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MARCO REGOLINI

A THEORETICAL MODEL OF

CENTROSOME FUNTIONING

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Short Forms

MC: Mother Centriole DC: Daughter Centriole MT: MicroTubule

MTOC: MicroTubule Organizing Center γ-TuRC: γ-Tubulin Ring Complex

PCM: Peri Centriolar Material RNP: RiboNucleo Protein

The centrosome at a glance

The requirements of a spherical reference system based on two orthogonal

protractors/goniometers show a surprising correspondence with the evidence

emerging from numerous experimental studies on centrioles and centrosomes: the

centrosome, as the main microtubule organizing center and because of the 9-fold

symmetry of its centrioles, their (transient) orthogonal arrangement and, above all,

their circumferential polarity (non-equivalence of spokes and triplets), may play the

role of a biological discrete and noise resistant interface, composed of two orthogonal

protractors, that recognizes and decodes morphogenetic instructions, or, more

generally, topogenic molecular targeting signals (frequently present at the N-terminus

of newly synthesized proteins or in the 3’UTR of mRNAs) and translates them by

delivering each targeted molecular complex (polarity and adhesion factors,

transmembrane receptors, mRNAs) into its expected 3D real location in the cell: like

an interface or a wiring device, the centrosome connects each targeting sequence with

the corresponding correctly-oriented microtubule: in this way morphogenetic

geometric (DNA coded) instructions are translated by the centrosome into actual

locations in cells, tissues and organs. Centrosome molecular geometry and

architecture imply its function: through the centrosome and its aster of robust

microtubules DNA can draw, build and “label” the intrinsic 3D grid line of the cell.

Centrosome, aster and primary cilium (its basal body is a centriole of the centrosome)

constitute the “hardware” of an interactive cross-talking system that manages

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geometrical communication inside the cell and between cells and establishes in

tissues coordinated and shared cell polarity. Targeting sequences and related receptors

constitute the “software”. In addition, the centrosome (the most chiral and

enantiomorphous cell structure) plays a geometric key role in left-right patterning:

mother centriole circumferential polarity, if reversely oriented, constitutes a likely

base for bilateral symmetry and symmetry breaking (asymmetry establishment).

The centrosome, discovered by Edouard Van Beneden in 1883 and studied by

Theodor Boveri few years later, is an organelle of animal cells that plays the role of

MTOC (MicroTubule Organizing Center), controls the cell-cycle and takes part to

mitosis; however it is not the only MTOC of eukaryotic cells: fungi and plants, that

do not possess centrosomes, use other structures and pathways to organize

microtubules (MTs). The centrosome, composed of dozens of highly conserved

proteins (“if conserved, they are important”) plays an important role in mitosis but it

is not indispensable and therefore not essential for cell division. So, a first question

arises: such a sophisticated and accurately conserved organelle must play any

important role, but which?

Centrosomes are made up of two orthogonal (during S, G2 and M phases of the cell

cycle) centrioles, disposed like the capital letter “L”: an axial ”Mother” (see later)

Centriole (MC) and an eccentric “Daughter” Centriole (DC:) embedded in an

(apparently) amorphous protein matrix named PeriCentriolar Material (PCM),

responsible for anchoring and nucleation of MTs: an “aster” of non-intersecting

robust MTs irradiates radially from the centrosome to the cell cortex, like, from the

central square of a city, many streets irradiate toward (and connect with) the

periphery. When centrioles disengage (interphase) the PCM persists around the MC.

MTs are nucleated by γ-TuRCs (γ-Tubulin Ring Complexes), displaced on the

centrosome surface and supported by protein scaffolds; the centrifugal direction of

each MT is the consequence of the orientation and inclination of its own γ-TuRC:

therefore the PCM is not an amorphous matrix but a well ordered frame of proteins

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able to orientate γ-TuRCs and their scaffolds (or docking platforms). Centrioles are

roughly cylindrical structures composed of nine blades of three parallel MTs

(“triplets”; some exceptions: the fruit fly Drosophila melanogaster has “doublets”, he

worm Caenorhabditis elegans “singlets”) arranged in a cylindrical or, rather,

prismatic barrel. All the properties of a biological spherical reference system small

organizer tool, based on two orthogonal protractors, are clearly showed, aren’t they?

…and a glance in a cell

In a cell there are approximately 1010

protein molecules (ten billions; Earth

population: ~7x109), subdivided into about ten thousand (10

4) different types. A cell

contains also millions of ribosomes, thousands of mitochondria, thousands and

thousands of surface receptors… Even more complex is the extracellular matrix that

surrounds cells, with dozens of different proteins and glycans (each type having many

different isoforms) showing astonishingly precise dispositions and orientations (the

cornea, for example: orthogonal layers, each one made up of parallel fibres). To

prevent an uncontrollable senseless chaos, eukaryotic cells have developed their inner

order: different membranes create compartments and the cell cortex too is

compartmentalized. “A living cell is not an aggregate of molecules but an organized

pattern, structured in space and in time… Some conceptual issues in the genesis of

spatial architecture: how molecules find their proper location in cell space, the

origins of supramolecular order, the role of the genes, cell morphology, the continuity

of cells, and the inheritance of order. The discussion is framed around a hierarchy of

physiological processes that bridge the gap between nanometer-sized molecules and

cells three to six orders of magnitude larger. Stepping stones include molecular self-

organization, directional physiology, spatial markers, gradients, fields, and physical

forces. The knowledge at hand leads to an unconventional interpretation of biological

order. I have come to think of cells as self-organized systems composed of genetically

specified elements plus heritable structures. The smallest self that can be fairly said

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to organize itself is the whole cell. If structure, form, and function are ever to be

computed from data at a lower level, the starting point will be not the genome, but a

spatially organized system of molecules. This conclusion invites us to reconsider our

understanding of what genes do, what organisms are, and how living systems could

have arisen on the early Earth” (Harold, 2005, in ” Molecules into Cells: Specifying

Spatial Architecture”). According to this point of view, an MTOC able to irradiate,

from its oriented γ-TuRCs, an aster of conveniently directed MTs, not overlapping

nor intersecting, each one distinguishable and labeled by a specific receptor that only

recognizes (and interacts with) the targeting sequence intended for itself and thus able

to univocally wire the cell, would be able to ensure the establishment of a controlled

global map firstly in cells (a “cell wide web” or a “cell grid line”) and then

reproduced in tissues and organs (controlled disposition and orientation of extra-

cellular matrix fibers): then a first quick glance at centrosome functioning is

necessary to look for the possible correlation between development (morphogenesis)

and centrosome, already evident in early zygote cleavage. In effect as we will see

better later, Azimzadeh and colleagues, in “Centrosome loss in the evolution of

planarians” (2012), write: "We hypothesize that centrosome loss occurred

concomitantly with the loss of the spiral cleavage and oriented cell divisions in the

ancestor of planarians and schistosomes… A significant difference can be found in

the mode of embryonic cleavage however. Macrostomum [whose cells do have

centrosomes] retained the ancestral spiral cleavage, also found in annelids and

molluscs, which relies on a stereotypical pattern of cell division orientation. In

contrast, planarian and schistosomes embryos undergo divergent modes of

embryonic cleavage, which apparently do not involve oriented cell divisions”

(Azimzadeh et al., 2012). Cleavage has its characteristic pattern in each Clade and

Taxon: it is radial in Amphibians, spiral in Molluscans, bilateral in Ascidians,

syncytial in flies, discoidal in birds, rotational in Mammals.

“The embryogenesis of freshwater planarians is equally intriguing: cleavage of the

fertilized egg was described as ‘anarchic’. No overt gastrulation or epiboly has been

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described.” (Sànchez Alvarado).

In mice, first embryonic divisions, described as irregularly rotational and

asynchronous, occur along unpredictable cleavage planes; in this stage, geometry of

cell arrangement is of little use; inner mass cell compactation does not follow any

architectural design and blastomeres lack centrioles that will appear only at the

blastocyst stage, when an evident embryo’s architecture emerges (orderly stereotyped

spatial disposition of cells).

A last number: Humans have ~1014

cells: ten thousand billion of (very complicated)

cells, organized in highly ordered tissues and organs. In each living organism there is

an absolute ”anarchy”: no Chief-cell, no Command-organ. Nonetheless living

organisms are the most ordered existing system. What is their architectural secret?

Shape and development: two main actors in morphogenesis

The aim and purpose of Metazoa development is to realize large organs and

organisms (able to run, fly, swim) making use of huge numbers of small dividing and

replicating units (the cells): the addition of thousands of little error in the 3D

displacement of the two new cells with respect to the position of the mother cell

would compromise (it is clearly incompatible with) the realization of high quality

architecture. What is the key to success in development and growth?

The biological mechanisms involved in tissue and organ development are highly

directional: division plane orientations, cell movements and convergent extension

take place according to precise directions; internal and external forces (osmotic

pressure, tension of extra-cellular fibers) stretch and bend cylindrical structures

according to the angle between cell axes and extra-cellular fiber directions; adhesions

between cells are not random but accurately localized and continuously remodeled

(differential adhesion); gradients of morphogens are formed using directionally

selective transport. Cells must be orientated and “informed” about their physical

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spatial position and about directions: cells must know the real physical location of

“up”, “down”, “front”, “rear” and these points of reference must be shared with the

neighboring cells; plants, like compasses and GPSs, use extrinsic point of references

or cues: not so in Metazoa which must generate their own (shared) points of

reference. “Centriole duplication is part of the mechanism by which the cytoskeleton

of the daughter cell is patterned upon that of the mother” (Harold, 2005). This is

astonishingly evident in the organization of Drosophila imaginal discs and in their

process of extroflection; topology of imaginal disc primordia (composed of a few

cells) corresponds to that of developed limbs; the leg imaginal disc is firstly divided

along two orthogonal axes (dictated by Wingless, Decapentaplegic and Hedgehog

gradients) into different domains; only a small number of cells, at the intersection of

these domains, form the distal pole tip of the forming leg; in imaginal disc, cells

arrange themselves in 3D concentric rings corresponding to the region of the adult

leg: the most outer ring corresponds to the most proximal leg region (coxa), the

bounding inner ring corresponds to the trochanter, followed by other internal rings

relative to the femur, tibia, tarsal segments, while the innermost central disc

corresponds to the claws (the most distal region); the position of the distal pole tip is

near to the center of the disc but a little off-centered; the disc is also lightly

asymmetric, oval or ellipsoidal; also each ring or annulus shows its own

characteristic 3D off-centering and oval shape (each elliptic ring having its own

eccentricity and position of major and minor axes and of focal points), like an

irregular odd archery target; off-centering and ellipsoidal ring shapes are bilaterally

symmetric in both left and right imaginal discs; in this way the future 3D tilt of the

proximal-distal axis of each region of the forming limb is determined: its orientation

in respect to the three axes of the body and adjacent limb regions is the consequence

of the controlled 3D off-centering and eccentricity of each annulus (designed by the

carefully forecast 3D disposition of cells) that orient and drive the corresponding

extroflection tilt; the accurate 3D “off-centering” and eccentricity seems to be

radially and centrifugally transmitted from the central few cells outwards to annuli,

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which are subdivided in some sectors like a dart board (clones or compartments),

controlled, step by step, by genetic programs carried out by cells able to manage their

own geometry.

The Drosophila mutants defective for the centriolar DSas-4 protein (Basto et al.,

2006) develop up to the adult stage, and, after using up maternal provisions of DSas-

4, are almost completely lacking in centrioles, at least in the brain, starting from the

third larval instar; the images of the adult mutant fly (see on the Internet the

comparative images of wild type vs. mutant in Basto’s free article “Fly without

Centrioles”) show an individual with monstrous deformities: the shape, the tilt and

the anomalous curvature of the wings certainly impede flight, just as the abnormal

angle between coxa and body cannot allow walking movements; what is the link

between morphogenesis (literally “shape-creation”) and centrosome? Metazoan cells

behave as if they had at their disposal an intrinsic (i.e. without external cues)

biological tool (the centrosome?), conceivable as roughly resembling and comparable

to a 3D-compass or 3D-GPS navigator (which, on the contrary, are driven by

external cues), able to grasp coded spatial indications (topogenic sequences) and

translate them to find and reach the intended directions and locations. Indeed, cell,

tissue and organ topology need, and cannot help but needing, such a specifically

dedicated “instrument”: effectively in migrating cells (in vivo and in vitro) the

centrosome reorients the cytoskeleton to reach the desired targets.

In multicellular Eukaryotes, a single fertilized oocyte (zygote) develops into an adult

organism (composed of billions of cells) which shows the characteristic shape of the

species: how is the correct species specific shape achieved? How are cells guided to

occupy their forecast position in the complex architectural plan of each organism?

Cell differentiation cannot explain how a particular shape is acquired: in effect

structures made up of the same type of differentiated cells show completely different

forms, as we can observe in skeletal stratified muscles, all composed of the same

differentiated type of cells and tissues (fibers of muscular tissue derived from

identical myoblasts, and connective tissue containing fibroblasts) but each one having

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its own characteristic conformation: pectoralis major is quite different from deltoid,

platysma is completely different from trapezius, and so on; can the difference of

origin and insertion dictate the shape of each muscle? The different shapes of muscles

appear to be due to the layers of connective tissue which surround it and its fibers:

endomysium and muscle fibers are almost identical in every muscle, whereas, in each

muscle, fascia, epymisium and perimysium have their own characteristic form

(spindle shaped, cylindrical, flattened) dictated by the orientation of extracellular

fibres; these connective layers are made up of collagen (and many other components)

fiber whose orientation is carefully controlled by fibroblasts. Similar considerations

can be made about bones, articulations and cartilages: same type of differentiated

cells and tissues, but very different forms. What dictates shapes and forms?

The shape of organs and organisms is the consequence of the spatial disposition of

cells and orientation of extra cellular fibers: our hands and feet (except wrists and

ankles) have very similar (if not the same) anatomical and histological structures

(confirmed by phylogenetics and embryology), nevertheless they have clearly

different shapes because of the diverse spatial disposition of the cells (osteocytes

above all) and the different geometry of the extra cellular fibers. In our skin, the

microscopic arrangement of the cells in sebaceous and sweat glands is different: each

type of gland possesses not only its own type of differentiated cells, but also its own

particular histological disposition of cells, easily recognizable through a simple

microscope; there are millions of these glands, often very close, and always and

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Fig. 1 Centriole and centrosome cycle.

On each line, on the left the respective position of centrioles is depicted: the MC has distal appendages, the

DC has distal ribs, the PCM is a light halo. On the right the position of the centrosome in a dividing cell is

schematized (N: nucleus; astral MTs are outlined only in anaphase); in non dividing (G0) non motile cells the

MC is the basal body of the primary cilium.

A) Phase G1: MC and DC are disengaged.

B) Phase S:

i) the DC begins to mature close to the MC proximal end;

ii) the DC, now close to the MC distal end, loses its distal ribs;

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iii) the DC acquires the distal appendages (now immature and short). It becomes a “new” MC; the

old MC orientates the new MC (“0°” mark coordination);

iv) from both MCs (old and new) a new procentriole-DC (cartwheel) arises; the diplosome

(MC+DC) containing the old MC maintains its orientation and is pulled by astral MTs towards

the forecast next spindle pole; the diplosome containing the new MC is displaced by astral MTs

(originating from the old MC) and pulled toward the forecast location of the new spindle pole.

C) Phase G2: procentrioles grow, becoming adult new DCs (distal ribs).

D) Prophase: both MCs form their own PCM.

E) Metaphase: both centrosomes are definitely positioned; the distal appendages of the new DC grow.

F) Anaphase: both MCs are completely formed (identical distal appendages) and their PCM is also

completely built. From both PCMs, astral MTs wire and map cell membranes of the two new cells.

G) Telophase: disengagement starts (only one cell is represented).

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everywhere each type of gland is built in accordance with its own characteristic cell

arrangement, suggesting that an intrinsic geometric equipment guides the cells to

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reach their correct position, or that a geometrical mechanism subdivides the cell

cortex and membrane in many different and non-equivalent compartments

(geometrically controlled to displace differentially adhesion complexes) in order to

adhere in a typical stereotyped fashion to neighboring cells (differential adhesion).

As every polyhedron has its characteristic shape with faces arranged in a fixed

position, each one with its own particular form, orientation and extension, anatomy

and histology show that cells, tissues and organs (and each microscopic structure like

the neprhon or the Corti’s organ) have their characteristic conformation and

topological arrangement; how do cells, tissues, organs and organisms achieve their

“geometrical-polyhedral” macro- and microscopic shape?

There are two main actors (hot topics) in morphogenesis: growth anisotropy and

heredity of forms.

As is known, anisotropy means that, given a material (a developing embryo in this

case), a physical quantity (growth rate, here) takes directionally dependent values.

When growth rate is rigorously isotropic (equal in every direction) spherical shapes

are formed; directional, but unpredictable, differences of growth rate (random

anisotropy) generate amorphous structures (neoplastic tissues are an example); to

realize well defined forms, anisotropy of growth rate must be attentively projected

and forecast: every direction shows its characteristic growth rate; so, growth is

orderly anisotropic from the earliest stages of zygote cleavage and becomes highly

anisotropic during organogenesis, resulting in structures that develop and grow in

predetermined directions; cell populations are correctly guided into fixed forecast 3D

positions, following programs characteristic of each species: cleavage, as we have

seen, can be radial, spiral, bilateral, syncytial, discoidal or rotational.

DNA: the first actor

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"Heredity of forms" means that the zygote’s genome contains and transmits to the

offspring all the necessary programs to control growth, capable of precisely

indicating the geometry, or, rather, the topology (accurately forecast, memorized and

stored in DNA) which growth must respect: fertilized eggs only generate organisms

that acquire the characteristic shape of the species (in the few crosses that occur

successfully, morphological characteristics are blended). The famous transfer of a

nucleus from a mammary gland cell of a Finn Dorset sheep (DNA donor) into the

cytoplasm of an enucleated oocyte of a Scottish Blakface sheep (DNA host) produced

Dolly, which showed the morphological features of a Finn Dorset sheep (the donor of

DNA). In snails, only one maternal gene is responsible for left- or right-handed spiral

cleavage. DNA (or the nucleus, if we want to include epigenetic, histonic and non

histonic, nucleo-proteins), the first actor in morphogenesis, controls growth and

development of organisms: it provides coded (and stored) “directional signals” that

guide cells to reach and occupy their forecast positions: thus the genome strictly rules

the orientation of cell movements, differential cell-cell adhesions and division planes;

in addition it masters the directional organization of fibers in the extra cellular matrix.

To better explain this concept, let’s think about a dividing cell: the respective position

of the two daughter cells can be dictated by the orientation of the division plane

(which is a geometrical process) or by a topological disposition of adhesion factors

on the cell membrane (which is a geometrical process too: topological disposition of

polarity and adhesion factors on a controlled grid line): both processes require that

the cell has been previously mapped and that a tool does exist, able to manage any

cell reference system (cross-talking interactively with DNA, whose language is made

of polynucleotides). Comparative anatomy and molecular phylogenetics indicate that

the homology of structures, organs and tissues is founded on the homology of

genomes: comparisons of whole genomes show high similarity levels (homology of

sequences) that fit in with anatomical and morphological features; morphological

taxonomy corresponds to homology of sequences. Therefore DNA contains heritable

morphogenetic (coded) guidelines that, by means of molecular targeting signals, drive

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and orientate populations of cells, imposing and dictating the correct direction that

cells must follow to reach their proper topological targets/locations and to correctly

assemble the extra cellular matrix: indeed the final result we can see in every adult

living being of every species is the correct stereotypical achievement of the forecast

species specific form, with every cell at its precise location (e.g. Bowman’s capsule

and loop of Henle in the nephron or Corti’s, Deiters’, Koelliker’s cells in the

cochlea) and extracellular fibers with organ or tissue characteristic orientation

(cornea, hairs, nails, beaks, claws). Then, how can DNA manage and supervise

developmental processes without a geometrical tool capable of recognizing,

understanding and translating (like an interface) its genetic topogenic instructions?

“The genetic instructions often include information pertinent to the localization of the

product. Targeting sequences direct proteins to the plasma membrane, nucleus,

mitochondria, or lysosomes. Certain proteins and mRNAs are transported

individually to particular locations in cell space, and this localization depends on

having an appropriate sequence. Transport vesicles recognize specific target

membranes, such as the Golgi, vacuole, or plasma membrane, with the aid of SNARE

proteins. But there is much more to growth and division than manufacturing the

parts. A rod-shaped cell must also elongate with constant diameter, construct an

efficient apparatus to partition its chromosomes, locate its midpoint, lay down a

septum, and undergo fission. In eukaryotic cells, targeted vesicle fusion requires, in

addition to the SNAREs, both a delivery system and a secretory apparatus” (Harold,

2005). For identifying precise locations in the cell cortex (apical, basal, anterior,

posterior) and reaching them, firstly the cortex must be “mapped” or “wired” (i.e.

subdivided in many non-equivalent compartments, orderly disposed on a virtual grid

line, somehow identifiable and recognizable through any kind of label), then the cell

must have at its disposal all the instruments necessary to manage this “map”: a tool is

necessary that can “understand” molecular geometric and directional coded signals

and “translate” them finding and physically reaching the intended cortical position.

“Structural and genetic studies suggest that asymmetry of the centriole (basal body)

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plays a critical determining role in organizing the internal organization of algal cells,

through the attachment of microtubule rootlets and other large fiber systems to

specific sets of microtubule triplets on the centriole…To understand cell organization,

it will be critical to understand how the different triplets of the centriole come to have

distinct molecular identities” (Marshall, 2012).

Whatever the molecular signals are (polynucleotides or polypeptides), how are they

recognized, decoded and translated, identifying with precision the desired direction,

location and orientation?

Centrosome: the second actor

Centrosome and morphogenesis are somehow correlated. Without the centrosome,

planarian and schistosome embryos cannot retain the ancestral spiral cleavage: they

undergo divergent modes of cleavage, without performing oriented cell divisions,

and, in addition, gastrulation fails.

Pathology shows that mutations in several loci coding for centriolar proteins cause

several morphogenetic disorders, from Protists to humans: Chlamydomonas bld

mutant does not have flagella, uni has only one flagellum, vfl shows multiple ectopic

flagella: they all present abnormalities in the cytoskeleton, location of the nucleus and

formation of the mitotic furrow; in humans, ciliopathies are associated with some

morphological disorders: renal and hepatic malformations, polydactyly, Meckel-

Gruber and Bardet-Biedel syndrome, etc. Cilia are assembled by basal

bodies/centrioles: what is the role of centrioles and centrosomes in development?

What is the link between the genes involved in morphogenesis and the architectural

organization of cells? Whatever the signal is (whether it is a cue to differentiate or a

factor to proliferate or a stimulus to move, etc.) the last step of each morphogenetic

process (beyond differentiation) is necessarily topologic, geometric and directional,

in order to drive cells and tissues toward the forecast architectural position they must

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occupy: forms and shapes are not the consequence of the kind or type of cells

(differentiation), on the contrary they are determined by the spatial disposition of

cells (geometrical architecture): in the Corti’s organ, the different type of cells is not

surprising and is the consequence of cell differentiation, but the precise orientation of

the basilar, tectorial and Reissner’s membranes is astonishing and cannot be

explained by cell differentiation. Let’s consider Drosophila gastrulation: no Gurken

signal from the oocyte to ventral follicle cells allows these cells produce Pipe; then a

long cascade of gene activities is triggered (gastrulation-defective, snake, easter,

spätzle, toll, tube, pelle, cactus, dorsal) till Dorsal protein (that is found everywhere

in the syncytial blastoderm) enters the nucleus only in ventral cells; this cascade of

gene activation (together many other – zerknüllt, tolloid, decapentaplegic, rhomboid,

twist, snail, fgf8 – that are activated or repressed depending on the level of

stimulating factors) can explain the different fates (differentiaton) of cells (dorsal-

ectoderm, lateral-ectoderm, neurogenic ventrolateral ectoderm, ventral-mesoderm),

but not movements: how ventral midline cells modify their cortical adhesion

junctions, and actin cytoskeleton to invaginate (with bilaterally symmetric

movements) at the central furrow and form the ventral tube? Morphogenetic signals

are molecules (sequences of nucleotides or amino-acids) that impose directions to

already polarized cells (receptors for Planar Polarity factors are not random

distributed on the cell membrane, but occupy defined locations): then, there must be a

noise-resistant structure, capable of precisely recognizing and identifying geometric

topological signals, decoding, interpreting and translating them to find and finally

reach the desired locations to drive cell movements. "The preceding interphase aster

centers and orients a pair of centrosomes prior to nuclear envelope breakdown, and

the spindle assembles between these prepositioned centrosomes…Current models for

cleavage plane determination propose that metaphase spindles are positioned and

oriented by interactions of their astral microtubules with the cellular cortex, followed

by cleavage in the plane of the metaphase plate. In early frog and fish embryos,

where cells are unusually large, astral microtubules in metaphase are too short to

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position and orient the spindle. Rather, the preceding interphase aster centers and

orients a pair of centrosomes prior to nuclear envelope breakdown, and the spindle

assembles between these prepositioned centrosomes" (Wühr et al., 2010).

Centrosomes are pulled up to their forecast position by astral (labeled and

distinguishable) MTs that ensure one-to-one correspondence between centrosomal

(labeled and distinguishable) and cortical compartments.

To drive cell movements, DNA (the operator) needs a “steering wheel”, a rudder that

transforms (translates) its orders into correctly oriented motions. This implies the

existence of a tool able to organize a three-dimensional reference system, the second

actor in morphogenesis, made up of real cellular structures; evidently, the classical

Cartesian reference system with three axes crossing the cytoplasm, does not exist

(this assertion is true for Metazoa, whereas in Plant parallel MT rings under the cell

wall design a real grid line, like a globe with designed parallel but without meridians,

something similar to a “cylindrical Cartesian system”); on the contrary, however, a

spherical reference system organizer does exist, which requires a structure, as small

as is desired, composed of two “protractors/goniometers” orthogonal to each other

and capable of generating oriented rays: this is the centrosome, with its two

orthogonal centrioles, built with a 9-fold symmetry and capable of assembling robust

microtubules (MTs) in oriented directions. May we suspect that differently directed

MTs are also differently labeled by specific receptors to play a useful role in mapping

and labeling cells? Indeed cells equipped with a non-labeled cytoskeleton seem more

confusing than cells without a cytoskeleton: imagine a bus, a railway or a subway

station with platforms lacking numbered information panels or an airport whose gates

have no numerals nor displays. In effect an MTOC that irradiates an aster of identical

undistinguishable MTs where motor proteins (kinesins and dyneins) walk up and

down would be a useless and chaotic obstacle for molecule diffusion. On the

contrary, through the centrosome, DNA builds and manages a real cell “subway

network”, made up of a real central station with numbered distinguishable platforms

(the centrosome ant its oriented and labelled γ-TuRC scaffolds), rails (MTs), trains

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(kinesins and dyneins) and different suburban stations (cortical compartments).

About cleavage and centrosome

“When centrioles are experimentally ablated, spindles drift within the cell”

(Azimzadeh and Marshall, 2010).

“Some characteristics of mouse early development could be linked to the absence of

centrioles: (1) the absence of regular cleavage planes during early development; (2)

the absence of any detectable axis of polarity within the blastomeres before the 8-cell

stage; (3) the random position of the spindle relative to the axis of polarity within the

blastomere during the fourth cleavage. Centrioles may act to keep PeriCentriolar

Material components in a precise position throughout the cell cycle and so be useful

in the control of the position of the axis of polarity and division. This may become

more important in differentiated cells, such as those found in the outer layer of the

blastocyst” (Gueth-Hallonet et al., 1993).

Let’s read again what Azimzadeh et colleagues write in “Centrosome loss in the

evolution of planarians” (2012): "The absence of centrioles in dividing cells implies

that planarians do not use the pathway for centriole duplication that underlies

centrosome reproduction in other animals, but only assemble centrioles de novo

during the differentiation of ciliated cells...We hypothesize that centrosome loss

occurred concomitantly with the loss of the spiral cleavage and oriented cell

divisions in the ancestor of planarians and schistosomes….It is remarkable that the

loss of such a conserved organelle as the centrosome occurred within not-parasitic

flatworms, as cellular and developmental processes appear largely conserved

between these species. A significant difference can be found in the mode of embryonic

cleavage however. Macrostomum retained the ancestral spiral cleavage, also found in

annelids and molluscs, which relies on a stereotypical pattern of cell division

orientation. In contrast, planarian and schistosomes embryos undergo divergent

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modes of embryonic cleavage, which apparently do not involve oriented cell

divisions”.

About spiral cleavage, Rabinowitz and Lander (2010) write:

“Spiralling embryos are found in a large group of invertebrate phyla but are largely

uncharacterized at a molecular level. These embryos are thought to be particularly

reliant on autonomous cues for patterning, and thus represent potentially useful

models for understanding asymmetric cell division. The series of asymmetric

divisions that produce the micromere quartets are particularly important for

patterning because they subdivide the animal-vegetal axis into tiers of cells with

different developmental potentials. In the embryo of the snail Ilyanassa, the IoLR5

RNA [Ilianassa obsoleta Long R5 RNA] is specifically segregated to the first quartet

cells during the third cleavage. Here, we show that this RNA, and later the protein,

are maintained in the 1q(121) cells and their descendents throughout development.

Some IoLR5-expressing cells become internalized and join the developing cerebral

ganglia. Knockdown of IoLR5 protein results in loss of the larval eyes, which

normally develop in association with these ganglia. Segregation of this RNA to the

first quartet cells does not occur if centrosomal localization is bypassed. We show

that the specific inheritance of the RNA by the first quartet cells is driven by a

discrete RNA sequence in the 3' UTR that is necessary and sufficient for localization

and segregation, and that localization of another RNA to the first quartet is mediated

by a similar element. These results demonstrate that micromere quartet identity, a

hallmark of the ancient spiralian developmental program, is controlled in part by

specific RNA localization motifs.”.

“One of the major types of mRNA transport in Drosophila embryos is the movement

of mRNAs involved in developmental pattern formation to the apical centrosome”

(Blower, 2013). It is well known (Scott, 2014) that different mRNAs are

asymmetrically distributed in Ilyanassa blastomeres by the centrosomes:

Decapentaplegic mRNA is delivered by the centrosomes to the macromeres whereas

micromeres receive by the centrosomes Long R5 RNA: the supposition that the

20

centrosome is equipped with different receptors to recognize targeting sequences is

plausible. We have just already seen (Wühr et al., 2010) that centrosomes, in the large

frog blastomeres, are positioned in such a way (through distinguished, oriented and

labelled MTs) that they look like trolley buses correctly connected to the two

polarized electric wires, orientated and properly front-rear positioned in respect to the

“electric city-skeleton” made of aerial-suspended wires: during their controlled

movements, guided and routed by a labelled MT cytoskeleton, they take and delivery

mRNAs to the same destination they are reaching.

"It came as a surprise to all of us that planarians could get rid of centrosomes

without affecting their regenerative potential, says Howard Hughes Medical Institute

and Stowers investigator Alejandro Sánchez Alvarado, Ph.D. It suggests to us that the

evolutionary pressure to maintain centrosomes may have very little to do with cell

division itself. There may be another function for centrosomes that is still

obscured…The fact that centrioles were retained in this organism while centrosomes

were lost, really speaks to the idea that centrioles evolved primarily for making cilia,

and not for their mitotic functions, says senior author Wallace Marshall“.

“Although the orienting cytoskeletal element is not yet known, this model

[intracellular origin of Left-Right patterning] provides a comprehensive, quantitative

synthesis of all the molecular and biophysical steps leading from Left-Right

orientation within single cells to asymmetric gene expression in the early embryo,

and it does not depend on ciliary motion. This scheme also parallels a model of

dorsal-ventral patterning, where an embryo-wide pattern arises from early

intracellular movement of Wnt containing particles by kinesin motor proteins along

oriented microtubule tracks” (Levin and Mercola, 2007).

“The centrosome has evolved in multicellular organisms from the basal

body/axoneme of the unicellular ancestor. It plays a major role in organizing the

microtubule cytoskeleton in animal cells. During interphase, the centrosome

organizes an astral array of microtubules that participate in fundamental cellular

functions such as intracellular trafficking, cell motility, cell adhesion and cell

21

polarity” (Azimzadeh and Bornens, 2007).

“There may be another function for centrosomes that is still obscured…” (Sánchez

Alvarado, 2012).

Another function for the centrosome: what is it?

”Is it possible to confirm this idea that the circumferential, morphological, structural

and molecular asymmetry of centrioles can be inferred from Mammals ciliated

epithelia? While the circumferential anisotropy of centrioles cannot be ascertained

within the centrosome, its existence can be inferred from the properties they express

during ciliogenesis, be it the formation of a primary cilium or of bona fide 9+2 cilia

in ciliated epithelia, some of which at least derive directly from the centrioles. As in

Ciliates and flagellates, these basal bodies nucleate appendages of various molecular

compositions (basal foot, striated rootlets, alarm sheets, etc, which anchor the basal

body to the membrane and to the cytoskeleton) and these nucleations arise at specific

sites of the basal body cylinder; in particular, the basal foot is located on triplets 5

and 6 corresponding to the side of the effective stroke of the cilium. What is

remarkable is that basal feet develop before the basal bodies reach their membrane

site and before they acquire their functional orientation“ (Beisson and Jerka-

Dziadosz, 1999).

Indeed the centrosome has a structure able to perform a different (unique and

peculiar) function, a logistic task: it looks like a “network switch”, or a “switching

hub”, the well-known computer networking multi-port device that receives

destination-addressed messages or frames from different equipment which it is

connected to (through one-to-one cables) and delivers each message only to the

(labelled) device which the message is addressed to: an “one-to-one” wired

connection links the switch to each device, each device is “labelled” and

distinguishable (private address) and each data is also labelled and addressed to only

one device. The previous considerations on the centrosome create the impression that

it plays the role of a molecular interface (see Fig. 4 and 5 on page 45 - 46) that

receives molecular complexes labelled by targeting sequences (ligands), “reads”

22

labels (signal-receptor interaction and capturing) through its γ-TuRCs (non-

equivalent) receptors and, by kinesins (motor proteins) that move along the

corresponding oriented MTs, delivers each molecular complex (transmembrane

receptors, polarity and adhesion factors, mRNAs above all) to where they are

destined. Thus it can be the cellular instrument used by DNA to manage cell, tissue

and organ topology. "Basal bodies and centrioles display structural and functional

polarities that play an important role in the spatial arrangement of the cytoskeleton

and hence the polarity of the cell" (Geimer and Melkonian, 2004). This is the key

idea: in Metazoa both mother’s and daughter’s centriole polarities (structural and

functional i.e. inclination and non-equivalence) are transmitted to the aster of

centrosomal MTs so that the aster is made of non-equivalent MTs (each MT is

distinguishable because of its own orientation and molecular labelling of its γ-TuRC:

one direction, one label) ; in Ciliates (Paramecium) centriole triplets are different and

distinguishable and acquire a precise and coordinated orientation with the complex

cytoskeleton: the triplet N° 9 links to the “postciliary ribs”, the triplet N° 4 is attached

to the “transverse ribbon”, the triplets N° 5-6-7 are connected to the “kinetodesmal

fibers”; similarly the (non-equivalent!) pins of a microchip are connected to precise

conductive tracks of a printed circuit board; as in Ciliates the centrioles organize the

“cyto”-skeleton, in Metazoa the two orthogonal centrioles of the centrosome organize

the architecture of the “PCM”-skeleton and confer to the centrosomal γ-TuRCs (or

their scaffolds) molecular complexes (labels) that on the one hand identify and

distinguish each MT with correspondence to its centrosomal geometrical location and

orientation, on the other hand allow an univocal interaction between targeting

sequences intended for cortical locations reachable through the oriented MT they

label. “It seems that in Protists and in Metazoa the triplets of basal bodies are not-

equivalent” (Beisson and Jerka-Dziadosz, 1999).

Plants and animal anatomy

23

Fixed in the ground, plants control their anisotropic growth by extrinsic reference

systems (gravity and light); animals, on the other hand, need an intrinsic self-made

reference system (something like an oriented cell grid line) to manage their geometry:

plants do not have orthogonal centrioles, animals do. Then it seems that the

centrosome is the intrinsic reference system tool of animals.

Plants, centrosome-free, have developed simple anatomical and histological

structures, with cylindrical or laminar arrangement: beautiful but anatomically

simple, repeated a large number of times. “The overall structural organization of

plants is generally simpler than that of animals. For instance, plants have only four

broad types of cells, which in mature plants form four basic classes of

tissues…organized into just four main organ systems” (Lodish 2012). In contrast

animals, centrosome equipped, have developed anatomical forms that are particularly

varied and complex (3D rather than 2D laminar arrangements) whose architecture

implies the existence of a right and proper geometric tool: the peacock’s livery, the

shells of crustaceans; animals show a high architectural accuracy and precision also

at the tissue level: kidney cortex and medulla or spongy bone osteons and trabeculae;

the same holds true for organs: skeleton and heart. In Vertebrates the shape of

structures that perform complex functions is astonishing: the curvature of cornea, lens

and retina strictly meets the need for projecting and focusing images; the inner ear -

labyrinth and cochlea- in Mammals and Birds has a shape perfectly suited to measure

the different vector-components of acceleration and analyze the frequency of

acoustical signals (the basilar membrane of the Corti’s organ performs, in a sense, a

“biological Fast Fourier Transform”).

Previous in-depth studies have investigated “what” centrosomes might be and

“what” might be their task: now the question is “how” centrosomes work.

A possible model of centrosome and centrioles function in cell and

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tissue topology: theoretical foundation

How cells control geometry of tissues and organs

“Several principles of construction of a microscopically small device for locating the

directions of signal sources in microscopic dimensions: it appears that the simplest

and smallest device that is compatible with the scrambling influence of thermal

fluctuations as are demonstrated by Brownian motion is a pair of cylinders oriented

at right angles to each other.” (Albrecht-Buehler, 1981).

“The centrosome has evolved in multicellular organisms from the basal

body/axoneme of the unicellular ancestor. It plays a major role in organizing the

microtubule cytoskeleton in animal cells. During interphase, the centrosome

organizes an astral array of microtubules that participate in fundamental cellular

functions such as intracellular trafficking, cell motility, cell adhesion and cell

polarity” (Azimzadeh and Bornens, 2007).

“A new centriole normally arises in a definite spatial relationship to an existing one

and at right angles to it” (Harold, 2005).

“It seems that in Protists and in Metazoa the triplets of basal bodies are not-

equivalent” (Beisson and Jerka-Dziadosz, 1999).

In order to coordinate these highly anisotropic, polarized and oriented functions, the

centrosome must have a suitable geometric structure, able to manage cell polarity and

decode “geometric” messages transmitted by DNA, to whose control all the previous

functions are subject.

The orthogonal arrangement of the centrioles in the centrosome suggests that this

organelle is the cell “reference system” organizer: a spherical-system builder based

on two orthogonal protractors/goniometers, one to manage geometry in the “x y”

plane, the second to manage geometry in an orthogonal plane containing the “z” axis.

25

Centrosome geometry and architecture must necessarily imply its function: as a

technical designer firstly squares a sheet, similarly, during the last period of each cell

division, through the centrosome, DNA firstly maps and wires the non-polarized and

homogeneous cell cortex: so, DNA can build the intrinsic 3D map of the cell,

transforming a (DNA-coded) “virtual” grid line in a real “actual” cellular grid (the

“cell wide web”) with intrinsic points of reference which dictate and orientate the

position of membrane polarity factors; DNA uses the centrosome to polarize the

whole cellular cortex and membrane in order to assume the control and the mastery

of the cellular and extracellular environment. Please pay attention to the expressions

“through the centrosome, DNA firstly maps” and “DNA uses the centrosome”: the

centrosome is only a sophisticated instrument in the hands of (controlled by) DNA,

then it does not work autonomously, but is strictly directed and managed by DNA.

Then we must look for a plausible molecular “hardware” (geometrical PCM

structure) and a corresponding molecular “software” (targeting sequences and

centrosomal receptors) able to perform such functions.

What are the requirements of a spherical reference system organizer made up of two

orthogonal protractors? How may the centrosome play the role of an interface,

composed by two orthogonal goniometers, making use of the 9-fold symmetry of

centrioles, their orthogonal arrangement and their circumferential polarity?

How must a “biological protractor/goniometer” be organized? Basic

characteristic of the protractors.

The difference between a simple ring and a protractor/goniometer (or a clock dial)

26

consists in the strictly ordered circumferential polarity and asymmetry of the

graduated protractor: like the dial of a clock is subdivided into an ordered row of

equidistant sectors and segments equipped with diverse (non-equivalent) marks,

similarly a protractor has different equidistant numerals, sequenced, in an ordered

fashion; if a homogenous ring is rotated about its axis, an observer will not perceive

any difference: the ring will appear always the same, identical and indistinguishable

from the original arrangement; on the contrary the observer will realize whether a

protractor (or a watch dial) has been rotated and will also estimate the angle of

rotation; “circumferential asymmetry” (or polarity) means that a disc or a circle are

made up of several different elements (arcs, sectors, segments) which are

distinguishable because of own individual label/marks, and then non-equivalent. One

mark (“0°” on the protractor, “12” on the clock) must be considered the beginning

(here it will be named the “0°” mark): it is fundamental for building and neatly

assembling the ordered sequence of the other (non-equivalent) marks, and essential

for orienting the protractor. A clock dial, marked by different and distinguishable

“Braille” characters and oriented in the space (horizontal, with the numeral “12” as

usually opposite to the user) allows a blind or a visually-impaired person to precisely

find a definite sector of the plane. Let us consider a protractor or a clock dial with

only nine equidistant, different, distinguishable Braille marks like the nine equidistant

triplets of the centriole wall that, at this moment of our analysis, we suppose to be

non-equivalent: why? So a sophisticated architecture, together with 9-fold symmetry,

costly and difficult to realize, would be meaningless and useless if their 9 components

were undistinguishable: in transverse sections, a centriole looks like a gear of a pump

or a shaft of a rotor or a drum of a turbine, but neither drills nor propellers can be

useful inside the cytoplasm and cells are neither mixers nor centrifuges; therefore we

now admit, but later we will face this argument, that the “non-equivalence” of the

nine centriolar triplets is an “informational non-equivalence” and this appears a

plausible, impressive and convincing reason (centriole works like a biological

informational protractor) to explain the centriolar and centrosomal complicated and

27

conserved architecture. Coming back to the “Braille” protractor, the plane containing

the protractor is divided into nine corresponding, ordered, labeled, identifiable (and

then non-equivalent) sectors like a dart board. After orienting the protractor (the “0°”

mark, like the numeral “12” on a clock dial, in the farthest segment opposite to the

user) a blind (or a visually-impaired) person that receives a vocal signal (a number),

through his fingers matches the signal with the corresponding Braille character and

individuates the sector of the plane corresponding to the signal: a signal (intended for

a desired location and containing the corresponding coded information) has been

“translated” into its real location on a plane through the interaction between the signal

and the corresponding Braille character operated by the blind person’s fingers. The

blind (or the visually-impaired) and the Braille clock dial are the elements of a set

which symbolizes the biological-protractor/centriole.

Left-Right (a first quick glance)

By reverting (clockwise > counterclockwise) the order of the sequence of the Braille

characters, the protractor becomes symmetric in respect to the original one. If the

blind (or visual impaired) has a “reverse” protractor (horizontal and orientated like

the original one, with the “0°” mark always in the same position, in front of him or,

better, opposite to him or, rather, on the farthest sector in respect to him, like “12” on

a clock dial), receiving the same vocal signal as before, matches the signal with the

corresponding Braille character but individuates a sector of the plane which is

symmetric, compared to that he would find through a non-reverse Braille protractor:

he “translates” the same coded signal into a symmetric location. By only a simple

reversion of the sequence of the marks, it is possible to realize bilateral symmetry,

without changing an enormous number of topogenic instructions; this is particularly

interesting from an evolutionary point of view: one single change in place of

thousands of changes is much more likely. Left-Right question will be deeply

28

analyzed later.

DNA, through the centrosome, generates ex novo a 3D oriented environment in

a previously homogenous cell

A “Braille marked” protractor is not used to measure, it is a translator of address-

signals into their corresponding locations in the plane; two such orthogonal

protractors perform the same identical task in 3D; in a cell, such instrument is an

interface, a biological geometric tool that receives molecular coded signals (input:

targeting or topogenic sequences), each one intended for a particular sector,

recognizes them through their tertiary 3D structure, matches each one with the

corresponding mark (ligand-receptor interaction) and returns (or indicates) the spatial

position (output) of the desired locations: any location can be easily reached through

an oriented ray arising from the selected mark. This comparison reveals other

important features of centrosome functioning; for a blind person, the space of an

empty room is homogeneous, without any point of reference, everywhere identical

and then “meaningless”; through an oriented 9-graduated “Braille” protractor, the

same space acquires nine intrinsic, autonomous (relative to the blind) and useful

points of reference (without external cues): it is no longer homogeneous but

subdivided into nine different and recognizable sectors and becomes a “meaningful”

space, a useful room, a detailed and usable environment. Similarly DNA, through the

centrosome, generates ex novo a 3D (autonomously oriented) labeled environment, a

grid line in a previously homogenous cell, transforming and converting it in a

mapped, wired, “webbed” and polarized in detail cell: an “useless” cell cortex

becomes an “useful and usable” space. This is the reason we have chosen the

expression “informational non-equivalence” for the different triplets. Through the

centrosome, a “blind” DNA becomes a “sighted” DNA: through the centrosome

DNA, so to say, turns on the light in the cell.

29

Orientation of the first protractor

Speaking about the symmetric “Braille” protractor, a lot of expressions have been

used to explain its position and orientation in respect to the user, in order to underline

how delicate the issue of orientation is; in effect protractors/goniometers must be

oriented: in a globe, one protractor is “horizontal” (equatorial), the other one is

“vertical” (meridian) and passes through the North and South poles. The first

protractor, arranged on the equatorial plane, lies on the “x y” plane of the spherical

reference system and its axis coincides with the “z” axis of the system: it is

responsible for indicating the longitude ( coordinate). The “0°” mark is used to

orient the protractor: on the globe it coincides, by convention, with the meridian

passing through Greenwich; on the “x y” plane it coincides with the “x” axis. Its nine

marks indicate nine meridian (or vertical) wedges. In a metazoan cell, as we have

already seen, DNA polarizes the cell cortex, often in the absence of any cue: there is

no extrinsic point of reference as in other systems (plants, compasses, GPSs), but

each species uses its own mode to polarize the cell: the “0°” mark can coincide with

the entry of the sperm or be positioned randomly, like a technical designer is free to

square a square sheet choosing randomly which side will be the “top” side.

Orientation of the second protractor

The second protractor, responsible for the latitude (θ coordinate), is vertical,

30

orthogonal to the first (Fig. 2 at page 35); it is possible to define its “top” and its

“bottom”: as in a clock on a tower the mark “12” is on the vertical axis and always at

the top, the diameter crossing the “0°” mark is vertical, parallel to the “z” axis (the

axis of the first protractor) and the “0°” mark is positioned at the top, aligned with (in

front of, facing) the “0°” mark of the first protractor. In a classic spherical reference

system, θ takes values from 0° to 180°, and then it is convenient to consider the

second protractor divided, by the “vertical” diameter crossing its “0°” mark, into two

halves (two facing symmetric hemi-protractors) the “right” one showing on its round

external border four marks (+40°; +80°; +120°; +160°) clockwise ordered starting

from the “0°” mark, and the “left” one showing the same four marks, but

counterclockwise ordered (-40°; -80°; -120°; -160°). So, these eight marks (four

“right” and four corresponding “left”) are symmetrically positioned relative to the

“0°” and its vertical axis : they divide the space into five parallel “horizontal” sectors

(two polar caps and three parallel disks): each “horizontal” sector (cap or disk) is

subdivided into nine parts by the first protractor while each meridian “vertical”

wedge is subdivided into five parts by the second protractor. It is not necessary that

both goniometer centres coincide. As on a globe, longitude covers the entire

circumference (2π radians or 360°; 9 meridian 40° wedges) whereas latitude covers

(symmetrically) only half circumference (π radians or 180°: π/2 or 90° North and π/2

or 90° South; 2 caps and 3 parallel disks: Fig. 3 at page 37). Note the eccentricity of

the two protractors: on a globe the protractors have the same center and so it is in the

canonical spherical reference system, but, in order to model the centrosome, we must

follow the eccentric disposition of the two centrioles. This “two-

protractors/goniometers-instrument” is sufficient to subdivide the 3D space into 45

pyramids (Fig. 3 at page 37) with the apex at the centre: each pyramid is identifiable

by its own longitude and latitude ( and θ coordinates, corresponding to the

protractors’ marks): each base faces and subtends a vertex solid angle of 4π /45

steradians, then its extension (4π r2/45), in a cell with a diameter of 10 μm (radius: 5

μm; surface: 4π r2 approximately 314 μm

2) corresponds to a cell cortex extension of

31

about 7 μm 2

(a circle with a diameter of 3 μm, or a square with a side of 2.6 μm).

These dimensions together with the physical properties of the MTs (bending-

resistance and rigidity) give an idea about the interesting order of magnitude of the

noise-resistance of this system and of its precision, much better than that of chemical

gradients: 45 cell cortex compartments (or rather poles) are much more than six poles

(anterior, posterior, dorsal, ventral, left and right) and assure a fine tuned polarity.

Fig. 2 Centrosome theoretical geometrical model: a spherical reference system composed of

two orthogonal protractors/goniometers.

A: frontal view of two orthogonal protractors/goniometers, subdivided into nine sectors, which

represents the two orthogonal centrioles: the first (horizontal) represents the base of the MC,

arranged on the equatorial “x y“ plane; its “0° ” mark is used to orient the protractor/centriole; the

second, the DC (vertical, orthogonal to the first), is closer to the reader: both “0°“ marks coincide; it

is convenient to consider the second protractor divided, by its “vertical” diameter crossing the “0°”

mark, into two halves (two opposite symmetrical hemi-protractors).

B: schematic lateral view of the proximal end of both centrioles (during S, G2) to show the

respective position of the above two sections.

An input-output spherical reference system tool based on two orthogonal

protractors/goniometers

32

A spherical reference system tool based on and built by two orthogonal

protractors/goniometers with nine notches, which is what the centrioles precisely are,

in order to recognize (input) coded geometric signals (often at the N-terminus of the

newly synthesized proteins or in the 3’UTR of mRNAs) and translate (output) them

by delivering each targeted complex into the desired final location, must possess: 1)

different marks (non-equivalent centriolar triplets); 2) a constant and ordered

sequence of marks; 3) a start mark; 4) a controlled orientation.

A centrosome will possess all these requirements if its two orthogonal centrioles,

built with 9-fold symmetry, organize the PCM in order to orient 45 scaffolds that

sustain γ-TuRCs (longitude and latitude inclination), and transfer to the PCM their

circumferential non-equivalence, labeling (in coordinated accordance with

neighboring cells) its 45 scaffolds with molecular receptors capable of recognizing

exclusively the targeting sequences corresponding to their orientation: the assembly

of robust MTs with corresponding oriented directions will be the last step.

As it will be better discussed later, Mennella (2012) found that “by using SIM and

STORM subdiffraction-resolution microscopies to visualize proteins critical for

centrosome maturation, we demonstrate that the PCM is organized into two main

structural domains: a layer juxtaposed to the centriole wall, and proteins extending

later away from the centriole organized in a matrix. Analysis of Pericentrin-like

protein reveals that its carboxy terminus is positioned at the centriole wall, it radiates

outwards into the matrix and is organized in clusters having quasi-nine-fold

symmetry. By RNA-mediated interference, we show that Pericentrin-like protein

fibrils are required for interphase recruitment and proper mitotic assembly of the

PCM matrix”. Centriole geometry is then well defined: through the assembly of

molecular complexes with centrifugal radial direction, centrioles are really able to

organize scaffolds/docking platforms for γ-TuRCs, transmitting their circumferential

polarity (non-equivalence of 9-fold rotational polarity is, for the moment, only

supposed): each scaffold (and its γ-TuRCs) assumes a double inclination imparted by

two orthogonal centrioles (longitude and latitude) to acquire its own orientation,

33

parallel to the local centrosome surface tangent plane and receives from centrioles

also the marks (molecular receptors) corresponding to its orientation. The surface of

the centrosome is compartmentalized into oriented and distinguishable (targeted or

labelled) docking platforms for γ-TuRCs (Fig. 3 on this page, 4 on page 43 and 5 on

page 44).

-------------------------------------------------------------------------------------------------------

Fig. 3 Centrosome theoretical geometrical model: discrete subdivision of the centrosome surface.

Nine meridians and four parallels subdivide the centrosome surface into 45 small areas (scaffolds for -

TuRC, which include SAS-4/CPAP, CNN, Asl and Pericentrin), each oriented in correspondence to its

position: their inclination is the result of the addition of two inclinations, one imposed by the MC (longitude)

and the other by the DC (latitude). As on a globe, longitude covers the entire circumference (2π; 9 different

meridians or 9 different meridian 40° wedges) while latitude covers (symmetrically) only half circumference

(π; 2 caps and 3 parallel discs).

-------------------------------------------------------------------------------------------------------

The centrosome-based wiring system could also function in the opposite way. As

before observed, according to this hypothesis, DNA acquires a complete command of

development geometry through the centrosome (and its role of geometrical interface).

Signals from other cells (gap junctions, adhesion molecules, signalling factors,

morphogens) in addition to their intrinsic signaling property can take interesting

information about their provenance, particularly useful, for instance, on the midline;

34

inwards carried by MT-linked dyneins, the direction of their provenance can be

interpreted by the spherically polarized centrosome and immediately used by DNA

which is thus able to integrate external inputs, cues and data (type of signalling

molecule, concentration level, provenance direction) with own genetic programs: a

very important interactively cross-talking between DNA, inner and outer

environments can be carried out by the centrosome and, as we will examine above,

the primary cilium, also connected to the centrosomal MC which constitutes its basal

body. Then, different cells (nearby or far away) can communicate interactively to

build complex organs and tissues (many experiments on competition between

genetically engineered clones in Drosophila wing illustrate this concept). Indeed,

something of the kind happens in the intraflagellar system of transport: Rosenbaum

and colleagues (1969) observed that, in Chlamydomonas (a bi-flagellated unicellular

green alga) following partial surgical ablation of one flagellum, the other is

immediately reduced in length, then re-growth occurs simultaneously in both flagella

until they reach the normal length. Evidently, the basal body organizes the formation

of the axoneme, and, in addition, it is able to decipher and decode information

coming from the periphery of the axoneme (Engel et al., 2012). “Our results reveal a

mechanism that orchestrates both the centriole-to-basal body transition and

subsequent cilia assembly through miRNA-mediated post-transcriptional regulation”

(Cao et al., 2012). The film by Ritter and Griffiths (2012), in which the centrosome of

cytotoxic T lymphocytes (CTL) “senses” the area of the cell membrane where the T

cell has recognized a tumor cell, is significant: this contact must be absolutely

strongly maintained, so the T cell response is the rotation, coordinated and directed

by the centrosome, of nucleus, cytoskeleton and cytoplasm in order to carry the killer

machinery close to the point of cell-cell contact. “The centrosome determines where

secretion occurs by contacting the plasma membrane at the point where the T cell

recognizes the tumor cell…Cytotoxic T lymphocytes are immune cells that destroy the

structural integrity of virus-infected or cancer-causing cells by releasing toxic

granules into them. At the point of contact between the CTL and its target cell an

35

immunological synapse is generated, through which the cells interact. Inside cells the

centrosome, where the cell skeletal elements are made, is responsible for moving

granules to the right place. Brought to the synapse in a CTL the centrosome ensures

that the toxic granules will hit their intended target when the immune cells dock onto

diseased cells. When the centrosome fails to move to the synapse, docking is

unsuccessful, and diseased cells cannot be discarded” (Griffiths and Wathne, 2012).

In conclusion, the finding of Mennella and colleagues, the evidence from Beisson and

Jerka-Dziadosz taken together with centrosome role in transferring different mRNAs

into different cells in Ilyanassa, indicates that our words “two orthogonal centrioles,

built with 9-fold symmetry, organize the PCM and transfer to it their circumferential

non-equivalence (γ-TuRC receptors) in order to orient 45 scaffolds that sustain γ-

TuRCs” are not off track; we are on the right rails.

This is “in nuce” (as ancient Romans said, that is “in embryo”, an expression which is

particularly apt and sounds good in this context) the geometrical model of

centrosome functioning. Now this embryonic and immature (“zygotic”) idea must

develop and mature into an adult presentable proposal. Until now we have conducted

an inductive reasoning, making some generalizations from theoretical and

experimental observations. From now on we will conduct a deductive analysis,

formulating hypotheses strongly founded on experimental evidences and testing the

possibilities to reach logical conclusions. To do that, it is necessary to ascertain more

deeply the theoretical and biophysical properties of a centrosome-based reference

system, starting from empiric data (experimental evidences and findings: from facts

to hypotheses and theories) .

The centrosome

The centrosome (Greek: κέντρον, center, and σωμα, body; “central body” because of

36

its recurring position near the center of the cell) is a sphere made of two orthogonal

centrioles embedded in a proteinaceous matrix (the PCM) from which many radially

(spherically, centrifugally) directed MTs originate (the “aster”).

Centrioles and basal bodies (at the base of cilia and flagella) are the same organelle:

the centriole of the spermatocyte becomes the basal body of the sperm, which, after

fertilization, is again a centriole in the zygote; in non-dividing cells, the MC becomes

the basal body of the non-motile primary cilium. Centrioles are cylinders (or, rather,

prisms, although the orientation of their faces is tilted: each face rotates inward

(about 55°) around its longitudinal edge); depending on the species, centrioles have a

height of 150 to 500 nm and a base diameter of 100-200 nm; their wall is made up of

nine longitudinal bundles (the faces of the prism), each consisting of three parallel

MTs that form the “triplets” (one MT, named “A”, is a complete cylindrical MT, the

other two, named “B” and “C”, parallel to the first one, are incomplete, in transverse

sections appearing like a capital letter C); inside, the structure of the proximal portion

of a new arising centriole has the appearance of a cartwheel, with a central hub and

nine spokes, each one radially directed towards the A-MT of a triplet.

The centrosome, found only in Metazoa and in multicellular algae but not in higher

plants and most fungi, is a sphere of electron-dense material inside which there are

two centrioles (orthogonal to each other during S phase and mitosis). The centrosome

shows many peculiar and unique characteristics: it is the only organelle that exists in

a single copy per cell, together with the nucleus and the primary cilium whose basal

body, in non-dividing cells, is (surprise surprise) the MC of the centrosome itself; it is

the only organelle that does not have a membrane: however the PCM (Peri Centriolar

Material), seemingly amorphous, is strongly organized in cylindrical layers and its

components do not diffuse into the cytoplasm, although some components show

remarkable turnover and high spatiotemporal variability; it is in contact through its

microtubules with each other organelle and each cytoplasmic and cortical location.

Up to now, more than 200 different molecular complexes, highly conserved from

Protists to Mammals, have been identified in centrioles and centrosomes. A recurring

37

question: why are so many different (and highly conserved) proteins orderly arranged

in coaxial cylinders around both centrioles in the PCM that compose the centrosome?

When a cell enters the S-phase, the two centrioles separate (disengagement) and,

orthogonally to each of them, a new one is assembled; the two new centrosomes,

each containing an old centriole, named “mother”, and a younger, newly assembled,

centriole, the “daughter”, participate (without being strictly indispensable) in mitosis

and form the mitotic spindle, of which they constitute the poles; each centrosome will

be inherited by one of the two daughters (sisters) cells. This unique semi-conservative

duplication is reminiscent of something similar to DNA, but it has been clearly and

definitively shown that centrioles and centrosome do not contain DNA and their

duplication does not occur by copying a template: on the contrary two different

pathways for centriole duplication have been described, one requiring a preexisting

MC that works like a platform to control the new DC assembly, and a de novo (“ex

novo”, to me, is a more correct Latin form, but it is rarely used in biological papers)

assembly pathway, turned off when a MC is present (with few exceptions, like

multiciliated cells). Such unusual and unique duplication modality (in which the self-

assembly capability of many macromolecular centriolar complexes is particularly

important) might allow the centrioles of the daughter (sister) cells to acquire the same

circumferential ordered polarity (positioning of the “0°” mark) and orientation of

their mother: so, from the zygote on, every cell could have its polarity coordinated

with the global polarity of the whole tissue and its architectural project.

The centrioles inside the centrosome are quite different: the older one, the ”mother”,

has nine external radial distal (“distal” is toward the centrosome surface, “proximal”

toward the centrosome center) and nine sub-distal appendages, while the younger one

(the “daughter”) has nine different small distal ribs (structural difference); only the

MC can form a “primary cilium” (functional difference); the orthogonality between

MC and DC is asymmetric: the daughter’s longitudinal axis, if prolonged, crosses the

other, so that the base of the DC faces the lateral surface of the MC’s proximal end,

but not vice-versa so that only the MC has a central pivotal position like a hub

38

(geometric difference: eccentricity). The centrosome is polarized: the “L” shape of

the two centrioles allows a proximal-distal axis to be identified (it coincides with the

MC axis), with a distal pole characterized by the described MC appendages, and a

second orthogonal axis along the DC. During centriole duplication, one spoke of the

“cartwheel” of the DC is parallel to the MC axis.

After mitosis, the MC, in non dividing cells, remains fixed, anchored to the cell

membrane by numerous MTs, positioned at the base of the primary cilium (of which

it is the basal body), whereas, during interphase in dividing cells it is often linked to

the nucleus; the DC is much more free in the cytoplasm.

The centrosome is the main cytoskeletal organizing center: from its PCM numerous

robust MTs emerge, centrifugally directed towards the cell cortex, assembled by rings

containing -tubulin (-TuRC, composed of -TuSCs: -Tubulin Small Complexes)

anchored through the participation of several proteins (SAS-4 and pericentrin, above

all) which form scaffolds or docking platforms. MTs are also associated with several

proteins: kinesins and dyneins are two families of motor proteins that utilize MTs as

rail tracks to carry organelles and macromolecules respectively outwards and

inwards; MAPs (Microtubules Associated Proteins) are a family of tissue-specific

proteins with different activity: MT (de)stabilization, linkage to the cytoskeleton and

association to the cell membrane.

MTs are long tubes whose walls are made up of polarized heterodimers of α and β

tubulin, arranged in 13 polarized longitudinal parallel filaments, with a ”minus” end

fixed (in vivo) on a -TuRC and a growing “plus” end, centrifugally outwards

directed: in vivo, α-β tubulin heterodimers are added to the “plus” growing end; what

is the function of the -TuRC-linked “minus” end? The -TuRC is clearly an

anchoring base and an oriented platform that dictates the direction of the MT.

The centrosome and its centrioles are likely the most sophisticated biological

structures: nevertheless still now the centrosome is a “character in search of an

Author” to use the title of the comedy by Pirandello. What the centrosome’s role is

and how it functions, it is still unknown.

39

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Fig. 4 Centrosome theoretical geometrical model: orientation and labeling of -TuRCs.

There is an absolute univocal and unambiguous one-to-one correspondence between targeting signal, -

TuRC receptor, -TuRC orientation, MT direction, cell cortex compartment. Signal: undulating line

(A) linked to a “twisted-chain” protein; the signal, also named in the text “geometric address” or “ targeting

sequence”, is encoded in DNA and, after being transcribed or translated, is contained and displayed in the

polypeptide or in the polyribonucleotide (twisted tube) destined for a pre-established cortical localization and

recognized by the -TuRC receptor (undulating line at the base of the hemi-circle structure, the scaffold of

the -TuRC disk on the scaffold); different -TuRC receptors (B,C) do not fit in with the “undulating”

line/signal: they mark -TuRCs having orientations corresponding to different directions; orientation of the

-TuRC itself, from which an MT (D arrow) originates, with a precise direction, points to the desired cell

cortex location (E) (thus implicitly encoded in each signal/address). A kinesin carrier (wheel) transports the

complex centrifugally. -TuRC orientation, MT direction and cortical compartments are the molecular

“hardware” of the system whereas signals and -TuRC receptors represent the molecular “software”.

40

Fig. 5 Centrosome theoretical geometrical model: functioning.

Small ellipses represent γ-TuRCs on the centrosome (large sphere): each one is identified by its own private

receptor (capital letters: A, B, C) which recognizes only the corresponding targeting sequence. Each γ-TuRC

has the orientation of the plane which, in that point, is tangent to the centrosome “spherical” surface. MTs

(arrows) are nucleated with directions imposed by the orientation of the corresponding γ-TuRC: like

orientation, like direction (one “discrete” orientation, one “discrete” direction). So, a molecular complex

(twisted tube) through its “geometric” targeting sequence, recognizes and links exclusively the receptor (A or

B or C) that marks that γ-TuRC which has the correct orientation to nucleate a microtubule directed to the

desired (corresponding: A or B, or C) destination, reached through a kinesin carrier (wheel): one targeting

sequence, one γ-TuRC receptor, one cortical compartment: one-to-one univocal correspondence.

-------------------------------------------------------------------------------------------------------

“The strange case of ”… the centrosome cycle

Like Dr. Jekyll, centrioles have a double identity: daughter in a cell cycle, mother in

the next. In Ciliates new centrioles arise using a pre-existing centriole as a platform:

instead in Metazoa, firstly the DC changes identity and matures into a new MC, then

41

from both MCs (old and new) two new DCs arise. The “old” MC, after

disengagement, during S phase assembles a new DC orthogonally, whereas the “old”

Daughter, after moving from the proximal end of its “old” Mother toward the distal

end, disengages from its “old” Mother, though maintaining a connection with it, is

transformed in a new MC (losing its ribs and acquiring the distal and subdistal

appendages characteristic of the MC) and, only after its maturation from Mother to

Daughter, it too assembles a new DC. The two new centrosomes, each one containing

two orthogonal centrioles, one old and one just newly formed, also maintain a strict

connection during S phase and prophase. This is a very strange case and, perhaps,

unique: other cellular organelles, structures and components, before cell division, are

divided or produced de (ex) novo or built copying a template, but each one maintains

its identity, its role and its function; DNA filaments are separated by DNA

helicase/polymerase but the old filament 3’-5’ remains in the new cell a 3’-5’ filament

(leading strand), and so does the other 5’-3’ filament (lagging strand), each one

conserving its role and its leading or lagging identity. As we have seen, centrioles,

that can be formed de (ex) novo, normally are assembled by using only the MC as a

platform and the new centriole arises always at right angle in respect to the MC: why

do Metazoa form a new centrosome through such a complicated, unique and

expensive process? (Fig. 1 on page 13). Embryo’s development is a very risky

process, above all for those species that use external fertilization, because of

predators: cleavage divisions have to occur very fast: 37,000 divisions in 43hours in

frogs, 50,000 divisions in 12 hours in flies, one every ten minutes; nonetheless this

unique, complicated and expensive mode of centrosome duplication has been chosen

also by those Metazoa that use external fertilization. Why? “If conserved, it is

important”: an excellent reason and an important explanation must exist. A last

observation about the eccentricity and uniqueness of centriole duplication: the MC of

a cell, after division, is inherited by only one of the two new sister/daughter cells,

which, at its turn, will transmit this same MC to one of its daughter cells: so, in a

clone of cells (derived from the same common ancestor cell) the MC of the ancestor

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survives (like a long-lived imperishable Phoenix) in only one cell of the group; the

age of each cell is the age of its MC: isn’t it very strange? In a sense it is possible to

affirm that every cell division is asymmetric: one cell remains a mother cell (that one

which conserves its old MC) whereas the other one is a real daughter cell with a new

MC: after each division there are not two sister cells, but a mother and a daughter

cell.

No centrosome? No gastrulation

“It is not birth, marriage or death, but gastrulation, which is truly the most important

time of your life” (Wolpert, 1986).

It is my personal conviction that this process of DC maturation (from Daughter to

Mother centriole) is evidence of an evolutionary event of exceptional importance: the

passage from already complex single-celled beings (many Protists show astonishing

complex shapes) or 2D multi-celled organisms to a complete 3D architecture (i.e. not

only simply laminar or tubular/cylindrical structures); this passage has deeply

involved centrioles and centrosomes. Multi-cellular organisms need coordinated and

common 3D polarity; gastrulation furnishes a clear example of 3D organization and

illustrates the fundamental difference of 3D architecture and dynamics in respect to

2D laminar processes: gastrulation requires a fine polarization of cell (differential

adhesion) and, above all an orderly orientation of the extracellular matrix fibers

which must be orientated according to common and shared directions: gastrulation

goes in parallel with the appearance of mesenchyme and mesoderm (and their

organized fibers), and, above all, with a well formed centrosome: “The

embryogenesis of freshwater planarians is equally intriguing: cleavage of the

fertilized egg was described as ‘anarchic’ by early developmental biologists. No overt

gastrulation or epiboly has been described in these embryos, yet they manage to

develop anteroposterior and dorsoventral axes without difficulty.” (Sànchez

43

Alvarado).

No centrosome? No gastrulation.

Lacking centrosomes, Planaria not only have lost the ancestral cleavage pattern, but

also the capability of performing gastrulation.

Shared and coordinated orientation of metazoan centrosomes

From facts and evidences (just now examined) to new hypotheses and theories.

“Centriole duplication is part of the mechanism by which the cytoskeleton of the

Daughter cell is patterned upon that of the mother” (Harold). The MC, before

disengagement, likely transmits to its old DC the information of orientation, and

physically orients its old DC in respect to the cytoskeleton; effectively also in Ciliates

the process of centriole duplication occurs at right angle and utilizes a pre-existing

centriole as a platform to orientate the arising centriole polarity in order to insert it

correctly in the complex cytoskeleton, something like a new trolley-bus (whose two

sprung trolley poles must be correctly connected to the two polarized electric wires)

is orientated and correctly (front-rear) positioned in respect to the “electric city-

skeleton” made of aerial-suspended wires; so the cells in a tissue become co-

ordinately polarized by co-ordinately oriented centrosomes: in Metazoa the

centrosome is the “intrinsic” (no external cues) reference system; plants, fixed in the

ground, use an “extrinsic” reference system (light and gravity), just as a compass uses

(extrinsic) Earth magnetism and a GPS utilizes (extrinsic) satellites: as an “extrinsic”

reference system is common to each receiver, similarly an “intrinsic” reference

system must be the same (identically oriented) in each cell; multicellular organisms

must possess a mechanism to transmit, share and co-ordinate their inside points of

reference (as we have seen, centrosomes increase cell polarity up to 45 poles) and this

function is performed through the orientation imprinted by the MC to its “old” DC

before disengagement, so that two co-oriented MCs build two co-oriented

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centrosomes before cell division: so, all the cells of a tissue have the same points of

reference to correctly build complex 3D organs. This unique behaviour of

centrosomes supports the idea that their main role is the translation of the virtual

(DNA coded) cell geometry into an actual real cell wiring system. When a new

procentriole arises (orthogonally and near the MC) the cartwheel is formed: 9-fold

symmetry and chiral (Guichard, 2013) non-equivalence of triplets (fundamental, in

the geometrical model of centrosome functioning, for left-right patterning) are

established co-ordinately and corresponding with those of the mother centriole:

"Whereas the cartwheel is thought to nucleate the nine fold rotational symmetry of

the microtubular triplets the acorn [see at page 51] might play an equally important

role imposing rotational asymmetry on the microtubular triplets, perhaps leading to

the asymmetric assembly of basal-body-associated fibers and hence cellular

asymmetry in general" (Geimer and Melkonian (2004). [Looking for “centriole

architecture” through any web search engine, it is possible (and convenient) to have

an updated idea on this continuously developing matter]. So, in tissues, all the

centrosomes maintain a common, shared and coordinated orientation to operate as

molecular geometric 3D interfaces that translate morphogenetic signals into precise

locations in the cell and in the whole tissue (extra cellular matrix fibers): their

biochemical structure is the “hardware” and their “software” consists in “targeting

sequences” and “labelled” γ-TuRC receptors; unfortunately, the comparison between

computers and living organisms ends here: in living self-replicating cells, each newly

formed geometric tool (centriole and centrosome) must “tuned” every cell division.

As we have already seen, through the centrosome, DNA organizes the cell cortex by

fine-tuning its polarity (45 cortical non-equivalent compartments) that must be

transmitted (and shared) from cell to cell.

About the non-equivalence of the triplets in centriole/basal bodies in Ciliates

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“Among flagellates, the appendages are also varied, biochemically and

morphologically; even microtubule appendages may have highly complex shapes as,

for example, in Physarum or in Ochromonas” (Beisson and Jerka-Dziadosz, 1999).

Non-equivalence of the triplets, their molecular-structural individuality capable of

distinguishing each other, is the main question to face.

Facts, above all: many studies on Protists have demonstrated that the nine triplets of

their centrioles/basal-bodies are different (not-equivalent) and arranged in an ordered

sequence: circumferential polarity in the arrangement of basal body triplets is

accorded with the disposition of the cytoskeleton. Ciliates contain only centrioles,

each at the base of a cilium or flagellum: they do not have centrosomes with two

orthogonal centrioles; orthogonality appears only during the assembly of a new

centriole, which arises and grows perpendicularly to a pre-existing one. The

biflagellate unicellular green alga Chlamydomonas reinhardtii has an ordered

location of its organelles: cilia, oral apparatus, nucleus, chloroplasts, pyrenoid,

eyespot, excretory vacuoles; this organization depends on the disposition of different

cytoskeletal fibers (four cruciform rootlets: two thick, made up of 4 MTs, and two

thin, made up of 2 MTs); the cell appears clearly polarized: an Apical-Basal axis from

the cilia to the pyrenoid, a Dorsal-Ventral axis orthogonal to the first, from the

nucleus to the oral apparatus; also a transverse axis of asymmetry (orthogonal to the

other two axes) is established because of the asymmetric position of the eyespot. In

Protists, centrioles organize the cytoskeleton (Feldman et al., 2007): structural

anomalies in centrioles cause disorders in the cytoskeleton (cruciform fibers lose their

normal composition or their orthogonal disposition). Chlamydomonas has two apical

flagella, whose movements are coordinated during planar 2D strokes, and during

conical-helical 3D rotations. The axoneme of its flagella is composed by the

canonical nine MTs doublets/blades (cilia and flagella have “doublets”, not triplets);

these blades are not equivalent: electron microscopy has allowed each one of the nine

doublets to be distinguished, each one showing its own morphological characteristic,

that identifies itself from the other, and its own fixed location relatively to the others;

46

the two central MTs of the axoneme are also different. Electron microscopy (Hoops

and Witman, 1983; Bui et al., 2009) has highlighted that the circumferential

asymmetry of the axoneme corresponds to (and is likely built by) to an even more

marked circumferential asymmetry of the basal body/centriole: it is possible to

distinguish each one of its nine triplets and their orderly sequenced arrangement,

determine the 180° rotation of one basal body compared to the second and observe

the connection between each triplet and particular fibers of the cytoskeleton: the

striated fibers of the “distal connector”, tie (or rather “connect”) and fasten the

triplets 9-1-2 of both basal bodies; the thick cruciform fibers are attached to the

triplets N° 3 and 4, the thin ones are linked to the triplet N° 8; the newly-forming

procentriol is always in front of the triplet N° 9. Geimer and Melkonian (2004) have

described an “acorn-like” structure in the inner distal part of the basal body, adhering

in a highly asymmetric manner to the triplets 2-1-9-8-7, and another structure, shaped

like the capital letter “V” in contact with the triplets 9, 5 and 4: "whereas the

cartwheel is thought to nucleate the nine fold rotational symmetry of the microtubular

triplets the acorn might play an equally important role imposing rotational

asymmetry on the microtubular triplets, perhaps leading to the asymmetric assembly

of basal-body-associated fibers and hence cellular asymmetry in general".

Thus, the process through which centrioles are built appears composed of two

different stages: first the 9-fold symmetry is firstly established (cartwheel) then

rotational polarity is imposed (acorn). By the way, there is a question with regard to

the cartwheel, which in Metazoa is formed only in the daughter centriole during its

building (“In vertebrate centrosomes, a cartwheel structure is present at the base of

procentrioles but is no longer seen in daughter and mother centrioles” Azimzadeh

and Marshall, 2010): if it were only a structural component of the centriole, it would

be present not only in the proximal portion of the nascent centriole and, in addition,

could not be absent in mature daughter and mother centrioles. It is likely the

cartwheel has, apart from its transient structural role in probasalbodies, other tasks:

establishment of the 9-fold symmetry and, perhaps, the arrangement of the molecular

47

platform for generating the non-equivalence of the 9-fold rotational symmetry; this

idea is supported by several measurements of the tilt angle of inward rotation of the

centriolar triplets blades (see “The centrosome” at page 40) that increases from the

proximal to the distal end: only the proximal region of the daughter centriole (where

the cartwheel is formed) is responsible for assembling the PCM around the DC, as we

will see later.

The shape of any structure is the consequence of its molecular composition: in C.

reinhardtii the polypeptide VFL1 coded by the gene vfl1 (Variable number of

FLagella), binds only to the triplet N° 1 (Silflow et al., 2001) confirming the

biochemical nature of the circumferential asymmetry.

Another Protist, Paramecium, has similar characteristics (Beisson and Jerka-

Dziasdosz, 1999): the high number of basal bodies (and cilia: about 4,000) is

accompanied by their ability to self-organize and to connect with each other in about

70 regular rows, always with the same orientation of the triplets (in order to beat with

coordination and synchronism), just using their circumferential asymmetry and

structural differences between the triplets; each new basal body arises at right angle

from an old one, then straightens up and rotates to acquire a precise and coordinated

orientation with its complex cytoskeleton: the triplet N° 9 links to the “postciliary

ribs”, the triplet N° 4 is attached to the “transverse ribbon”, the triplets N° 5-6-7 are

connected to the “kinetodesmal fibers”. This role of basal bodies in organizing the

arrangement of cortex and cytoskeleton agrees with the movements of the DC

described in many Metazoa (cortical cytasters: Salinas-Saavedra and Vargas, 2011)

and in Mammals (Piel et al., 2000), where it seems to organize in detail specific

peripheral cell sectors. Interventions of the centrioles/basal bodies in a complicated

cortical organization have also been described in Trypanosoma (Lacomble et al.,

2010), in which a characteristic rotation of the new DC around the MC has been

observed.

Chlamydomonas basal-bodies are also capable of regulating the length of the two

flagella: Rosenbaum and colleagues (1969) observed that, following partial surgical

48

ablation of one flagellum, the other is immediately reduced in length, then re-growth

occurs simultaneously in both flagella until they reach the normal length: basal-

bodies organize axonemal components, attentively regulating the activity of kinesins

and dyneins through a highly sophisticated mechanism, the Intra Flagellar Transport.

Summarizing, in protistan centrioles, built with 9-fold symmetry, each triplet shows

its own morphology, its fixed position and linkage to the cytoskeleton and even a

molecular individuality has been proved for the triplet N° 1; furthermore, centrioles

are univocally oriented in the cytoplasm, in respect to the cytoskeleton: all of the

theoretical requirements of a “biological” protractor are satisfied. And in Metazoa?

V.I.P. Very Important Proceedings

Two studies have opened a new scenario for the centrosome: (1) the first (Dodgson,

2013) faces the problem of cell cortex compartmentalization that allows cells to

achieve a more detailed polarity (indeed Anterior-Posterior and Dorsal-Ventral axes

are too few to build complex organs); interestingly, the compartmentalization of the

centrosome surface (45 small areae) quantitatively corresponds to the cortical

compartmentalization shown by this study (one-to-one correspondence between

centrosomal and cortical compartments); (2) the second (Blower, 2013) highlights the

role of the centrosome in binding and delivering mRNAs into defined cytoplasmic

localization.

These works introduce the idea of a centrosome that operates like a mail-sorting

machine: zip-codes (alpha-numeric characters not able to be recognised by the optical

devices of the machine) are firstly read by a scanner and transformed into barcodes

(stripes of vertical bars printed onto the envelopes) able to trigger the devices that

control the entrance in the correct lane. DNA (in exons, or in introns or in other part

of the sequences that flank a gene) stores the code for the cortical position where an

mRNA or a protein (transmembrane receptors, polarity and adhesion factors above

49

all) must be located: this code is transcribed into RNA (3’ UTR, miRNAs?), which

can match and accompany mRNAs and proteins, or can be translated into the protein

itself (N-terminus targeting sequences/ligands) so that the final 3D shape of each

code is easily recognized by -TuRC receptors (see later); for instance nanos and

bicoid mRNAs are localized in the fly oocyte cytoplasm through MT transport,

driven by their 3’UTR sequence. Let’s then read these findings:

1) “The polarity machinery of fission yeast is arranged into cortical clusters that are

dynamic and persistent…This suggests that the interaction between different polarity

factor species may be an actively regulated feature, and not simply occur as a default

when polarity factors reside within a same general domain at the cell cortex. Future

work should aim to clarify how the various polarity factors are targeted to different

clusters. This may be accomplished through post-translational modification of certain

polarity factors through competitive binding interactions. Thus, cortical

compartmentalization of proteins into discrete clustered domains may be a general

feature exploited by cells to control spatiotemporal signaling events with high

fidelity…Cortical compartmentalization of proteins into discrete clustered domains

may be a general feature exploited by cells to control spatiotemporal signalling

events with high fidelity. As we observe similar polarity factor clusters in

Saccharomyces cerevisiae and Caenorhabditis elegans cells, the clustered

organization of polarity factors within cortical subdomains and regulated cluster

segregation may be key regulatory features across many organisms. In the case of cell

polarity, cortical nodes and their spatial segregation could contribute to robust ‘on’

or ‘off ’ switching of polarity at the right place and time in cells, following intra- or

extracellular signals…This suggested that localized microtubule delivery (of polarity

factor Tea1) and/or oligomerization could suffice for the formation and maintenance

of cortical nodes of both Tea1 and its interactor Mod5…A quantitation of node

number in Tea1-GFP, Tea3-GFP, Tea4-GFP and GFP-Mod5 cells showed that a

typical cell end consistently organizes 20–30 nodes of each protein dispersed along

the cell cortex” (Dodgson et al.).

50

2) “Localization of mRNAs to specific destinations within a cell or an embryo is

important for local control of protein expression. mRNA localization is well-known to

function in very large and polarized cells such as neurons, and to facilitate embryonic

patterning during early development. However, recent genome-wide studies have

revealed that mRNA localization is more widely utilized than previously thought to

control gene expression. Not only can transcripts be localized asymmetrically within

the cytoplasm, they are often also localized to symmetrically-distributed organelles.

Recent genetic, cytological, and biochemical studies have begun to provide molecular

insight into how cells select RNAs for transport, move them to specific destinations,

and control their translation…One of the major types of mRNA transport in

Drosophila embryos is the movement of mRNAs involved in developmental pattern

formation to the apical centrosome. Movement of these mRNAs occurs in a dynein-

dependent manner and requires Egl and BicD for transport. However, little was

known about the mechanism of RNA anchoring at the centrosome... Microtubules are

used for the majority of long-distance transport within cells. Microtubules are

important for the localization of the majority of known localized mRNAs (with the

notable exception of localized mRNAs in Saccharomyces cerevisiae, which require

actin-based transport) through the action of various motor proteins. However, several

studies suggest that microtubules are not just a highway for transporting mRNAs, but

can also serve a destination for some localized transcripts. Purification of

microtubules from a variety of organisms (sea urchin, frog, human) has demonstrated

that hundreds of mRNAs co-purify with microtubules. The majority of microtubule-

localized mRNAs code for proteins that appear to function in cell cycle and

microtubule-related processes. Our group recently tested this idea directly by

knocking down the mRNAs for 10 uncharacterized microtubule-localized transcripts

in HeLa cells. We found that the majority of these mRNAs coded for proteins required

for proper microtubule organization during both interphase and mitosis. Work in

Xenopus oocytes has also found that both spindle localization and translational

control of a subset of mRNAs are important for completion of both meiotic divisions,

51

highlighting the link between mRNA localization and translational control. In

addition to containing mRNAs that control the microtubule cytoskeleton,

microtubules also contain a number of transcripts that appear to be translationally

repressed and are likely to be passive cargo on the spindle rather than active

participants in controlling microtubule-related events. This idea is consistent with

recent work looking at RNA localization in early cell divisions of the snail Ilyanassa

obsoleta. In this work, the authors used RNA FISH to examine several mRNAs

important for early development. Some of these transcripts show an unequal

distribution during cell division by selectively associating with one of the two

centrosomes of a dividing blastomere. This suggests that unequal segregation of

important developmental mRNAs by the mitotic spindle could be an important

mechanism for the establishment of early patterning asymmetries. While many

mRNAs are known to localize to meiotic and mitotic microtubules little is known

about the sequences or proteins involved in this process” (Blower).

Facts and evidences, these, from which hypotheses can be formulated: Dodgson

(control his schematic in his article, free on the Internet) models the process of

cortical compartmentalization in such a manner that agrees completely with our

images (Fig. 4 and 5). From RNA localization to centrosome and its alternative

differential delivering it is plausible to formulate the hypothesis of the geometrical

role of the centrosome as a biological interface.

It is convenient, now, to review other evidence.

“While centrioles are dispensable for spindle assembly, they are more important for

spindle positioning. When centrioles are experimentally ablated, spindles drift within

the cell” (Azimzadeh and Marshall, 2010).

In Drosophila embryos all syncytial mitotic divisions are not randomly oriented, but

strictly controlled by the centrosomes that remain linked to their own nuclei (if

centrosomes are experimentally damaged, development stops immediately): the first

4 divisions generate nuclei that remain radially equidistant from the center and form a

sphere; then, during cycles 4-6, the division planes are oriented in such a manner that

52

nuclei distance themselves along the AP axis, transforming the sphere into an

ellipsoid whose marginal nuclei are symmetrically equidistant from the cortex.

During the stages 7-10 a characteristic symmetric migration towards the cortex

occurs; Baker and colleagues (1993) have proposed that "cortical migration is driven

by microtubule-dependent forces that repel adjacent nuclei". A network of

interdigitating microtubules (like the polar MTs that in metaphase connect the two

opposite spindle poles, overlapping their oppositely directed “+” ends) forms between

yolk cells centrosomes (not-migrating) and peripheral centrosomes (migrating): this

geometric network of MTs carries nuclei to the cortex while their final ordered

position appears to be due to astral MT population (unlikely polar MTs, astral MTs

with reversely directed polarity do not overlap: boundary MTs of different asters go

parallel with their plus ends pointing in the same direction). "In Drosophila the

movements of nuclei to the embryo cortex are mediated by forces acting on the

centrosomes rather than on the nucleus itself. Asters are presumably the main target

of such forces. It is then conceivable that MTs, nucleated on either side of the

centrosome or which display different characteristics, are nucleated under the

influence of opposite sides of the centriolar shaft, just as different appendages arise

from basal bodies. The situation in S. cerevisiae gives some support to the idea: the

spindle pole body, functional equivalent of the centrosome, displays a marked

structural and functional bipolarity with an intranuclear spindle and an aster of

cytoplasmic microtubules. Like in Metazoa, defective astral microtubules lead to

defective nuclear positioning and defective budding. The biochemical and

physiological differences between the two microtubule arrays are already well

documented. Different gamma-tubulin binding complexes interacting with the inner

or outer plate respectively, are involved in the nucleation of the two microtubule

arrays” (Beisson and Jerka-Dziadosz, 1999). The ordered separation of nuclei, the

controlled asymmetry of their arrangement, in anterior-posterior direction, and their

division into two cortical halves (Right and Left) have been highlighted in a study

based on the differential spatio-temporal beginning and speed of mitosis N° 14,

53

defining domains in which cells start to divide simultaneously (Foe, 1989); 25 left

and 25 right domains with different form and extent are evident: "all the domains

described also occur as pairs. Whether paired or not, every domain is bilaterally

symmetric." A clear midline is evident both dorsally and ventrally; domains show an

interesting link between centrosomal and cleavage geometry (very surprising are the

images by Foe, 1989, in: “Mitotic domains reveal early commitment of cells in

Drosophila embryos”, freely available on the Internet). Strikingly, domains appear

arranged according to the theoretical model of the centrosome in longitudinal

wedges, one on the midline, four “left” or “Occidental, Western” (so to say, if one

prefers geographical terms) and four “right” or “Oriental, Eastern”, intersecting two

polar caps and three parallel rings; it appears that the cortex of the embryo is mapped

and compartmentalized by the zygote centrosome: both maps (theoretical centrosome

compartmentalization showed in Fig. 3 on page 37 and fruit fly embryo cortex at 14th

mitosis) coincide; as we have seen, through the centrosome DNA “invents a

spherically organized space”, creates a 3D design upon an equal, homogenous,

equivalent and nameless cortical surface and draws a labeled grid line: a featureless

and unidentified cell cortex, mapped and wired by the centrosome aster, acquires a

useful labeled compartmentalization: it becomes polarized in detail.

From these studies an extraordinary and surprising correspondence emerges with the

theoretical geometrical model of centrosome functioning, about both the centrosome

“hardware” (spherical compartmentalization and one-to-one correspondence between

centrosomal and cortical compartments, and therefore 3D inclination of γ-TuRC

scaffolds) and the centrosome “software” (different centrosomal receptors, differently

located on the centrosome to bind different ligands for differently delivering them in

the cytoplasm).

Morphogenesis and thermal fluctuations in the cell environment

54

“We hypothesize that centrosome loss occurred concomitantly with the loss of the

spiral cleavage and oriented cell divisions in the ancestor of planarians and

schistosomes….It is remarkable that the loss of such a conserved organelle as the

centrosome occurred within not-parasitic flatworms, as cellular and developmental

processes appear largely conserved between these species. A significant difference

can be found in the mode of embryonic cleavage however. Macrostomum retained the

ancestral spiral cleavage, also found in annelids and molluscs, which relies on a

stereotypical pattern of cell division orientation. In contrast, planarian and

schistosomes embryos undergo divergent modes of embryonic cleavage, which

apparently do not involve oriented cell divisions” (Azimzadeh et al., 2012). As we

have seen on page 46, centrosome loss occurred concomitantly with the loss of

gastrulation too. To create the correct “stereotypical pattern of cell division

orientation”, evidently the species-specific instructions for positioning the spindle

poles in each cell division are encoded and stored in DNA: in effect we have already

seen that only one gene is responsible for left- or right-handed spiralian cleavage. The

centrosome receives any recognizable signal from DNA and, through its MTs,

nucleated by properly oriented γ-TuRCs, positions the poles of the spindle in such a

way that cleavage is, as forecast by DNA, radial, spiral, bilateral, syncytial, discoidal

or rotational. During cleavage, the size of blastomeres can vary in a continuous

fashion (starvation, abundance of nutrients, temperature) but the angle between two

subsequent division planes is precisely and discretely fixed, always constant for each

species and not continuously distributed in an interval of values: to give an example,

the angle between the planes of two successive early meridian divisions in sea urchin

embryos (from 2 to 4 cells, and continuing to 60 cells) does not vary around a main

value, it always has the same identical precise value, whatever the size is of the

zygote; after the surgical separation of the two first blastomeres of a sea urchin or a

frog embryo, two complete, but smaller (about half-size) embryos develop,

nonetheless the plane of each cleavage division occurs following and maintaining the

same precise stereotyped pattern (orientation), characteristic of the species: size

55

changes, directions do not, like vectors; and so it is during the first stages of organ

development. It seems that metazoan cells possess a “discrete” instrument able to

precisely read angle values from DNA instructions (specie specific, then genetic,

pattern of cleavage division orientations) and realize 3D, bilaterally symmetric when

necessary, angles (spindle pole positioning) having the programmed value: in

addition, angle amplitude appears to be chosen in a limited number of discrete values;

consider for example left and right semicircular canals and their striking directional

precision: the macroscopic result (high spatial precision of anatomical structures)

descends from the addition of many and many microscopic arrangement of cells,

developmental microprograms or modules which organize the assembly of a few

cells with an extraordinary level of precision (as in cleavage); the addition of many

different modules is necessarily affected and conditioned by different factors (e.g.

diverse cell size due to random localized abundance/deficiency of nutrients). Indeed

about the word “precision” a comment is necessary: 45 cell cortex compartments are

much more than 10 thousand dots per inch (dpi) that is a very high graphic precision;

however the surface of each compartment (a square with a side of 2.6 μm) is

enormous if compared to the dimensions of a protein (the average diameter size is

about 3-6 nm); so in metazoan organisms, composed of thousands billion cells (1014

),

we can see high precision of shapes but not absolute identity; Metazoa utilizes that

level of precision which necessity and sufficiency require to achieve high quality

stereotyped reproducibility, but not identity.

Let’s come back to the work of Dodgson and colleagues: “The establishment of

domains of polarity factors occupies and confers different identity and function to

restricted areas of the cell cortex”: like the centrosome surface, the cell cortex too

appears to be compartmentalized into non-equivalent distinguishable areas.

...“Complexes are delivered to cell ends by growing microtubule tips”: one-to-one

correspondence between corresponding centrosome and cortical compartments is

assured by MTs originated from oriented centrosomal γ-TuRCs.

...“Intriguingly, nodes did not appear to correspond to similarly distributed lipid

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microdomains...,Thus, oligomerization can trigger cluster formation and enable

cortical enrichment of polarity factors in cells”: the large dimension of the cortical

compartments with respect to the protein diameters is compensated for by self-

oligomerization (self-assembly of homo- and hetero-monomers).

...“What could be the physiological advantages of spatially confining polarity

regulators to nodes? One possibility is that nodes could provide a means for cells to

control polarity at the cortex in space or in time, by regulating or preventing polarity

factor interaction, or by segregating certain node populations from others....In

summary, the polarity machinery of fission yeast is arranged into cortical clusters

that are dynamic and persistent, and may be formed by oligomerization (direct or

mediated by an interacting partner). Many polarity factors can be found in

neighbouring but separate cluster populations, with this spatial segregation

potentially key to their function. Although the clusters are dynamic, they are also

persistent and appear relatively immobile, and it is not yet clear what the functional

significance of that persistence/immobility might be. One possibility is that it may

allow polarity factors to maintain a stable domain of localization and function.

Alternatively, it may ensure that certain polarity factor clusters only interact with

others at specific locations and times within the cell, as exemplified by Tea1 and

Tea3. This suggests that the interaction between different polarity factor species may

be an actively regulated feature, and not simply occur as a default when polarity

factors reside within a same general domain at the cell cortex”. Fine tuned polarity is

absolutely necessary in Metazoa: an accurate and careful control of polarity at the

cortex in space and in time is the most important characteristic of differential

adhesions, indispensable in convergence and extension, epiboly, invagination.

The “software”

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The idea about the spatio-temporal dynamics of cortical compartments can explain

another property of the centrosome: we must not think of cells like globes mapped

once and for all: on the contrary the centrosome (which really is compartmentalized

once and for all), in different cells and in different phases of the cell cycle and life,

can assume different (controlled, never random) positions and, through it, DNA can

“design” a newly oriented cortical grid line (e.g. in migrating cells that respond to

differently localized chemoattractants); when the centrosome is near the center of the

cell, one of its 45 compartments nucleates an MT directed toward a particular cortex

area (e.g. that one where one spindle pole must be positioned in order to dispose the

division plane with a desired angle with respect to the proximal-distal axis of a

developing limb); differently, when the centrosome is near the cell membrane, for

reaching the same cortical area, another γ-TuRC must be chosen, that one which, in

this different configuration, is properly oriented. The centrosome can change its own

orientation (not randomly but under control) the orientation of the cytoskeleton and

the global polarity of the whole cortex (like in migrating cells) but cells always know

their orientation and the position of the centrosome; in DNA the cell map and its

relative virtual grid line, that DNA “physically and really” draws in the cell through

the centrosome, is stored and coded: DNA chooses, step by step, the most convenient

orientation; on this data, during evolution, new geometrical steps (targeting sequences

calculated in accord with the position of the centrosome) have been added to

developmental programs in order to build more and more complex organs and

organisms. Step by step, stage by stage, new targeting sequences, appropriate to the

spatio-temporal position of the centrosome, have been added (“approved” by

purifying selection) to developmental programs in such a way that cells are correctly

guided and positioned to realize very complex organs. Targeting sequences are not

“absolute” (like North, West, etc.) but relative to the centrosome (known) position

and cortex compartmentalization (known) orientation: to reach an area with a given

angle respectively to the Dorsal-Ventral axis and a given θ angle respective to the

plane containing the Dorsal-Ventral and Anterior-Posterior axes, in a developing

58

embryo, different targeting sequences are chosen (and have been selected during

evolution) from time to time, depending on the position of the centrosome and, as a

consequence, on the γ-TuRC (labelled once and for all by its receptors) that is

properly oriented to nucleate an MT correctly directed. Something similar occurs in

GPS devices: when we turn, the map on the screen rotates in order to show the actual

position of “forwards” or “straight on”; our “straight on” direction is not “absolute”

and always the same and does not point towards a constant direction, but its

orientation depends on the position and orientation of our car. Topogenic sequences

do not indicate a fixed position of the cell cortex, but one fixed centrosome

compartment; the choice of one particular topogenic sequence is relative to the

centrosome location.

The language used by metazoan systems for their morphogenetic programs must be

made of targeting sequences and written with some basic rules: the correspondence

between targeting sequence and γ-TuRC receptors must be invariable (constant and

static) while the correspondence between γ-TuRC receptors and cortical

compartments must be univocal (one-to-one) but time-variable: cortical

compartmentalization too is dynamic, variable, nonetheless always under control,

never random. The one-to-one correspondence between targeting signals and γ-TuRC

receptors is absolute, constant and invariable, whereas the one-to-one

correspondence between targeting signals (and related γ-TuRC receptors) and cortical

compartments is strictly univocal but time-variable (it is then a “relative” concept):

by moving (off-centering) the aster, the correspondence between compartments

remains one-to-one (from a given centrosome compartment it is possible to arrive

univocally into only one cortical compartment) but the same centrosome

compartment can correspond, from time to time, to different cortical compartments,

and vice-versa, depending on the controlled position of the centrosome. Off-centering

of centrosomes explains why, although centriole geometry is based on the 40°angle,

the first meridian division planes in sea urchin embryos occur at 90° angle and not at

80° or 120° as expected if the centrosome in the cell maintains a central position.

59

This fits in very well with an evolutionary model of “genetics of morphology”:

purifying selection has firstly approved the choice of a particular targeting sequence

added, for instance, to polarity or adherence factors only if the consequences were not

dangerous, then, through natural selection, the fittest shapes have established.

Evolutionary morphology is a tale of targeting sequences, added, changed, erased, in

order to test and evaluate new spatial disposition of cells; thus genetics of

morphology is the genetics of targeting sequences.

Growth is a highly anisotropic process, in which polarity and direction are always

regulated by precise forecast programs. Identical objects (matches or sticks for

instance) can compose many different geometric plane figures (perimeters) when they

are assembled following each other, each one oriented with a particular tilt angle; if

only the right angle is permitted (and its useful multiples: 0°; 90°; 180°; 270°; four

degrees of freedom) it is easily possible, for example, to compose all the Arabic

numerals (as in digital displays); if only the 45° angle is allowed, (and its multiples:

0°; 45°; 90°; 135°; etc.; eight degrees of freedom) all the capital letters of the English

alphabet can be easily composed. Fibroblasts can control the disposition and

orientation of the collagen fibers they produce, making fasciae of different shapes

that force the homogenous muscular tissue to take the form characteristic and typical

of each skeletal muscle. It is worth recalling the work of the mathematician biologist

D'Arcy Wentworth Thompson: in his famous “On growth and form”, written many

years ago, in 1917, he wrote a chapter -“The comparison of related forms”- to explain

the importance of mathematical transformations of forms in related animals: physical,

mathematical and mechanical laws are the basic determinant of the form; between the

mathematical transformations he examined, “share-mapping” is particularly

intriguing, because it is generated by changing the 2D angle between axes (rectangle

> parallelogram, for example): applied to the shape of organisms, through 2D “share-

mapping” only one of the two coordinates of each landmark (landmark-based

geometric morphometrics) changes and this sustains the difference of forms.

Thompson’s ideas did not have biological and molecular bases; the geometric role of

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the centrosome can fill this gap: new species can arise because targeting sequences

have been added, changed, erased and new coded values for growth vector directions

have been performed.

Morphogenesis: a tale of angles

Growth velocity vectors are well defined for each point and stage of a developing

organism: vector module (the intensity of growth, or growth “speed”, which can be

considered the “scalar” component of growth “velocity”), can vary around a main µ

value (Gaussian distribution) under the control of many agents, from genetic

programs to growth factors and hormones. On the contrary, growth vector orientation

is always precisely predetermined and fixed so that adult organisms and organs can

reach different size but have always the same characteristic shape (“geometric

similarity”: left and right mammalian limbs, cochleae and eyes are good examples).

Size can be different in two different individuals (in each species the expected or

main value and the standard deviation are defined for each organ) but only very small

variations, and only in the last stage of development, are permitted in the single

(healthy) individual whose pair symmetric organs are highly similar, about identical:

the dimensions (size) of limbs, fingers, ears are always the same in the left and right

half of the same individual whereas the Darwin’s tubercle, on the helix of the

auricular pinna, can be different in the two ears because it arises at the last stage of

pinna formation. A fundamental morphogenetic rule in Metazoa: scalar quantities,

subject to many controllers, can vary continuously around a species-specific

“Gaussian” main µ value (with a typical standard deviation σ value for each process

of organ morphogenesis), whereas vector orientations are precisely predetermined,

chosen in a limited number of values, in each species and for each stage and point of

the developing organism and their very subtle variations are only due to thermal

fluctuations.

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Illacme plenipes has 750 bilaterally symmetric legs

Illacme plenipes (Myriapoda) has up to 750 legs all arising from a fixed point of the

cylindrical body circumference and all with the same (bilaterally symmetric)

orientation of the proximal-distal axis; if the angle between the proximal-distal and

the anterior-posterior axis were continuously variable about a main value, we would

see 750 legs not parallel, but in Illacme plenipes the legs of the same side are

absolutely parallel, in each individual; two individuals are substantially identical: the

number of legs can vary, like size, around a main value, but the tilt of the proximal-

distal axis in respect to the anterior-posterior axis is always invariable. Different

organs have their own spatio-temporal values for the magnitude (“scalar” component)

of growth in an interval of permitted species-specific values (accordingly with the

species-specific standard deviation): growth magnitude can be positive, null (no

growth) or even negative (apoptosis) and is independent from the intensity of other

organs: as is well known, growth occurs through the addition of many interacting

developmental elementary microprograms or modules (something similar to the

microprogramming in computer architecture), like morphogenetic fields and imaginal

discs: few cells in a restricted space; as a consequence, when the final (macroscopic)

result depends on the interaction of several (microscopic) modules, external forces

can influence the correct angles imposed by growth programs. As we have seen,

microscopic programs are extremely precise, however macroscopic results can show

differences: the more complex (larger and bigger) organisms are, the more variable

the ultimate results become. Large organs and big organisms cal mislead us showing

forms that vary in size and in angle too: if we look at cleavage (from 1 to 16 cells) of

a frog embryo, we can see (control on the Internet) a sequence of precise angles

between two successive division planes; but cells are never identical in size (they are

subject to the action of growth factors whose local concentration is, in turn, subject to

thermal fluctuations and then variable) and therefore can distort the final shape (think

62

to a cube with only one face a little larger than others). In limbs, the bones are the

leading structures and do not compete with others; differently, teeth can be

programmed with a size that does not fit in well with the size of facial bones: so teeth

can be too crowded or too sparse in respect to jaw’s or maxilla’s size and each tooth

can be subject to external forces (by other close teeth) that perturb the original

orientation of growth velocity vectors: variations of directional growth angles are

imposed by the concurrence of external cues.

Which molecules and which organelles are involved in directional architectural

management?

A surprising aspect of development is how cells are capable of forming

morphologically different organs and organisms (millions diverse species, from

worms to humans) by using (often for different purposes) the same (and highly

conserved) few signaling pathways (Wnt, Notch, TGF-β, Hedgehog, etc.),

morphogens (retinoic acid; bicoid and nanos mRNAs etc.) and structural molecules

(tubulin, actin, etc.). Why is it possible to realize so many and so different shapes

through the same molecular gradients? Where is direction-information coded?

The only “driving motor” that moves molecules in solution is thermal fluctuation

(Brownian motion) and the only “helm” that directs molecules in different directions

is the result of enormous numbers of random collisions between molecules that allow

a molecule to find sooner or later the correct orientation and direction: the

randomness is compensated for by the frequency of collisions, the speed of molecules

and the mean free path. Let’s recall some values calculated in gases at ambient

temperature and pressure: the average time between two collisions is of the order of

10-10

s, therefore 10 billion collisions per second; the mean free path between two

consecutive collisions is of the order of 10-8

m, or 10 nm; the average speed has

values of 1000 (103) km/h, higher than the speed of sound in air. Such high numbers

make it possible for each molecule to be quickly directed in the desired direction but

without any predictable time precision: we must consider that the Gaussian

continuous distribution of values in systems based on solutions and concentrations

63

does not agree with the precise 3D order necessary for biological structures that must

be stereotypically reproduced: e.g. the orientation and direction of extracellular

matrix fibers (cornea), or limb and organ shape (inner ear: malleus, incus, stapes,

cochlea, semicircular canals, utricle, saccule); only one out of infinite possible angles

is sought and, to do so, other types of arrangement and order are necessary: enormous

numbers of very small cells always obtain the same architectural result, laying

themselves out correctly to compose very complex organs whose size is

incomparable with cell size. “The spatial resolution of gradients based on diffusible

molecules has fundamental limitations set by the ability of receptors to discriminate

small differences in ligand concentration, such that sensitivity to concentration

changes in one part of the gradient comes at the cost of saturation in the rest of the

gradient. Such considerations lead to the idea that global positional information

might provide at most a low-resolution map of position within the cell that must then

be refined by local determination of structure and organization” (Marshall, 2011). In

addition to these limits we must also wonder how receptors can evaluate directional

information, if any, of ligand concentrations. Two similar geometric figures (a 2D

polygon or a 3D polyhedron) can show different dimensions of sides, areas and

volumes (scaling), but do not change their (plane or dihedral) angles (homothety)

indispensable to maintain their similar shape: by changing the angles, a square is no

longer a square but is transformed into a rhombus, like a rectangle becomes a

parallelogram. From the proposed geometrical model of the centrosome, a cell wired

by the aster emerges, mapped (really and physically compartmentalized under the

direction of the virtual grid line coded and stored in DNA) and capable of precisely

carrying 3D developmental programs out, in which the centrosome plays the role of a

geometric interface between (discrete) address codes, encoded and memorized in

DNA, similar to postcodes, and the relative spatial (also discrete) localizations like

the cortical compartmentalization of proteins into discrete clustered domains. It is

thus possible to obtain the assembly (controlled by DNA) of large and extended

structures and systems (cells, tissues and organs) with very high levels of order and

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precision, highly stereotypically reproducible in organisms composed of hundreds of

thousands of billions of cells (1014

), bypassing the limits imposed by the

thermodynamics of solutions.

About “precision” and a biological “anti-aliasing” theoretical filter

Centrioles/protractors/goniometers are instruments equipped with discrete, non-

continuous, polarity (with nine degrees of freedom) that limits, but at the same time

makes precise and reproducible, the controlled execution of morphogenetic programs

(oriented cell division, tube morphogenesis, migration, extracellular fibers

disposition, convergence and extension, adhesion, etc.). One-to-one correspondence

between centrosomal and cortical compartments assures the precision of

reproducibility of forms: let’s recall Albrecht-Buehler’s words: “Several principles of

construction of a microscopically small device for locating the directions of signal

sources in microscopic dimensions: it appears that the simplest and smallest device

that is compatible with the scrambling influence of thermal fluctuations as are

demonstrated by Brownian motion is a pair of cylinders oriented at right angles to

each other”: in metazoan organisms we see high precision in reproducing shapes and

executing stereotyped oriented processes but not identity, because thermal

fluctuations cannot be eliminated. To understand how cells control angles and

directions we can observe only those developmental microprograms carried out by a

few cells: cleavage, gastrulation and neurulation furnish clear geometrical

information. Indeed the 9-fold symmetry of the centriole, taken together with the cell

size and the numbers of cells necessary to build metazoan organisms, seems to be the

best choice for building stereotyped organs and organisms (then successful,

controlled and purified by evolutionary selection); if the symmetry of centrioles had

an order of magnitude more than 9, thermal fluctuations (MTs are stiff and bending-

resistant but very long in a viscous cytoplasm crowded with organelles and

65

membranes) would cause overlapping of cortical domains (considered as the area in

which an MT subject to thermal fluctuations can arrive and “land”): during evolution,

“experiments” have been performed (but without success) as showed by Riparbelli

and colleagues (2009) who found in Acerentomon microrhinus centrioles composed

of 14 doublet microtubule blades, used to form cilia and flagella or mitotic and

meiotic spindles; the 9-fold symmetry has been chosen because it is, so to say, the

cellular “anti-aliasing” filter (to borrow something from the well known Nyquist–

Shannon Information Theory sampling theorem) to avoid overlapping (and disorder)

of cortical compartments, and, at the same time, the best choice to obtain the best

topological and morphological reproducible results: maximum output with minimum

effort.

As I have said, the objective and the purpose of development is to realize very large

organs and organisms making use of very small units (cells): the addition of

thousands of little errors, due to continuously variable values of directional

parameters, in each stage of growth, is incompatible with the realization of high-

quality architecture.

We move from a continuous distribution of degrees of freedom, subject to gradient

levels, to a discrete, precisely programmable distribution, limited but precise and

constant for each step, in the execution of a program and therefore resistant to the

“background noise”; thermal fluctuations are therefore restricted and limited around a

fixed (discrete) number of degrees of freedom: subject to thermal fluctuations, the

MT nucleated by a γ-TuRC will not reach precisely the center of the corresponding

cortical domain but it will arrive, like an arrow directed at a target, in a point that is

surely inside the compartment; to better explain this concept it is convenient to recall

the atom model by Bohr (omitting the successive considerations of Quantum

Mechanics): electrons orbit around the proton with canonical periods into different

shells depending on their energy, but they are only permitted to have discrete values

of energy, so they can stay on one delimited shell or on another; similarly, the MT

“landing” point onto the cortex fluctuates around the center of a compartment in 2D

66

annuli or rings of different probability densities (higher near the center) but only one

(discrete) cortical compartment is reachable from one centrosomal compartment

(one-to-one univocal correspondence, although spatio-temporally variable, as we

have seen before); the Gaussian distribution consequent to thermal fluctuations

appears restricted and limited to a small area around the center of the cortical

compartment like a small rifle target: the cell cortex is then composed of several

discrete neighbouring non-overlapping “rifle targets“ (cortical compartments), each

one connected to only one centrosomal compartment (one-to-one discrete

correspondence). In organisms composed of 1014

cells, stochastic processes

algebraically sum variations due to thermal fluctuations so that size varies

continuously but inside an interval; not so forms: a thumb is a thumb and an index

finger is an index finger; a limited “discrete” one-to-one correspondence between

discretely orientated centrosomal compartments and discrete cortical compartments

restricts and limits the effects of thermal fluctuations. Organs are composed of very

large numbers of cells, organized in different tissues: the ultimate result is the sum of

many, many sub-programs or elementary micro-programs so that forms could appear

different; indeed the previous considerations about homothety must be referred only

to elementary programs: the high precision of the control of 3D angles during the

stereotypical pattern of orientation of cleavage division planes furnish a glaring

example of simple basic micro-programs: cleavage is a typical microprogram

whereas gastrulation and neurulation, although simple, are composed of some

elementary programs; organogenesis is the sum of a lot of microprograms. This is a

clearer explanation of the concepts of continuous, controlled distribution of

probability density, high precision and identity. The theoretical definition of “discrete

cortical compartment” is: “the cortical area where MTs arrive, subject to thermal

fluctuations, started from the corresponding centrosomal compartment”. To borrow

something from Quantum Physics, cell cortex polarity is “quantizated”: its

“quantum” could be obtained (only when the centrosome is well-centered in the cell)

by multiplying the squared cell radius by π/45 (0.07 might be the “cell polarity

67

constant”), but the frequent off-centering of the centrosome changes its value. More

than nine triplets imply more than 45 centrosomal and cortical compartments, but

thermal fluctuations overlap the cortical areas where MTs arrive started from the

corresponding centrosomal compartment”, destroying the one-to-one correspondence

(aliasing). I am tempted to add a few words to Albrecht-Buehler’s cited sentence: “It

appears that the simplest and smallest device that is compatible with the scrambling

influence of thermal fluctuations as are demonstrated by Brownian motion is a pair of

9-fold-discrete-symmetry-cylinder oriented at right angles to each other”. To find

solutions for fighting entropy and limiting the disorder caused by thermal fluctuations

is the fundamental extraordinary ability of living beings.

Precision and constant reproducibility, particularly in very small confined spaces like

cells, are reached with difficulty by chemical concentrations (solutions constitute

typical examples of continuous distributions of density rates: where and when they

exceed a threshold value is unpredictable with high precision and out of a 3D

directional control: uncertainty and “noise” are inevitable; “The spatial resolution of

gradients based on diffusible molecules has fundamental limitations” Marshall,

2011); in addition, chemical concentrations, substantially isotropic, are not useful for

transferring or transmitting the angle information of 3D highly anisotropic growth

processes (compare bicoid, nanos, hunchback and caudal mRNAs gradients in

Drosophila embryos to the MT cytoskeleton that can discretely and “precisely” wire

small cells: the firsts are one-dimensionally controlled, whereas a labelled

cytoskeleton is three-dimensional). “Regulated spatial segregation of polarity factor

clusters provides a means to spatio-temporally control cell polarity at the cell cortex”

(Dodgson et al., 2013)

The gradient of a scalar field (density) is a vector pointing in the direction of the

greatest rate of increase: its components are the first partial derivatives (x,y,z) of the

field; supposing that cells could precisely control the rate of increase along a

direction (being able to create a 3D directionally oriented increase of concentrations,

read a 3D directional increase, 3D directionally respond and react), then cells must be

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able to manage x, y, z coordinates, and a spherical reference system tool would again

be necessary (see the next paragraph: “About the primary cilium”).

A discrete, limited but precise organelle is the essential aspect of the centrosome

geometrical model. By observing the spinal column of mammals (in reptiles and fish

the number of vertebrae is even larger) we can check the preceding statement: we do

not see a variable continuous distribution of the form, but its precise (and discrete)

distribution, so that the more cranial vertebra is always the atlas, followed by the

epistropheus and gradually by the characteristic vertebrae for size and position in the

column, always predictable and discrete (cervical, thoracic, lumbar), that maintain

their typical (cervical, thoracic, lumbar) forms; like polyhedrons, each vertebra (in

different individuals of the same species), can vary in size but not in shape. Through

the geometrical molecular architecture of the centrosome (hardware: γ-TuRC

inclination) and topogenic sequences interacting with γ-TuRC receptors (software),

DNA has acquired the capability to store (and transmit to descendants) geometric

directional developmental instructions (understood and translated by the centrosome)

and has achieved a complete mastery and command to accomplish developmental 3D

programs. The orientation of first cell divisions (cleavage) in Metazoa confirms this

assertion: “When centrioles are experimentally ablated, spindles drift within the cell”

(Azimzadeh and Marshall, 2010); without two orthogonal few-degrees-of-freedom

“geometric” organelles, planarians cannot carry out the orientation of cell division

planes, typical of the spiral cleavage of their ancestors. Gastrulation is also

compromised. As we have observed, growth directions are fixed and invariable in the

elementary programs: when a lot of nested microprograms belonging to different

developmental modules are added up, the final results could show differences, also

considering the random local variability and fluctuation of cell dimensions and their

number (size and division rates are subject to several growth factors and hormones),

but, as we will soon see, the fine control of angles has achieved exceptional results

during evolution.

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Quercus has about 500 species

Quercus has about 500 species, because of the enormous differences of shape; in each

individual of the same species, branches and roots have locations and orientations

(direction of the proximal-distal axis) whose values are continuously distributed:

branches can arise from any point of the circumference of the trunk and be oriented in

any direction, showing continuously variable tilts (compare to Illacme legs); only in a

few genus - Larix, Abies, Cedrus, Cocos, Phoenix, Agave - branches arise with a

characteristic inclination (but from any point of the circumference of the trunk), and

this order is already lost in twigs: not so for the 750 legs of Illacme pleniples, all

arising, as I have said, from an invariable constant point of the body circumference

and all with the same (bilaterally symmetric) parallel orientation of the proximal-

distal axis. In plants a different reference system, sensitive to different cues, inner

(MT disposal) or outer (light and gravity) but not controlled by “discrete” organelles,

drives their orientation and development, without a fixed (but precise) number of

discrete degrees of freedom (which is the main characteristic of the animal

centrosome): so words like “Ventral, Dorsal, Left, Right”, when referred to plant

anatomy, are meaningless. On the contrary, “tube elaboration in the Drosophila

embryo is highly stereotyped and often genetically determined… Recent studies of the

branching program of the mouse lung reveal that the branching patterns of complex

mammalian tubular organs animals can be highly stereotypical. Metzger and

colleagues (2008) examined hundreds of fixed mammalian lungs to generate a 3D

reconstruction of mouse lung morphogenesis at different developmental stages. They

demonstrated that from animal to animal, the pattern of lung branching is highly

reproducible and involves only three modes of branching used reiteratively in only

three different subroutines to pattern the entire lung. The modes of branching were

described as (1) domain branching, (2) planar bifurcation, and (3) orthogonal

bifurcation“ (Andrew and Ewald, 2010). Unlike plants, metazoan limbs do not arise

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from any point of the body (and neither do cranial and spinal nerves, etc.), but their

location and their orientation have a fixed, highly reproducible, stereotypical value

(chosen between the permitted degrees of freedom).

A precise order and control and an extraordinary fine tuning of inclination and

direction is strikingly evident in fruit fly imaginal discs (page 14), in feathers

(maintained from the rachis to barbs and barbules) in limbs (leg, paw, claw) and even

in hairs, from flies (bristles) to humans (in our eyebrows and eyelashes, hairs show a

locally controlled - bilaterally symmetric - direction, and also in moustaches where

hair tilt is carefully and locally controlled, as hair inclination is characteristic and

stereotypically reproduced in the beard); Metazoa need a precise architecture for the

locomotion apparatus to perform extraordinarily difficult and highly directional tasks

in order to balance, walk, run, fly, swim. So metazoan organisms are capable of

developing their sophisticated 3D bilateral symmetry because precise, discrete,

stereotyped and programmed instructions for position and direction are “translated”

by an enantiomorphous “discrete” centriole. Illacme plenipes, as I have already said,

has 750 legs arising from a fixed point of the cylindrical body circumference with the

same (bilaterally symmetric) orientation: all individuals are about geometrically

identical. And so is it in Paramecium tetraurelia with its thousands of cilia arranged

in dozens of parallel longitudinal rows in every individual, each hardly

distinguishable from others: the number of basal bodies and rows (similarly to

Illacme legs) can vary, but not their geometrical arrangement. On the contrary, two

trees of the same species are neither similar nor have an identical distribution of

branches, which are free to arise from any point of the trunk and with variable

direction.

Human opposable thumbs: a great success of 3D angle control

Morphogenesis and chemical gradients do not agree: the first requires a discrete and

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precise disposition and orientation of cells and extracellular fibers, the second do not

possess 3D information.

In nephrons, sweat or sebaceous glands, middle and inner ears we see the result of a

coordinated and precise hystological architecture; in limbs, which in Vertebrates are

composed of a very large number of cells, we can see an even more astonishing

precision in the management of angle geometry.

A very simple experiment: open your hand and point the tip of the thumb towards

your eyes: it is rotated of ~80° in respect to the other fingers (compare to the big toe

(hallux) orientation in your foot which is identical in all the five fingers):

The bilaterally symmetric repositioning of the thumb axes, properly oriented in order

to build an opposable finger, has been a milestone of extraordinary importance for the

evolution of Humans, an extraordinary result achieved by the fine control of angles;

this had been possible because of the high capability of precisely managing 3D

angles, a fundamental characteristic of metazoan cells. Is it conceivable to obtain a

similar result (bilaterally symmetric) through morphogen gradients? In addition: a

simple (and then likely) mutation in only one gene coding for a targeting sequence

recognized by the corresponding γ-TuRC receptor of “right” and “left” symmetric

centrosomes, as proposed by the geometrical model of centrosome functioning (see

later), can sustain the evolutionary variation of an angle (like in right- or left-handed

developing snails): what evolutionary event can represent the molecular base of

morphogen gradients able to realize the appearance of new organisms equipped with

bilateral symmetric opposable thumbs?

The centrosome: an input-output cellular spherical reference system tool

“When centrioles are experimentally ablated, spindles drift within the cell”

(Azimzadeh and Marshall, 2010).

“Our results suggest that selective pressure to maintain the centrosome in animals

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comes from the need to coordinate specific developmental processes rather than a

fundamental cellular requirement for the organelle” (Azimzadeh, 2012).

No centrosome? No order.

At this point of the theoretical analysis an initial summary is convenient:

compartmentalization of the cell cortex and segregation of mRNAs (localization of

translation) are mediated by MTs; the fundamental role of the centrosome consists in

operating like an interface between DNA coded geometric instructions (the cell

biochemical mapping “software” consisting in targeting or topogenic sequences, or

ligand-“zip-codes” that interact with the corresponding γ-TuRC receptors) and the

corresponding final locations in the cell, reached by oriented MTs, conveniently

nucleated and irradiated by bi-oriented (longitude + latitude) γ-TuRCs to wire the cell

cortex (the cell biochemical mapping “hardware”: orientation and inclination of γ-

TuRC scaffolds).

Now we can lay the theoretical foundation of the model.

A first model of the centrosome

Equivalent or not equivalent, that is the question

“Centriole duplication is part of the mechanism by which the cytoskeleton of the

daughter cell is patterned upon that of the mother. It is probably not correct to say

that one centriole provides a template to make another (and there are instances of

centrioles arising de novo), but some kind of copying appears to be involved...

Examples of self-organization have long been familiar to biochemists under the

heading of self-assembly. Ribosomes, microtubules, microfilaments, virus particles,

and lipid bilayers come to mind” (Harold, 2005).

“Centrioles may act to keep PeriCentriolar Material components in a precise

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position throughout the cell cycle and so be useful in the control of the position of the

axis of polarity and division.” (Gueth-Hallonet et al., 1993).

“It seems that in Protists and in Metazoa the triplets of basal bodies are not-

equivalent” (Beisson and Jerka-Dziadosz, 1999).

Equivalent or not equivalent, that is the question. Rather, it is the main fundamental

problem we must face. As already observed, the sophisticated 9-fold symmetry

architecture (very difficult to build) would be meaningless, useless and

incomprehensibly costly, if their 9 components were undistinguishable. If Metazoan

centriolar triplets are diverse and not equivalent like in Protists, as supposed by

Janine Beisson and Maria Jerka-Dziadosz, centrioles will operate like “biological”

protractors/goniometers also in Metazoa. Vorobjev and Chentsov (1982) presented in

their cited article, interesting pictures of the appendages of the “mother” centriole in

mammalian cells that may support the idea of the non-equivalence of the mammalian

centriolar triplets: each triplet appears different in shape in comparison with the

others and the nine ribs of the “daughter” centriole are also different. Unfortunately,

studies on centrioles in Metazoa are difficult because centrioles are embedded in the

proteinaceous matrix of the PCM.

”Is it possible to confirm this idea that the circumferential, morphological, structural

and molecular asymmetry of centrioles can be inferred from Mammals ciliated

epithelia? While the circumferential anisotropy of centrioles cannot be ascertained

within the centrosome, its existence can be inferred from the properties they express

during ciliogenesis, be it the formation of a primary cilium or of bona fide 9+2 cilia

in ciliated epithelia, some of which at least derive directly from the centrioles. As in

Ciliates and flagellates, these basal bodies nucleate appendages of various molecular

compositions (basal foot, striated rootlets, alarm sheets, etc, which anchor the basal

body to the membrane and to the cytoskeleton) and these nucleations arise at specific

sites of the basal body cylinder; in particular, the basal foot is located on triplets 5

and 6 corresponding to the side of the effective stroke of the cilium. What is

remarkable is that basal feet develop before the basal bodies reach their membrane

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site and before they acquire their functional orientation “(Beisson and Jerka-

Dziadosz, 1999).

Some certainty, at last (but does any certainty exist in science?): rather, some clear

experimental evidence. Mammalian centrioles have non-equivalent triplets that

nucleate divers (morphologically and functionally) appendages before reaching the

cell membrane. We have before supposed an informational non-equivalence of

triplets because our theoretical analysis had accompany us to this conviction: now we

have a first demonstration we were right. However this is true only for mammalian

centrioles and basal bodies. What happens inside the centrosome?

It is not hazardous trying to face the previous question, following this path: the

theoretical analysis of a spherical reference system based on two orthogonal

protractors/goniometers gives significance and meaning to the highly sophisticated

structure and rotational polarity of centrioles and indicates how a centrosome could

operate; if centrosome behavior in Metazoa agrees with the functioning of a

theoretical spherical reference system organizer, it is possible to hypothesize that its

geometrical role is likely. Indeed many studies (see references) confirm the

geometrical role of centrosomes in defining cell polarity, orientation of division

planes, differential cell-cell adhesion, migration, apical constriction, convergence and

extension by intercalation, extracellular fiber disposition. Centrosome’s geometry

implies its function: metazoan triplets appear not equivalent.

Centrioles in Ciliates and centrosomes in Metazoa: biophysical and architectural

considerations about non-equivalence

“Among the conserved proteins involved in the biogenesis of the canonical 9-triplet

centriolar structures, SAS-6 and Bld10 have been shown to play central roles in the

early steps of assembly and in establishment/stabilization of the ninefold symmetry.”

(Jerka-Dziadosz et al., 2010).

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As we have already seen, centrioles are present in eukaryotic cells, but not in higher

plants and most fungi; unicellular organisms have only centrioles/basal bodies, each

one independent, whereas in multicellular algae and Metazoa two orthogonal

centrioles are embedded in the PeriCentriolar Material that forms the centrosome.

Protists show rotational, cylindrical (or rather circumferential) symmetry, but also

asymmetry is frequent whereas they never show bilateral symmetry [pay attention to

the difference between “180° rotation” of a geometric 2D figure (the sequence of

marks remains unaltered) that seems, but is not, bilateral symmetry, and “180°

reflection (or overturn)” that is really bilateral symmetry (the sequence is reversed or

opposite): the axes around which the two figures move are diverse, in the first case

being orthogonal to the plane in which the figure lies, whereas in the second case the

axis lies on the plane containing the figure]. On the contrary, Metazoa show bilateral

symmetry and a 3D architecture of their organs and limbs; Ciliates have cylindrical

centrioles, Metazoa have two orthogonal cylindrical centrioles embedded in a

spherical centrosome: the second centriole, orthogonal to the first, adds the capability

of completely controlling the third dimension, indispensable for managing the

arrangement of cells in multicellular organisms. The idea is that Metazoa have

developed new pathways to adapt Ciliates’ sophisticated molecular mechanisms in

order to transmit the 9-fold symmetry and polarity of two orthogonal cylindrical

centrioles to the spherical wedges and sectors of the centrosome (or rather of the

PCM): so Metazoa could assemble once and for all, a tool through which they can

control, direct and organize their 3D anisotropic growth. In fact, to use a spherical

reference instrument based on two orthogonal protractors/goniometers, like a globe, a

two-step process is necessary: firstly the longitude of a point ( coordinate) must be

found, then its latitude (θ coordinate) can be identified, but only after a rotation of the

vertical protractor around its vertical axis that aligns the protractor inner border in

correspondence with the found longitude; this appears particularly complex and

difficult (and frankly unlikely) in a cell; on the contrary, if a little sphere (always

maintained in a controlled position and orientation) like the centrosomal PCM is

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organized only once and for all in each cell and built with its surface subdivided and

compartmentalized into 45 small areas (as we have seen in the above geometrical

analysis) each one oriented and labelled by molecular receptors that recognise the

geometric (molecular) signals intended for the corresponding longitude and latitude

(and, consequently, for the corresponding cytoplasmic pyramid too), the problem of

spatial orientation in the cell environment has a very easy solution. Like on a globe,

parallels and meridians are marked on its surface once and for all to facilitate the task

of finding a point of given coordinates, so the 9-fold symmetry of two orthogonal

cylindrical centrioles, transmitted and impressed on the centrosome surface once and

for all, permits an easy translation of molecular geometric signals (in which the

intended coordinates are coded) into their corresponding localizations in the

cytoplasm, only by the usual signal-receptor interaction between targeting sequences

and γ-TuRC (or scaffold/docking platform) receptors located on the centrosome

surface. Obviously, this must happen maintaining fixed (or variable but, in any case

under control, that is never random) the orientation of the centrosome in the cell,

which is in accordance with the described mobility of the only DC: after building the

PCM surface, the MC controls its position and orientation, while the DC disengages

and is quite free in the cytoplasm. “Once and for all” are words that sound bad in

biology, because molecular turnover is the fundamental biophysical base for

managing variation of concentrations (thresholds); although many centrosome

components show high turnover rates, centrioles are very stable structures, effectively

built “once and for all”, and so it may be supposed for the PCM skeleton which

organizes orientation and labelling of γ-TuRC scaffolds. Therefore “once and for all”

means that the molecular PCM skeleton responsible for the inclination of γ-TuRC

scaffolds and the localized delivery of γ-TuRC receptors is somehow transferred to γ-

TuRC scaffolds in order to orientate and molecularly label each PCM compartment

only once per cell cycle, just like centrioles are built only once per cell cycle.

A regular polygon of 9 sides (nonagon or enneagon) has 9 internal angles of 140° and

is composed by 9 isosceles triangles (radially disposed) whose vertex (or central)

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angle measures 40° (Fig. 2 on page 35). Ciliates possess advanced biochemical

mechanisms (with high predisposition for self-assembly) to assemble and build two

angles: the right angle and the angle of 140°; the first is evident in the orthogonal

arrangement of MC and DC during duplication and in the orthogonality between each

cartwheel spoke and the A-microtubule of the corresponding triplet of the centriolar

wall; the second (and its supplemental of 40°) is evident in the 9 fold symmetry of

cartwheel spokes and triplets: in the transition zone of Chlamydomonas basal bodies,

where the axoneme is organized, there is an astonishing “stellate structure” (well

described by Geimer and Melkonian through a beautiful electronic microscope image

in their cited article, free on the Internet) composed of 9 isosceles triangles (nonagon)

with a vertex angle of 40° and two identical angles, each of 70°: the base of each

triangle forms an angle of 140° (70° + 70°) with the base of the consecutive triangle.

In Mammals the right angle is also shown by some Microtubule Associated Proteins

(MAP-2, MAP-4, Tau-MAP). Kitagawa and colleagues (2011), van Breugel and

colleagues (2011) and Gönczy (2012) have shown that the N-terminal domains of

SAS-6 dimers (a conserved protein indispensable for centriole building) naturally

interact between themselves at 140° (internal angle) to form polygonal oligomers,

rings and helices (left- or right-handed); SAS-6 has been found in every model

organism: Chlamydomonas, C.elegans, D. rerio, X. laevis, M. musculus, G. gallus, H.

sapiens. "Intriguingly, when Drosophila SAS-6 is over expressed together with Ana2

(ortholog of SAS-5), the two proteins can assemble into well-ordered tubules that

bear a striking resemblance to the cartwheel" (Cottee et al., 2011). Then, SAS-6 is a

powerful and quasi-autonomous (self-assembling) tool to build angles of about 140°.

The case of the hexapode Acerentomon microrhinus is interesting in which Riparbelli

and colleagues (2009) found ” large centrioles composed of 14 doublet microtubules

that serve as templates for cilia and flagella and organize mitotic and meiotic

spindles”: self-assembly of SAS-6 in cooperation with other molecular complexes

allows cells to build other symmetries (a regular polygon of 14 sides has 14 angles of

154.28°), when necessary: centrosomes and centrioles with non-9-fold symmetry can

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perform (as well as, or perhaps better) tasks like axoneme or spindle formation,

different from their fundamental morphogenetic role as geometrical interface:

metazoan morphogenetic 3D programs are written in “140° language” (or 40° vertex

angle) and must be interpreted by a “compatible” 9-fold symmetry interface

(remember the considerations about the “biological anti-aliasing filter”, genetics of

targeting sequences and “genetics of morphogenesis”); centrosomes of somatic cells

of Acerentomon microrhinus possess 9-fold symmetry MCs able to organize DCs

equipped with different symmetry to perform particular functions, different from

morphogenetic ones: “Strikingly, daughter centrioles contain a transient cartwheel

that is lost after maturation. The length of radial spokes is like that found in 9-fold

cartwheels, whereas the diameter of the hub varies according to the dimensions of the

centriole cylinder. This suggests that the hub may dictate the master plan for

centriole geometry. Finally, the finding that 14-doublet centrioles arise from 9-

doublet mothers points to an alternative model for centriole assembly” (Riparbelli

and colleagues 2009). Guichard and colleagues (2010) have shown a 110-nm stalk

that connects at 90° the central hub of the DC procentriol to the MC in human

centrosome; Chlamydomonas Bld-10p, a component of the cartwheel-spoke tip,

connects the triplets to the spokes and maintains them orthogonal to the spoke.

Picone and colleagues (2010) have identified dynamic centrosomal MTs that mediate

homeostatic length control in Metazoa cells, like Chlamydomonas manages axoneme

length. Geometrically, the management of 90° and 140° angles, together with the

capability of controlling distances and the predisposition for self-assembly of rings

and curved structures, are sufficient for the cylindrical (or, rather, prismatic)

symmetry of two orthogonal centrioles to be transferred to a spherical (or, rather,

polyhedral) shaped centrosome; some models (schematics in Piel et al., 2000 and in

Bornens, 2002, 2012, free on the Internet) clear and confirm this idea, showing that

centrioles, through the nucleation of a “fan-shaped” structure made up of MTs lying

on planes passing through the axis of the centriole and the A-MT of the triplet-blade

and having different tilts (like some radii of a circle starting with an angle of 40°

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between themselves: something like the fan-shaped structure schematized in Fig. 11)

can transform the longitudinal rectilinear shape of each blade of their walls into a

curved spherical surface; note that the geometry of 140° (40° supplemental angle) is

respected in this model; the schematics and images proposed by Gopalakrishnan and

colleagues (2011) in “SAS-4 provides a scaffold for cytoplasmic complexes and

tethers them in a centrosome.” (Nature Commun.), Mennella and colleagues (2012)

in: “Subdiffraction-resolution fluorescence microscopy reveals a domain of the

centrosome critical for pericentriolar material organization” (Nature Cell Biol.),

Lawo et al.(2012) in ”Subdiffraction imaging of centrosomes reveals higher-order

organizational features of pericentriolar material” (Nature Cell Biol.), are consistent

with this idea. Centrosome architecture reminds us of fullerenes: both self-manage an

angle (140° in centrosomes, 109.5° in fullerenes) and build cylindrical or spherical

structures taking advantage of their aptitude for self-assembly. Also the self-

assembled “baskets” of clathrin triskelia (vesicles) that show angles of 120° have

something in common with centrosomes: intriguingly, the N-terminal of the human

SAS-6 shows 40% identity (65% positives) with the central domain of the clathrin

light chain; this can support the previous considerations about Acerentomon

microrhinus: 14-fold symmetry (as we have seen a regular polygon of 14 sides has 14

angles of 154.28°) may be realized through the cooperation of molecular complexes

that force the basic interaction of SAS-6, whose most thermodynamically stable

configurations are about 140° ±10%. Rodrigues-Martins and colleagues (2007) have

shown that self-assembly is required in centriole formation: "centriole biogenesis is a

template-free self-assembling process triggered and regulated by molecules that

ordinarily associate with the existing centriole. The MC is not a bona fide template

but a platform for a set of regulatory molecules that catalyzes and regulates DC

assembly". Song and colleagues (2008) arrive to similar considerations, finding a

mutual cooperation between the PCM and the centrioles: “the PCM itself may direct

the formation of the DC”. In mice, first embryonic divisions occur with unpredictable

cleavage plane positions and blastomeres lack centrioles (they will appear only at the

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blastocyst stage) but possess PCM and γ-TuRCs to form spindles: evidently the

kernel or nucleus of the PCM necessary for mitosis is autonomously self-assembled

in each new cell until the stage of 64-blastomeres, when centrioles begin to be formed

and build a complete centrosome. Kubo and colleagues (1999) and Dammermann and

Merdes (2002) observed that pericentriolar satellites, after recruiting proteins

indispensable for anchoring γ-TuRCs to their centrosomal docking platform (centrin,

pericentrin, ninein, SAS-4 etc.), are transported to the centrosome by MT-linked

dynactin. Centrosomes of Spisula, after chemical disassembling (1.0 M KI) lose γ-

TuRCs, but maintain their PCM skeleton (built once and for all) intact: after

incubation with oocyte extracts containing γ-TuRCs, they recover: "This recovery

process occurs in the absence of microtubules, divalent cations, and nucleotides"

(Schnackenberg et al., 1998). Ou and colleagues (2002) found that the PCM is

organized in an ordered and geometric fashion, showing a characteristic “centrosomal

tube”, closed at one (the inner) end and open at the other end, with a diameter of 1.5

μm and a depth of 2 μm, dimensions that are larger than centrioles height and width

but comparable to the dimensions of the centrosome: "A subset of PCM proteins have

been shown to be arranged in a tubular conformation with an open and a closed end

within the centrosome... Microinjection of antibodies against either CEP110 or ninein

into metaphase HeLa cells disrupted the reformation of the tubular conformation of

proteins within the centrosome following cell division and consequently led to

dispersal of centrosomal material throughout the cytosol (CEP250/c-Nap1,

pericentrin, γ-tubulin and ninein)" (Ou et al., 2002). Alliegro and Alliegro (2008)

have identified in Spisula solidissima several non-coding centrosomal RNAs: the

importance of non-coding RNA in organizing protein complexes is well known

(spliceosomes, ribosomes, and nucleoli). Unlike fullerenes and clathrins vesicles,

which are spherical layers, centrosomes do not possess an accurately spherical

surface: the PCM grows around centrioles (the core components of the centrosome)

and organizes perfectly oriented γ-TuRCs on an irregularly spherical surface. It seems

that only one centriole might be sufficient for organizing the PCM; indeed, a second

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centriole, orthogonal to the first, is indispensable for transmitting correct “latitudinal”

inclinations and marks (or latitude receptors responsible for angle θ) to the parallel

caps and rings (Fig. 3 and 6). In the geometrical model, as already hypothesized, cells

use mechanisms to manage 90° and 140° angles.

The transition from unicellular Protists to multicellular Metazoa is founded on

the orthogonal disposition of two centrioles.

So, it seems that Metazoa have empowered the sophisticated centriolar molecular

apparatuses of Ciliates (capable of ordering and arranging new cell structures under

the influence of others, already existing: assembly of microtubules, centrioles

duplication, assembly of axonemes and IntraFlagellar Transport) to spherically

organize their centrosomes (the diameter of the centrosome is about only two times

the height of centrioles, then not so different) in order to build 3D complex organs

and organisms: Metazoa arrange spherical disks and wedges around two orthogonal

centrioles, by the only operational control of 90° and 140° angle. In Ciliates

centrioles perform three main functions: 1°) as basal bodies they manage the

assembly of the axoneme, transmitting their 9-fold-symmetry, controlling axoneme

length and organizing the complex IntraFlagellar Transport; 2°) as centrioles they

build and maintain the cytoskeleton; 3°) as Mother centrioles they are used as

platforms by new arising procentrioles. The addition and the successive fusion of

these three functions have prepared and paved the way for the next step: building a

centrosome. The transition from unicellular Protists to multicellular Metazoa is

founded on the orthogonal disposition of two centrioles (see the paragraph “Shared

and coordinated orientation of metazoan centrosomes” on page 46). As in

Chlamydomonas and Paramecium the rotational asymmetry and non-equivalence of

the triplets is used to build axonemes and complex cytoskeletons made up of

different fibers each one linked to a particular triplet, so in Metazoa the two

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orthogonal centrioles, after assembling a “quasi-spherical” PCM skeleton, recruiting,

attaching, orienting and anchoring γ-TuRCs to impose spherical polarity and

asymmetry, cooperate to “label” γ-TuRCs. So, γ-tubulin rings are anchored, oriented

and labeled by the participation of many proteins –SAS-4, ninein, centrin,

pericentrin– each one present in several isoforms: the high number of these proteins

confirms that the process of γ-TuRCs anchoring is not a simple docking process: this

process establishes the sophisticated (and indispensable) spatial orientation of γ-

TuRCs: this function is the evolution of Ciliates’ 1°)-function of axoneme assembly.

Like in Ciliates’ 2°)-function each centriolar triplet uses its own unique 3D molecular

shape to recognize and bind its particular ligand (one of the several cytoskeletal

components), metazoan triplets have molecular structures to recognize and bind their

proper ligands in order to correctly transmit located receptors to γ-Turcs, already

oriented on their scaffolds/docking platforms. In Ciliates the centrioles (one or more)

manage the cyto-skeleton, in Metazoa the centrioles (two per cell) manage and

organize the PCM-skeleton which, in turn, builds and manages the cyto-skeleton.

Metazoan centrioles organize the geometrical architecture of the PCM (oriented

scaffolds for γ-TuRCs: centrosome “hardware”) and transmit their non-equivalence

by displacing to each scaffold/γ-TuRC the receptors corresponding to its inclination.

The evolutionary process is: from only one centriole > to two orthogonal centrioles

(diplosome); from Protists “centriole>cyto-skeleton” to Metazoa “diplosome>PCM-

skeleton”.

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The only “true” centriole is the mother centriole: the daughter centriole is an

intermediate product between a procentriole and a “true” centriole, only useful

for cooperating orthogonally with the MC to form the PCM of a 3D reference

system organizer, the centrosome.

Ciliates duplicate their centriole, 3°)-function, using a complete centriole as a

platform near which a new procentriole arises at right angle and, when it is

completely formed disengages: this is already a diplosome, likely used to polarize the

new centriole in the same manner than the “mother” centriole (here we utilize the

term “mother” to underline the similarity of the centriole cycle in Ciliates and in

Metazoa) in such a way that a coordinated orientation (positioning of the “0°” mark)

between mother and daughter centrioles is maintained and the new centriole is

correctly inserted in the cell to avoid that an uncoordinated orientation causes

distortions in their complex cytoskeleton (Paramecium); the task of positioning a

basal body with nine different triplets, each one connected to a specific cytoskeleton

component, has something in common with the insertion and connection of the pins

(several and, above all, functionally different!) of an integrated circuit (microchip)

into an electronic circuit: each pin must be precisely connected to a defined

conductive track on the printed circuit board. It seems that Metazoa have empowered

and developed this very important stage: in Metazoa the centriole cycle is temporarily

stopped at the stage of orthogonality (diplosome) to build and organize the PCM and,

successively, restarts and finishes only in the next S phase. Follow carefully this point

of view: in late S phase, after the process of maturation of the DC, two new MC

generate and correctly orientate two new procentrioles (like in Ciliates) but the

process of maturation of procentrioles is blocked, interrupted, suspended: making use

of this convenient orthogonal disposition, each diplosome forms the PCM and cell

division occurs, each new cell having a MC associated with a “pro-/daughter-“

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centriole; the process of centriole biogenesis will be re-activated and completed in the

next early S phase (definitive DC maturation into a complete, ultimate MC). The only

“true” centriole is the MC, whereas the DC is an “aid-centriole” an intermediate

product between a procentriole and a “true” centriole, only useful for cooperating

orthogonally with the MC to form the PCM of a 3D reference system organizer, the

centrosome. Before we have used the expression “addition and successive fusion”:

addition of 1°) Ciliates’ function (axoneme assembly) to 2°) function (cytoskeleton

building) occurs during the orthogonal disposition of the arising procentriole and the

“mother” centriole: this stage has been prolonged and, in a sense, is overlapping and

not in phase with the metazoan cell cycle; this can help us understand the strange

centriole/centrosome metazoan cycle.

Whether centrosomes and MTs are involved in AP polarity formation in C. elegans

embryos and in other organisms has been a subject of controversy: Tsai and Ahringer

(2007) have cleared up this problem demonstrating that “polarity only occurs when a

small, late-growing microtubule aster is visible at the centrosome; MTs deliver

positional signals and are required for establishing polarity in many different

organisms and cell types. In C. elegans embryos, posterior polarity is induced by an

unknown centrosome-dependent signal". This is a fundamental milestone: in Metazoa

the spherical polarity of centrosomes and centrioles is transferred through the

cytoskeleton to the whole cell cortex.

As we have seen, to satisfy the basic requirements of a spherical reference system, in

order to recognize coded geometric signals and translate them into their desired final

locations, “cellular protractors/goniometers” must possess: 1) different marks; 2)

constant ordered sequence of marks; 3) one start mark; 4) controlled orientation of

the tool in respect to reference points: “In C. reinhardtii the polypeptide VFL1 coded

by the gene vfl1 (Variable number of FLagella), binds to the triplets 9-1-2 near to the

triplet N° 1… Further evidence of rotational polarity comes from the asymmetric

attachment of various appendages to specific triplets in the basal bodies and from the

site of daughter basal body formation adjacent to defined triplets in the mature

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organelles” (Silflow et al., 2001): evidently in C. reinhardtii the triplet N° 1 has its

own unique and distinguishable triplet marker. Surprisingly Yoshinori and Yukio

(2010) found a human ortholog of Chlamydomonas Vfl1 protein and other correlated

centrosomal proteins: “the bibliography as well as database searches provided

evidence that the human proteome contains at least seven centrosomal leucine-rich

repeat proteins;… we identified a centrosomal protein called CLERC (Centrosomal

leucine-rich repeat and coiled-coil containing protein) which is a human ortholog of

Chlamydomonas Vfl1 protein. The bibliography as well as database searches

provided evidence that the human proteome contains at least seven centrosomal

leucine-rich repeat proteins including CLERC. CLERC and four other centrosomal

leucine-rich repeat proteins contain the SDS22-like leucine-rich repeat motifs,

whereas the remaining two proteins contain the RI-like and the cysteine-containing

leucine-rich repeat motifs. Individual leucine-rich repeat motifs are highly conserved

and present in evolutionarily diverse organisms”.

There are then surprising correspondences between the geometrical model of the

centrosome (nine meridian wedges, each one subdivided in five parallel areae) and

many reported findings: the compartmentalization of the cortex in Drosophila

embryo during its 14th mitosis (one impair meridian wedge, four right and four left

meridian wedges, each one subdivided in five parallel areae), the

compartmentalization of the cortex in yeast (about 50 cortical domains); the role

played by the centrosome in asymmetric delivery of mRNAs in I. Obsoleta; the role

played by centrosomal microtubules in segregating different mRNAs into different

cytoplasmic regions; the centrosomal proteins found by Yoshinori and Yuko.

Then, now it is the time to set the hypotheses of the centrosome geometrical model.

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Fig. 6 Centrosome theoretical geometrical model: from 2D rotational polarity to 3D spherical polarity.

A: (top view): the MC (internal circle subdivided in 9 intensely coloured sectors) is responsible for

“longitude” that is transmitted to the whole PCM (external annulus, weakly coloured), whose -TuRCs

(small bars) acquire an inclination parallel to the corresponding centriolar blade; each MC blade faces one

meridian wedge. In each wedge, all the -TuRCs have the same longitudinal inclination. B: after the

intervention of the DC, that imposes a rotational inclination corresponding to that of its blades, each -TuRC

acquires also the latitude inclination which is added to that of longitude. There is a double inclination: first

each -TuRC is parallel to the corresponding blade of MC, then it acquires the inclination parallel to the

corresponding DC blade; the eccentric positioned DC is responsible for “latitude” (two opposed spherical

caps and three parallel spherical disks): this second centriole/protractor is composed of two symmetric hemi-

protractors/goniometers. C: all the -TuRCs contained in the same cap or disc (coloured circles) whatever

their longitudinal orientation, are rotated to acquire the same latitudinal orientation, identical in the same cap

or disk. So, two 2D circumferential-rotational polarities are merged to realize a 3D spherical polarity

First hypotheses:

- Centrioles have a circumferential ordered and discrete asymmetry as a consequence

of macromolecular differences of their triplets.

- Centrioles are platforms for a set of regulatory molecules that assist and facilitate

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the semi-self-assembly of the PCM.

- The MC transmits its 9-fold symmetry (longitude-dependent inclination:

coordinate of a spherical reference system) to PCM -TuRC scaffolds /docking

platforms.

- The DC transmits its 9-fold symmetry (latitude-dependent inclination: θ coordinate

of a spherical reference system) to PCM -TuRC scaffolds /docking platforms.

- Each -TuRC on a centrosomal scaffold/docking platform is oriented in accord with

the tilt of the local tangent plane: scaffold’s (and -TuRC’s) inclination is the addition

of the latitudinal tilt (DC) to the longitudinal (MC); on the same scaffold there are

several -TuRCs.

- Both centrioles transmit to the PCM their circumferential asymmetry and impress

their molecular non-equivalence.

- Each -TuRC (or its centrosomal scaffold/docking platform) receives from both

centrioles the receptors (longitude and latitude) corresponding to its own position and

orientation.

- Each -TuRC (or its centrosomal docking platform) displays its receptors to

recognise the signal (a molecular ligand with a particular targeting sequence)

corresponding to its own orientation and to the intended location in the cell cortex.

- The direction of centrosomal MTs depends on the orientation (tilt) of the -TuRCs

by which they are nucleated.

- Each signal (ligand) has a 3D shape that recognises only the receptors of that -

TuRC that is oriented in order to nucleate an MT with the desired direction: there is a

precise and invariable one-to-one correspondence between geometric signals and -

TuRC receptors.

- The centrosome is the cytoskeletal organizing center; it is polarized and its

orientation and position in the cell are strictly controlled.

- The correspondence between centrosomal and cortical compartments is univocal

(one-to-one) but time-variable, since it depends on the position and orientation of the

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centrosome: a same -TuRC can be connected, at different times, to diverse cortical

compartments.

- The one-to-one correspondence between targeting signals and γ-TuRC receptors is

constant and invariable, whereas the one-to-one correspondence between targeting

signals (and related γ-TuRC receptors) and cortical compartments is time-variable.

- The centrosome is a geometric discrete interface that receives geometric coded

signals (input), matches each one with the corresponding -TuRC receptors

(decoding: ligand-receptor interaction) and nucleates oriented MTs (translation) to

reach the required locations (output).

- Aster, cytoskeleton and cell cortex receive from the centrosome the same spherical

asymmetry (mapping or polarization).

- Centrioles are chiral structures as a consequence of their rotational reversible

asymmetry.

About the primary cilium

The primary cilium (only one per cell) is a non-motile cilium whose basal body is the

MC of the centrosome, which, in G0 non-dividing and non-migrating cells, moves

towards the cell membrane (maintaining its orientation) [“non-motile” does not mean

“motionless, static”: motile cilia of the multiciliated cells in the respiratory

epithelium, like propellers, produce an extracellular intense flow; non-motile primary

cilia do not, however they can bend when subject or exposed to flows]; in epithelial

cells it is positioned near the center of the apical surface; if cells re-enter mitosis, the

cilium is reabsorbed and sheds: motile cilia are formed ex novo, primary cilium does

not, it is unique (one-per-cell) as the MC that is its basal body and follows the strange

cycle of the MC. It is involved in cell-cell signaling pathways: in Vertebrates, unlike

other Metazoa, Hedgehog receptors are positioned on the primary cilium. Motile cilia

of the Hensen’s node cells generate a flow, involved in left-right asymmetry, which is

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“sensed” by primary cilia of neighbouring cells. Avasthi and Marshall (2013) and

Wood et al. (2013) hypothesize that primary cilia, like antennas, are capable of

receiving and transmitting too.

Indeed it seems possible that the direction of provenance (the location of signal

sources) is an understandable “geometrical information” of a signal, like in planar

cell polarity or in cells near the midline: this information does not consist in any

molecular signal but it is simply implicitly furnished by the spatial direction of a

flow: it can be deciphered and decoded only by receptors associated with (or

corresponding with) the oriented blades of the basal body, i.e. receptors located not

randomly but in precise positions of cilium circumference, in correspondence of one

of its 9 doublets. The important task of maintaining the midline in its correct position

or repositioning a new midline (after first blastomeres splitting events or during

regeneration after surgical or accidental injuries) can take advantage of information

about the provenance of signals (deciphering if they arrive from the left or from the

right) in order to drive the process; as we have observed before, Carbajal-Gonzales

(2012) has shown that “in Eukaryotic cilia and flagella, radial spokes are different

from each other, but conserved across species”: the primary cilium radial spokes may

be circumferentially polarized by its polarized MC/basal body. Cao and colleagues

(2012) reported that a sophisticated mechanism organizes the centriole-to-basal body

transition and cilia assembly through miRNA-mediated post-transcriptional

regulation.

Why only one primary cilium per cell? Only one primary cilium is convenient for

“understanding” different directions of provenance of a regular (quasi-laminar) flow

of molecules: many cilia, random or orderly displaced, are not because a space

crowded with cilia cause flow turbulence with unpredictable bounces and collisions

(recall the values of molecular speed seen on page 60) of signalling molecules subject

also to electric (+/- charges) or chemical (hydro-phobic/-philic groups) forces during

impacts with cilia membranes, able to alter and modify the direction of hits between

molecules and cilia (noise). A pinball machine with its cylindrical spring active

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bumpers illustrates this concept.

Receptors that enrich the primary cilium, exposed to a morphogen flow, are

stimulated by signal kinetics (concentration levels going over threshold). Hedgehog

(Hh) signalling, as I have said, in Vertebrates occurs in primary cilia, involving

kinesin (KIF7) and dynein transport of many molecules (Smoothened, Patched,

SUFU, Gli): downstream Hh signalling, in Vertebrates as in Invertebrates similar

processes occur, but only in Vertebrates (the most complex 3D organisms) does Hh

signalling need receptors positioned on the primary cilium. In order to better

appreciate the following considerations, it is interesting to review some numbers:

concentration of Sonic hedgehog (Shh) in chick embryo neural tube decreases from

15 nM to 0.5 nM; 1 nM concentration corresponds to about 1 molecule/µm3 (0.6 to be

precise; a simple addition of exponents: 1M means 6.022 x 1023

molecules per liter or

dm3; 1 nM is 1 x 10

-9 M or 6.022 x 10

14 molecules; 1 dm

3 contains 10

15 μm

3: that is

6.022 x 10-1

or 0.6 molecules per μm

3); the volume that faces a primary cilium (with

the same size of the cilium: 7 µm length and 0.3 µm diameter) measures about 2 µm3;

molecules of Shh in a volume of 2 µm3

vary from 18 to 0.6; Shh gradient is capable

of signaling at a distance of 30 cell diameters; protein diameter average size is about

3-6 nm; primary cilium circumference measures 1,900 nm (1.9 µm) , and its height is

(as just seen) 7,000 nm (7 µm); compare to Acetylcholine concentration [5*10 -4

M] in

the synaptic space [1 µm3] -> 300,000 molecules, and to hormones concentration

[10-8

M] -> 6 molecules/µm3 (average density of receptor: 300/µm

2, 9*10

4/cell); recall

also the values of molecular speed and collisions (page 60), considering that 1 µm3 of

gas at standard conditions (0°C or 273,15° K) contains a number of molecules of an

order of 107

(like Acetylcholine) but the temperature in Vertebrate cells is higher. The

gradient of Hedgehog is attentively controlled through N-terminus palmitoylation

which increases its hydrophobicity and facilitates its binding to cell membranes,

limiting its diffusion. Could receptors, randomly positioned on the cilium surface

(even on the opposite face), be able to interact with very few (and so small in respect

to primary cilium dimensions) molecules? Often in cell biology only small quantities

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of solutes are necessary: 250 protons are enough for lysosome acidification. In order

to sense, “measure” and graduate the responses to very low concentrations of

important signaling molecules which move at high speed (addition of Brownian

motion and flow speed), cells use sophisticated strategies: the HER family of

receptors for epidermal growth factors can dimerize in such a manner that only one

molecule can activate some dimers while two ligand molecules are necessary to

trigger other types of dimers: then different dimers are activated by different

concentrations. Flows of very low concentrations of signalling molecules can better

and more quickly interact with receptors if these are correctly positioned in

correspondence of no more than two or three consecutive doublets, oriented towards

the flow and directly exposed to it: this is possible through the geometric role of the

rotationally polarized MC/basal body. “A structure at the ciliary base appears to have

all the features required for compartmentalization and which we thus call the ciliary

partitioning system (CPS). This complex consists of the terminal plate, which serves

as a cytosolic ciliary pore complex (CPC)… a plate-shaped structure containing nine

pores through which the microtubule doublets of the basal body pass. Each pore

expands from the doublet B-tubule into an opening well suited for the passage of

intraflagellar transport particle” (Ounjai et al., 2013). Receptors can be placed only

in correspondence to one or two doublets in order to coordinate the cell fast response

to a forecast source direction, and reduce noise: when a very weak signal is expected

from a forecast provenance, it is convenient to orient receptors towards the foreseen

direction (in migrating cells, for example). “In vertebrates, centriole position appears

to respond to planar cell polarity cues, consistent with the localization of some

planar cell polarity proteins at centrioles” (Montcouquiol and Kelley, 2003). When

receptors are placed everywhere on the cilium, through intra-flagellar transport,

activated signal molecules or signal transduction molecules can be carried, along the

corresponding doublets (primary cilium compartments), to the circumferential

polarized basal body, labelled with a targeting sequence coding the “number” of the

doublet and sent to the nucleus to be elaborated: qualitative analysis (spatial

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orientation and type of morphogen gradients) can be added to quantitative analysis

(number of receptors stimulated in a temporal interval). Such a mechanism is

probably indispensable to allow epithelial cells, which have only one side free to

receive signalling molecules, to feel and estimate the direction of origin of very low

concentrated morphogens or to “sense” very few morphogen molecules from a

particular (forecast) direction. Primary cilium basal body is supposed to have been

previously oriented in the “mapped” cortex in such a way that each axonemal doublet

is located in a fixed and controlled position in respect to the cytoskeleton and

coordinated with the other cells of the epithelium: the basal body of the primary

cilium is the MC of the centrosome, that, already oriented during the last cell

division, has migrated to the cortex, maintaining its orientation, so that it can easily

arrange and orient its transition fibers, basal feet, and ciliary rootlets to anchor itself

to the membrane and maintain the correct orientation. So through a polarized primary

cilium, morphogen gradients (mathematically defined as vectors oriented toward the

source) can be deciphered, interpreted and translated by basal bodies: a controlled

rotational disposition of receptors can cooperate to increase the differential response

to variation of concentration rates (using thus three factors: concentration gradient,

receptor density and receptor circumferential position). Signaling pathways can

interfere with the number and circumferential position of primary cilium receptors in

order to better fine-tune the cell response to gradients of morphogens or to flows (see

left-right and the role of Hensen’s node cells): a primary cilium, circumferentially

polarized by its polarized basal body, can organize its receptors in such a way that it

can operate as a directional antenna or, rather, a directionally programmable antenna.

Left-Right

A role of centrosomes and centrioles in left-right patterning has been proposed by

many researchers:

“What sub cellular component is responsible for the crucial orientation event that

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defines “leftward”? One likely possibility is that the coordination of the 3 axes is

performed by a cytoskeletal organizing center such as the centriole or basal

body...The sharp midline separation suggests that the first cell cleavage in X. laevis

may produce L and R halves that inherit differential chiral information.“ (Vanderberg

and Levin, 2009).

“An intrinsically chiral structure, perhaps the centrosome, serves as a template for

directing polarity in the absence of spatial cues. Such a template could help to

determine left–right asymmetry and planar polarity in development” (Xu et al.,

2007).

Cilia are considered the initiators of asymmetry: the flow generated by the motile

cilia of Hensen's node cells induces asymmetry in many internal organs (heart, liver).

What role can centrioles play in left-right patterning? Brown and Wolpert (1990)

hypothesized a molecule or a cellular chiral structure, named “F”, capable of adding a

Left-Right axis perpendicularly to the AP and DV axes.

An extraordinary answer to this question arrives from the geometrical model of the

centrosome, considering its role of interface that translates targeting sequences into

their location in cells, through labelled γ-TuRCs: MCs, if assembled with reverse

circumferential sequence (clockwise/counterclockwise), can generate a real true

enantiomorphous organelle (likely the only one in the cell) right-/left-handed, able to

symmetrically translate morphogenetic instructions (topogenic sequences). Let’s

come back to the set (a blind or a visually impaired person and a Braille clock dial

maintained horizontal) which symbolizes biological protractor/goniometer

functioning; let’s suppose that two blind or visually impaired individuals start from

the same point of the plane: one has a normal Braille dial whereas the second has a

dial built with a counterclockwise disposition of the Braille characters (“12” is in

front of him like in the other instrument, but the other eleven numerals are disposed

counterclockwise: “1” is in the sector normally reserved for “11”, “2” in the segment

normally occupied by “10”, and so on); vocal signals indicate the direction of their

steps: the two individuals will execute the received (identical) instructions in a

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symmetric fashion: their paths will be bilaterally symmetric. Therefore the answer to

the left-right patterning question has been defined “extraordinary”: a little change in a

cell organelle instead of thousands and thousands of changes in morphogenetic

programs is capable of generating bilateral symmetry. Same signals, two symmetric

pathways: same morphogenetic programs, two symmetric organs.

A new hypothesis

- Reverse or opposite rotational polarity of the MC is the base of Left-Right

patterning and bilateral symmetry.

Both the problems about Left-Right patterning and bilateral symmetry are easily

resolved by the centrosome geometrical model: a centriole with a reversible

circumferential polarity (default or opposite, standard or overturned, clockwise or

counter-clockwise) is a clear chiral, enantiomorphous structure; its role as an

interface whose output is the spatial delivering of targeted molecular complexes

assures the realization of bilaterally symmetric architecture (output) as a response to

the same input that drives the default architecture (realized by non-reverse or default

MC).

Mirror symmetry of two 3D objects is very much easier than one might suppose: it

consists of the opposite sign of only one coordinate: any point P (with coordinates “x,

y, z”) belonging to one object, is symmetrical to the point P’ belonging to the

symmetric object (in this case the plane of symmetry is the “y z” plane) whose

coordinates are “ –x, y, z ” (note the sign “–“ before the “x” only); in a spherical

reference system, only the sign of the coordinate changes. The MC of the

centrosome, if built with reverse polarity (mirror symmetric in respect to a “default”

MC) matches each targeting sequence with the same corresponding mark which is

symmetrically positioned in respect to the default MC, and assembles aster and

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cytoskeleton with the same reverse polarity of its triplets, and this is so for the

disposition of cell landmarks, polarity complexes, receptors and signalling molecules

and, above all for the direction of extracellular fibers: the whole polarization of cells

and tissues is symmetric and the morphogenetic processes of paired and unpaired

organs are carried out mirror-symmetrically: the reverse circumferential polarity of

the MC is transmitted to tissues and organs that grow bilaterally symmetric. In snails,

only one maternal gene is responsible for the left- or right-handed spiral cleavage: it

is surprising that only one gene is able to completely reverse (with perfect mirror

symmetry) the arrangement and orientation of cleavage planes in many many cells,

however mirror symmetry consists only in the sign “-“ before the coordinate “”; a

simple molecular mechanism must necessarily exist capable of reversing MC

circumferential polarity: this matter will be examined more deeply later.

Plants do not show bilateral symmetry or left-right polarity. Unlike animals, plants

and trees do not have evident and true bilateral symmetry, a left and a right half or

side; only the shape of leaves and flowers could seem nearly symmetric (although 2D

only), but the curvature of the two leaf edges (particularly near the petiole and apex),

the edge indentation, the position of petiole, the apex tilt, the arrangement of the

veins that start alternately from the central vein and, above all, meristem histology

and developmental biology exclude the existence of a true bilateral symmetry. Also

the flowers of zygomorphous plants (orchids for example), described as roughly 2D

bilaterally symmetric, after a thorough morphological and developmental analysis,

lead to the same conclusions: bilateral symmetry of paired sepals and petals, as

symmetry of the two halves of unpaired structures (especially for the arrangement of

veins and pigments) is only apparent, not supported by anatomical, histological and

developmental foundation; the two cotyledons (in dicots) have different shapes too;

other symmetries frequently appear, with several reflection planes. A similar apparent

but false symmetry, like in the petals of zygomorphous flowers, appears also in each

of our fingers: a finger seems itself a symmetric object composed of two symmetric

halves and shows an “apparent” midline and an “apparent” (sagittal, proximal-distal)

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plane of symmetry, but anatomy, histology and embryology do not support this idea:

each finger is mirror symmetric to its opposite finger of the other limb. It is known

that the apparent bilateral symmetry of zygomorphous flowers has an advantage in

attracting pollinator insects (which curiously, take note, are Bilateria): thus, during

evolution, zygomorphous plants have developed quasi-symmetric flowers, modifying

their plans for building laminae and layers, as we will see later. Indeed, plants

dispose, under their cell wall, parallel MT rings that compose a real grid line; so they

can manage somehow both the third dimension and anything like mirror symmetry:

fixing some points of reference along their cortical MTs after cell divisions, and

controlling the distance from the equator, through MAPs, they have the possibility of

using the third dimension (orthogonal to the array of cortical MTs) in order to locate

the spindle poles along the circumference of cortical MTs. It is possible to model how

2D bilateral symmetry could be generated in laminar tissues without centrosomes by

using MTs and MAPs, like plants, devoid of centrioles, or like acentrosomal

planarians: after the first (or another “particular” division in plant meristem or in

regeneration blastemas) the two new cells can mark their respective side of contact:

this is already a midline and both cells, in respect to this side, are bilaterally

symmetric between themselves; this side-mark and the opposite spindle pole position

(symmetric, in the two cells, in respect to the midline), reproduced and transmitted by

the offspring, represent the cues that orient the planes of division; descendant cells

orient the spindle poles following autonomous independent programs (automatically

alternating longitudinal and transversal divisions), to generate division planes

bilaterally symmetric between two close or distant cells having the same lineage but

located one in the “right” and the other in the” left” half. In effect, in plants, this

supposed apparent mirror symmetry is local-depending: unlike animals, in which

bilateral symmetry is globally oriented in respect to the sagittal plane (shared

orientation of centrosomes), the orientation of “quasi-mirror-symmetric” organs

(flowers) is random and local (not global and shared), so they can look up or down,

or toward East or West. Without centrosomes, 3D developmental processes cannot be

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realized: Planarians do not perform gastrulation. Compare plant development to that

of Drosophila wings (although the fruit fly possesses only an “ancient” and

incomplete type of centrosome with doublets instead of triplets and is a simple

organism with a little connective tissue, without bones and cartilages): when a cell is

genetically engineered to grow faster than others, its clone of descendant cells forms

a larger part of the wing, but the final result are two bilaterally symmetric wings

showing the canonical shape: a “geometrical” interactive cross talking between

genetic programs and extracellular environment has happened to form two

stereotypical normal wings (in addition mirror symmetric). So in zygomorphous

plants, a quasi-bilateral 2D symmetry of flowers can be achieved through non-

regulative development. “Bilateral (3D) symmetry” means that two (possibly distant)

structures (the hands or the ears, for instance) show anatomical, histological, cellular

and sub-cellular mirror symmetry; in the two mammalian cochleae of the same

individual, the general shape is clearly symmetric: furthermore also symmetric is the

disposition and orientation of membranes (basilar, tectorial, Reissner’s), of cells

(Corti’s, Deiters’, Koelliker’s) and of their cytoskeletal MTs too (MT bundles in pillar

cell). In C.elegans, morphogenesis of the intestine shows that the two first cells (Ea

and Ep) divide transversally (the plane of cytodieresis contains the AP axis) and

generate their bilateral counterparts: from now on, right and left cells will have mirror

symmetric shape, polarity, dimensions, movements, orientation of cleavage planes,

and cell-cell adhesions; on the contrary, during C.elegans vulva formation, the first

divisions occur longitudinally (the plane of cytokinesis is orthogonal to the AP axis)

and an “apparent” bilateral symmetry (anterior-posteriorly oriented) appears:

however developmental differences are detectable between the anterior and posterior

halves, the anterior one growing faster than the posterior, and cells have different

dimensions, different cell-cell contacts and adhesions.

As we have already said, centrioles are present in eukaryotic cells, but not in higher

plants and most fungi; unicellular organisms have only centrioles/basal bodies, each

one independent, while in algae and Metazoa two orthogonal centrioles are embedded

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in the PeriCentriolar Material that forms the centrosome: only the centrosome can be

equipped with left/right MC.

An accurate bilateral symmetry and a definite left-right polarity have been established

only in Metazoa.

Drosophila right and left wings reproduce, with mirror-like feature, the same shape,

edge curvature, compartments and arrangement of tracheae and their anastomoses

(symmetry breaking and superimposition of asymmetry is reserved at the latest stages

of wing formation: see Levin M., Palmer A.R. 2007: “Left-right patterning from the

inside out: widespread evidence for intracellular control”, BioEssays); Ultrabithorax

mutants, instead of halters, develop a pair of additional wings that are built with the

same bilateral symmetry. Inserting the human ortholog gene LHX2 into apterous

mutant embryos (the mutant phenotype lacks wings) the normal wild-type phenotype

is rescued, with two bilaterally symmetric wings (Strachan and Read, 2010); it is

clear that, upstream, the same genes and the same signals act, but downstream there

are two different ways (or, rather, two symmetric tools) left- and right-handed that

symmetrically carry the same instructions out; development confirms that wings

originate from symmetrical primordia, the imaginal discs: after introducing the idea

that MC reverse symmetry is the most likely organizer and builder of metazoan

bilateral symmetry it is not surprising that imaginal discs topology not only

corresponds to that of developed appendages, but is bilaterally symmetric too.

Bilateral symmetry of Metazoa has clear anatomical, histological and developmental

foundations: if Metazoa (bilaterally symmetric) possess centrosomes and plants (non

mirror-symmetric) do not, this cannot be a fortuitous and meaningless coincidence.

Obviously, the inevitable variability of biological processes, due to several cues,

thermal fluctuations above all, especially when enormous numbers of cells are

involved, (very high precision, as we have seen, does not mean identity) can originate

very small differences between left and right: our faces, frankly bilaterally

symmetric, can show a slight (controlled) asymmetry (but our legs have the same

precise -bilaterally symmetric- length!).

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Bilateral symmetry in Metazoa is more marked than it may appear: it is evident in the

unpaired bones, cranium, vertebral column, pelvis and thoracic cage, but also the

unpaired internal organs (e.g. digestive or respiratory apparatuses), originated from

unpaired (e.g. archenteron) or symmetrical paired primordia (e.g. somites, somatic

and splanchnic mesoderm), keep this symmetry until, during development,

asymmetric movements, rotations and twists, oriented in only one of the two possible

directions (clockwise or counterclockwise), intervene, or developmental adaptations

are superimposed in only one half of the body. Indeed Metazoa are often described as

superficially symmetric but interiorly asymmetric: my personal opinion is that in

Metazoa bilateral symmetry is a fundamental basic property (and an essential

requirement) of their locomotive and sensorineural (movement driving) apparatuses:

bilateral symmetry is the simplest and the most efficient way to assure balance, drive

and control the direction of movements and localize perceived signals (differential

stimulation of two equal bilateral effectors or receptors); without bilateral symmetry,

the control of balance in fast-running/-flying animals (prey and predator change

directions at a great rate) would be a quite difficult problem; this seems to have been

the reason for the extraordinary evolutive success of bilateral symmetry in mobile

organisms; on the contrary, the asymmetry of high brain functions, like hemispheric

lateralization of language or face perception, is superimposed on the basic sensorial

bilateral symmetry; in effect the initial inevitable bilateral symmetry of internal

organs is only a consequence of the establishment of a general symmetry plan

(gastrulation, neurulation, gut formation) but, unlike in locomotive and sensorineural

apparatuses, does not have functional significance: Vertebrates have developed and

adopted asymmetry in many internal organs to solve, for example, the non-

elementary problems of the anatomy and physiology (fluid dynamics) of the great

vessels (systemic and pulmonary circulation). Also in other organs and in other Phyla

limited asymmetries have been described, for instance in Drosophila wings (Levin

and Palmer, 2007), confirming that a downstream process of symmetry breaking is

superimposed to an upstream bilateral symmetry plan.

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Summarizing, the extraordinary property of two reversely polarized MCs is: “same

input, two symmetrical outputs”.

Bryant (1981: for review see also: Gilbert, 2010, Baker, 2011) proposed the “Polar

Coordinate Model of Positional Information in the Developing and Regenerating

Limb”: in this model, cells are supposed to have a circumferential organization and

adjacent cells “sense” neighbouring signals (recall also the considerations about the

primary cilium and its role as a rotationally programmable –receiving and

transmitting– antenna). When developing tissues or cells, normally non-adjacent, are

juxtaposed, duplications arise: Bryant's polar coordinate model forecasts the

orientation of duplicated limbs; the graft of a left limb bud (or a left regeneration

blastema) on the contralateral right stump, causes three areas of re-growth that

produce three limbs; a central left limb, composed of the transplanted left cells that

maintain their circumferential value (reversed regarding right stump cells) and their

characteristic left-handed tilt and (shared common) orientation of their three axes;

other two abnormal external right limbs growth, composed of stump right cells,

conserving the AP and DV axes typical of the right limb, but with the PD axis

described as rotated respectively of about ± 90°; cells try to normalize circumferential

cell-cell contacts inducing the arising of correctly polarized cells interpolated

between graft and stump cells); cells that are differently patterned (left/right) respond

differently to the same morphogenetic stimulus: they build the forecast structures

(cells maintain the state of differentiation that is permitted in the species: re-growth is

species specific), but through their own polarity; the orientation of the proximal-distal

axis in limb buds depends on the spatial topological position (orientation of

circumferential values) of the neighbouring cells from which the blastema is induced.

Bryant’s “shortest intercalation rule” shows that the juxtaposition of surface receptors

(circumferentially ordered; remember again the considerations made about the

primary cilium) “senses” incorrect cell-cell contacts and stimulates the correct

differentiation and intercalation of cells with correctly oriented rotational polarity.

Bryant’s model completely agrees with the statements of the geometrical model of

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centrosome functioning: i) cells possess a circumferential global polarity, imposed by

the centrosome which organizes the cytoskeleton and compartmentalizes cell cortex

and membrane (polarity and adhesion factors, signalling receptors); ii) reverse

polarity of the MC is the molecular foundation of left-right patterning and bilateral

symmetry. Bryant's model indicates that the “chiral structure” that determines the

left-right pattern (Xu et al., 2007) and the “cellular component” that specifies the

difference between left and right sides (Vandenberg and Levin, 2009) must possess

not only a simple generic enantiomorphism but a complete “rotational” chirality: this

supports the idea that only the MC (which is circumferentially polarized) has such

properties.

Germ cells and, consequently, every zygote, have a MC built with “default” rotational

polarity, clockwise- or counterclockwise-oriented, depending on the species: in

Xenopus zygotes, Danilchik and colleagues (2006) filmed in vivo their

circumferential asymmetry: rotational equatorial cortical movements

(pharmacologically induced) are oriented in a single fixed (“default”) direction in the

zygote and in parthenogenetically activated oocytes, whereas, after the first mitosis,

the two blastomeres show similar equatorial cortical movements but with opposite

direction between them; a left-right symmetric polarity had been established in left-

and right-handed symmetric blastomeres. Every zygote has the same “default”

pattern: so situs viscerum solitus is the same in every adult, not 50% as expected in

case of random left/right patterned zygotes.

Breaking of bilateral symmetry

During the early stages of development, cilia of cells in the Hensen node (or its

functional equivalent in other phyla) rotate unidirectionally, producing a (default)

flow that activate genes encoding transcription factors only in the cells of the left part

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of the organism that are reached by this flow. Thus many internal organs in

Vertebrates are asymmetrical: heart, great vessels, lungs, spleen, cerebral cortex,

digestive apparatus and its accessories (liver, pancreas). Situs viscerum solitus is

established: the spleen and the heart on the left, the liver on the right. Studies carried

out on the Zebra fish (Danio Rerio) have filmed the rotation and migration events

that occur during heart early development and that are superimposed on the original

bilateral symmetry. In these organs, originated from primordia with bilateral

symmetry, during a certain phase of development different processes are performed

that involve only one half of the organism: heterochelia, the difference in shape

between the two (right and left) chelae in Crustaceans, is a good example; one of the

two chelae, used in courtship, is larger and has a more suitable shape for cutting,

while the other specializes in grasping. It appears that there is a common “default”

program for both bilateral primordia: later, during development, in the left half this

“default” program is silenced and replaced (or overlapped) by a modified program,

reserved uniquely for the left half (left-reserved program), that conserves the left-

handed modality of execution (carried out by left patterned cells). Errors in this phase

cause “heterotaxia”: in the rare cases of cardiac right isomerism, two both right atria

develop (the “default” program is not silenced in the left half and the left-reserved

program is not activated), while in left cardiac isomerism two both left atria develop

(the “default” program is silenced also in the right half and the left-reserved program

is activated in the right half too): surprisingly, in both cases, the two atria (whatever

they are both right or both left) are mirror-images of each other (bilateral symmetry):

thus in right isomerism there are two symmetric right atria (both with the

characteristic anatomical features of a right atrium) one built by left-handed cells, the

other built by right-handed cells and therefore bilaterally symmetric; and this is so in

left isomerism (Hildreth et al., 2009); this can confirm that cells, determined to be

right (circumferentially polarized by the MC), transmit their polarity to aster and

cytoskeleton, and execute any morphogenetic program in right-handed modality,

whereas left cells translate the same instructions in left-handed modality.

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It is remarkable the importance of gap junctions between left- and right-patterned

adjacent cells: the pioneering experiments on frogs performed by the first

embryologists (Wilhelm Roux in 1888, Oskar Hertwig in 1893) more than a century

ago showed that if one of the two first blastomeres is burnt off while the other one

continues to sense its membrane receptors (gap junctions), only a half embryo

develops; on the other hand, if the two first cells are separated, each cell can no

longer “sense” the other one through the gap-junctions and two complete organisms

arise. “When separated at the 2-cell stage, Newt embryos exhibit 89% incidence of

organ laterality reversal in one of the twins”. (Takano et al 2007): one blastomere is

“default” patterned, the other one is already oppositely patterned (situs viscerum

inversus). “The sharp midline separation suggests that the first cell cleavage in X.

laevis may produce L and R halves that inherit differential chiral information”

(Vanderberg and Levin, 2009): left and right centrosome have real differential chiral

information contained and “coded” in the reverse sequence of MC non-equivalent

triplets. However, left and right cells with chiral information (during the very first

stages of development) are able to “reset” and restart from an “original” condition: in

fact, 16-cells-blastulae of sea urchin, artificially divided into two halves (one Ventral

and one Dorsal) produce two complete larvae: the Ventral one conserves Animal-

Vegetal and Dorsal-Ventral axes, whereas the Dorsal one maintains only the original

A-V axis, but acquires a new repositioned D-V axis and reverse L-R polarity

(resetting of the cells which will differentiate into blastopore primordium); the graft

of the Spemann organizer shows that the blastopore possesses L-R inductive

capability, being able to induce receptor cells to form duplicated ectopic structures,

bilaterally symmetric along a new midline, from neural tubes to complete heads. In

these experiments the blastopore appears to control the positioning of the midline and

to possess a unique role in managing L-R polarity (symmetry conservation or

symmetry breaking induction); so, normally, it can maintain the natural L-R

patterning with a fixed midline or can intervene to “reset and restart” imperfect

blastulae in order to save very early splitting-events (twins): this is a powerful

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mechanism that greatly improves the survival of defective blastulae and the success

of the reproduction. The blastopore, unpaired positioned on the midline, its bilateral

symmetric inducing activity and its developmental connection with the Hensen node

(or its equivalent) shows its important role in L-R symmetry and in symmetry

breaking mechanisms; in Mammals, during gastrulation, left-right patterned cells

from the epiblast primitive node (on the midline) invaginate and, directed from the

midline to the Left or Right embryo half, replace the previous hypoblast cells (likely

not left-right determined) to form the embryo endoderm; a second wave of entering

of left-right patterned cells forms the mesoderm, many cells moving laterally and

some directed forwards to form the notochord on the midline, whose inducing

activity is well known (neural plate, somites, intermediate and lateral plate

mesoderm, prechordal plate: all these structures are formed through bilaterally

symmetric morphogenetic processes); also well known is the role of nodal cells in

Left-Right symmetry breaking (unidirectional flow of perinodal fluid due to

unidirectional/default rotation of nodal cells primary cilium). In Bryant’s “Polar

Coordinate Model of Positional Information in the Developing and Regenerating

Limb” it appears that cells try to normalize circumferential cell-cell contacts, by

inducing the arising of correctly polarized cells that interpolate between graft and

stump cells: this indicates a left-right pattering-inducing activity also in limb buds

and in regenerating blastemas (probably triggered by signals from gap-junctions as

we have seen in the experiments of Roux and Hertwig).

Left-right determination is an epigenetic process that has something in common with

sex chromosomes and sex determination: in the two sexes the majority of organs have

the same shape but the morphogenetic programs characteristic of genital organs of

one sex are strictly reserved to and expressed in this one only and silenced in the

other one. Similarly, in the two halves of an organism, many organs are similar

(symmetric) but others are characteristic and strictly reserved to one half only

(chelae, spleen, bicuspid and tricuspid valve, left and right heart ventricle). In both

cases this means that only in one sex or in one half of the body, is access allowed to

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that part of the genome which is reserved only to that sex or that half. The link

between alterations in the normal functioning of sex chromosomes and left-right

patterning is interesting: it is present in CHILD syndrome (images presented by

Vanderberg and Levin, 2009, free on the Internet) and in gynandromorphism

(astonishing images are presented by Palmer, 2010, also free on the Internet). It is

useful to remember that teratomas, when derived from germ cells, occur in testes or

ovaries, whereas, when derived from embryonic cells, occur on the midline.

Symmetry breaking and asymmetry establishment have singular features in

Echinoderms like sea stars: larvae are clearly bilaterally symmetric (plutei) whereas

adults show an apparent and misleading 5-fold symmetry: indeed the adult is almost

entirely composed of left-half derived cells; rather than a radial symmetry, this

phylum seems to have adopted an unusual circular metamerism (different from the

longitudinal metamerism, like segments in D.melanogaster, or somites in Vertebrates)

and to have enormously amplified the left-right asymmetry. Also in fruit flies left-

right patterning shows singular and surprising features: as we have seen in Foe’s

study, the domains described occur as pairs and, paired or not, each domain is

bilaterally symmetric: so a clear midline is evident dorsally and ventrally; the

preblastodermic syncytial development in Drosophila is not so unusual: it is a

bilateral symmetric blastula quite similar to that of other Metazoa (Xenopus, sea

urchin, etc.) but with blastomeres without a membrane: its polarity and global

compartmentalization is dictated by its centrosomes.

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Discussion of the model

Critical points of the proposed geometrical model

The previous theoretical structural hypotheses about the centrosome have highlighted

how accurately they fit in with several geometric, morphogenetic and thermodynamic

requirements of complex organisms composed of very large numbers of very small

units (cells): for instance, bilateral symmetry and left-right patterning can be easily

resolved by the centrosome geometrical theoretical model in agreement and accord

with the statements of cell and evolutionary biology. However, from the proposed

(theoretical) model some important criticalness (biochemical feasibility) emerges and

questions arise: then answers (and new questions) must be searched for and, if it

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possible, found.

Here our aim is to ascertain the biological, biochemical and biophysical foundation of

our hypotheses.

Q&A

Above all there is the problem of the non-equivalence of the nine centriole triplets:

what is the biochemical basis of such an unusual biological process, the assembly of

an ordered sequence of nine similar but non-equivalent structures?

In addition, other queries:

i) The symbols for the hours on a clock are orderly sequenced (circumferential

polarity) and the symbol for “12 o’clock” is always at the top to guarantee the global

orientation of the whole structure: which known biochemical mechanism can create

the circumferential polarity of the nine centriole triplets, ordering, arranging and

aligning them in accordance to a predefined sequence and a pre-established global

orientation?

ii) In the proposed model, the reverse orientation of centriole polarity is the basis of

3D bilateral symmetry: which known biochemical mechanism can carry this function

out? In other words, how is it possible to assemble in an opposite sequence

(clockwise > counterclockwise) nine radial spokes and nine centriolar blades?

iii) The centrosome has been supposed to be spherical while the PCM is organized in

cylinders, coaxial to the centrioles: how is the correct quasi-spherical -TuRC

inclination achieved?

iv) How can the centrosome map the whole cortex if the nucleus, to which it is often

close and which is not crossed by MTs, hides more than half of the cortex?

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v) How do the macromolecular complexes (3-6 nm in diameter), destined for a

precise position in the cortex or the cell membrane, quickly find their respective -

TuRC receptors, interspersed among many others over the large (2x106 nm

2)

centrosome surface?

i) Molecular basis of triplet non-equivalence (centrosome software)

From Geimer and Melkonian (2004) ”The ultrastructure of the Chlamydomonas

reinhardtii basal apparatus: identification of an early marker of radial asymmetry

inherent in the basal body”:

“At the distal end of the basal body (bb), exactly at the transition between the

microtubular triplets of the bb and the doublets of the transitional region, a filament

of about 10 nm diameter is attached to the microtubular doublets (rarely triplets) in a

rotationally asymmetric pattern linking A-tubules of doublets 7, 8, 9, 1 and 2. From

doublet 2, the filament arches back to doublet 7, passing through the lumen of the bb.

The overall outline of this closed structure resembles that of an (capless) acorn with

its broad base located between doublets 1 and 2, and its pointed tip at doublet 7. At

doublets 2 and 7, the acorn has a prominent knob through which linkage with the A-

tubule is established. The side of the acorn that is not attached to bb doublets/triplets

will, in the following, be called the `lumenal' side of the acorn. A second, V-shaped,

system of filaments of about 8 nm diameter is present in this region of the bb. Two

filaments extend from triplets (rarely doublets) 4 and 5 into the bb lumen, bisect the

lumenal side of the acorn and, in the center of the bb lumen, connect to another

filament that runs perpendicular to the two filaments, extending down from the

proximal end of the stellate structure in the transitional region. The positional

relationship of the acorn to these filaments is best seen in longitudinal sections

through bbs. In such sections, the acorn is seen as two asymmetrically positioned

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electrondense dots. The filaments extend from triplets 4 and 5 at the level of the acorn

and bend downwards with an angle of about 35° after reaching the lumenal side of

the acorn. They continue to the other side of the bb, making contact with triplets at

the level of the distal connecting fiber attachment with the bb. In cross sections

through bbs, depending on the sectional plane, these filaments can be seen to contact

triplets 8, 9 and 1.

Most interestingly, both systems of filaments were already present at the distal end of

the probasal bodies.”

The last words completely agree with the geometrical model of centrosome

functioning: the process of centriole duplication through the characteristic orthogonal

disposition and the MC role as a platform are considered the mechanisms responsible

for transmitting the same coordinated orientation of rotational asymmetry

(correspondence of MC and DC “0° marks); as we have seen in “Centriole/Basal

bodies in Ciliates” (on page 53, about Paramecium) the distal end of the basal body

(immediately under the axoneme) is the same end which, during centriole formation,

is close to the pre-existing centriole, used as a platform for self-assembly; a new

centriole, once correctly and coordinately oriented by its mother/platform, can be

easily inserted into the fragile structure of the cytoskeleton maintaining a coordinated

mother/daughter orientation without causing any distortion: 4000 basal bodies, made

up of nine different triplets each one having high propensity for binding different

elements of the cytoskeleton, must be guided and oriented to avoid a tangled jam. To

underline its importance, we have compared before this apparently strange but

fundamental and unique process of centriole duplication to the introduction of a new

trolley-bus into the aerial-suspended electric town-circuit or to the insertion of an

integrated circuit onto a printed circuit board.

We will come back to this theme.

The idea underlying the completion of the geometrical model of the centrosome has

something in common with the process of coordination of the rotational polarity of

the arising procentriole and the MC; the idea is that the biochemistry of non-

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equivalence does not consist in a structural difference of triplets (or radial spokes),

but in a mechanism able to differentiate and “decorate” nine identical sectors,

apposing nine different and orderly sequenced molecular complexes, which, in turn,

distinguish and render different both triplets and radial spokes. Thus, non-equivalence

is not imposed by the tertiary structure of the centriolar blades and spokes, on the

contrary their quaternary structure is responsible for their non-equivalence. A ring is

certainly the most likely structure and the “acorn” described by Geimer and

Melkonian is particularly appealing; a ring of an informational macromolecule able to

contain information (a linearly ordered sequence of equi-spaced markers) appears to

be the most suitable structure: a ring of RNA? Indeed no polypeptidic ring has been

found in centrioles and centrosomes, whereas “within the core of the basal body a

twisted or looped 90 Å diameter fiber, or more probably pair of fibers, RNase-

sensitive, in association with dense granules is observable (Dippel, 1976):

1 RNA loop + 9 protein dense granules = 9 RiboNucleoProteins (RNPs) markers.

The work “Structure and non-structure of centrosomal proteins” (Dos Santos et al.,

2013) presents the finding that “centrosomal proteins tend to be larger than generic

human proteins since their genes contain in average more exons (20.3 versus 14.6).

They are rich in predicted disordered regions, which cover 57% of their length,

compared to 39% in the general human proteome… These residues predicted to be

both disordered and coiled-coil may represent disordered regions that lack stable

structure unless they interact with a binding partner, and take coiled-coil structure

only upon binding”. Disordered protein domains frequently bind nucleic acids

(Vuzman and Levy, 2012): then the propensity of centrosomal proteins to bind RNA

is exciting (like CLERC, centrosomal leucine rich and coiled coil containing proteins,

studied, as we will see soon, by Yoshinori and Yukio: leucine rich domains and coiled

coils have high propensity to bind RNA): RNAs appear to be the fittest candidate to

be the biochemical basis of the centrosome “software”. Nine triplets (and also nine

cartwheel radial spokes), if structurally identical, can be easily self-assembled around

the SAS-6 ring without a fixed order of appearance, and, in a later moment, each of

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them acquires its own individuality: so identical triplets and spokes become

distinguished (and therefore non-equivalent) because of the presence of nine different

marks (like RNA hairpins, stems, loops, etc.) aligned in an orderly sequence, easily

coded, memorized and stored in a linear macromolecule. A ring of RNA is therefore a

very good candidate to realize the molecular basis of triplet non-equivalence: nine

diverse marks can be linearly coded in DNA (realizing an orderly sequence) and

distanced by “spacers”; the mark defined as the “0° mark” (the reference mark used

to orient the ring like the numeral “12” on a clock) can be formed by the

juxtaposition of the two ends of the molecule, then in a fixed position in respect to the

other eight marks and arranged in the centriole under the control of the MC used as a

platform: this fits in with the idea that the reason of the strange centrosome cycle

consists in the process for coordinating shared orientation). Many biochemical

pathways constitute the complex cross-talking between DNA and centrosome to

control and regulate the cell cycle: an RNA ring, transcribed but not translated, is

faster and fitter than a protein. A DNA sequence transcribed into an RNA ring allows

nine RNA-based markers (receptors), different from one another, to be arranged and

equally spaced around the SAS-6 ring (cartwheel): other PCM macromolecular

complexes, like miRNAs or RiboNucleoProteins (RNPs) recognize these triplet

markers in order to be arranged into that sector of the centrosome which is radially

contiguous to (or in front of) each centriolar blade (Fig 6). Indeed self-assembly is a

property characteristic of identical macromolecules, monomers, or of a few different

units (heterodimers and heterotrimers) that form the quaternary structure of proteins:

nine MT blades, which, in addition, are different and must be orderly sequenced, are

too many to be self-assembled together, especially because the precise constant

sequential order is a very difficult and frankly unlikely self-assembly process. “To get

deeper insight into centriolar wall formation, we examined the order of appearance

of the nine A-microtubules in the nascent procentriole. The formation of the first A-

microtubules was not directly related to a specific position. Moreover, the position of

each A-microtubule at the centriole wall did not correlate with its size, arguing

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against a sequential growth process. These findings suggest that each A-microtubule,

and thus each blade in a procentriole, assembles in an independent manner”

(Guichard et al., 2010). According to this finding, the nine triplets are, originally,

structurally identical: after their (random-arising) self-assembling, they become

different and orderly distinguishable because of the decoration by an RNA ring. As

already cited, “In C. reinhardtii the polypeptide VFL1 coded by the gene vfl1

(Variable number of FLagella), binds only to the triplet N° 1” (Silflow et al., 2001):

evidently in C. reinhardtii the triplet N° 1 has its own unique and distinguishable

triplet marker. Yoshinori and Yukio (2010) “identified a centrosomal protein called

CLERC (Centrosomal leucine-rich repeat and coiled-coil containing protein) which

is a human ortholog of Chlamydomonas Vfl1 protein. The bibliography as well as

database searches provided evidence that the human proteome contains at least seven

centrosomal leucine-rich repeat proteins including CLERC. CLERC and four other

centrosomal leucine-rich repeat proteins contain the SDS22-like leucine-rich repeat

motifs, whereas the remaining two proteins contain the RI-like and the cysteine-

containing leucine-rich repeat motifs. Individual leucine-rich repeat motifs are highly

conserved and present in evolutionarily diverse organisms”. Coiled-coil containing

proteins and leucine-/cysteine-rich regions have highly propensity to bind RNA.

Centrosomal RNA

“The centrosome and spindle as a ribonucleoprotein complex” (Alliegro, 2011).

“An intriguing morphological and developmental parallel between certain

procentriolar elements and an RNA-containing component of the Paramecium

kinetosome occurs during centriolar production and development in embryonic chick

tracheal epithelial cells” (Dippel, 1976).

Hiedemann and colleagues (1977) reported their observations on the formation of an

incomplete and not functional aster, following the implant of basal bodies of

Chlamydomonas Rheinardtii in Xenopus eggs: after the treatment of the basal bodies

with weak concentrations of RNase, the formation of a partial aster was found to be

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completely suppressed and only the capacity for lengthening of the centriole MTs

remained; the -TuRC function (nucleation of astral MTs) appeared to be sensitive to

the RNase, whereas only the MTs of the triplets of the centriole wall, after removal of

the CP110 cap, could still grow in length (in vitro) because of the addition of α and β

tubulin dimers at the “+” end. What is the functional association between RNA and

centrosomal -TuRCs ? Laane and Haugli (1974) had already studied the association

of RNA with centrosomes in Physarum, and Hartman and colleagues (1974) in

Tetrahymena pyriformis; Snyder (1980) showed that RNase inhibited microtubule

nucleation in PtK1 cells. Finally centrosomal RNAs (cnRNAs), not coding and absent

from the remaining cytoplasm was identified in the centrosome of Spisula

Solidissima (organism clearly bilaterally symmetric) (Alliegro et al., 2006).

Chichinadze and colleagues (2012) have continued the studies on Spisula cnRNAs

concentrating on characteristics that are particularly worthy of in-depth examination,

following the observation by Alliegro and colleagues (2006) that “a substantial ORF

[Open Reading Frame] was readily mapped in the antisense strand. The predicted

polypeptide encoded in this ORF includes a highly conserved 200 amino acid-long

reverse transcriptase domain. This domain exhibits striking homology (P=e-75

) to Zea

mays putative polyprotein, a member of the RNA-dependent nucleotide polymerase

family of proteins, Pfam00078. In addition, a ribonucleoprotein consensus RNA-

binding site (RNP-1) was found downstream from the reverse transcriptase domain.”

The importance of RNA for centrosome to work correctly emerges from another

study (Ishigaki et al., 2013): “RBM8A (Y14) is carrying RNA-binding motif and forms

the tight heterodimer with MAGOH. The heterodimer is known to be a member of

exon junction complex on exporting mRNA and is required for mRNA metabolisms

such as splicing, mRNA export and nonsense-mediated mRNA decay. Almost all

RBM8A-MAGOH complexes localize in nucleoplasm and shuttle between nuclei and

cytoplasm for RNA metabolism. Recently, the abnormality of G2/M transition and

aberrant centrosome regulation in RBM8A- or MAGOH-deficient cells has been

reported. These results prompt us to the reevaluation of the localization of RBM8A-

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MAGOH in human cells. Interestingly, our immunostaining experiments showed the

localization of these proteins in centrosome in addition to nuclei. Furthermore, the

transiently expressed eYFP-tagged RBM8A and Flag-tagged MAGOH also co-

localized with centrosome signals. In addition, the proximity ligation in situ assay

was performed to detect the complex formation in centrosome. Our experiments

clearly showed that Myc-tagged RBM8A and Flag-tagged MAGOH formed a

complex in centrosome. GFP-tagged PLK1 also co-localized with Myc-RBM8A. Our

results show that RBM8A-MAGOH complex is required for M-phase progression via

direct localization to centrosome rather than indirect effect”.

Hypothesis: circumferential polarity is generated by an RNA ring

“Structural and genetic studies suggest that asymmetry of the centriole (basal body)

plays a critical determining role in organizing the internal organization of algal cells,

through the attachment of microtubule rootlets and other large fiber systems to

specific sets of microtubule triplets on the centriole…To understand cell organization,

it will be critical to understand how the different triplets of the centriole come to have

distinct molecular identities” (Marshall, 2012).

“The overall outline of this closed structure resembles that of an (capless) acorn with

its broad base located between doublets 1 and 2, and its pointed tip at doublet 7. At

doublets 2 and 7, the acorn has a prominent knob through which linkage with the A-

tubule is established” (Geimer and Melkonian, 2004).

“Within the core of the basal body a twisted or looped 90 Å diameter fiber, or more

probably pair of fibers, RNase-sensitive, in association with dense granules is

observable…The apparent extraction, from the above structures, of RNA-containing

material by pronase and of protein-containing material by RNase is particularly

puzzling and intriguing… The apparent removal of both RNA and protein from this

basal body structure by either of the two corresponding enzymes suggests an unusual

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organization of the two components.… authors suggest that the filament might

contain "informational macromolecules" for assembly of the cores and centrioles… If

the RNA plays a structural rather than a translational role, then does it provide

scaffolding or dictate the order of assembly of the subunits in protofilament

formation, or serve as a recognition center for protein aggregations giving rise to

nucleation sites? Or does the RNA have some unique morphogenetic function which

our present preconceptions about assembly mechanisms have not permitted us to

envisage?”(Dippel, 1976). The “acorn” of Geimer and Melkonian and the “looped

fiber” of Dippel show similar diameters: 10 nm (acorn) and 90 Å (remember the

equivalence: 1 nm = 10 Å).

“Perhaps less tangible but still a likely cause for lingering controversy is that the

presence of nucleic acids in the spindle or centrosomes will require us to look

differently at these structures from a functional, and more to the point, evolutionary

standpoint ” (Alliegro, 2011).

Warning: the non-equivalence of the triplets concerns exclusively the “software” of

centrosome functioning, i.e. γ-TuRCs labelling; the orientation and inclination of γ-

TuRCs (centrosome “hardware”) is not controlled by the mechanisms examined in

this section.

To better develop the geometrical model of centrosome functioning, it is necessary to

deeply analyze the idea that the biochemistry of non-equivalence does not consist in a

(biochemically unlikely) structural difference of triplets (or cartwheel radial spokes),

but in a single linear macromolecule - RNA - capable of assuming different 3D

conformation: such molecule is able to bind different proteins (markers or receptors)

in order to decorate the base of the centriole and differently label the nine triplets and

the nine spokes, juxtaposing nine different 3D structures (ribonucleoproteins, RNPs:

Figs. 7 and 8) to spokes and triplets: as we have seen, the idea that the non-

equivalence of triplets and spokes does not consist in their different structure or

molecular composition (primary, secondary and tertiary structures are identical and

equivalent: this is a more likely and canonical property of the centriolar blades), but

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in the collocation of nine different polyribonucleotidic-marks at their base that can, in

turn, bind different proteins (non-equivalence of the quaternary structure) seems

plausible and convincing.

A single-stranded filament of RNA, because of its chemical-physical properties and

the frequent modification of the bases, exhibits, like proteins, a variety of

thermodynamically favourable secondary structures (hairpins, stems, loops, knots,

pseudoknots: Fig. 7): these, in turn, create particular 3D tertiary configurations.

Transfer-RNA is a well-known example: its secondary (two-dimensional) cloverleaf

structure (three different stems, each ending in a loop, and a fourth variable loop), is

encoded linearly (i.e. one-dimensionally sequenced) in DNA and in the pre-tRNA

transcript; a 3D tertiary “L” shaped conformation similar to a chaise longue is the

final result after splicing: these properties enable it to interact with extreme precision

with its cognate amino-acyl-tRNA-synthase and with the appropriate site of the

ribosome. This is an evident discrete system, highly resistant to noise, based on codes

recognized by their 3D structure, with an almost negligible margin of error. Similar

secondary and tertiary structures have been highlighted also for introns and in many

small nuclear and nucleolar RNAs. “The acridine-orange fluorescence studies

showed reduction of the yellow-green basal body fluorescence by RNase but not by

DNase, and a shift from yellow-green (indicative of double-stranded RNA or DNA) to

orange-red (indicative of single stranded RNA) when staining followed

mercaptoethanol or pronase treatment” (Dippel, 1976): a ring of single-stranded

RNA with nine different double-stranded hairpins or knots (Figs. 6, 7) linked to

proteins (RNPs) is strongly consistent with these observations. Centriolar triplets

non-equivalence, supported by RNPs, is transmitted to the whole neighbouring

sector of the corresponding PCM and especially to the elaborate scaffold of γ-TuRCs:

γ-TuRCs are similar to cones, with the circumference of the base composed of a γ-

tubulin ring; γ-tubulin is incorporated into a heterotetramer (γ-tubulin small complex

or γ-TuSC) which, in turn, is composed of two molecules of γ-tubulin and two other

conserved proteins, DGrip84 -91 in Drosophila; [Grips means γ-Ring Proteins also

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called GCPs, acronym of γ-Complex Proteins; other different Grips, Dgrip-75, -128

and -163 in Drosophila, link γ-TuSCs to organize -TuRCs]; pericentrin fibrils

(Mennella, 2012) and SAS-4 (Gopalakrishnan, 2011) connect radially centriolar

blades and γ-TuRC scaffolds.

As before stated, to satisfy the basic requirements of a spherical reference system

organizer, in order to recognize coded geometric signals and translate them into their

desired final locations, “cellular protractors/goniometers” must possess: 1) different

marks; 2) constant ordered sequence of marks; 3) one start mark; 4) controlled spatial

orientation of the entire structure. A single-stranded RNA ring has all the

characteristics to be the molecular platform of the non-equivalence of the nine

centriolar blades: (a) it is memorized linearly in DNA, which can thus encode nine

different molecular labels; (b) these different molecular labels (hairpins or knots) are

orderly (linearly) sequenced and equally spaced (DNA spacers), suitably distanced so

that they fit in structurally with each of the nine spokes/triplets; this is comparable to

a strip of conveniently distanced numerals that follow each other in an orderly

manner and that can decorate the face of a clock, comprising the characteristic

numeric ring; (c) an RNA ring is equipped with structures that allow it an

unambiguous orientation: like the acceptor stem of tRNA, 5’ and 3’ cnRNA ends can

be used as anything like a handle-stem that identifies the so-called “0°” reference or

start-mark (it can be compared to the figure “12” which is always at the top on a

clock). Indeed a mechanism to form a ring of single-stranded RNA, connecting its

ends (3’ poly(A)-tail and 5’ m7G cap) is used during the first stages of translation in

eukaryotes: several poly(A)-tail-binding proteins, joined to the 3’mRNA poly(A)-tail,

are bound by the eukaryotic translation Initiation Factor 4G (eIF4G), while the

5’mRNA m7G-cap is bound by eIF4E; both eIF4G and eIF4E are joined by eIF4B,

producing a circular molecule (often very large) of mRNA. It is well known that

many regions of human non protein-coding DNA are transcribed into pre-mRNA:

cnRNA11 (see later) possess 3’UTR- poly(A)-tails and 5’UTR- m7G caps and can be

assembled into a ring conformation, following usual mRNA processing.

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Fig. 7 RNA 3D structures.

Because of its chemical-physical characteristics and the frequent modification of its bases, an RNA

molecule, from its earlier linear configuration (A), acquires diverse local secondary, thermodynamically

favourable, structures (stems, loops, hairpins, knots as showed in: B > I) with canonical and non-canonical

base-pairings, and corresponding different tertiary 3D structures

-------------------------------------------------------------------------------------------------------

ii) Chirality and bilateral symmetry: RNA, through an event of

retrotransposition, might have generated the reverse polarity of the MC

Let’s summarize again the hypothesis about left-right patterning, which will be faced

here. In the geometrical model of centrosome functioning, the MC is considered the

chiral structure responsible for realizing bilateral symmetry: indeed the MC,

polarized with reversed, opposite circumferential sequence (clockwise/

counterclockwise), seems to be the only rotationally enantiomorphous organelle, the

unique biological structure able to play a geometrical role in left-right patterning and

bilateral symmetry establishing, which are indisputably geometrical processes.

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Centrosomes, with opposite polarity of the MC, are geometrical interfaces which

receive the same input (signals with the information for the value of the coordinate)

and translate them symmetrically (output); during organogenesis, they transmit their

intrinsic chirality to each mirror symmetric organ. As we have already said, only the

MC has the property of being assembled with opposite polarity, on the contrary, the

DC has always the same rotational polarity in every cell: mirror symmetry changes

only the longitude ( coordinate) of a point, never its latitude (θ coordinate). An MC

with reversed sequence of the triplets and therefore, with circumferential polarity,

organizes a “counterclockwise polarized PCM”, transmitting its reverse polarity to

the γ-TuRC receptors. In each meridian wedge of the “reverse” centrosome, the γ-

TuRC receptors remain structurally the same but are bilaterally symmetric in respect

to the “default” centrosome, like in a ”reverse” clock dial the numeral “1” takes the

place of the numeral “11”, “2” takes the place of “10” and so on; longitudinal -

TuRC receptors are always the same but reversely (symmetrically) positioned: their

3D configuration, their shape and form maintain their characteristic and remain

unaltered and unchanged. -TuRC inclination too remains unaltered and so the

associated latitudinal receptors: in a clock dial decorated by Roman numerals, “II”

identifies a sector positioned at “60° -clockwise rotation- from XII”, whereas in a

reverse/symmetric dial (overturned) the Roman numeral “II” does not change its

shape, only identifies a mirror symmetric position “60° -counterclockwise rotation-

from “XII”) [Overturning Roman numerals creates some problem: IV,VI,VII,VIII,

and IX, when overturned, are different; not so if we make use of capital letters: A, H,

I, M, O, T, U, V, W, X,Y]. The reversely polarized centrosome, compared to a

“default” centrosome, has the extraordinary property to translate the same DNA

morphogenetic geometric instructions – 3D signals or targeting sequences - into 3D

bilaterally symmetrical locations: one input > two reversely rotationally polarized

MCs > two symmetric outputs. Note that left and right centrosomes are built through

a variation in a part of their “software” (opposite or reverse polarity of longitudinal -

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TuRC receptors) whereas their “hardware” (-TuRC scaffold inclination and

orientation) remains completely unaltered. This hypothesis fits in very well with

evolutionary biology statements: a simple, small, easy change is much more likely

than conspicuous and large genomic variations: to change only the sequence of nine

marks of an RNA ring is very much more likely than to collect, store and conserve “a

lot” of variations in “a lot” of morphogenetic programs, until two complete sets of

instructions (one Left and one Right, coding for the correct bilateral symmetry of “a

lot” of symmetrical organs) make it possible to build an entire bilaterally symmetric

organism: and this for millions species (million is much more than “a lot”). Ease

passes the examination of natural selection: like in computer programming simple

languages and concise algorithms are preferred, so in evolutive competition easy

solutions are more stable and sure than complicated programs, and, to say, “win the

award”.

A question: to be effectively evolutionarily likely, a change must be simple, small and

easy: how “simple”? At this moment of our analysis, to reverse a sequence of

nucleotides does not seem so “easy”.

Each geometric signal for the longitude or angle “” (encoded in the related targeting

sequence), recognized by a -TuRC receptor on a counter clockwise labeled

centrosome, is decoded and translated as the symmetrical negative angle “-”,

whatever is its angle θ (its latitude). By reversing the only angle , perfect bilateral

symmetry is realized: “Basal bodies/centrioles are an excellent candidate for an

intracellular “F-molecule” [the chiral molecule hypothesized by Brown and Wolpert

(1990)], because they function as a microtubule-organizing center to direct

asymmetric localization of maternal components” (Levin and Palmer, 2007).

Left/right centrosomes are capable of building bilaterally symmetric cytoskeletons

that wire and map cell cortex compartments in a corresponding mirror symmetric

fashion.

As just seen, the biochemistry of non-equivalence does not consist in structural

differences of triplets (or radial spokes), but, more likely, in a single ring of RNA: to

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change only the sequence of nine marks of an RNA ring is easier than to change the

orderly sequence of nine bulky radial spokes or nine different awkward triplets, each

made of three long, hulking, unwieldy MTs: how “easier”? What known biochemical

mechanism can easily carry out the overturn of this ring or the reversal of its

nucleotide sequence, indispensable to realize an opposite, reversed polarity in the

MC? In other words, how is it possible to assemble in an opposite sequence

(clockwise > counterclockwise) nine RNA/RNP structures which decorate nine radial

spokes and nine centriole blades? In this respect it is convenient to imagine the RNA

ring like a very large molecule of tRNA having 9 loops in lieu of 3 and with a short

handle-stem similar to the tRNA acceptor stem, containing different 3’ and 5’ ends

(like a plug equipped with two differently shaped prongs or blades or pins).

What known biochemical mechanism can carry out the reversion of MC polarity?

“Gedankenexperiment” (thought experiments)

This term, introduced by the Danish physicist Hans Christian Ørsted, became famous

through Einstein’s and Schrödinger’s mental (or conceptual) experiments.

We too will perform three virtual experiments in which an observer is in front to

different couples of similar (near identical) objects: two similar thin plugs (having flat

large faces and two short pins), two similar house keys (having a large bow like a thin

disk and a very short blade), two similar images of a tRNA secondary structure,

designed on a sheet.

1) Both plugs have the name of the manufacturer impressed on one face only, and

nothing impressed on the opposite face: both pugs lay on the plane of a table, have

the pins pointing toward the observer, and show the side with the manufacturer’s

name; watching them the observer sees the name of the manufacturer on both the

plugs and notes a little difference in the pins: one plug (that we name “A”) has on the

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left (of the observer) a short and thick pin, whereas the other pin is longer and

thinner; the second plug (“B”) has similar but reversed pins: the short and thick one is

on the right (of the observer), the longer and thinner on the left; to enter into their

socket which has two vertical holes (at the top the large one, at the bottom the small

one) the pins must fit in well with the holes; after entering, the observer sees that the

name of the manufacturer in the “A” and “B” plugs appears on the mirror (or

opposite) side, on the left side in one, on the right side in the other: the plugs appear

as symmetric.

2) Both keys are a little strange: they have a very large bow (disk shaped) and a very

short flat blade; on one side of the bow there is a “head”, on the other a “cross”;

watching the keys, the observer sees that both show the same side with the head but

in the blades (which point both toward him) the observer notes a little difference: one

key (that we name “A”) has a blade showing at the left (of the observer) a smooth

straight border or edge, whereas the other border has a knob or a little tooth; the

second key (“B”) has its blade edges reversed: the knob or tooth is at the left of the

observer; to slide into the keyhole or keyway (supposed horizontal) and enter into the

lock, the keys must have the knob on the same side, on the right of the observer (Fig.

8); after entering, the “heads” in the “A” and “B” keys are on the mirror/opposite

sides (one up, one down) and the observer sees “head” on one key bow and “cross”

on the other; the bows (disks) have been overturned.

3) Both tRna secondary structure images are designed with the anticodon loop at the

bottom, the “D” loop at the left and the “T” loop at the right of the observer; only a

little difference in the stems(top) is perceived by the observer: in one image (named

“A”) the terminal sequence “CCA” is at the right of the observer in the 3’ tRNA end,

while in the figure “B” the terminal sequence “CCA” is at the right of the observer, in

the 5’ tRNA end; the acceptor stems can enter and interact with the active site of the

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amino-acyl-tRNA synthase only if the “CCA” sequence is (we suppose, here) on the

right (of the observer); after taking the correct position into the enzyme housing, in

both secondary RNA structures, the sequence “CCA” will be at the right (of the

observer) and the two molecules will show “T” and “D” loops symmetrically located

in respect to the observer and an usual anticodon in one image while in the other it is

opposite (reversed).

Fig. 8 Centrosome theoretical geometrical model: chirality.

A: a key with nine clockwise sequenced numbers on the edge of its bow, and with a short blade that has a

bulge or a knob pointing toward the number “3” can correctly fit in its lock; B: a second similar key built

with a reverse, symmetric, blade (the bulge points towards the number “9”) has the same clockwise sequence

of numbers on the edge of the bow, but cannot enter (large X) in its lock; C: after overturning the second

key, it becomes compatible with its lock but the sequence of the 9 numbers on the edge of the bow is now

reversed and symmetric to the ring in “A” (the nine numbers are counter clockwise sequenced).

D, E: an RNA molecule has all the characteristics to be the molecular basis of chirality: it is memorized

linearly in the genome, which can thus encode the ordered sequencing of nine different molecular “labels”

(see also Fig.6); this molecule can assume a 3D shape made of a ring of 9 orderly sequenced “labels” and a

“stem” (used to orientate the ring) which fit in the housing (active site) of its scaffold ; two cnRNA rings

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with the same sequence, but having their short “handles/stems” symmetric (D,E), after fitting into the

housing structure are reversely oriented, showing a bilaterally symmetric sequence of their nine loops,

hairpins etc.

These experiments demonstrate that very little changes only in a small part of a large

object are responsible for the overturn of the whole object: by changing only four or

five nucleotides in a tRNA molecule it is possible to realize the overturn of the entire

molecule. As already observed, a little evolutive change is more likely than a big one.

A ring of RNA composed of a little stem and a large circle (like a tRNA with nine

loops), can be easily front > rear overturned like a coin (head > tail): this overturned

ring, with a short stem and a large circle containing 9 equi-spaced different 3D loops

is symmetric in respect to the not overturned ring (Fig. 8); what molecular process

can overturn an RNA ring? Changing few nucleotides at the ends of a RNA sequence

is three time easier than for an polypeptide sequence (one amino-acid is coded by

three nucleotides): from this point of view an RNA ring is better than a protein ring.

The Brown and Wolpert’s “F” chiral structure

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Fig. 9 theoretical geometrical model: chirality.

A: model of the cnRNA default ring (here arbitrarily named “right”); its handle/stem (3’ + 5’

juxtaposed ends) is the “F” Brown and Wolpert chiral structure.

B: “left” version of the cnRNA ring; the sequence of the nine markers is unaltered, identical to A;

the only difference consists in the reverse (or opposite) direction of the two horizontal hyphens of

the capital letter “F”.

C: the same “left” ring of B after the overturn necessary to position correctly the F shaped

handle/stem to fit in well and interact with the housing of the corresponding molecular structure: the

sequence of the nine markers is opposite, clockwise>counter-clockwise reversed, mirror (or

bilaterally) symmetric.

Let’s imagine, as just seen, the RNA ring and its handle-stem like a common house

key having only the border (or the circumference) of the bow (a large “ring shaped”

bow instead of a “disk shaped” bow) with nine different (radially outward or inward

directed) jutting notches, and a short asymmetric blade (something similar to a big

“F”); to better explain this concept, let’s suppose that the nine different jutting

notches have shapes which do not change when they are head>tail reversed or

overturned, like the following capital letters “A; H; I; O; M; T; V; X; Y” (more

convenient than Roman numerals, we before used in a clock dial); the large key bow

(with its nine different notches/letters) symbolizes the large cnRNA ring with nine 3D

structures (loops or hairpins shaped in such a way that their form remains the same

when they are overturned) while the short blade is the short cnRNA stem (Fig. 9).

This handle stem is exactly the Brown and Wolpert’s “F” chiral structure composed

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of a vertical segment and two horizontal hyphens: in the “default” configuration

(which, here, we name “right”) these hyphens are in the usual position showed by the

letter “F”, whereas in the “left” configuration they are reversely (or oppositely)

oriented. The Brown and Wolpert’s “F” chiral structure is made up of few nucleotides

belonging to the 3’ and 5’ ends of the cnRNA transcribed sequences.

This is a first answer to the precedent question: “how simple is this small, easy

change?” The change is small because it concerns only a minimum part of the whole

object. Probably the easiest solution of the problem of two opposite or reversed –

clockwise > counterclockwise – sequences of RNA consists in a very little difference

of the stem/handle: two identical large RNA rings with nine marks, identically

orderly sequenced, but with little differences in their short 3’-5’ termini, so that their

two short stems have symmetric 3D conformations; these two rings can be managed

as two symmetric RNA rings (Fig. 8); when their symmetric stems are arranged in

such a way that their 3D configurations appear identical to the observer and are both

compatible with the housing-structure in which the stems must be positioned (the

active site of a molecular complex), the two RNA rings are overturned, head-tailed,

symmetric, with opposite and reversed -clockwise > counterclockwise- sequence of

their 9 double stranded structures. These nine 3D loops, like the jutting notches/letters

of the key bow, after overturning can interact with the same molecular complexes that

interact with the not overturned loops. Then, little differences in the terminal ends of

the cnRNA ring (about 1% of nucleotides are different) realize the overturn of the

entire RNA ring that can easily decorate symmetrically the MC with “opposite”,

reversely oriented, clockwise > counter clockwise disposition of its nine marks.

Something similar can be observed in cytoplasmic dynein, where two monomers

containing a ring-shaped structure and a stem, bind together, juxtaposing their stems

in such a fashion that the rings are symmetrically disposed (one “default”, one

overturned).

Summarizing: the mirror symmetry of the short handle-stems of two large identical

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rings (like two protractor/goniometers) is responsible for completely overturn the

entire structure (protractor/goniometers oppositely graduated).

What mechanism can perform a little change only in the ends of a sequence,

maintaining conserved the whole long sequence? The most likely (known) process is

a transposition event, followed by independent evolution of 5’ and 3’ ends: two loci,

having the same sequence and free to evolve separately, maintain the same general

sequence through purifying selection while a little change, permitted only in their 3’-

5’ ends, can create two short stems having a symmetric 3D shape: it is not necessary

that the two terminal sequences are precisely identical and reversed because different

short sequences of RNA, after covalent modifications of their nucleotides and non-

canonical pairing, can assume the same 3D shape in order to realize two 3D

symmetrical configurations compatible with the housing-structure in which the stem

must be positioned (Fig.8). This is a second answer to the precedent question: “how

simple is this little, easy change?” Such an evolutionary event able to introduce

bilateral symmetry in Metazoa is extremely easy, little and simple, then very likely:

mutation of only a few nucleotides at the ends of the DNA sequence coding for

cnRNA. Paraphrasing Descartes‘famous sentence “Cogito, ergo sum”, we may say:

“Facile, ergo verisimile” [easy, therefore likely]. Indeed it is quite more conceivable

and plausible that a single and simple, casual, random, fortuitous event (mutation of

four or five nucleotides) is the base of bilateral symmetry of “all” the organs (paired

or unpaired) of “all” metazoan species, instead of an infinite number of complicated

casual mutations (in millions of species and for each organ) able to “write” bilaterally

symmetric building programs, choosing, step by step, the proper symmetrical cell

location.

Left ring and Right ring, left MC and Right MC, Left centrosome and Right

centrosome, Left half and Right half of organisms. The overturned RNA ring

transmits its opposite, reversely oriented sequence of marks to the PCM surrounding

the MC and to the already orientated -TuRCs (as we have said, orientation and

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inclination of -TuRCs in left and right centrosome are the same; only the longitude

labels of -TuRCs are symmetrically positioned): from the reverse MC, -TuRCs

receive reversely ordered longitude receptors: two identical cnRNA rings with

opposite sequence of their 3D structures create two bilaterally symmetrical

centrosome; bilateral symmetry is not a property of -TuRC orientation but a property

of -TuRC longitude labelling. “The data are consistent with models in which the

early cytoskeleton is nucleated by a chiral structure that orients itself with respect to

the other two axes, and thus biases the intracellular transport of key determinants

along the LR axis” (Lobikina et al., 2012). “In the intracellular model, an early

component of the cell-polarity system (likely involving the cytoskeleton) orients the

transport of key molecules within cells that ultimately creates an LR difference in the

embryo… This intracellular model shows how physiological mechanisms integrate to

produce large-scale LR gradients from initial subcellular polarities. Although the

orienting cytoskeletal element is not yet known, this model provides a comprehensive,

quantitative synthesis of all the molecular and biophysical steps leading from LR

orientation within single cells to asymmetric gene expression in the early embryo,

and it does not depend on ciliary motion” (Levin and Palmer, 2007).

My personal opinion is that in Bilateria, during very early cleavage stages, probably

during the first zygote division itself (but this depends on the Clade), Left-Right

pattern is defined, and a midline imposed, through a genetic/epigenetic process

memorized in each cell, so that many genes are, at the same time, switched “ON” in

left cells and “OFF” in right, while other are switched “OFF” in left cells and “ON”

in right: the difference between “Left” and “Right” cells consists only in the state

“ON/OFF” of probably only one upstream gene (or an enhancer/silencer sequence)

which controls a cascade of many other genes and DNA sequences (some of them are

“ON” in Left cells and “OFF” in right and others are “OFF” in Left and “ON” in right

cells). So, some signal molecules, produced only in left cells and deciphered by

receptors directionally positioned on a polarized primary cilium of right cells, or

transmitted through gap junctions (Levin and Mercola, 1999) interact with nuclear

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receptors (expressed only in the right half), producing a “left-right interactively cross-

talking” in order to confirm and maintain a correct midline and to face events of

embryo splitting by restarting, resetting or recovering left/right patterning.

Downstream there are different cascades of left/right gene expression: lefty and

nodal, for example, are expressed normally, only in the left half. One component of

this differential cascade is the transcription, from only one of the two different loci, of

the Left or Right cnRNA molecule, which drives the assembling of Left or Right

MCs and allows Left cells to carry morphogenetic instructions out, mirror

symmetrically compared to Right cells. This transcription event not necessarily must

occur already at the stage of two blastomeres, it is simply one of the events that

belong to the Left or to the Right cascade of downstream left/right genes: in mice,

centrosomes appear at the stage of 64 blastomeres, but cells maintain epigenetic

memory of their Left or Right identity, previously acquired.

“Yet one key question remains: how is the chiral cytoskeletal architecture interpreted

to localize ion transporters to the left or right side?... we found that endogenous

Rab11 mRNA and protein are expressed symmetrically in the early embryo. We

conclude that Rab11-mediated transport is responsible for the movement of cargo

within early blastomeres, and that Rab11 expression is required throughout the early

embryo for proper LR patterning” (Vandenberg et al., 2013).

Left-right determination, as we have already seen, is an epigenetic process that has

something in common with sex chromosomes and sex determination: Left and Right

cells run the same morphogenetic programs in a mirror symmetrically fashion

(bilateral symmetry) or perform different programs which are reserved only to one

half of the organism and, consequently, asymmetrically expressed (asymmetry).

Then, during later stages, in the development of some organs, Left-Right bilateral

symmetry is broken (in a species-specific fashion, not always conserved) and

asymmetry is defined (situs viscerum solitus/inversus) in such a way that cells in the

left half follow different developmental instructions than “right” cells and run left-

reserved programs (differential cascades of DNA transcription and signalling

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pathways, “ON/OFF” switched genes). Perturbing the cytoskeleton, the primary

cilium, and, above all, MT structure causes problems to the mechanism (the

centrosome “hardware”) that firstly imposes and, later, breaks Left-Right symmetry:

“Recent findings in Arabidopsis thaliana have shown that mutations in α-tubulin and

in a γ-tubulin-associated protein (Tubgcp2 [a -TuRC component]) play an important

role in the symmetry properties of the plant axial organs. Wild-type A. thaliana axial

organs do not twist during normal elongation, and its flowers are radially

symmetrical. This symmetry can be broken by mutations in tubulin and tubulin-

associated protein complexes. The tubulin mutations spiral1, spiral2, and spiral3

produce right-handed helical growth mutants. Lefty (lefty1 and lefty2) mutants were

found to be suppressor mutants of spiral1 and when outcrossed displayed a

prominent left-handed helical growth. Both α-tubulin and γ-tubulin complexes are

ubiquitous in eukaryotes and are involved in the formation and nucleation of

microtubules. Here, we characterize the laterality phenotypes induced by the same

mutations in a vertebrate (the frog Xenopus laevis), the nematode Caenorhabditis

elegans, and mammalian cells, supporting a fundamental role for tubulin in the cilia-

independent generation of LR asymmetry” (Lobikina et al., 2012). Left-Right

“asymmetry” (that consists in “bilateral symmetry” breaking), imposed by a

genetic/epigenetic mechanism, is performed through any chiral structure (primary

cilium or other centriolar or MT derived structures). As we have already said chirality

is not the same as “bilateral symmetry”, it is the basis to build bilaterally symmetrical

organs; α-tubulin and γ-tubulin mutations interfere with MT rings disposition in

plants and with centrosome building in Metazoa.

Assuming that cnRNA is the organizer for the creation of circumferential polarity, the

concepts of non-equivalence of the centriolar triplets and chirality (left-right

patterning) overcome the barrier of their biochemical feasibility.

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cnRNA11 bioinformatics

Alliegro and colleagues have described various centrosomal RNAs (cnRNAs),

including two cnRNA11: an mRNA11 of 3863 nucleotides (nt), GenBank:

DQ359732, coded in the Plus strand and another (“Minus” strand coded) RNA11,

GenBank: DQ363378, of 638 nt. Data banks conventionally supply the sequence of

the Plus/+ filament, numbering nucleotides from 5’ to 3’. Here “long dcnRNA11” is

the short form for “DNA locus coding for the long cnRNA11”: in this case the locus

is on the Plus/+ strand; “coding locus” here is the sense, non-template and non-

transcribed 5’>3’ sequence, whereas its antiparallel complementary strand is the

antisense, template and transcribed 3’>5’ sequence; “short dcnRNA11” is the short

form for “DNA locus coding for the short cnRNA11”: in this case it is on the Minus/-

strand. The words “sense/non-sense and template/non-template” (referred to the

entire filament) are not used because transcription may happen on both filaments,

depending on each locus: the long dcnRNA11sense sequence is on the Plus filament,

whereas the short dcnRNA11 sense sequence is on the Minus; Plus and Minus strands

are antiparallel (and so are their respective numbering by data banks): if imagined

like written lines (as presented by data banks) in the Plus strand the order of the

letters is (and numbering increases) from the left end to the right end (5’>3’) whereas

in the Minus strand the letters ( and numbering) start from the right end. Aligning

(with blastn algorithm) these two dcnRNA11 coding sequences, the longest one (from

the 2255th nt to the 2880th nt of its Plus filament) corresponds to the sequence from

the 630th nt to the 3rd of the shortest one (Minus filament), with clearly reverse

alignment (Minus/Plus), a non-perfect correspondence (93%), 6 indels (in-sertion del-

etion) and, above all, the substitution of some original terminal nucleotides (2 from

the 3’ end, 8 from the 5’ end of the short dcnRNA11): these are therefore two very

similar but not identical sequences, then coded and stored in two different loci, one,

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long, in the Plus strand and the other, short, in the Minus strand. Pay attention to the

alignment direction: both sequences, although not identical but very highly similar,

have their corresponding nucleotides aligned in the same 5’>3’ direction, respectively

on the Plus and Minus filament: as we have said these sequences are antiparallel,

left>right on the Plus strand, right>left on the “Minus” one, but both 5’>3’. They are

not perfectly identical to each other (especially because of the two deletions and four

insertions in the short dcnRNA11), and are reversely oriented in a sense as we might

expect from a Plus > Minus retro-transposition event (transposition does not change

the nucleotide sequence: original and transposed loci, if read in the same 5’ > 3’

direction (that in Plus and Minus strands are opposite or antiparallel) have the same

identical sequence; therefore the reverse alignment of two sequences, one on the Plus

filament and the other on the Minus is only apparent). Taken together these findings

support the retro-transposition hypothesis, which maintains 5’ > 3’ order, requires the

intervention of nucleases (reverse transcriptase is an RNase family member) and,

strikingly and surprisingly, completely agree with the previous considerations about

the little changes in 3’-5’ ends necessary and sufficient for an RNA ring to create two

short 3D symmetric stems. Therefore, we must deduce that the 638 nt cnRNA11 is

not a part of the 3863 nt cnRNA11: these two dcnRNA11 loci, after transposition,

have independently evolved with significant changes (6 indels in little more than 600

nt are not negligible), however maintaining their substantial sequence identity

through purifying selection (except for the ends). The different ends of the transposed

short cnRNA11 can assemble a stem with a 3D shape that is bilaterally symmetric in

respect to the stem of the original cnRNA1: it is not necessary that the two terminal

sequences are precisely identical and reverse because not identical short sequences of

RNA, as we have already said, after covalent modifications of their nucleotides and

non-canonical pairing, can assume similar 3D shapes; after entering into the

housing/active site of the MC, the transposed cnRNA11 ring is necessarily overturned

(Fig. 8) and the sequence of its nucleotides is opposite and reversed. The long

cnRNA11 is transcribed from its antisense non-template (in this case the 3’ > 5’

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Minus filament) strand, and shows a sequence corresponding to its 5’ > 3’ sense

(“Plus”) coding strand (as known RNA polymerases “walk” on the antisense template

filament in direction 3’ > 5’ and synthesize a new RNA chain from 5’ to 3’), whereas

the short cnRNA11 is transcribed from its antisense non-template (in this case the 5’

> 3’ Plus filament) strand, read by RNA polymerase from the 3’ end, and shows a

sequence corresponding to its 3’ > 5’ sense (“Minus”) coding strand (Fig. 8). [Do not

confuse the expression “ 5’>3’ “ when it is used to show a direction and when it is

used to identify a DNA strand: the 5’>3’ filament is the leading “Plus” filament

during DNA replication, whereas the 3’>5’ filament is the lagging or “Minus”

strand]. Exploring the nucleotides which flank the matching sequence in both

dcnRNA11, very surprising findings emerge: the two stems show a really symmetric

3D sequence because of the symmetric position of a consensus sequence. It is better

to establish some point of reference: let us consider as “START” (the beginning of

the region of similarity) the sequence (5’>3’: left>right) “TGACG” which in the long

dcnRNA11 Plus (coding) strand goes from the 2255th to the 2259th nt, and as

“STOP” (the end of the region of similarity) the sequence (5’>3’: left>right)

“GCTAG” which in the long dcnRNA11 Plus strand goes from the 2876h to the

2880th nt (Fig. 9). On the Plus strand of the short dcnRNA11 (the only one reported in

data banks; in this case it is the non-coding antisense template filament) we find the

sequence (5’>3’: left>right) “CTAGC” (3rd >7th nt) that is complementary but

opposite (antiparallel) to the previous “STOP”, and the sequence (5’>3’: left>right)

“CGTCA” (626th >630th nt) that is complementary and reverse (also antiparallel) to

the previous “START”. Reading the Minus (coding) sense strand of the short

dcnRNA11 (Fig. 9) and following the direction 5’>3’( now right>left), we can read

identical sequences as in the long dcnRNA11: the “START” “TGACG” sequence

(630th >626th nt; Fig. 8 reports the sequence 3’ > 5’; numbering is always the same

as the Plus strand) and the “STOP” sequence “GCTAG” (7th >3th nt). If now we

read (always 5’>3’) the nucleotides which are after the “STOP” sequence on the long

dcnRNA11 Plus strand, we find “TTGAGTTA”. A closely corresponding (5’>3’:

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right>left) sequence precedes the “START” in the short dcnRNA11 Minus strand

“ATGGAAG”: because their opposite antiparallel alignment (5’>3’ vs 3’>5’), the

sequences (both read in 5’ > 3’ direction) “AGTTA” and “AGGTA” are surprising

similar (consensus sequence) but positioned on the opposite ends (3’ end of the long

cnRNA, 5’ end of the short cnRNA: Fig. 9). If we represent the two rings of

cnRNA11 with their stems corresponding (not symmetric, both showing the

consensus sequence at the right of the observer, like in the third virtual experiment),

their sequences are clearly reversed (Fig. 10): the overturn of the RNA ring is

obtained through only little nucleotide differences in the stem. in effect only very few

nucleotides are normally enough to precisely fit in with the active site of a

polypeptide.

Still more extraordinary is the fact that the antisense filament that codes the long

3863 nt cnRNA11, along its length, contains a sequence similar to a reverse

transcriptase, therefore indicating the concrete possibility of a retro-transposition

event. But there are still more surprises because, as we have already seen, “a

ribonucleoprotein consensus RNA-binding site (RNP-1) was found downstream from

the reverse transcriptase domain” (Alliegro et al., 2006): this long mRNA appears to

be similar to a LINE (Long Interspersed Nuclear Element, a not Long Terminal

Repeat retro transposon) even if shorter. Thus, the previous analysis confirms the

possibility that a transposition has originated the short cnRNA ring which can be used

in an overturned fashion (front > rear or head > tail in respect to the corresponding

similar sequence of the long cnRNA11), creating a symmetric decoration of the MC:

this might represent the (easy, simple and evolutionary likely) biochemical basis of

bilateral symmetry: transposition has generated two DNA loci (cnRNA-coding) that

have evolved differently, generating two similar cnRNAs, displaceable, through their

diverse ends, in two different symmetrical fashions (head/tail, front/rear).

What length should we expect for an RNA ring that ensures a receptor at the base of

each triplet? The ring composed of nine SAS-6 N-terminal dimers (Kitagawa, 2011)

has a diameter of 23 nm and a circumference of 72 nm; the ring formed by 9

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complete SAS-6 dimers (with their radially arranged coiled-coil C-terminal domains)

has a diameter of 43 nm and a circumference of 135 nm; (the “acorn” of Geimer and

Melkonian has a diameter of 10 nm: it is possible that the RNA ring is inscribed into

the SAS-6 ring); estimating a linear length of 0.34 nm occupied by each nucleotide in

a linear polynucleotide chain, and about 16 bases for each of the 9 stem-loops (as in a

tRNA arm), 400 nt should be sufficient to cover the entire circumference of 9 SAS-6

N-terminal dimers and to generate the 9 signals (600 nt for the complete ring, C-

terminals included). These dimensions correspond to those of the various cnRNAs

described by Alliegro and colleagues (Alliegro et al., 2006, 2010; Alliegro and

Alliegro, 2008; Alliegro, 2011), except for the long 3863 nt RNA, whose meaning

seems much more general; in fact: 1) it can no longer be seen after the first zygote

division; 2) it is present during the formation of the first two centrosomes which, in

the author’s model, in agreement with the observations of Danilchik and colleagues

(2006), Levin and Mercola (2007) and Venderberg and colleagues (2013), distinguish

the first two blastomeres in a Left-Right sense (in species whose first blastomeres

contain centrosomes); 3) it includes the reverse transcriptase; 4) it contains a

sequence that is quite similar but not identical to the 638 nt cnRNA 11.

“In Spisula oocytes, most of these [cnRNAs] are not detectable before oocyte

activation, but several were found to be present in unactivated oocytes as a distinct

hybridization patch associated with the nucleolinus. As the nuclear envelope breaks

down, the newly formed centrosomes are found to be embedded within, or closely

apposed to, the nucleolinar patch…The nucleolinus is an RNA-rich compartment,

closely apposed to or embedded within the nucleolus…. The nucleolinus is a unique

cellular compartment containing centrosome and spindle-associated RNAs” (Alliegro

et al., 2010). Because of this long cnRNA11 (3863 nt) location, the nucleolinus (in

which firstly centrosomes are embedded) appears to be the (temporary: only once per

cell cycle) nuclear location for pre-cnRNAs maturation (like the nucleolus is the

location for pre-rRNAs maturation and spliceosomes are the locations for pre-

mRNAs maturation): using several gene-finding programs - GenScan (MIT pattern

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scanning gene finder), GeneMark (Georgia Tech gene finder), NCBI ORF finder and

FGENESH (HHM-based gene finder from Soft Berry - to predict exons + introns,

this long cnRNA11 shows to possess introns and then it may reasonably be

considered as a very long and immature pre-cnRNA.

How many different types of cnRNA should there be in the centrosome? We

obviously expect three distinct types of cnRNAs, one for the MC (invertible to

support the Left-Right difference: therefore 2, slightly different, MC cnRNAs) and

one invariable, for the DC. These three cnRNAs should have the duty of marking

each radial spoke and each triplet in order to be able to transmit the non-equivalence

to other structures, like the PCM wedges. Other cnRNAs may comprise the receptors

associated to the -TuRCs (hypothesizing, as seems logical, that these receptors are

also polyribonucleic or ribonucleopolypeptidic): 9 different cnRNAs would comprise

the receptors for the longitude (nine centrosomal meridian wedges) and 5 more for

the latitude (two centrosomal caps and three parallel rings); a further receptor that

“captures” all the macromolecules that must be distributed in the cell by the

centrosome and display a centrosomal localization targeting sequence (see below:

centrosome trafficking) can also be envisaged. These are 18 different cnRNAs; it

cannot be excluded, and is in effect very probable, that the wiring system generated

by centrioles, centrosome and aster MTs, if used also in a centripetal sense (with

dynein molecular motors), as already mentioned, might require a similar number of

small RNAs (located near the -TuRCs) that would accompany molecular messengers

coming from particular compartments of the cell membrane (and taking the

fundamental information of “cortical compartment of provenience”) to the nucleus;

this makes it possible to code the geometrical information (cortical compartment of

origin) into a molecular structure (a particular miRNA able to bind with suitable DNA

sequences or with other proteins involved in the regulation of the genes). In their

work, Alliegro and colleagues (2008) found a similar number of different cnRNAs:

“This subset of 39 sequences that exhibited database identities could be divided into

three categories. The largest group (19) matched uncharacterized BAC [bacterial

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artificial chromosome] clones, hypothetical proteins, or other uncharacterized

chromosomal sequences from a wide variety of species. Sixteen of the 39 identities

were related to nucleic acid or genome structure and metabolism. Examples include

nucleotide polymerases (cnRNAs 65, 118), an Entamoeba snRNP (cnRNA48), clam

(Venus) and pig microsatellite sequences (cnRNAs 123, 154, 226), and retroelements

from a variety of species (cnRNAs 15, 93, 142, 171). The third category containing

only four sequences had no clear relationship to centrosomes, the cytoskeleton, or

nucleic acid metabolism...A subsequent screen for centrosome-associated RNAs in

Ilyanassa embryos resulted in the identification of approximately 50 additional

molecules” (Alliegro 2011).

A) Short dcnRNA11 “Plus” 5’ ag|ctagc…………cgtca|cttccatc 3’

B) Short dcnRNA11 “Minus” 3’ tc|gatcg…………gcagt|gaaggtag 5’

C) Long dcnRNA11 “Plus” 5’ ttcatctaa|tgacg... ..gctag|ttgagttac 3’

D) Long RNA11 3’ AUU|ACUGC……CGAUC|AACUCAAU 5’

Short RNA11 3’ CUACCUUC|ACUCGC……CGAUC|GA 5’

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E) Long RNA11 3’ AUU|ACUGC……CGAUC|AACUCAAU 5’

Short RNA11 5’ AG|CUACG……CGUCA|CUUCCAUC 3’

Fig. 10.1 dcnRNA11.

“START” sequence is underlined; vertical bars separate the matching sequence.

A) Plus / + / antisense / template strand locus for the short cnRNA11 (638 nt): 5’ (left) > 3’(right).

B) Minus / - / sense / coding strand locus for the short cnRNA11 (638 nt): 3’(left) > 5’( right).

C) Plus /+ / sense / coding strand locus for the long cnRNA11 (3863 nt): 5’ (left) > 3’(right).

D) 5’ (left) > 3’(right) long and short cnRNA11 alignment: “START” and “STOP” coincide. Consensus

sequence (bold) at opposite ends.

E) Opposite (reversal) alignment of both cnRNA11: “START” and “STOP” are at opposite ends (reversed).

Consensus sequence (bold) at the same side.

long cnRNA11 short cnRNA11

5’ 3’

U U

A A

A C

C C

3’ U 5’ U

A:::::::C A:::::::U

U:::::::A G:::::::C

U:::::::A c A

A c u C

C u a U

U a c G

G c g C

C g .. ..

.. .. .. ..

.. .. ……………

…………… Fig. 10.2 cnRNA11 stems.

When the stems of both short and long cnRNA11 correspond (consensus sequence in bold) the two rings are

overturned: “START” and “STOP” sequences are mirror symmetric.

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Further researches have been carried out on the 3863 nt cnRNA11: the short sequence

between the 2054th and the 2089th nt

“CTGGTGCTGTTGCTGCGGTTGCTGCTGTTGCTGCTG”

has an enormous diffusion in all the genomes and is present in dozens loci in all

organisms. If we examine this sequence, it does not appear to be similar to any

known localization targeting sequence (mitochondrial, lysosomal, etc. actually

present in “Signal Peptid Resourches Data Base” [proline.bic.nus.edu.sg/spdb] and in

“Prediction of signal peptides” [www.predisi.de]), it is not similar to a “CG isle”, and

cannot be compared with sequences often found in introns, enhancers and silencers; it

does not contain tandem repeated trinucleotides (trinucleotide tandem sequences in

Homo sapiens, although not frequent nor very long are much more ordered, with very

few, if any, variations in the repeated trinucleotide sequence).

It seems not to be itself, in toto, a repeated sequence (no repeats found using

“Tandem repeat finder Program”): it is 98% identical, from nt 1 to 36, to Jockey-

6_DK, (from nt 511 to 546) which is a non-Long Terminal Repeat /Jockey in

Drosophila kikkawai, defined as a "apurinic-like endonuclease and reverse

transcriptase"; this strengthens the supposition that the long cnRNA11 is a non-LTR

retrotransposon. Inserting this cnRNA as a query and using “blastn” to look for

generic correspondences both in the “Nucleotide collection” and in the “Genome”

databases (specifying each time the restriction of the research to one single model

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organism) a great number of correspondences appears every time; it is astonishing

that this sequence is the only section of the long cnRNA11 with such an abundant

correspondence: being a brief sequence, there is always the suspicion that it is a case

of random correspondence, but in 3863 nt there should be other 36 nt sequences that

are randomly aligned with various other sequences of several genomes. For example:

by using” blastn” to seek alignments corresponding to this 36 nt sequence (from the

2054th to the 2089th nt of the long cnRNA11) in the chromosomes of a model

organism like Mus musculus (taxid:10090), we obtain similarities in dozens of

different loci for each chromosome, belonging to many proteins (some of which very

interesting because they concern, for example, histone-methylases, transcription

factors, nuclear receptors, extracellular sulphatases) or situated at different distances

from genes; there are correspondences also in short interspersed repeated sequences

(SINE), this last circumstance being very interesting from the point of view of

development and morphology, if we think that the morphological differences between

canine races are almost exclusively dictated by genomic differences relating to

SINEs, as demonstrated by Wang and Kirkness (2005).

Alliegro consider this cnRNA 11 an mRNA: therefore, trying to translate this

sequence into a polypeptide and, considering that the lack of a start codon does not

allow an Open Reading Frame (ORF) to be identified, we obtain the following 6

amino-acid sequences:

1) 5'>3' Frame 1st: L V L L L R L L L L L L;

2) 3’>5' Frame 2nd: S S N S S N R S N S T;

3) 5'>3' Frame 3rd: G A V A A V A A V A A;

4) 3'>5' Frame 4th: Q Q Q Q Q Q P Q Q Q H Q;

5) 5'>3' Frame 5th: W C C C C G C C C C C;

6) 3'>5' Frame 6th: A A T A A T A A T A P.

The meaning of these short polypeptides is very problematic: it may be a question of

a consensus sequence of centrosome localization, similar to those present on the

fibers surrounding nuclear pores in which phenylalanine and glycine, both non-polar,

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alternate; five sequences are either completely hydrophobic (the first, third and fifth:

Leucine, Alanine or Cysteine) just like the filaments connected to nuclear pores or

decidedly hydrophilic (the second and the fourth: Serine and asparagiNe or

glutamine, Q); the sixth sequence alternates two amino acids, but one is hydrophobic

(Alanine) and the other is hydrophilic (Threonine) producing an amphiphilic

sequence. Since this 36 nt sequence recurs in positions far away from the genes, it

seems probable that it is part of regulatory domains and, then, non-coding and

untranslated.

In conclusion, the idea that non-equivalence is a property of the quaternary structure

of nine triplets with identical tertiary structure seems to be supported by common and

known biological mechanisms; same observation can be made for the second idea,

the reversion of the orderly sequence of non-equivalent markers, whose opposite

disposition may be the structural base of bilateral symmetry. Then, if both ideas are

sustained by simple and common biochemical processes, they cannot be speculative

suppositions: they appear plausible. The findings and evidences discussed, taken

together, turn the proposed ideas into something more than a hypothesis. I hope.

iii) PCM molecular architecture (centrosome hardware)

“In top-views of centrioles, of the 18 proteins analysed in this study, 4 (Centrin, SAS-

6, STIL and Plk4) revealed compact dots. All other proteins were disposed in ring-

like patterns around the centriole and, as shown for γ-Tubulin and NEDD1, CPAP

showed both ring and central dot localization” (Sonnen et al., 2012).

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Now it’s the turn of the centrosome “hardware”. In the centrosome, the two centrioles

maintain their orthogonal configuration during S and G2 phase and in the first stages

of mitosis: at this time the centrosomes and their PCM are formed and acquire all

their geometrical properties.

The main task of both metazoan centrioles appears to be the assembly of the PCM;

the MC is also responsible for forming cilia and maintaining centrosome orientation

during G1: in non-dividing cells the MC becomes the primary cilium basal body.

The centrosome, which has long been described as a spherically-shaped organelle, on

the contrary, appears to be not spherical but structured in cylindrical, coaxial, layers

around the centrioles; then two considerations must be made:

- the aster is a spherical structure and the direction of the astral MTs is clearly

spherical-radial, centrifugal: this implies that the orientation of -TuRCs must be

parallel, at the point of nucleation of each MT, to the centrosome “spherical /

polyhedral” surface (or rather, parallel to the local surface-tangent plane); the surface

would then be spherical and the PCM too would therefore have a spherical /

polyhedral shape; [warning: here and later, the word “γ-TuRC” stays for “the ring-

shaped base of γ-TuRCs”: only this ring, lying on a plane, can be “parallel” to a

tangent plane; the word “parallel” would be meaningless if referred to the whole

structure of a γ-TuRC, similar to a cone].

- in contrast, the organization of the PCM around the MC is indisputably cylindrical:

Sonnen and colleagues (2012), using 3D-structured illumination microscopy to

analyse the molecular architecture of the PCM, have demonstrated that its structure

consists of coaxial layers around the MC, confirming a similar description already

expressed by Ou and colleagues (2002). The quantity of PCM around the DC is much

less than around the MC and the position of the DC is decidedly eccentric (Fu and

Glover, 2012). The DC too organizes its modest PCM circumferentially and

orthogonally to the MC.

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Both centrioles possess a 9-fold symmetry: the PCM and the whole centrosome,

organized by them, must necessarily conserve the same 9-fold symmetry. The MC

organizes circumferentially the PCM and subdivides it into 9 sectors (meridian

wedges) corresponding to the nine MT blades of the MC (Fig. 6; this schema is

confirmed by the images presented by Mennella and colleagues 2012, free on the

Internet); the DC also organizes circumferentially the PCM and subdivided it into two

caps and three parallel rings or discs (Figs. 6B, 6C,).

Then there are two main geometrical problems to be addressed and faced:

(1) MTs show an astral, centrifugal, radiating 3D (spherical) and, above all, non-

intersecting direction: then, a biochemical mechanism must exist capable of orienting

-TuRCs in such a way that each one is parallel to the centrosome’s surface tangent-

plane in order to nucleate a radially oriented microtubule towards the cell cortex: in

other words, -TuRCs do not show the same cylindrical symmetry as centrioles, on

the contrary each -TuRC shows an inclination that is the addition of two

inclinations, one (longitude) imposed by the MC, one (latitude) by the DC. (2) The

longitude inclination and the relative labeling information can be transferred radially

(cylindrically) by the MC whose position in the PCM is central: not so for the

latitude-information that from each DC blade must reach all the -TuRCs included on

the same cap- or disc-sector (comprised between two “parallels”) and positioned on

different meridian wedges: a biochemical mechanism must exist capable of

transmitting the same “latitude-information” to -TuRCs which have the same

latitude but different “longitudinal location”.

A logical explanation might be that the spherical / polyhedral shape is not a property

of the whole centrosome but that it is restricted only to -TuRCs, whereas the

centrosomal PCM structure consists of roughly cylindrical, coaxial layers around the

MC. It seems that -TuRCs are orientated in two step modality: whatever their

latitude, because of the organization imposed by the MC and its central pivotal

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position inside the centrosome, like a hub, -TuRCs are initially parallel to the MC

blades (centrioles should be imagined as prismatic rather than cylindrical), acquiring

the orientation corresponding only to the longitude (Fig. 6 A): the contribution of the

DC would then consist in revolving -TuRCs, so as to transmit and superimpose the

orientation relative to their latitude. This hypothesis is based on the observation that

the aster is composed of MTs that do not intersect (O’Toole et al., 2012) but have an

ordered radial, 3D (spherical, centrifugal) direction, necessarily resulting from the

orientation of the -TuRC from which each MT originates: like orientation (longitude

+ latitude), like direction (or, rather: one -TuRC “discrete” orientation, one MT

“discrete” direction; one-to-one correspondence between -TuRC “discrete”

orientation and MT “discrete” direction). Molecular complexes capable of orienting

each -TuRC must therefore exist and the cylindrical organization of the PCM around

both centrioles agrees with the hypothesis of centriole-driven orientation of γ-TuRCs;

γ-TuRC structure fits in well with this hypothesis: its centripetal portion is a long

cone that is inserted into the PCM and therefore comes in contact with various other

molecules. “Several centrosomal proteins have γ-TuRC anchoring function at the

centrosome, including pericentrin B, CG-Nap (also known as AKAP350 and AKAP

450)….Additional proteins including PCM-1, CEP135 or BBS4 are required for the

formation and maintenance of a radial microtubule array anchored at the centrosome

in interphase” (Delgehyr et al., 2005); “Complex containing the centrosome proteins

CAP350 and FOP, and EB1, has also been proposed to play a role in anchoring MTs

at the centrosome” (Azimzadeh and Bornens, 2007).

It seems, as before observed, that Metazoa have improved the molecular control of

three quantities (already well managed by Protists): the right angle, the angle of 140°

(and its supplemental of 40°) and MT length: combining these three geometric

quantities by assembling their biochemical supports, they can manage the architecture

to realize and regulate the double inclination (longitude and latitude) of centrosomal

-TuRCs. Control of the angle of inclination corresponding to the longitude and

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latitude can only (or, rather, must necessarily) derive from the transmission of the

orientation corresponding to the geometry of the centriolar blades (9-fold symmetry):

each MC blade is in effect already oriented (parallel) towards the corresponding

wedge/meridian sector, and each DC blade is already oriented towards the

corresponding cap or a parallel disk (Figs. 6, 2); transmission of this information

must take place through simple known mechanisms: “The centrosome from G1 cells

is composed of a MC and a DC linked by a matrix. Matrix assembly is assumed to be

triggered by centrioles through two subsets of microtubule-binding proteins, one able

to bind centriole proximal minus ends, and one able to bind centriole walls in a

polyglutamylation-dependent manner….A large pericentriolar cloud of additional

components can be accumulated in a microtubule-dependent manner, leading to an

extended boundary” (Bornens, 2002). The presence of -TuRCs with different

functional value has been suspected for a long time (Fouquet et al., 1998): some of

them act as MTOCs (nucleating cytoplasmic MTs) while others only have functions

in organizing the centrosome. “The dual distribution of the γ-tubulin could indicate

two different abilities of MT nucleation. PCM γ-tubulin is considered to be involved

in the nucleation of cytoplasmic MTs. Centriolar γ-tubulin must be involved in the

unknown functions of the centrioles … Moreover this γ-tubulin γ-TuRCs labelling [by

immunogold electron microscopy] was initially present only in centrioles and then it

becomes predominant in the PCM” (Fouquet et al., 1998). The role of this “unknown

functions of centriolar γ-tubulin “ must be faced. From two different populations of γ-

TuRCs, one of centriolar identity (nucleation of centrosomal MTs that remain

confined in the centrosome), and one of PCM identity (nucleation of cytoplasmic

MTs), arise two diverse populations of MTs, PCM-MTs, confined and restricted in

the PCM, useful to impose the correct orientation to each γ-TuRC scaffold and

transfer to each γ-TuRC, through kinesin-mediated transport, the receptors of

longitude and latitude, accordingly with γ-TuRC position in respect to MC and DC

triplets, and cytoplasmic-MTs that reach the cell cortex. It is important remembering

that several MAPs (e.g.Tau and MAP-2, both neuronal, or MAP-4 that is expressed in

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many cell types) have a typical “right angle” shape, with a side parallel and

longitudinally bound to the MT and the other orthogonal to the MT axis: one or more

“right-angle MAPs” at the tip of a radial “centrosomal, PCM-restricted” MT can be

the molecular structure able to orientate γ-TuRCs orthogonally to the “centrosomal

virtual radius”. The cylindrical organization around the MC may occur by

maintaining and transmitting the geometrical subdivision of the centriole wall and its

9-fold symmetry. The poor use of the DC as a cytoplasmic-MTOC in G1, and the

presence of γ-tubulin in close proximity to its wall (Sonnen et al., 2012), suggest that

the few MTs (nucleated by -TuRCs of centriolar identity only) originating from this

centriole are useful to transmit latitude inclination (and corresponding receptors) to

the -TuRCs of the PCM, reached with centrifugal and straight-line direction during

last stages of mitosis (centrosome maturation): ”There are no foci of convergence of

microtubules around the second (daughter) centriole in interphase until the middle of

the G2 period ….the centriole as such is not the center of microtubule formation;

instead, microtubule-organizing centers are formed on it or in contact with it”

(Vorobjev and Chentsov, 1982). The problem still needs to be addressed of how this

information about latitude is transmitted from the DC to all the γ-TuRCs included in

the same parallel disk, but located in different meridian wedges (of different

longitude: Fig. 6 C). The MC can easily transmit its 9-fold symmetry to the entire

PCM, independently from latitude, because of its central/axial position in a

cylindrically organized PCM (Fig. 6 A); the DC, because of its eccentric position

(Fig. 6 B), must transfer the latitude-information of its blades to γ-TuRCs having

different longitude: a simple “radial” transmission from an eccentric DC is not

sufficient: it would only reach the γ-TuRCs of two (opposed) meridian wedges. As

we have already said, this is the main geometrical problem: plant cells, larger than

animal cells, make use of parallel cortical MTs (very similar to the parallels on a

globe) and control the MT distance from each other (e.g. to form the pre-prophase-

band) in order to manage, in some way, the third dimension; metazoan small cells

must transfer the circumferential symmetry of their orthogonal centrioles to -TuRCs,

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being successful in imposing on them the 3D spherical symmetry indispensable to

organize their 3D cytoskeleton; then a molecular 3D structure must exist capable of

forming something like a little “aster” inside the PCM, with its centre at the proximal

end of the DC, that reaches all the -TuRCs, whatever their longitude.

The cylindrical layers around the MC reach a diameter of about 560 nm, accordingly

with Sonnen and colleagues (2012) and Fu and Glover (2012) and form almost the

whole PCM. On the other hand, the DC is surrounded by layers with maximum

thickness of 200-250 nm containing also γ-tubulin (Fu and Glover 2012); both the

centrioles have an external diameter of 170-180 nm: the DC is surrounded by very

little PCM, which is nevertheless able to nucleate few MTs originating from -TuRCs

placed almost on the centriole wall itself. This is consistent with the notion that the

DC is not a real MTOC; even the distance between the γ-tubulin and the DC wall

(Sonnen et al., 2012) fits in with the preceding observations. So what is the use of an

orthogonal centriole (DC) if it produces only very few MTs (Bornens, 2002; Vorobjev

and Chentsov, 1982)?

The DC eccentricity leads me to think that on the proximal end of each MT blades

there exists an MT structure (the “large pericentriolar cloud of additional

components can be accumulated in a microtubule-dependent manner, leading to an

extended boundary” hypothesized by Bornens) able to transmit, by means of PCM-

restricted-MTs, the latitudinal inclination and the relative receptors (characteristic of

each DC triplet) to all the γ-TuRCs of each corresponding disk (or cap) whatever

their longitude. Since the 40° angle-based geometry must be respected (as in

centriolar 9 fold symmetry: 360°/9 = 40°; the central dihedral angle of each wedge

measures 40°) it seems logical to take into consideration a structure composed of five

SAS-6 dimers, whose molecular structure is responsible for the 9-fold symmetry

constructed on an internal angle of 40° and on its supplemental external angle of

140° (polymerization angle of SAS6 dimers N-termini: Kitagawa et al., 2011; Van

Breugel et al., 2011; Gönczy, 2012); these authors have demonstrated the capacity of

SAS-6 dimers to self-assemble in polymers from 3 to 10 units whose N-terminal ends

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bind together to form a 140° angle. As already anticipated, unlike fullerenes and

clathrins vesicles, which are quasi-spherical objects, centrosomes do not build an

accurately spherical surface: the PCM grows around the centrioles (the core

components of the centrosome) and organize perfectly oriented -TuRCs on an

irregularly spherical surface. Surprisingly SAS-6 is not only inside the DC lumen

(during DC formation) where it appears in a larger quantity to organize the cartwheel

or the central hub, which have a certain length, but it is also outside the same

procentriole, in close proximity to the proximal end of the centriole wall.

Gopalakrishnan, Guichard and colleagues in “Self-assembling SAS-6 multimer is a

core centriole building block” (2010) show very interesting electronic images and

histograms (free on the Internet) about the clear presence of SAS-6 immediately

outside the centriolar wall: the differences between cross and longitudinal sections

agree with the hypothesis that SAS-6 localizes also in the PCM near the proximal end

of the procentriole; the authors furnish interesting diagrams to show the percentage of

SAS-6 found inside and outside the centriole wall, and these values agree with the

expected ones. Also the localization of CEP 135/Bld10 (which acts as a bridge

between SAS-6 and radial spokes) is more external than was previously believed, γ-

TuRCs are very close to the surface of the DC and γ-tubulin is present inside the

centriole (Sonnen et al., 2012) and immediately outside (Fouquet et al., 1998).

A model to explain how the “about-spherical” shape of the centrosome might be

organized is conceivable: a half ring of 25 nm diameter (Fig.11) of five SAS-6 dimers

(through 140° interaction between their N-termini ), lying on the plane containing the

axis of the daughter centriole, and the A-MT of each triplet-blade, positioned

(outside, but very close to the centriole wall) near the proximal centriole pole, along

the MT blade, can radiate five MTs (from the C-terminals of the SAS-dimers) starting

with an angle of 40° between themselves, like the cartwheel spokes. These MTs, like

radii, are lye on a plane orthogonal to the centrosomal surface, and a molecular

complex similar to Chlamydomonas Bld-10 or MAP-2/ MAP-4 can assure the

orientation of the corresponding -TuRCs (or their docking platforms), orthogonal to

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MTs and parallel to the local tangent plane. This can be the skeleton of a semicircular

(half-round) structure lying on this plane: a similar process from each blade (near the

proximal poles, then close to an ideal centre of the centrosome) can constitute the

structural basis of a “spherical” centrosome, or rather the platform on which

centrosomal proteins are “spherically” assembled. This is not far from the

“hypothetical model of how centrioles could organize the centrosome matrix”

proposed by Bornens (2002). Several other proteins cooperate with SAS-6 to build

the 9-fold centriole structure and the 140° angle: together they organize, as we have

said, along each DC blade, a half-ring fan-shaped structure that reach, radially, the γ-

TuRCs and superimpose their DC inclination (latitudinal) on that already imposed by

the MC cylindrical structure (longitudinal); so the DC, through this 140°-fan-shaped

SAS-6 half ring and centrosomal MTs, can transmit its latitudinal symmetry and

relative receptors to γ-TuRCs having different longitude.

“In late G2 or M phase cells, Cep135 staining could be seen to extend from MCs to

the area occupied by SAS-6 and STIL. This indicates that Cep135 progressively

associates with the proximal ends of DC, concomitant with their growth during the

cell cycle…taken at face value our data suggest that the number of Cep135 proteins

at cartwheel structures is likely to be low in comparison to the amount of Cep135 that

can be detected by 3D-SIM at MCs. It is tempting to speculate that the latter Cep135

population is important for centriole stabilization” (Sonnen et al., 2012).

The DC 140°-fan-shaped structure is likely composed of few layers of half ring of

SAS-6 and related proteins for a total thickness of 36 nm, compatible with the blade

width. The procentriole central hub has a periodicity of 12 nm because of its

composition of about ten layers of SAS-6 rings: “the central tubule is a polymer of

repeating subunits” (Gopalakrishnan, 2010, Guichard et al., 2010). Nine (temporary)

such 140°-fan-shaped structures along each DC blade constitute a small aster inside

the PCM able to correctly orient all the γ-TuRCs (Fig. 11). It is also known (Jakobsen

et al., 2001) that the PCM has a high turnover of its components: the repeated

movements of splitting and joining of the rather more mobile DC (Piel et al., 2000),

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in respect to the MC, which is always well anchored in its fixed position in the cell,

ensure the participation of the DC in the correct turnover of the PCM components

under its control.

Considering again Albrecht-Buehler’s cited (and already modified) sentence: “It

appears that the simplest and smallest device that is compatible with the scrambling

influence of thermal fluctuations as are demonstrated by Brownian motion is a pair of

9-fold-symmetry-cylinder oriented at right angles to each other”, I am tempted to

add some other words: in effect it is very difficult to think to a tool like the

centrosome equipped with two orthogonal centrioles, one of which is not eccentric;

necessarily, one centriole, the MC, is a central hub while the second cannot form with

it a cross (literally crossing and intersecting the MC wall: two orthogonal hubs are

very difficult to build and seem useless because a clutched contiguity or an extreme

proximity cause barrier/hiding problems –Fig. 11–) but must assume any eccentric

configuration: the most simple arrangement appears to be the known juxtaposition of

the ends because, as it is possible to appreciate in Fig. 11, the MC is not a barrier and

does not impede that the DC reaches every PCM wedge and transmits to each wedge

its inclination information; furthermore this type of eccentricity allows the MC to

control the orientation (shared and coordinate tissue polarity) of the DC at the time of

its maturation into a new MC. Therefore the DC requires and needs the particular

“140°-fan shaped structure” to realize “a large pericentriolar cloud of additional

components accumulated in a microtubule-dependent manner, leading to an extended

boundary” to borrow Bornens’ words for my own use. So the Albrecht-Buehler’s

sentence (I hope in his indulgent permission) can sound: ”It appears that the simplest

and smallest device that is compatible with the scrambling influence of thermal

fluctuations as are demonstrated by Brownian motion is a pair of 9-fold-symmetry-

cylinder oriented at right angles to each other, one axial and one eccentric whose

base faces the distal wall of the first”. The particular property of the DC to be an

intermediate product between a procentriole and a “true” centriole, extremely useful

because of its orthogonal position in respect to the MC, is strengthened.

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In conclusion: in the theoretical geometrical model of the centrosome, the MC

arranges cylindrically γ-TuRCs, corresponding to its 9 “prismatic” faces; the

eccentric DC “compels” all the γ-TuRCs contained in the same cap or disk (between

two “parallels”) to assume also the inclination corresponding to their latitude,

creating the spherical polarity (double inclination) of γ-TuRC scaffolds.

Evolutionary “work in progress”

In my opinion cells without centrioles and centrosomes can perform only simple

laminar morphogenetic processes (including the creation of elementary tubes) making

use of the cytoskeleton and through their ability to control their simple and rough

polarity and MT disposition by different cues: light, gravity, “automatic

repositioning” of cell-cell contacts organized through MAPs, etc. (Wasteneys and

Ambrose 2009: ” Spatial organization of plant cortical microtubules: close encounters

of the 2D kind”); as we have seen “the overall structural organization of plants is

generally simpler than that of animals. For instance, plants have only four broad

types of cells, which in mature plants form four basic classes of tissues…organized

into just four main organ systems” (Lodish et al., 2012, Ch. 20). Plants possess and

use many cytoskeleton factors common with Metazoa: “Remarkably, formins appear

to be not only important regulators of the actin cytoskeleton, but also prime

candidates for mediating the co-ordination between microfilaments and microtubules

also in plants, despite using mechanisms of microtubule interaction different from

those of their metazoan counterparts” (Cvrčková, 2012). Microtubule Associated

Proteins (MAPs) can arrange MTs parallel and constantly distanced from each other:

“Cellulose synthases in etiolated Arabidopsis thaliana hypocotyl cells move

bidirectionally in the plasma membrane along tracks that are typically defined by

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cortical microtubules. However, examples are known in which, vice versa, cellulose

microfibrils impose orientation on newly formed cortical microtubules….At near

weightlessness, tubulin polymerizes into microtubules in vitro, but these microtubules

do not self-organize in the ordered patterns observed at 1g. Likewise, at near

weightlessness cortical microtubules in protoplasts have difficulty organizing into

parallel arrays, which are required for proper plant cell elongation. However, intact

plants do grow in space and therefore should have a normally functioning

microtubule cytoskeleton. Since the main difference between protoplasts and plant

cells in a tissue is the presence of a cell wall, we studied single, but walled, tobacco

Fig. 11 Centrosome theoretical geometrical model: transmitting the same latitudinal receptors to

γ-TuRCs with different longitude.

A) Along each DC blade a 140°-fan-shaped MT-structure, SAS6 and -tubulin based, is positioned near the

proximal centriole end and lies on the plane containing the axes of the centriole and the A-MT of each

triplet-blade: it is supported by a half ring of five SAS-6 dimers (reverse “T”) and other proteins cooperating

to build the 140° angle; through SAS-6 dimers C-terminal coiled coils (“T” stems) and -tubulin/MT , this

140°-fan-shaped MT-structure reaches and organizes -TuRCs (ellipsoidal disks) localized in different

meridian wedges (with different longitude) and superimposes DC radiality (latitudinal inclination) on the

longitudinal inclination already imposed by the MC cylindrical structure.

B) Schematic centrosome cross section at MC proximal end with a nascent procentriole (DC): view from the

MC distal end. The 140°-fan-shaped structures (dotted lines) starting from the DC PCM (close to one triplet

blade) can reach five (1-5) wedges (separated by lines) of the MC PCM (-TuRCs: ellipsoidal disks); a

similar structure (not represented) on the opposite (symmetric) DC PCM (close to the corresponding triplet

blade) can reach five corresponding wedges of MC PCM: two symmetric DC blades transmit the same

latitude; 140° geometry is the same for MC PCM and DC 140°-fan-shaped structure. As depicted, the

presence of the cylindrical MC is not a barrier.

C) View from the DC distal end of a schematic orthogonal (in respect to B) representation of geometrical

disposition of the nine 140°-fan-shaped structures (dotted lines): from the DC PCM each one reaches the

corresponding cap or parallel ring of the MC linked PCM (-TuRCs: disks); symmetric DC blades transmit

the same latitude; 140° geometry is the same as in A, and the presence of the cylindrical MC is not a barrier.

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154

BY-2 suspension-cultured cells during an 8-day space-flight experiment on board of

the Soyuz capsule and the International Space Station during the 12S mission

(March-April 2006)…. Microtubules could be aligned by cues from an anisodiametric

cell shape, anisotropical mechanical stress, moving cellulose synthase complexes, a

pre-existing cell wall pattern, or maybe gravity” (Sieberer et al., 2009). “One

emerging concept is that the ability to organize decentralized microtubule arrays

depends to a large extent on microtubule self-organization. This may be coordinated

largely by the activities of motor proteins, which in plants include a remarkable

variety of minus- and plus-end directed kinesins…Without centrosomes, plant

microtubule arrays are largely self-organized by the relative activities of microtubule-

associated proteins. The recent discoveries of katanin p60 and MOR1 provide

important clues about how microtubule assembly and stabilization are achieved,

particularly in the cortical arrays that regulate growth polarity and cell wall

deposition in interphase and terminally differentiating cells” (Wasteneys, 2002).

One centriole alone can organize organisms with circumferential (rotational)

symmetry; the intervention of a second orthogonal centriole enables the careful

management of the 3D of tissues and organs, because it governs the orientation of γ-

TuRCs in accordance to the latitude angle, which is added and superimposed to that

of longitude. This is true also for some particular Metazoa: during Drosophila

segmentation, centrosomes are indispensable (segmentation is a 3D process) but in

later stages of fly development they are dispensable: laminar (2D) morphogenetic

processes and creation of elementary tubes do not require 3D precise controls.

There is a wide taxonomic range of “work in progress” in which centrioles and

centrosome have different degrees of development with different structures (the

unicellular green alga Chlamydomonas has centrioles with triplets, like other

unicellular Protists, but Caenorhabditis elegans centriole has singlets and Drosophila

has doublets). As observed by Azimzadeh and colleagues (2012), cellular and

developmental processes are conserved in flatworms, but planarians have lost the

centrosome and develop by making use of different pathways which allow them to

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build only laminar tissues (like the leaves in Plantae) or elementary tubes and to

maintain an extraordinary ability for regeneration. Acerentomon microrhinus builds

axonemes with 14-fold symmetry; Cnidaria and Ctenophora appear radially

symmetrical, but they are quite different: they are Radiata, not Bilateria and have

only two germ layers, ectoderm and endoderm (Diploblasts); they have centrioles and

cilia, but the behaviour of their centrosomes is quite different than in Bilateria

(Bornens, 2012): Ctenophora fertilization is naturally polyspermic and many

centrioles are utilized contemporaneously in the same cell; Cnidaria zygotes lack

cytasters (Salinas-Saavedra and Vargas. 2011). In this taxonomic area - and in the

corresponding evolutionary phase - some genetic changes need to complete the final

centrosome structures take place. It is clear that although the number of genes is quite

similar in different metazoan Clades, on the contrary, their 3D complex organization

goes in parallel, hand in hand, with non-coding DNA amount and centrosome

structure development.

“Πάντα ῥ εῖ ” [everything flows] (Heraclitus)

The continuous flow of developing and not completely mature mechanisms and

structures (and their molecular base) is characteristic of evolution, and allows what

has been generated previously to be conserved and reused by superimposing small

but important modifications (transposons, duplications, exon exchange between

different genes –gene shuffling–, unequal cross-over, etc.) in order to achieve

surprising results. So, depending on the success in surviving (purifying selection)

different species show differently developed centrosomes and different pathway to

control centrosome’s “hardware and software”: if the origin of bilateral symmetry

may be a simple evolutionary event, quite more complicate are the control

mechanisms; in every species coding DNA is much shorter than the set of sequences

that control gene expression. Everything flows…

But, sometimes, something comes back: “ Nihil sub sole novum” [nothing new under

the sun] (Ecclesiastes).

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iv) mapping the whole cortex

Two different cycles must be followed: the centriole and the centrosome cycle (pay

attention to distinguish “centriole cycle” and “centrosome cycle” when you read the

following lines).

Centriole cycle:

Vorobjev and Chentsov (1982) have clearly described the centriole cycle as follows

(Fig. 1):

“- The structures of the two centrioles differ throughout interphase; the MC has

appendages, the DC does not.

- In the distal part of the DC, there are peculiar outgrowths (ribs). Unlike

appendages, these ribs remain unaltered in two to four serial sections. The above

structure of the DC remains constant to the end of telophase.

- Throughout the S period, differences are observed in the structure of the two MCs,

i.e., one of them contains satellites and appendages, while the other has note. The

structure of the second centriole changes somewhat in the S period: it loses ribs

situated in the distal part.

- Thus, in the next cycle, the new (ex-daughter) centriole differs from the former

(mother) only by the absence of appendages. This difference, however, is functionally

significant…Appendages are probably needed for bridging the centriole to the

membrane, which is also evidenced by the fact that when they become attached to the

membrane their position and outward appearance are somewhat changed.

- Two MCs situated in the two poles of a cell differ somewhat in structure: one

contains distinctly visible appendages, whereas the other lacks them…In anaphase,

the general structure of spindle poles hardly changes. But by this time both MCs have

appendages which are less distinct than in metaphase.

- Despite the fact that in G2 two MCs become equivalent with respect to

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microtubules, the difference between them, i.e., the presence of appendages on one

and their absence from the other, persists throughout the G2 period and during the

first half of mitosis”.

Centrosome cycle:

Ou and colleagues (2002) have described the centrosome cycle as follows (Fig.1):

“- Thus, in late S phase cells that had two separated centrosomes, the MC centrosome

had two regions of CEP110 (centriolin) staining, whereas the Daughter centrosome

had only one site.

- In random cultures, centrosomes initiating duplication can be identified by the

appearance of a structure at the margin of the centrosome. When cells displaying this

stage of duplication were stained for CEP110, this protein was found at the site of

duplication as well as at the open and closed ends of the MC centrosome tube.

- Further, we showed that, following centriole separation at G1-S, the DC moves

along the MC and come to reside at the site of centrosome duplication. Importantly,

the addition of these proteins to the open end of the Daughter centrosome tube

coincides with the transition of the Daughter centrosome to a mature centrosome

which is capable of duplication and acts as a microtubule organizing center.

- Thus, our study, for the first time, identifies a specific region of the centrosome that

is modified in its protein composition during the process of centrosome maturation, a

process that is completed following cell division”.

During the process of maturation (Fig. 1), the DC moves along the MC towards the

distal end of the MC (where MC appendages are): after losing its ribs, it is formed by

9 equivalent and identical triplets: then, the old DC, now new MC, matures near the

old MC to maintain a coordinated orientation of centrosomes (based on non-

equivalence of triplets), indispensable to coordinate the development of complex

organs. Let’s recall Harold’s words: “Centriole duplication is part of the mechanism

by which the cytoskeleton of the daughter cell is patterned upon that of the mother”.

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A question: is it possible that the proximal end of the ex-DC becomes the distal end

of the newly formed (or, rather, maturated) MC? In this case some receptor might

distinguish the old and the new centrosome and perform asymmetrical delivery of

transcription factors and mRNAs during mitosis, as we have seen in Ilyanassa.

“Further, we showed that CEP110 appeared at only one site (the site of CEP250/c-

Nap1) within the Daughter centrosome from the time of its initial formation until

prophase” (Ou et al., 2002). “In anaphase, the general structure of spindle poles

hardly changes. But by this time both MCs have appendages which are less distinct

than in metaphase” (Vorobjev and Chentsov, 1982). So, in late anaphase/beginning

telophase, when the new centrosome is mature but the nucleus has not yet formed and

DNA is still packed into chromosomes, there is the physical space for the two

centrosomes, through their asters, to be able to map and wire cortical compartments

in the two daughter cells without the impediment of the nucleus which will, only

subsequently, distort the perinuclear MTs: these, unlike other MTs, will no longer be

substituted in G1, because their intrinsic rigidity does not allow new ones, incapable

of bending in order to move around the nucleus, to be nucleated: “Our study suggests

that perinuclear microtubules are a separate and relatively stable subpopulation of

the total population of cytoplasmic microtubules and may serve a function different

from that of the more variable not perinuclear microtubules” (Park et al., 1984).

Stable MTs show acetylation of a lysine and C-terminal detyrosylation of α-tubulin.

As we have already seen, aster MTs constitute a particular population of stable MTs

whose function consists in mapping and wiring the whole cell.

The maturation timing of the DC and new centrosome (that forms around it, using it

as a “new” MC), gives a response to query iv): the nucleus does not obstruct the

“mapping” process of the entire daughter cell because the process takes place in

anaphase-telophase, when the chromosomes are still compact, endoplasmic reticulum

and Golgi membranes are restricted in small vesicles, both centrosomes are mature

and both asters can easily reach the whole daughter cell cortex.

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v) Centrosomal trafficking

“Functional centrioles and intact subdistal appendages are required for the

recruitment of PCM proteins in animals” (Esparza et al., 2013).

“In eukaryotic cells, targeted vesicle fusion requires, in addition to the SNAREs, both

a delivery system and a secretory apparatus” (Harold, 2005).

As we have seen, Kubo and colleagues (1999) and Dammermann and Merdes (2002)

observed that pericentriolar satellites, after recruiting proteins indispensable for

anchoring γ-TuRCs to their centrosomal docking platform (centrin, pericentrin,

ninein, SAS-4 etc.), are transported to the centrosome by MT-linked dynactin.

The fifth query to be dealt with concerns the “crowded” presence of many

differently-oriented astral MTs, originating from centrosomal γ-TuRCs: how are the

macromolecular complexes, destined for a precise position in the cell membrane,

quickly guided toward the respective γ-TuRCs, interspersed among many other on a

large polyhedral surface? Up to now, we have discussed the subject of wiring

precision: to assure the needed speed, each γ-TuRC and its MT must be reached

easily and quickly. The “astral” MTs are nucleated by γ-TuRCs that are suitably

oriented and equipped, in accordance to the model, with receptors corresponding to

their latitude and longitude. As we have seen, the only “motor” that moves molecules

in solution is thermal fluctuation and the only “helm” that directs the molecules in

different directions is the result of random collisions with other molecules. The

process by which a macromolecular complex finds the γ-TuRC it is destined for,

localized on a spherical structure that in many cases makes a complete

“circumnavigation” of the centrosome necessary, frankly seems to be too complicated

and slow, if not impossible: protein diameter average size is about 3-6 nm,

centrosome diameter is about 800 nm, its equator then measures approximately 2,500

nm and its surface about 2,000,000 nm2. It appears necessary a multi-step process:

firstly a centrosomal receptor seems to be necessary, situated at one pole of the

centrosome, able to recognize (and to be recognized by) a targeting sequence placed

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on those molecular complexes that must use centrosome and aster to be correctly

located in the cell.

“The identification and localization of two populations of both CEP110 and ninein

within the centrosome has some functional implications. First, the function of

CEP110 and ninein is, at least in part, centriole-based. Second, previous studies have

suggested that ninein plays a role in microtubule anchoring at the centriole and acts

as a cap for microtubule ends. If so, the presence of ninein at the open end of the

centrosomal tube suggests that microtubule anchoring or capping functions may

occur within this region as well, at least at some point during the cell cycle. The

absence of ninein from the daughter centrosomes would therefore limit their ability to

anchor or cap microtubules at the open end of the tube. Such a relationship may

explain in part why previous studies failed to identify microtubules in association

with immature centrosomes. The observations described here raise the possibility that

ninein plays a larger, and perhaps more diverse, role within the centrosome than

previously thought” (Ou et al., 2002). These authors seems to adapt the hypothesis

supported, amongst others, by Bornens (2002) about PCM restricted MTs (MTs

would start only from MC subdistal appendages) and have developed the

observations by Vorobjev and Chentsov (1982) about the role of the whole MC-

linked-PCM (from which cytoplasmic MTs would start) and MC appendages, where

ninein could play the role of catching the molecular complexes directed to the

centrosome (ninein plays a larger, and perhaps more diverse, role within the

centrosome).

Studies on centrosomal targeting sequences of different ninein isoforms and on the

ability of ninein to bind different kinases and γ-TuRCs themselves, carrying out a

larger, and perhaps more diverse, role within the centrosome than previously thought,

are attractive. “Our study of GFP-tagged full-length hNinein reveals that four

domains are required and sufficient for centrosomal targeting” (Lin et al., 2006). In

this sense, the Cep 164 complexes of distal appendages and of ninein-CEP110

(centriolin), present on the 9 subdistal appendages of the MC, may have the role of

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sites for recognizing centrosome localization signals, presented by macromolecular

complexes, with the consequent capacity to route these complexes, after binding them

to the centrosome, on the sector having the required longitude. We have already seen

that Kubo and colleagues (1999) and Dammermann and Merdes (2002) observed that

pericentriolar satellites, after recruiting proteins indispensable for anchoring γ-TuRCs

to their centrosomal docking platform (centrin, pericentrin, ninein, SAS-4 etc.), are

transported to the centrosome by MT-linked dynactin.

“We propose that Cep164 is targeted to the apical domain of the MC to provide the

molecular link between the MC and the membrane biogenesis machinery that

initiates cilia formation” (Schmidt et al., 2012). This same molecular link could have

been adapted to drive molecular complexes (centrosome targeted) onto the desired

centrosome wedge.

An in-depth study on the role of ninein “in MT nucleation and MT anchoring at the

centrosome” was carried out by Delgehyr and colleagues (2005): “Ninein is targeted

to both centrioles by its C-terminus and stabilized at the MC by its N-

terminus...These data suggest that a subset of microtubules could be nucleated and

later anchored at the subdistal appendages. Based on our results, we propose that

microtubules nucleated in a γ-TuRC-dependent manner at the centrosome would have

different behaviours. Microtubules nucleated far from the subdistal appendages

would be transiently anchored by the γ-TuRC but then released from the centrosome

in a manner possibly dependent on specific factors. Indeed, many microtubule seeds

are produced and released from the centrosome. By contrast, microtubules nucleated

at the vicinity or on the subdistal appendages would become anchored more readily

at these structures on the MC. Therefore, ninein, a component of these appendages,

might favour microtubule nucleation (by docking the γ-TuRC), followed by

anchoring”.

In accordance to this hypothesis, subdistal appendages might have the role of

capturing the complexes directed to the centrosome through their own “centrosomal”

MTs (arising from γ-TuRCs of centriolar identity: Fouquet et al., 1998) like

162

mechanical molecular antennas and distributing them, through “centrosomal” actin to

the final corresponding γ-TuRC from which the “cytoplasmic” MT, directed to the

cortex, will originate. “The recycling endosome associates with the appendages of the

MC” (Hehnly et al., 2012). As we have seen, during its first stages of cleavage, in

Ilyanassa obsoleta long RNAs are linked to only one of the two centrosome before

mitosis to be delivered exclusively and asymmetrically to micromeres: differential

targeting leads the new arising centrosome in that sector of the cell where the position

of the spindle pole is programmed and the same targeting sequence guide RNAs to

the same sector (together with the centrosome).

It is an attractive hypothesis that several centrosome targeting sequences exist, placed

on those macromolecular complexes (RNA 3’ UTR or N-terminus of polypeptides)

that must be routed towards prefixed cell locations through the appropriate MTs.

Such mechanism is quite similar to that used for translocation of proteins in

mitochondria, where different targeting sequences, present on the proteins that must

enter the mitochondrion, are sequentially decoded in order to reach the expected

location (the external mitochondrial membrane, the internal one, the inter-membrane

space or the matrix); it is well known that in fly oocyte bicoid and nanos mRNA are

localized through their 3’UTR sequence and delivered by MT transport. When a

polypeptide or polyribonucleotide complex (spindle poles binding proteins, cell

adhesion complexes, integrins and other extra-cellular fiber receptors, maternal

mRNAs, etc.) must be sent by means of the centrosomal MTs into a certain cortical

compartment, should first of all have a centrosomal localization signal that is easily

recognizable in a particular (easy accessible) area of the centrosome: the cap where

the distal end of the MC is present with its subdistal appendages, where the open end

of the centrosomal tube (Ou et al., 2002) is and where the ninein-linked MTs are, is

the most likely one. Here a second receptor placed on the appropriate “wedge”

appendage can recognize a second targeting sequence that identifies the meridian and

can send the macromolecular complex along the expected sector (wedge), where

molecular motors present in the centrosome (centrosome localization of myosin-V

163

and centractin - an ARP i.e. Actin Related Protein - is well known) can lead it towards

the latitudinal receptor corresponding to its third targeting sequence. At each

recognition of a targeting sequence by the appropriate receptor, different kinases or

proteases (Urbé et al., 2012) may deactivate or remove the targeting sequence that

has been read and recognized, leaving room for the next recognition, exactly as

happens in mitochondria, in which the choice of one among many destinations poses

quite similar problems.

From its ancestral function of anchoring to the membrane and generating the

axoneme, the MC distal end has evolved to acquire new structures in order to link to

adjacent centrioles (Chlamydomonas, Paramecium, Tetrahymena) and interface with

them and with other cytoplasmic fibers, in accordance to a precise geometric design;

Vorobjev and Chentsov (1982) observed that “appendages are probably needed for

bridging the centriole to the membrane, which is also evidenced by the fact that when

they become attached to the membrane their position and outward appearance are

somewhat changed”. In non-ciliated cells the appendages (distal and subdistal) seem

to perform other and new functions, such as orienting the centrosome in the cell

(coordinately, as we have already seen, with the polarity of neighboring cells),

anchoring it to the nucleus, correctly orientating the daughter centrosome, capturing

and routing of macromolecular complexes equipped with “address-signal” (targeting

sequences) towards the correct γ-TuRC; membrane linked centrosome maintain their

orientation and can perform their geometrical role of biological interfaces.

164

Conclusions

Let’s then summarize the results:

i) The centrosome is an ordered tool whose surface is made up of 45 oriented

scaffolds for γ-TuRCs; each scaffold is labelled by its own receptor able to recognize

(and interact with) the targeting sequence intended for the cortical compartment

reachable through the MT nucleated by its oriented γ-TuRCs. One-to-one invariable

correspondence is established between targeting sequences and γ-TuRC molecular

labels. One-to-one univocal but time-variable correspondence is established between

γ-TuRs and cortical compartments, depending on the (known and controlled)

centrosome position in the cell.

ii) Two centrioles, arranged with eccentric orthogonality during S G2 and M phase,

transmit their 9-fold symmetry and non-equivalence of the triplets to the PCM (γ-

TuRC scaffolds).

iii) A ring of RNA, composed of nine different and equi-spaced loops (markers) is

responsible for the non-equivalence of the centriolar triplets.

iv) A transposition event of the gene coding for the RNA sequence responsible for the

non-equivalence of the centriolar triplets has generated a similar sequence with a

little difference in its ends so that its transcript’s 3’ and 5’ terminals, once juxtaposed,

compose a stem whose 3D structure is mirror symmetric to that of the original

transcript. The interaction between the RNA ring stem and the corresponding

molecular centriolar complex must occur through a typical disposition of the stem:

this causes the overturn of the ring transcribed from the transposed locus with

consequent reversal of the sequence of the triplet markers.

165

Future perspectives: From cell geometry to organ geometry. Toward a global theory

of morphogenesis in Metazoa

In fibroblasts, procollagens and proteoglycans are delivered through trans-Golgi

derived secretion vesicles, carried to the cell membrane by MT linked kinesins: these

vesicles converge and coalesce to form long and deep grooves on the outer face of the

cell membrane, where procollagens auto-assemble into long fibrils. The orientation of

grooves and surface collagen binding molecules determine the spatial orientation of

future collagen fibers. Taken together, the geometrical model of the centrosome, its

role in mapping and wiring the cell cortex (one-to-one correspondence between

centrosomal and cortical compartments), the coordination of the shared common

centrosome orientation in every cell of a tissue make it possible to hypothesize that

the shape of organs is modeled by connective tissues through genetically

programmed orientation of extracellular matrix fibers, whose geometrical orientation

and direction are achieved by means of controlled exocytosis of procollagen and

proteoglycan: this may be possible because of the centrosome and its role of

geometric, noise resistant, 3D interface that translates morphogenetic signals into

precise locations in the cell. Intriguingly, fibroblast secretory granules and grooves,

membrane areas forecast by the centrosome model and cortical domains found in

eukaryotic cells have compatible size. This may be the transition from cell geometry

to organ geometry.

166

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