Adaptive self-organization during growth of bacterial colonies

Physica A 187 (1992)378-424 North-Holland

Adaptive self-organization during growth of bacterial colonies

Eshel Ben-Jacob, Haim Shmueli, Ofer Shochet and Adam Tenenbaum School of Physics and Astronomy, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel

Received 11 February 1992

We present a study of interfacial pattern formation during diffusion-limited growth of Bacillus subtilis. It is demonstrated that bacterial colonies can develop patterns similar to morphologies observed during diffusion-limited growth in nonqiving (azoic) systems such as solidification and electro-chemical deposition. The various growth morphologies, that is the global structure of the colony, are observed as we vary the growth conditions. These include fractal growth, dense-branching growth, compact growth, dendritic growth and chiral growth. The results demonstrate the action of a singular interplay between the micro-level (individual bacterium) and macro-level (the colony) in selecting the observed morphologies as is understood for non-living systems. Furthermore, the observed morphologies can be organized within a morphology diagram indicating the existence of a morphology selection principle similar to the one proposed for azoic systems. We propose a phase-field-like model (the phase being the bacterial concentration and the field being the nutrient concentration) to describe the growth. The bacteria-bacteria interaction is manifested as a phase dependent diffusion constant. Growth of a bacterial colony presents an inherent additional level of complexity compared to azoic systems, since the building blocks themselves are living systems. Thus, our studies also focus on the transition between morphologies. We have observed extended morphology transitions due to phenotypic changes of the bacteria, as well as bursts of new morphologies resulting from genotypic changes. In addition, we have observed extended and heritable transitions (mainly between dense branching growth and chiral growth) as well as phenotypic transitions that turn genotypic over time. We discuss the implications of our results in the context of the evolving picture of genome cybernetics. Diffusion limited growth of bacterial colonies combined with new understanding of pattern formation in azoic systems provide new tools for the study of adaptive self-organization and mutation in the presence of selective pressures. We include brief reviews of both the recent developments in the study of interfacial pattern formation in non-living systems and the current trends in the view of mutation dynamics.

1. Introduction

W e a r e s u r r o u n d e d b y e n d l e s s p a t t e r n s a n d s h a p e s , r a n g i n g f r o m t h e g r o w t h

o f s n o w f l a k e s to t h e a g g r e g a t i o n o f s o o t p a r t i c l e s , f r o m d e n d r i t i c g r o w t h d u r i n g

0378-4371/92/$05.00 © 1992- Elsevier Science Publishers B.V. All rights reserved

E. Ben-Jacob et al. / Adaptive self-organization during growth of bacterial colonies 379

solidification of metals to the formation of coral reefs. Understanding the spontaneous emergence of these patterns from an orderless environment has long been a challenge to scientists [1,2]. One wonders whether each of the diverse forms found in nature is a result of unique cause and effect, or if there are unifying underlying principles. During the last decade, we have witnessed the emergence of such principles and the development of a unified theoretical framework of interfacial pattern formation in diffusion limited growth [3-5]. Such developments should have an impact on several fields, including industrial applications and the natural and medical sciences. Here, we present an application to the study of adaptive self-organization during diffusion-limited growth of bacterial colonies [6-10].

In the last decade, the cornerstone of developments in the study of interfacial pattern formation is the recognition of the nature of the interplay between the microscopic interfacial dynamics and the external macroscopic forces (growth conditions) in determination of growth patterns. We now understand that for diffusion-limited growth, the resulting patterns originate from a competition between the diffusion field and the interface kinetics (expressed as surface tension, surface kinetics and anisotropy). This led to a new insight: the observed patterns can be grouped into a small number of "essential shapes" or morphologies, each reflecting a different "compromise" in the competition. The same morphologies are observed in different systems and over many different length scales. At the same time, different morphologies are observed in the same system as we vary the growth conditions. Examples of some of the typical shapes discussed here are shown and characterized in fig. 1.

Does the study of interracial pattern formation in azoic systems bear relevance to biological systems? The pioneering studies of Fujikawa and Matsushita [6,7] have demonstrated that the growth of bacterial colonies on thin agar plates is an example of a quasi-two-dimensional biological growth process which is diffusion limited (diffusion of nutrient towards the colony). First they have shown that in the limit of very low nutrient level and a very long diffusion length the colonies adapt a fractal structure which resembles the one derived in simulations of diffusion-limited aggregation (DLA) [11-14]. Varying the growth conditions, they have observed dense-branching morphologies (DBM) [15-17] and compact (Eden-like [18,19]) growth. Both were very similar to patterns which were predicted and observed during diffusion limited growth in azoic systems.

This made us wonder, whether the new understanding of interfacial pattern formation in azoic systems can help us reach a new understanding of biological systems. The studies presented here were motivated by the assumption that it would.

Growth of a bacterial colony presents an inherent additional level of

Fig. 1. The "essential shapes". As explained in the text, the endless array of shapes can be grouped into a small number of characteristic shapes reflecting different dominant effects. The same shapes are observed in different systems and on different length scales. Here (a)-(c) are results of Hele-Shaw experiment [5] and (d ) - ( f ) are from electrochemical deposition. The Hele-Shaw cell is a simple yet elegant device for studying pattern formation. It consists of two closely spaced plexiglass plates sandwiching a layer of dyed glycerol. Through an inlet at the center of the top plate, air is injected into the glycerol. The ECD cell also consists of two plexiglass plates with an electrolytic solution sandwich in between. It has two electrodes, one at the center and the other one along the outer boundary. Voltage is supplied for deposition on the inner electrode. (a) and (d) show a fractal-like structure similar to that of DLA simulations [11-14]. It is characterized by its fractal dimension (the mass distribution as a function of radius). This shape reflects the diffusive instability, it is typical in the limit of small surface tension, large noise and long (longer than the system size) diffusion length. The structure was produced by ECD at low voltage [72,97-99]. In the Hele-Shaw experiment it results from grooving of a random lattice on the bot tom plate. (b) and (e) show the dense branching morphology [5, 15]. This is the characteristic morphology in the absence (or for weak) crystalline anisotropy. It reflects the competition between the diffusive instability and the action of surface tension and surface kinetics. The structure has a well defined shape-preserving envelope that moves at constant velocity. In the ECD experiment, a mixture of ZnSO 4 and CuSO 4 was used to reduce the anisotropy. Each of the fingers is made of a fine structure of narrow branches. (c) and (f) show dendritic growth. In the Hele-Shaw experiment a 4-fold lattice was grooved on the bottom plate [49]. The dendrites are characterized by a main trunk (referred to as needle-crystal) with a parabolic tip moving at constant velocity. The trunk is feathered with side-branches which grow outward while being stationary in the laboratory frame. It is observed when anisotropy is dominant.


complexity compared to azoic systems, since the building blocks themselves are living systems. In a bacterial colony, the individual bacteria can go through major changes during the growth of the colony in response to the growth conditions. It has been shown by Shapiro et al. [20-22] that macro-level changes (the morphology of the whole colony) go hand in hand with changes in the micro-level organization. We have classified three types of changes in the macro-level structure of the growing colony: (i) sharp and extended (all around the interface) transitions, which look like morphology transitions observed in non-living systems; (ii) sharp and localized transitions (not observed in non- living systems); (iii) gradual changes over a fraction of the interface.

It is suggestive that the first type is due to a phenotypic change of the bacteria [23]. It represents adaptation of the colony, as the change leads to a new morphology with self-organization which is better adapted to the imposed growth conditions. We expect the second transition (which will be referred to as a burst of new morphology) to arise from an inheritable change. The mutation improves the colony's adaptation (faster growing morphology) and becomes the dominant genotypic phase (it takes over spatially-fills the petri dish). We have performed many studies (via reinoculation of bacteria from different original morphologies, before and after the transitions) to relate the morphology transitions with phenotypic and genotypic changes. As expected, the bursts of new morphology indeed seem to result from genotypic changes, while the first transition is phenotypic. However, this is not always the case. We also observed sharp and extended, inheritable and phenotypic transitions that turn genotypic after a time delay.

Morphology selection during the growth of the colony reflects an interplay between the tendency of the individual bacterium (micro-level) and the tendency of the colony as a whole. The external growth conditions are imposed on the colony. The environment of the individual bacterium is set by the colony's dynamics. Thus, whether we have a phenotypic, genotypic or new type of changes, we are facing an adaptive self-organization of the colony. Hence, diffusion-limited growth provides us with a new test of selection and adaptation.

We present our results to researchers from different disciplines. Therefore we provide a brief review of the last decade developments in the study of interracial pattern formation in azoic systems (section 2), as well as a summary of the classical identifications of phenotypic and genotypic changes. A brief review of the conventional view of mutation kinetics and the recent trends put forward by Shapiro et al. [24], Cairns et al. [25,26] and Hall [27,28] is also presented. In both sections, we made an effort to bridge the terminology barriers.

In section 4 we present the various observed morphologies and comment

382 E. Ben-Jacob et al. / Adaptive self organization during growth of bacterial colonies

about modeling of the bacterial growth. We also show dendritic growth in the presence of anisotropy, and morphology transitions due to phenotypic changes. Bursts of new morphology are discussed in section 5. Chiral growth is described in section 6, as well as transitions between tip-splitting growth and chiral growth. We comment on the possible interpretations of our observations and their implications towards the new picture of genome cybernetics (section 7). We conclude with comments about further directions of study derived from our preliminary findings (section 8).

2. Interfacial pattern formation in azoic systems: brief review

The transfer of information from the microscopic (atomic) level to the macroscopic (observed) level is evident in the beautiful six-fold symmetry of a snowflake. The symmetry of the flake is determined by the six-fold symmetry of the underlying ice crystal. The decoration and complex structure result from the action of the diffusion field instability (explained below). The principal mystery is how the microscopic dynamics, operating on the scale of angstroms, is amplified to such an extent that in a diffusion-limited growth it controls the macroscopic shape on a scale of centimeters. A qualitative understanding can be reached by considering the principles of nonequilibrium growth, which are reviewed in this section.

2.1. The diffusion field instability and fractal growth

During growth, a stable phase will "propagate" into an unstable or meta- stable one. Thus, during the formation of snowflakes, the stable solid phase propagates into the unstable, super-saturated with water vapor atmosphere. The growth rate of the stable phase is limited by a diffusion process: the diffusion of water molecules towards the snowflake (in the above example), diffusion of heat away from a growing solid (in the case of solidification from undercooled melt [29]) or diffusion of nutrients towards the bacterial colony (during growth on thin agar). In all of these examples, the velocity of the interface between the two phases, v n, is proportional to the gradient of the diffusion field u,

v. ~Vu. (1)

The kinetics of the diffusion field u is governed by the diffusion equation

Ou DV2u (2) Ot


where D is the diffusion constant. The diffusion field drives the system towards decorated and irregular shapes, and acts to intermingle the two phases on many length scales. This effect is a manifestation of the basic diffusive (Mullins-Sekerka) instability [30] shown in fig. 2. Assume that we start with a circular interface perturbed by a sine wave in the absence of microscopic effects. That is, the value of u along the interface (denoted by us) is some constant u 0 (e.g. in solidification u 0 is the melting temperature). At the tips of the bulges, the gradient of u is larger, and consequently the bulges grow outward faster than the other parts of the interface. In fig. 2b we give the results of linear stability analysis, which show that the rate of growth of perturbations of mode number m is proportional to m. Hence, the diffusive instability is stronger for the shorter wavelengths. When it is the only acting mechanism (in the absence of microscopic effects), then any noise or fluctuations cause the interface to break into ever-growing bulges, which develop many smaller bulges and so on, ad infinitum. In the Laplace limit of eq. (2), and in the limit of zero driving force A (e.g., the dimensionless supercooling (T M - T~)/TM in the solidification from melt, the dimensionless supersatura-

4O

20

10

(a)

I . . . . I . . . . L b ' ' ' T . . . . I . . . .

loo2 o

I®®~gg~ C+++ 3 ÷+* **+_. _ c * + .

20 40 60 80 100 (b) Mode number m

Fig. 2. (a) Schematic illustration of the Mullins-Sekerka instability [30]. The solid is a 4-fold sine wave deformation (that is, the mode number rn = 4) of a circular interface (dashed line). The four bulges are closer to the outer boundary (the circle with radius R0) , hence the velocity (illustrated by the arrows) is larger. (b) Results of the linear stability analysis, showing the initial growth rate as function of the mode number m for a sinusoidal perturbation of a circular interface. Line (1) is for constant u 0 along the interface (no surface tension and no surface kinetics), line (2) is when surface tension is included and line (3) is in the presence of surface kinetics. Note that in the latter case there is no fastest growing mode. Line (4) is in the presence of both surface tension and surface kinetics. In the absence of microscopic effects (line 1) all modes are unstable. When surface tension and surface kinetics are included, the short wavelength modes (high m) become stable. In addition, there is a specific mode number m that is the most unstable (the fastest growing mode).

384 E. Ben-Jacob et al. / Adaptive self-organization during growth of bacterial colonies

tion ( c ~ - C e q ) / ( 1 - Ceq ) in solidification from supersaturated solutions [31- 34] #~, etc.), the two phases intermingle without any characteristic length scale or ordering leading to a fractal growth [11-14,35]. For a finite driving force, in the case of a diffusion equation there is a characteristic length l =- D/v where v is the average growth velocity. The growing morphology has a fractal structure on scales smaller than l, and a constant density (set by A) on the larger scales [36,37].

2.2. The dense branching morphology

The microscopic effects, when present, compete with and channel the diffusive instability. The most common of these effects are surface tension, surface kinetics and anisotropy (The latter is present when the growing phase has a crystalline structure, which will be discussed in the next section.) Phenomenologically, the microscopic effects change the boundary conditions at the interface, which become [5,29,38]

u~ = u0(1 - d0K - /3 , ,v . ) , (3)

where K is the local curvature of the interface, d o is the capillary length, which is proportional to the surface tension, and/3 o is the kinetic coefficient, which is proportional to the rate of phase transition at the interface. The microscopic effects introduce additional length scales (d 0 and/30D ), and time scales (d~/D and do/30), and modify the stability of the interface as shown in fig. 2. When present, they lead to a new characteristic morphology, the dense branching morphology [5,15,16,39,40], in which the growth is via a cascade of tip- splittings (fig. 1). The latter represents the "compromise" in the competition between the tendency of the macroscopic and microscopic effects, while the characteristic branch widths reflect the balance between these effects [39] (smaller as the diffusion field "wins").

2.3. Anisotropy, singular perturbation and dendritic growth

For many years, the research effort in interfacial pattern formation centered around the question of selection with respect to dendritic growth. (The motivation was to predict the nature of dendritic growth during solidification of metals, which had practical implications.) Back in 1947, Ivantsov [41] studied the problem of solidification from melt, ignoring interfacial effects (set the surface temperature to be the melting temperature T M all along the interface).

#' Ceq is the equilibrium concentrat ion and c~ is the concentrat ion at the boundaries. The solid

concentrat ion is taken to be 1.


He found that, for any value of the undercooling A, there exists a continuous family of steady state solutions with parabolic shape. There were thin fast ones, and fiat slow ones, such that the product of the tip radius R 0 and the velocity v 0 was constant, i.e.

Roy o = func(A). (4)

Both the parabolic shape and the prediction of propagation at constant velocity fit well with the characters of the observed dendrites. However , the Ivantsov solution specified only the product of the radius of curvature of the tip and the tip velocity, but could not predict either one alone. For example, the 1976 experiments of Glicksman et al. [42] demonstrated that under controlled conditions, for a given undercooling, the same dendrite (i.e., same tip velocity and radius of curvature) is reproducibly observed. This implied a "selection problem": for a given undercooling, the Ivantsov solution allows a continuous family of parabolic solutions, and yet, for specified conditions, only one is observed. Today we understand why there could not be one solution in the limit of constant surface temperature. The reason is that the only length scale in the problem is the dynamical diffusion length 1 = D/u. As it is the only one, the radius of the tip must be proportional to it, leading to a relation of the form Rv = const. To obtain selection of one specific solution, an additional length scale must enter the problem.

In 1963, Mullins and Sekerka have shown that, in addition to the above difficulty, all of the Ivantsov solutions are linearly unstable (due to the diffusive instability), so none of them can be observed. Sensibly, the first attempts to resolve the stability problems were based on the assumption that incorporation of surface tension would involve only minor shape corrections of the Ivantsov parabolic fronts, while stabilizing all parabolas below a characteristic length scale. However , the selection problem remained inherent in this. In 1973, Oldfield [43] proposed that the selected dendrite was the one moving with the minimum speed (or maximum radius of tip) for which the surface tension can stabilize the underlying needle-crystal. Oldfield's idea was revived and elabo- rated in 1977 by Langer and Mul le r -Krumbhaar [44,45], who performed extensive calculations in order to find this marginally stable operating point.

At first, it seemed as if the selection problem had been solved [44]. However , this was not the case. One difficulty was that no reference to the anisotropic aspect of solidification had been made. Hence, different substances were predicted to share similar selected dendrites, which was obviously not the case. The problem of solidification had to wait six additional years before the next significant progress could be made, with the development of sufficient computing power and the subsequent application of more advanced mathe-


matical methods. The surprise was that, despite their small size, surface tension and surface kinetics are singular perturbations which may totally change the character of the interfacial dynamics; hence, the microscopic dynamics cannot be treated as a small correction to solutions initially determined from the macroscopic dynamics. When surface tension and surface kinetics are isotropic, dendritic growth does not occur. Instead, "tip-splitting" of growing fingers occurs, leading to the dense-branching morphology (fig. 1). Anisotropy is required in the interfacial dynamics to produce dendritic growth [46-53]. This picture is now confirmed by both experimental [54] and theoretical results

[3-51. The above can be understood as follows: Starting from a parabola (or any needle-crystal-like shape), if we "turn on"

the surface tension the tip becomes the coldest point along the interface. Heat flows along the interface toward the tip and causes it to slow down. At the same time, two points on either side of the tip will move faster, leading to the tip-splitting dynamics (this is the singular nature of surface tension). In order to avoid that and allow dendrites to form, the heat flow towards the tip must be suppressed. This is exactly the effect provided by the crystalline anisotropy (which is also a singular perturbation). For large enough anisotropy (of the order of 1 percent or so), the tip is no longer the coldest point along the needle-crystal, and as the anisotropy is increased the coldest point moves away from the tip to a point with a different growth direction. It leads to a rather subtle interplay between the anisotropy and the possible needle-crystal. For a given anisotropy, only a needle-crystal with the right tip velocity and tip curvature will feature the coldest point at the right temperature and the right distance from the tip (in terms of arc-length) to exactly balance the original tip-splitting dynamics. The result is that, instead of the original (Ivantsov) continuous family of parabolas, only a discrete set of needle-crystal solutions (with close to parabolic shape) can satisfy the subtle interplay, giving rise to a "solvability" criterion [3-5,55-63].

The heuristic argument and its mathematical treatment explain that, when anisotropy is included, steady state needle-crystal-like solutions can exist. But, how does this lead to dendritic growth composed of a needle-crystal trunk decorated with side-branches [64-69] and the observation of a specific dendrite? if we perturb the needle-crystal, say by introducing a bulge near the tip, the perturbation will grow as a result of the diffusive instability. The bulge grows outward at a fixed position in space, and when the tip advances the bulge moves backward relative to the tip. Only for the fastest needle crystal does the bulge move backward faster than its growth rate, so the tip restores its shape while the perturbation keeps growing. This mechanism results in decorating the fastest needle-crystal with the side branches, hence turning it into the observed


dendrite: the only one that can exist, only this specific dendrite can satisfy the competi t ion between the diffusive instability and the growth rate of the needle-crystal.

2. 4. Morphology selection and morphology transition

With the discovery of the new "microscopic solvability" criteria, the con- sensus was that the problem of dendritic growth was finally solved. There was already an understanding of the basic mechanisms controlling either dendritic growth or tip-splitting growth. Yet, this was far from being the full picture. For one, the new criteria referred only to the tip of an isolated dendrite. The dendrite is far from being just a "needle-crystal". It looks more like a "backbone" decorated with a complex structure of well developed side branches. Moreover , the stable phase forms many dendrites growing in a self- organized manner, to create the global structure or the morphology. Similarly, tip-splitting is only a basic element of the growth process that leads to the characterization of the resulting morphology. Hence, a new understanding, of how to go from the individual stem to the morphology in a self-consistent manner , and an appropriate characterization of the morphology are called for. At present, while the picture is not yet complete, we know the following: Both for dendritic growth and for the dense branching morphology (DBM), the growth is within a well defined envelope [39]. The latter is shape-preserving and propagates at constant velocity. For both cases, the morphology has a constant density that is set by the level of A.

In addition to the relation between the stem and the morphology, there is another nagging problem. According to the solvability criteria, as long as anisotropy is present, needle-crystal solutions exist for any value of undercooling za. However , in numerical simulations and in experiments it was found that, as the undercooling is changed at some critical value Ac, the emerging pattern is no longer dendritic. Instead, tip-splitting occurs [5,39].

The observation of the DBM under growth conditions, for which we know (according to the solvability criteria) that dendritic growth can exist, means that the two morphologies can theoretically coexist. Thus, the "microscopic solvability" can clearly be only part of the picture, and a more general principle is needed to distinguish between different morphologies and to determine the one to be selected. Ben-Jacob et al. [5,15-17] have proposed that the fastest growing morphology is the dynamically selected one. This means that if more than one morphology is a possible solution, only the fastest growing one is nonlinearly stable and will be observed.

It was proposed that, as the growth velocity measures the rate of approach

towards equilibrium, its average can serve as a response function. (By the term


"average velocity" one should refer to the velocity weighted according to the geometry of the interface, and thus take into account the global shape of the object.) A fundamental question that remains is whether the "average velocity" is the only variable, or whether there are two counterparts, one of them representing the branching dynamics and scaling, and the other on the microscopic level, representing the equilibrium properties of the interface and the selected growing stable phase. In other words, either the velocity plays an analogous role to the entropy (for systems in equilibrium), or it is the analog of the free energy [39,70].

The existence of a morphology selection principle implies the existence of morphology diagrams, in analogy with phase diagrams in equilibrium. For phases in equilibrium, for a given set of conditions, the phase that minimizes the free energy is the selected one, irrespective of the prior history of the system. The concepts of a selection principle and a phase diagram go hand in hand. By contrast, non-equilibrium growth processes are time dependent, so it is not clear a priori that a morphology diagram should exist (that is, that the shapes will depend only upon the growth conditions and not on the history). However, if it does exist, then a given morphology is reproducible for a given set of growth conditions and therefore a selection principle must exist. The existence of a morphology diagram has been confirmed experimentally in various systems, suggesting that a selection principle must exist. Whether this principle is the fastest growing morphology hypothesis remains to be seen [70].

The analogy with systems in equilibrium may be carried out even further. The existence of a morphology selection principle also implies the existence of morphology transitions. That is, a sharp transition between morphologies as we vary the growth conditions. Similarly, observation of a sharp transition between morphologies would imply the existence of a morphology selection principle. At present, there are many experiments in various systems that clearly demonstrate morphology transitions [5].

2.5. Changes in the microscopic organization during morphology transition

Just as the microscopic dynamics can determine the macroscopic morphology, so can the macroscopic dynamics reach down and affect the micro-structure of the growing phase. In other words, the macro-level and the micro-level organization have to be determined in a self-consistent manner. At present, there is no theoretical handling of the micro-level organization. Yet, we have much experimental data that lead to the emergence of a consistent singular feedback scenario.

Zinc is highly anisotropic, hence it usually does show dendritic growth, while copper, which has lower anisotropy, ordinarily develops into a DBM. The


different morphologies on the macroscopic scale go hand in hand with different micro-level organizations. In fig. 3 we show electron microscope pictures of zinc and copper grown in electro-chemical deposition. The zinc (fig. 3a) shows long range crystalline order and dendritic growth down to the micro lengtt

Fig. 3. Electron microscope view of zinc (a) and copper (b) grown via electro-chemical deposition. On the macro-level, (a) shows dendritic growth and (b) is a DBM.


e~

~.~. .~ =~ ..

• "~ 0

0 ...~ ~

" ~ 0

~ . ~ . . ~ _ = ~ - o ~ ' " ~ .

o ~.-~.~ ~ ~ . _

~ u~ .t3 0

~ . ~ - ~ .

~ ..~ ..0 . _ 0 0

• ,~ . ~ "*0 0

• ~ = -~


scales. The copper, on the other hand (fig. 3b), shows short range (tens of nanometers) Crystalline order and a different organization on the micro-level.

Similar changes are observed as we vary the growth conditions. In fig. 4 we show transitions during electro-chemical deposition [5,71]. The global structure changes go hand in hand with micro-level changes. For example, the black color of the DBM of zinc is due to the fact that it is made of about 100 ~ size crystallites with random orientation. The dendritic growth has a silver color typical of single crystal zinc. In other studies [72] it was also shown that under high applied voltage the zinc adopts a new super-lattice.structure.

The general scenario of the singular feedback indicates that, as we drive the system further from equilibrium in a manner that amplifies the micro-macro interplay, we observe a more complex global structure together with a higher level of micro-level organization. With respect to bacterial growth it means that we should expect the following: as the imposed growth conditions are more extreme and complex, better adapted growth will be that in which the bacteria interaction may lead to a higher level of micro-level organization.

3. Phenotypic vs. genotypic changes and current trends in the study of mutations: brief review

In the growth of a bacterial colony, the building blocks themselves are living systems (the individual bacterium) that can go through significant changes in response to imposed growth conditions. As we mentioned in the introduction, an essential goal in our studies is the clarification of the interplay between changes in individual bacteria and morphology transitions of the whole colony. In this section we briefly review the classical def ini t ions-with respect to bacteria - of phenotypic (noninherited) and genotypic (inherited) changes. We also describe another kind of change transgressing the classical s c h e m e - epigenetic inheritance [73,74]. These classifications are directly related to the assumed kinetics of mutations, so we describe also the conventional view of mutation kinetics as well as the recent novel trends in the study of mutations in the presence of selective pressures.

3.1. Phenotypic vs. genotypic changes

Bacteria with identical genetic phase, that is material, structure, conformation and function or state of activity (to distinguish from genetic code, which refers only to the DNA sequence), represent a specific genotype [23]. Each specific genotype can exhibit a spectrum of different characters and properties when exposed to different environments. These are defined as the phenotypic


expressions of the specific genotype. Accordingly, a genotypic change is a transition from one genotype to another, while a phenotypic change is a transition from one phenotype to another, both still belonging to the same genotype. A classical, or ideal, phenotypic change represents an adaptation of each individual to constraints imposed by the environment during its life-cycle. Ideally, all bacteria of a specific genotype will go through identical phenotypic changes when exposed to identical environmental constraints. The classical phenotypic change is also a reversible process: when the external conditions invoking the change are switched back to the original ones, the individual responds by changing back to its original phenotype.

The common definition of genotypic change is a change in the genetic code (referring usually to the DNA sequence). It exhibits a nondeterministic and undirected response of the genome. The decisive test in biology for identification of a change as being genotypic is on the molecular level. Alternatively, the following simple, but only approximate, test is commonly used: colonies of bacteria of both k i n d - t a k e n from samples before and after the c h a n g e - are grown under identical growth conditions. The appearance (physical structure, physical functions, etc.) of the bacteria in the two colonies is then compared. Similar appearance is correlated with phenotypic change, while different appearance is correlated with genotypic change. However, different genotypes may have phenotypes with similar appearance (phenocopy). Therefore , similar appearance for certain growth conditions does not prove that the two colonies belong to the same genotype, and the test has to be performed for a spectrum of growth conditions and many generations.

3.2. Epigenetic variations

In recent years there has been a renewed interest in those variations that do not accord with the classical identification of phenotypic and genotypic changes [73,74]. At present, there are yet neither generally accepted classifications of these variations nor accepted and satisfactory explanations for the entire spectrum of observations. The most commonly used concept in this connection is that of epigenetic variation. It is well known that different kinds of somatic cells (of eukaryotes) with the same genetic code (identical D N A sequence) maintain by heritage their different identities over many cell divisions. Such transfer of information is an example of epigenetic inheritance. Most generally, it is defined as any inheritance which is not transferred via the D N A sequence. That is, transfer of information encoded in the chromatin conformation, genes functional state, etc. [78]. Epi is also used to refer to information stored not

within the genome (agenetic). For example, there are unicellular organisms whose cortical structure serves as a nucleation center to initiate the same


structure in their progeny [74]. When the cortical structure of these organisms is modified, the modification can be inherited for a number of generations. The above mechanism is common in ciliates, and it might be that other agenetic inheritance mechanisms function in other organisms.

3.3. The conventional view o f mutation kinetics

A mutation, in its most general definition, is any detectable and heritable genetic change. However, commonly a mutation designates alterations in the DNA sequence, whereas other changes in the genetic phase are referred to as epimutations or epigenetic inheritance [74]. Mutations are also classified according to their causal mechanisms: spontaneous (naturally occurring) and tailored (by genetic engineering methods). Spontaneous mutations are assumed to occur randomly with close to uniform distribution. It is established experimentally that mutation probabilities (rates) per gene range within 10 -4 - 10 ~2. Ordinarily, it is assumed that the mutation rates are not affected by the environmental conditions (we refer to direct influences on the bacteria, and not induced changes in the DNA, i.e. via radiation).

At present, according to the conventional view, mutations are viewed as errors that occur spontaneously during the replication phase of the organism. During its life cycle, selective forces do determine the success of the mutant to survive and to transmit the mutated structure to future generations. Thus a clear dichotomy is assumed between the event of mutation and the process of selection.

3.4. Re-examining the conventional view

Recently, there have been new experimental observations, whose interpretation within the conventional view poses substantial difficulties. These have led to re-examination of basic preconceptions about mutation kinetics.

Back in 1984, Shapiro [24] undertook a pioneering step. He induced a specific tailored mutation that prevented the bacteria from consuming a certain nutrient. By exposing the bacteria to a large amount of that nutrient, pressure was exerted on the colony to undergo a specific mutation, in order to re-enable consumption of the available nutrient. He concluded from his observations that most mutants arise after the bacteria were grown on selective plates (prevent- ing usual consumption of nutrients and demanding specific mutations capable of consuming the available nutrients). Shapiro's measurements indicated that, under these selective constraints, the frequency of genetic mutations was higher by at least two orders of magnitude than the frequency under nonselective conditions.

Following Shapiro, Cairns et al. [25] (1988) also studied several types of


"appropriate" mutations during the growth of E. Coli colonies, and noticed higher mutation rates of advantageous mutants when exposed to specific constraints. The results have been further supported in recent experiments by Hall [27,28]. The new experiments might support the view that environmental constraints exert direct influence to increase the rate of advantageous mutations. Yet, at present, there is an ongoing controversy [76-78] as to what extent the experimental findings are sufficient and indeed call for reexamina- tion of the conventional view.

In section 7, we present the interpretation of our observations (discussed in sections 4, 5 and 6) using the concept of self-guided genome transformations.

4. Morphology diagram: phenotypic adaptation

4.1. Description of the basic morphologies

In fig. 5 we show three of the basic morphologies that we have observed: compact growth (like Eden [18,19,79]), tip-splitting growth (like DBM [15- 17]) and fractal growth (like DLA [11-14]). The observations can be summar- ized in a morphology diagram (as was studied by Fujikawa and Matushita [6,7]) as a function of nutrient concentration, temperature, humidity and agar level. As we have mentioned, the existence of a morphology diagram implies the existence of a morphology selection principle. The latter implies a selection of the colony as one unit. This assists in identifying the colony as a single organism.

For a given strain, the same morphology is reproducibly observed for the same growth conditions, irrespective of initial conditions (provided that no mutation occurred during inoculation). Microscopic studies reveal that the micro-level dynamics and the bacteria appearance are different for the different macroscopic morphologies. That is, each morphology is characterized by specific geometrical properties of its global structure (the compact growth is characterized by the fractal structure of its interface [19,79]; the tip splitting growth has a well defined shape-preserving envelope that advances at constant velocity [38,39,70]; the fractal growth is characterized by its fractal dimension#Z), as well as by a specific phenotypic phase of the micro-level. It means that the morphology selection involves a phenotypic adaptation that can lead to the better fitted self-organization according to the imposed growth conditions. Such adaptation reflects an interplay between individual and colony adaptation, which is the biological manifestation of the singular feedback explained for azoic systems. It is known that an isolated bacterium (Bacillus

~' Detailed studies of the geometrical properties will be presented in ref. I80]


Fig. 5. Three of the basic morphologies. (a) Eden-like growth. Grown on a high level of nutrients and relatively dry agar. (b) Dense branching morphology. (c) Fractal-like growth (low nutrients and dry agar). The initial dense growth in (c) resulted from initial higher humidity. Close up of tip-splitting growth. (d) and (e) show the tip-splitting dynamics via 2D and 3D views. (f) 500x magnification shows the individual bacterium after staining the colony.

sub t i l i s ) becomes longer and reproduces less f requent ly under condit ions of

p o o r nutr ients . U n d e r even more ext reme condit ions, it turns f rom a vegetat ive

m o d e to a spora. For the colony, it is advantageous to be more branching u n d e r condi t ions of poor flow of nutrients. Hence , the b a c t e r i u m - b a c t e r i u m

interact ion and the bacter ia density must be modif ied accordingly. The final o rgan iza t ion has to be selected via a solvability criteria (compromise be tween the var ious tendencies) , as we explain in the next section.

Microscopic studies of a D B M (fig. 5) show that, inside each of the colony tips (where mos t of the reproduc t ion takes place), the mot ion of the bacter ia


looks like a random motion of fluid molecules. Close to the boundaries, the motion is more organized. Further down the "finger" (older parts) the density of bacteria is higher, the movement is slower and the mean free path is much shorter. The individual bacterium has a rod-like shape (vegetation mode) of about 0.6 Ixm width and about 2-3 ixm in length. The length is sensitive to the level of nutrient concentration (longer for low concentration) and to the age of the bacteria (short for "old" bacteria). The motion of longer bacteria shows a higher degree of internal correlation. In the very old parts (non-active parts) of the colony, the bacteria turn into spora. The similarity between the tip-splitting dynamics and that of non-living systems indicates that there is a strong bacterium-bacterium interaction, which can be viewed as an effective surface tension and surface kinetics. In the limit of fractal-like growth, the motion of the bacteria seems to be organized in small cells. Hence, the envelope is less pronounced, and probably the effective surface tension is much smaller. In this limit, the diffusion length of the nutrients is much larger than the branch width and is comparable to the size of the system (or even longer). This is different from the DBM case, where the diffusion length can be smaller than the typical branch width.

4.2. Comment about the modeling

Here we are mainly interested in the range of parameters where the growth dynamics is via a cascade of tip-splitting, leading to a dense-branching morphology (DBM). As was mentioned earlier, for this range of parameters the growth is diffusion limited. Generally speaking, the reproduction rate which determines the overall growth rate is limited by the level of nutrient concentration available for the bacteria. The latter is limited by the diffusion of nutrient towards the colony. Hence, the process is similar to a diffusion-limited growth in other azoic systems, such as solidification from a supersaturated solution, solidification from undercooled liquid, growth in a Hele-Shaw cell, electro-chemical deposition, etc. However, there are at least two essential differences. First, the concentration field of the nutrient, c, extends into the colony. Second, the bacteria may secrete substances whose concentrations could affect the dynamics of the bacteria, including the formation of a well-defined envelope. For a given phenotypic phase of density p (as projected on 2D) and a single secreted substance with concentration u, the model has the following typical structure:

0p =V[Do(u, Vu, p, Vp) Vpl + r(o, Vp, c) (5) Ot au 0~- = D"VZu + s(p, u, c), (6)


O__~c = DcV2C + f ( p , /), Vp, c) (7)

Ot

where Do(u , Vu, p) , D u and D c are the diffusion parameters of the bacteria, the secreted substance and the nutrient, respectively. The functional form of D o plays a crucial role in determining the dynamics. Its dependence on u can lead to a collective motion. The dependence on p can reflect direct physical bacterium-bacterium interaction (e.g. via long protein molecules). The rate functions r, s and f represent reproduction of the bacteria, production of the secreted substance and food consumption, respectively.

In a forthcoming publication [81] we present a study of a simplified version of the model, assuming that u is proportional to p and that the rate functions do not depend on gradients. That is

0 p = at V[Do( P ) Vp] + r(p , c) , (8)

Oc = DcV2 c + f ( p , t3, c) . (9) Ot

To include the possibility for different phenotypic phases we have to add a field q~ (order parameter) that represents the various phenotypic phases. In this case, Dp and the rate functions all become functions of q~, whose time dependence is given by

cqt = D't 'V2~ + g((/)' C) . (10)

The function g is derived from a potential like G(q~, c). The minima of G represent the various phenotypic phases. Hence, G represents the selectivity of the environment with respect to the phenotypic phases. For given growth conditions, the time evolution of the model will select simultaneously a morphological structure together with the most appropriate phenotypic phase. Therefore, it will describe phenotypic adaptation of the colony.

Above, we described continuous models. A complementary approach (as is the case in the study of interfacial pattern formation in azoic systems) would be to develop "atomistic", or discrete versions of the models. The latter is more efficient in the study of highly decorated morphologies. In our preliminary studies, we found the recently developed diffusion-transition scheme [38,39,70] to be a very useful additional approach.

4.3. Dendri t ic growth

An essential part of the new understanding of interfacial pattern formation


in azoic systems has to do with the role of anisotropy. Anisotropy is needed in order to have dendritic growth rather than a cascade of tip-splitting. In the case of solidification, the anisotropy is provided by the symmetry of the crystalline structure of the growing phase (the solid). In the Hele-Shaw experiment, anisotropy was imposed via engrooved channels on one of the plates. In other Hele-Shaw experiments, anisotropy was imposed locally at the growing tip via small droplets [82] or inserting a string in the fluid [83]. These experiments demonstrated that, irrespective of the form of the imposed anisotropy, it can lead to a similar dendritic growth. Hence, an additional important test of the similarity of bacterial growth to interfacial pattern formation would be to impose anisotropy on the growth of the bacteria, and to look for dendritic growth.

As a first step, we have imposed anisotropy via ripples on the agar. When the agar is dried rapidly, wrinkles and ripples are formed as shown in fig. 6a. When pronounced, they channel the growth of the colony (fig. 6b) and provide anisotropy sufficient for dendritic growth. In fig. 6c,d we show some examples of bacterial dendritic growth similar to those developed in non-living systems. Microscope studies of dendritic growth show higher level of coordination in the bacterial movement.

The results provide additional support to the similarity between bacterial growth and interfacial pattern formation in non-living systems. They demonstrate that singular perturbation and singular feedback do play a crucial role during the growth of bacterial colonies. The ripples on the agar break the symmetry in the motion of only few bacteria, in the immediate vicinity of the ripples. Yet, this minute asymmetry (or local anisotropy), being a singular perturbation, is sufficient for the existence of dendritic growth. At the same time, via the singular feedback, the macroscopic dendritic growth leads to a correlated motion of the bacteria on the micro-level in other parts of the colony. Recently, we have found a way to impose controlled anisotropy on the surface of the agar. Preliminary results show that indeed it leads to dendritic growth for a certain range of growth conditions. So, currently we are searching for the optimal conditions that will lead to the most pronounced dendritic growth.

4.4. M o r p h o l o g y transitions due to pheno t yp i c changes

In section 2 we have explained that the existence of a morphology selection principle implies sharp transitions between the growing morphologies, as we vary the growth conditions. Observations of morphology transitions during the growth of the bacterial colony is perhaps the most crucial test for the similar aspects with interfacial pattern formation in azoic systems. In many cases,


Fig. 6. (a) Examples of ripples on agar that was dried rapidly. (b) Adjustment of growth (on the macro level) to the ripples on the agar. (c) and (d) Examples of dendritic growth of the bacterial colony resulted from spontaneous anisotropy.

s p o n t a n e o u s m o r p h o l o g y t rans i t ions were obse rved . These t r ans i t ions , which

a re r e m i n i s c e n t of the H e c k e r t r ans i t ion [71] o b s e r v e d dur ing e l ec t ro -chemica l

d e p o s i t i o n , resu l t f rom changes in the humid i ty and nu t r i en t c o n c e n t r a t i o n


Fig. 7. Phenotypic transitions: (a), (b) spontaneous; (c) induced by temperature change (taken out of the incubator); (d) induced by increasing the nutrients level.


during growth. The transitions are very sharp and extended, that is, they occur simultaneously all around the morphology front (fig. 7). Re-inoculation of either morphologies (before and after the transition) on the same agar plate leads to the same morphology, irrespective of origin (fig. 8). Hence, we

Fig. 8. Testing the transition. Shows similar growth for reinoculation from two morphologies (before and after the transition) for various growth conditions: (b) and (d) low level of nutrient; (a) intermediate level; and (c) high level.


identify the transitions as phenotypic morphology transitions (see appendix B for more details).

For controlled phenotypic transitions, we varied either the temperature or the nutrient concentration. The former was done by placing the agar plates outside the incubator in the middle of growth. For the latter we have started the growth on low-nutrient agar. Then (after the colony reached 1 ~-~ of the

plate radius) we added high-nutrient agar along the outer boundaries of the

petri dish. The existence of a morphology diagram and the sharp transitions between

the morphologies imply the existence of a morphology selection principle that governs the bacterial growth. The latter provides a biological adaptive force with respect to phenotypic changes, and a biological selective force with respect to genotypic changes (next section). Revealing the nature of the selection principle is one of our future tasks. Yet, as we show in sections 5 and 6, the preliminary observations hint that it is similar to the "fastest growing morphology" principle proposed for azoic systems.

S. Bursts of new morphologies: genotypic adaptation

5.1. Description of the phenomenon

In fig. 9 we show a novel phenomenon observed during growth of the bacterial colony, which is not observed in non-living systems. A new morphology bursts at a localized point along the advancing front of the colony. The new morphology has higher growth velocity, outgrows the original morphology and becomes the dominant one. The bursts were observed when the original morphology slowed down as a result of decrease in the nutrient concentration or humidity (which occurs during the growth). The fact that the transition is localized suggests that it is not due to phenotypic change. In several cases (see appendix B for details) that we studied, re-inoculation of colonies, whose ancestors came from the original colony and from the burst, led to different growth patterns under the same growth conditions. Hence, while additional studies are needed, it is suggestive that the burst is due to a genotypic change, and the bursts of new morphology represent a genotypic adaptation of the colony. As the burst is the faster growing morphology, it appears that the morphology selection principle governing the bacterial growth (the biological selective force) is similar to the "fastest growing morphology" principle in azoic systems.

Not always do we observe a localized and sharp transition. In some cases the transition seems to be gradual. It appears that a new mutation starts at a given


Fig. 9. Bursts of new morphologies.


point, and thereafter, over a certain range, both genotypes coexist until, via composition competit ion, one of the genotypes becomes the dominant one. We expect this scenario to take place when both genotypes have similar adaptivity to the growth conditions. In other cases, due to a local variation in the growth conditions (agar thickness, humidity, etc.), a new genotype becomes locally dominant , but then it is outgrown by the original genotype.

At present, we do not know under which growth conditions a genotypic change is more likely than a phenotypic one. Moreover, in some cases we

Fig. 10. Simultaneous bursts.


observe simultaneous bursts (fig. 10) at a number of localized points along the growing front. Such behavior seems to be in between phenotypic and genotypic changes.

5.2. Comment about individual and colony adaptation and selection

Let us assume that the burst of a new morphology indeed results from a muta t ion of a new genotype. Each of the individuals of the new genotype is not necessarily bet ter fitted to the environment. The fact that the morphology of

the new genotype can grow faster (as a result of different bacteria movemen t and bac t e r ium-bac te r ium interaction) means that the colony as a whole is be t te r adapted to the imposed growth conditions. (In other words, the colony self-organization of the new genotype is bet ter fitted to the environment .) As a result, the new colony will outgrow the original one and will survive. Hence , we are facing a process of colony selection. It differs from the ordinary picture of natural selection of the individual in response to the environment , which is a crucial part in the current view of evolution. At present, there are two common strategies to study mutat ion dynamics: (i) selection applied to cells growing in liquid; (ii) immobilized cells covering an agar plate. In both cases, the study focuses on individual selection (recently, as was ment ioned in section 3, with emphasis on ext reme selective environment) . Diffusion-limited growth pre-

sents a new strategy for studying colony selection. Moreover , the observat ion of muta t ion during growth provides additional information about the time of occurrence of the mutat ions and spatial correlations.

For a manifestat ion of the burst of a new morphology, a finite size nucleation of the new genotype has to be formed. Hence, we are facing the question of nucleation rate of mutat ion vs. mutat ion rate. The simplest possibility is that the new mutant is stationary and has a reproduction rate which is much higher than that of the original genotype (which we do not think is the case). If this is true, a single mutant will directly lead to a finite size nucleation. On the other hand, if the new mutant is not stationary and has a reproduction rate comparab le to that of the original genotype, the transition from a single mutant to a finite nucleation calls for new theoretical inquiries. An interpretat ion in

accordance with the conventional view of mutat ion kinetics poses a difficulty. This being the case, it would be suggestive that an autocatalytic-like (mutation

in one bacter ium leads to mutat ion in its neighbors) process or co-mutat ions (mutat ions via genetic cooperat ion amongst several bacteria) seem to be opera t ive here, as we explain in section 7.

To conclude, it is crucial to moni tor o n the micro-level the burst of a new morphology. Relying on a spontaneous occurrence of a burst is not feasible. Instead, we intend to use micromanipulat ion to plant a single bacter ium of


different genotype and monitor the dynamics of mutation nucleation. It will also enable us to obtain information about the nature of the selection principle.

6. Chiral growth

6.1. Description of the morphology

In fig. l l a , b we show another interesting morphology that is observed during the growth of bacterial colonies - chiral growth, in which the colony consists of branches all having the same handedness of twisting. Chiral asymmetry (which was first discovered by Louis Pasteur) exists in the whole range from subatomic particles to human beings, and seems to have played an important role in the evolution of living systems [84, 85]. Hence, it is not surprising that bacteria display chiral property. Back in the seventies, Mendelson et al. showed [86-89] that long cells of Bacillus subtilis can grow in helices, in which the bacteria form long strings that are twisted around each other. These observations show that the bacteria possess chiral properties. In other observations they have

shown also that the chiral characteristics affect the structure of the colony. Our optical microscope observations indicate that during chiral growth the

colony consists of moving bacteria (unlike the static helices). The individual bacteria are longer than those in the case of tip-splitting growth, and have a string-like shape, but the individual ones do not show (on this level) chiral structure (fig. l l c ,d ) . In addition to the string-like bacteria we also observe some fraction of shorter rod-shaped ones. The leading parts (active parts) of the colony consist almost entirely of long bacteria. The micro-level dynamics show a slow swarming of the long bacteria. Unlike the case of tip-splitting growth, the motion is coordinated. The bacteria seem to move along parallel trails following each other. There is a pronounced tendency for twist, as if under the action of a force perpendicular to the motion (like a magnetic force acting on a moving particle). Hence, to model the growth one has to add a perpendicular drift term to the diffusion of p in eq. (5). For a defined handedness, the bacteria have to be able to distinguish between up and down. The growth in an upside-down petri dish shows the same chirality while colonies grown at the bot tom of the agar show the opposite handedness. Therefore , we think that the determination of up vs. down is done via the vertical gradient of the nutrient concentration.

Chiral growth is also observed in organic (but non-living) systems: 2D solidification of phospholipids consisting of single handed isomers [90-93]. The mechanism in which the micro-level handedness is transferred to the macro- level is not yet understood. It is important to note that the chiral behavior is


.=.

.=.

e . o

×

c q

o

v

o

E

0

e,,

e -

~ Z


not unique to the Bacillus subtilis. Such dynamics is also observed in other bacteria (such as Proteus [94]).

Next, we studied the dependence of the chiral morphology on the growth conditions. The motivation was to find out whether it exists for a specific range of parameters (growth conditions) on the morphology diagram. We found that this is not the case. Instead, it turned out that the occurrence is dependent on history: the results are different when we start from chiral growth or from tip-splitting growth, as explained below.

6.2. The transitions between chiral and tip-splitting growth

The generic transition from tip-splitting to chiral growth appears as a genotypic burst of the chiral morphology (fig. 12). The transition is fast and localized. We inoculated two colonies on the same agar plate, one from tip-splitting ancestors and one from chiral "parents". Both colonies grow as their ancestors, and keep doing it for many cycles of reinoculation (see appendix B for details). From the above observations one would conclude that the transition from tip-splitting to chiral growth is due to a genotypic change. In fig. 13, we show the reverse transition, that is, back from chiral to tip-splitting growth. This transition looks like a phenotypic change, as it occurs simultaneously over a finite fraction of the advancing front. Indeed, when we re-inoculate colonies from the chiral growth, and from the tip-splitting that originated from chiral growth, both evolve into a chiral morphology.

The above observations fit the classical identification of phenotypic and genotypic changes. However, we have the following additional observations (details are given in appendix B). (i) Non-symmetric but very frequent transitions between the same modes: tip-splitting growth and chiral growth. (ii) Extended and simultaneous genotypic transitions. (iii) Phenotypic change that becomes genotypic over time. We inoculated on one petri dish two colonies: a tip-splitting and a chiral. At the first stage, they each grew (at a certain level of nu t r i t i on - see appendix B) like their ancestors. At a later stage, at the same moment , simultaneous extended transition occurred in both colonies, to a ramified tip-splitting morphology. The tip-splitting that evolved from the chiral growth had similar appearance to the one that evolved from the original tip-splitting (fig. 14). Surprisingly, reinoculation from both outer regimes led to chiral morphology. Other studies we performed showed that the chiral genotype exhibits tip-splitting dynamics at certain growth conditions. Hence, the chiral to tip-splitting transition is phenotypic, but the transition from the (original) tip-splitting to the (new) tip-splitting is genotypic. The latter means that we have observed a simultaneous and extended genotypic transition. Another surprising result has to do with a time delay. The chiral-tip-splitting


Fig. 12. (a) and (b) show bursts of chiral growth from tip-splitting growth. (c) and (d) show a combinat ion of a phenotypic transition and burst of chiral growth from a single location.


Fig. 13. Spontaneous phenotypic transition from chiral growth to tip-splitting growth.

transition seemed to be modified over time. Inoculation from the tip-splitting that evolved from the chirai colony, more than two weeks later, led to a tip-splitting growth. Moreover, the phenotypic tip-splitting now shows (genotypic) tip-splitting growth for all the growth conditions that we have studied.

To conclude, we emphasize that the above are preliminary results and as such should be viewed as anecdotal observations, demanding more intensive study.

6.3. Comments about possible interpretations

The extended simultaneous genotypic transition can be explained according to the conventional view if we also add the element of composition competition. At an early stage of growth of the colony, a new genotype appears via ordinary mutation. From that point on, the colony is composed of two genotypes - say majority type A and minority type B. At a later stage a change occurs in the growth conditions, to which type B is better adapted. Hence, B becomes the majority type, and we observe a morphology transition. The composition competition can also explain the phenotypic change that was modified over time. For example, it is possible that after the new morphology stops expanding, genotype A becomes the dominant one in the vertical growth, and the composition changes again. However, the composition interpretation poses some difficulties. Under growth conditions of similar selectivity (the two pure colonies grow at the same rate) to the two genotypes we expect the morphology to consist in a combination of the two original types. We have observed such combined morphology when we performed dozens of reinocula-


Fig. 14. Extended transition from chiral growth and tip-splitting growth to a new tip-splitting growth. In both cases the new morphology has similar appearance. It also shows the differences between C and T during the initial growth. In (b) CT indicates a location at which a mixture of C and T was inoculated.

t i ons at s im i l a r s e l e c t i v i t y w i t h a m i x t u r e p r e p a r e d f r o m t h e t w o g e n o t y p e s ;

o t h e r w i s e th is was n o t t h e g e n e r i c case .

A n o t h e r i n t e r p r e t a t i o n , w h i c h is still w i th in t he c o n v e n t i o n a l v i e w , is t ha t t he

g e n o t y p i c c h a n g e s a r e ac tua l l y e p i g e n e t i c v a r i a t i o n s o r p h a s e v a r i a t i o n s . B o t h


have much higher rates than ordinary mutations rates. This can explain extended and simultaneous transitions. However , epigenetic variations exist over a finite number of generations, so one would expect a genotypic-like change that turns into a phenotypic one. Instead, we observe the reverse scenario. We also observed asymmetry in the transitions, while phase variations are symmetric.

If we are willing to go beyond the conventional view, there are numerous possible interpretations. For example, let us assume self-designed genetic changes guided by the environmental conditions which are brewing during the life cycle of the bacteria. Within the colony, part of the environment of each bacterium is its surrounding bacteria. Hence, we can expect synchronized and autocatalytic genetic changes or co-mutations that can lead to the observed extended transition (see next section and ref. [95]). In this case, the biological "selective forces" are the singular feedback mechanism for self-consistent mic ro -macro organizations.

As we have mentioned earlier, at present we lack sufficient information for strong support of the above or any other interpretations. Yet, it is sufficient to demonstrate that a new look at the phenotypic vs. genotypic changes is called for, and that the diffusion-limited growth of bacterial colonies combined with new understanding of pattern formation in azoic systems provide new tools for the study of adaptive self-organization and mutation in the presence of selective pressures.

7. Comment about the evolution of the theoretical framework

Since the classical experiments of Luria and Delbr/ick [96], mutations are commonly viewed as randomly occurring errors during the replication phase of the organism. There is a well-founded understanding at the molecular level of the occurrence rates of errors, and its predictions are consistent with the observed rates of mutation occurrence. These rates, regulated by internal molecular mechanisms, are assumed to be neutral with regard to the environmental conditions. The latter do present, however, selective forces acting on the various mutants during their life cycle. They determine which of the mutants is successful in survival. This dichotomy between mutation and selection, replication and life-cycle, is an essential part of the conventional view [77]. This is the framework used for the design and interpretation of most experiments in genetics. Yet, it has never been directly tested and demonstrated [24,25]. The Luria and Delbriick experiments as well as most of the following ones have actually demonstrated the existence of random mutations during neutral (nonselective) growth, but did not show it to be the only type, as


mutat ion rates during growth under selective pressures were not tested. Only recently new experiments (see section 3) were designed and performed to test this issue of growth in the presence of selective pressures. At present, there is an ongoing controversy [76-78] as to what extent the new experimental observations call for a different theoretical framework.

Our studies bring a new angle to this issue. As we explained above, diffusion-limited growth presented here belongs to the same general category of growth in the presence of selective pressures (the singular feedback acts as the biological selective pressure). In this sense the growth situation is compatible to the one in the recent studies of mutation kinetics under environmental pressures. We emphasize that most sides in the controversy agree that it is easier to interpret the results if one is willing to go beyond the conventional view of mutation dynamics. We are facing a question of strategy: should we avoid any new theoretical framework because of the fact that it yet lacks a specific molecular-level support? Or should we choose the theoretical framework that appears to provide the simplest explanation and then, in parallel, test it by characterizing the molecular-level mechanism that is needed and design experiments in order to reveal it? It is important to note that the conventional view was developed historically in a similar manner: The molecular mechanism was discovered after the development of the theoretical f ramework of mutation kinetics.

Let us assume that the current conventional view has a finite range of applicability. For example, assume that it is applicable as long as the selective pressures are below a certain level. Motivated by the preliminary observations, one may define a more extended theoretical framework within which further experiments will be designed. The results of the observations will then provide the basis for a new theoretical iteration, and so on. Abiding this strategy, and motivated by the experimental results mentioned in section 3 and by our own observations, we propose the following example for a plausible theoretical f ramework and an example of new implied experiments.

To extend the theoretical framework we make the following essential assumptions: (i) The genome-media has two basic roles. One is the well founded and accepted role as data storage device for the genetic information. Another role is information processing: it can perform information analysis (about the internal and external conditions) and accordingly perform designed changes in the stored information. That is, the genome can be viewed as an adaptive cybernetic unit. (ii) There are two basic kinds of mutations which reflect the two roles. The first are errors (in the information transfer) that occur during the replication phase of the bacteria and are not affected by the environment . The second kind are changes in the genome, self-guided by the adaptive constraints of the environment, that occur specifically for better


adaptation to the externally imposed conditions. (iii) Changes of the second kind brew during the life cycle of the organism.

During the growth of the colony, the environment of the individual bacterium is set by the colony dynamics and the bacter ium-bacter ium interaction (which can range from physical interaction to transfer of genetic material). Along the above assumptions, the colony organization (being the environment) can directly affect the genetic metamorphosis of the individuals. Hence, we expect to observe synchronized, autocatalytic and cooperative genetic variations of the colony, either spontaneous or in response to imposed growth

conditions.

8. Comment about further empirical enquiries

Prior to a serious search for molecular level mechanism, it is most desirable to design and perform more experiments on the macro-level for a crucial test of the new ideas. First we have to repeat the experiments presented here in a more quantified manner (detailed measurements of the growth rate, accurate geometrical characterizations of the morphology, especially the chiral one, etc.), more intensively and within a wider range of statistics. It is also important to test the generality of our observations on other kinds of bacteria. As a second step, it is important to perform the experiments proposed in sections 4, 5 and 6; especially to monitor the dynamics of mutation nucleation on the micro-level via continuous optical microscope observations. The following are a few of many examples for new experiments which will provide additional testing: (i) Diffusion-limited growth in combination with the experiments described in section 3. That is, growth on agar that consists of two types of food, say A (at low level) and B (at high level). One should start a colony of a genotype that can consume food type A, but cannot consume food type B unless it goes through a genotypic change. (ii) The same experiment as (1), but providing food B only to a confined area on the agar. (iii) Similar to (1), but with implementation of bacteria after the genotypic change (to a phase that can consume food B) in the original colony. These experiments should demonstrate if indeed the occurrence of a mutation compatible with food B is

synchronized and autocatalytic. In addition and perhaps and most exciting test would be to observe whether

imposed anisotropy will lead to a genotype that shows dendritic growth. We have seen that anisotropy exerts pressure on the bacteria towards coordinated motion on the micro-level, which is needed for dendritic growth. Would anisotropy direct a mutation whose new genetic property is co-ordinated motion? To find out, we should grow bacterial colonies in the presence of


imposed anisotropy, for several reinoculation cycles. We will then have to grow it under isotropic conditions. If a self-guided mutation did occur, the colonies should show dendritic growth under the new conditions. The empirical efforts call for further theoretical investigations both of the growth of colonies (via the models we have presented developments of new "atomistic" models, models for chiral growth, etc.) and of mutation kinetics and nucleation.

Let us close with some words on the nature of the research presented in this manuscript. The area of investigation will involve long term studies and a level of risk which is not faced in regular disciplinary activity. However, we believe that despite the risk, such an interdisciplinary approach has great potential for major new understanding. We hope that the new approach will stimulate additional empirical studies that will open new avenues for theoretical inquiries and further scholarly endeavors.

Acknowledgements

We are most grateful to Prof. M.J. Matsushita for many useful discussions and communicating with us his results prior to publications. We thank E.Z. Ron and J.A. Shapiro for introducing us to the "world" of bacterial growth and for their encouragement, many discussions and comments on our manuscript. We are thankful to G. Segal for his technical assistance in developing the straining procedure. Special thanks to O. Shmueli for her assistance in performing the experiments, her comments on the manuscript and many discussions. We have also benefited from conversations with Y. Aharanov, M.Y. Azbel, Y. Elkana, E. Jablonka, M. Kaiser, Y. Kantor, R. Kupferman, G. Landan, S. Lipson, R.G. Mintz, and M. Sternberg. E. Ben-Jacob and O. Shochet thank the KFA Jiilich for hospitality during part of this research. This research was supported in part by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development, and by the Program for Alternative Thinking at Tel-Aviv University.

Appendix A. Experimental methods

The experimental methods that we have used are very similar to those used by Fujikawa and Matsushita [6]. The bacteria were grown on agar substrate in standard plastic petri dishes with a diameter of 88 mm. The medium consisted of 5 g of sodium chloride, 5 g of tri-kaliumphosphat-3-hydrat (K3PO 4 • 3H20 ) and an amount of peptone (Bacto-peptone; Difco Laboratories) ranging from 0.4 g (poor nutrient) to 10 g (rich nutrient) and 15 g of agar (Bacto-agar; Difco)


in one litre of distilled water at pH 7.0 + 0.2. The mixture was autoclaved for 30 min. The agar is poured into the petri dishes (about 20 ml per plate). The

plates were dried at room temperature (23-25°C) for 24 to 48hours. The

amount of water evaporated was about 22% per day of drying determined by

weight measurement. The bacteria we used were Bacillus subtilis. Originally,

we have started the experiments with strain 168. Inoculation was on the surface

of the agar, usually at the center of the petri dish (unless more than one colony

was grown to study competition). The colonies were incubated in a closed

incubator at a temperature of 37 -+ 1.5°C. For photography, the colonies were stained with 0.1% Coomassie Brilliant

Blue R (Sigma Chemical Co.) in methanol:acet ic acid:distilled water

(50 :10 :40) . The strain was then washed using the same mixture without the

stain. Microscopic observations were performed using an optical microscopic (Olympus BH2-UMA) with ultra-long range objectives of up to 500x magnifi-

cation. For higher magnifications we used a scanning electron microscope,

utilizing the method developed by Shapiro [20].

Appendix B. Detailed description of the transitions

B. 1. Phenotypic changes

Tables I - I I I show three examples of testing a morphology transition for

being due to phenotypic change. The source plates (J30, K17 and V14) show

transition between two types of tip-splitting growth. Plates of poor (0.4 g/l) ,

Table I Source plate J30.

Plate I O

p5 T T 0.4 g/1 p6 T T growth within 4-6 days p13 T T p14 T T

q5 T T 2 g/1 q6 T T growth within 3-4 days q13 T a) T "~ q14 T T

u5 T T 5 g/l u6 T T growth within 1-2 days u13 T ") T ") u14 T T

~) Edges of the tips show slight chirality.

E. Ben-Jacob et al. / Adaptive self-organization during growth of bacterial colonies

Table II Source plate k17.

417

Plate I O

n6 T T 0.4g/l n8 T T growth within 3-5 days

k38 T T 2g/1 k39 T T growth within 1-2 days k40 T T

130 T T 5 g/l 134 T T growth within 1 day 135 T T

Table III Source plate V14.

Plate I H O

pl T T T 0.4g/l p2 T T T growth within 5-6 days p9 T T T pl0 T T T

ql T T T 2g/l q2 T T "~ T growth within 3-4 days q9 T T T ql0 T T T

ul T T T 5g/l u2 T T T growth within 1-2 days u9 T T T ul0 T T T

a) Changed into C after 5 days of growth.

m e d i u m ( 1 - 2 g / l ) and rich ( 5 - 1 0 g / l ) level of b a c t o p e p t o n e were i nocu la t ed

wi th b a c t e r i a f rom the or ig ina l m o r p h o l o g y ( d e n o t e d by I for inner) and f rom

the new m o r p h o l o g y ( d e n o t e d by O for ou te r ) . F r o m V14 we i noc u l a t e d also

f r o m a r eg ion of the or ig ina l m o r p h o l o g y , but ve ry close to the t r ans i t ion

( d e n o t e d by H ) . I n o c u l a t i o n of the co lon ies on the s ame pe t r i dish g u a r a n t e e s

s imi la r g r o w t h cond i t ions for bo th colonies . Some of the p la tes were d r i e d at

r o o m t e m p e r a t u r e for 24 hours , the o the r s were no t d r i ed at all. In all cases ,

the co lon ie s tha t g row on the same pe t r i dish had s imi lar a p p e a r a n c e (see fig.

11). Th is was also the case for o t h e r p h e n o t y p i c changes tha t we have s tud ied and a re no t r e p o r t e d here .

B.2 . Geno typ i c transit ions

In fig. 15 we shown an e x a m p l e of " t r e e " of a t ip -sp l i t t ing g rowth (T) and o f

ch i ra l g r o w t h (C) tha t b u r s t e d f rom it. The iden t i ty o f the m o r p h o l o g y , e i the r

418 E. Ben-Jacob et al. / Adaptive self organization during growth of bacterial colonies

Fig. 15. The "genotypic tree" used to identify genotype T and C. In all cases T and C led to T and C respectively. Plates (d), (f) and (v) are with 0.4g/l of peptone and plate (k) with 2g/l.

T or C, did no t change over five cycles of re inoculat ions and at different

nut r ien t levels. In addit ion to the " t ree- l ike" test, we have also pe r fo rmed tests

of isolated colonies inoculat ion, after the bacteria were first placed in a liquid

env i ronmen t . These results suppor t the identification of T and C as two dif ferent genotypes .

B.3 . The chiral- t ip-spl i t t ing transition

In figs. 13 and 14 we show some examples of the chiral growth to tip-splitting g rowth transitions. T h e y look a spon taneous phenotyp ic changes. In fig. 16 show two examples for inoculat ions on the same plates f rom the two morphologies , before and after the transition. As we can see, bo th colonies show similar chiral growth. Such similar appearance is characterist ic of pheno typ ic

changes . In table IV we show an example of one test f rom a source plate (D12) . The

lat ter had a s t ructure similar to that shown in fig. 14a. The points T, C i and C o deno t e inoculat ions f rom the inner par t of the tip-splitting growth, the inner


Fig. 16. Examples for testing the chiral to tip-splitting transition. (i) and (o) indicate inoculations from regimes before and after the transition.

pa r t o f the chiral g rowth and the ou te r par t of the chiral g rowth (after it c h a n g e d to t ip-spli t t ing growth) , respect ively. In fig. 17 we show examples of the resul ts of the test at a low nutr ient level (chiral g rowth is p re fe r r ed ) . It c lear ly shows that the inoculat ions f rom C i and C O lead to morpho log ie s with s imilar a p p e a r a n c e , while the inocula t ion f rom T leads to t ip-spli t t ing growth.


Table IV

Source plate d12 ( l s t experiment).

Plate T C~ Co

j4 - C -

j5 - - c j6 T C C

j7 T C C j8 T C C

k4 - C -

k5 T C C k6 T C C

k7 T C C

k8 T C -

15 - - C

16 T C T (?)

17 T C C 18 T - -

i2 T ? C i3 T ? C

i4 T C C(?) i5 9 ? C

0.4 g/I

2 g / I

5 g / I

? means partial or total loss of information due to overgrowth. - m e a n s no innoculation from a specific zone.

According to this test, it seems that T and C are different genotypes and the chiral to tip-splitting transition is due to a phenotypic change.

Table V shows a surprising result. We have repeated the same test as shown in table IV more than two weeks later. This time the chiral to tip-splitting transition assumed a genotypic character. It seems as if the phenotypic change turned into a genotypic one over time. Similar results were obtained from all the other plates that we have tested.

Table V

Source plate d12 (2nd experiment; after 19 days).

Plate C~ C,,

w13 C - 0 . 4 g / l

w14 C - growth within 3 days w15 C -

x13 C T 2g/1 x19 C T growth within 2 -3 days x20 C T

y13 C T 5 g / l y14 C T growth within l day y15 C T


Fig. 17. Innoculations from inner parts of tip-splitting growth T chiral growth C and tip-splitting growth that evolve from chiral growth CT. Both plates have 0.4 g/l of peptone. The relative sizes of T and C indicate that the chiral morphology is the biologically preferred one for these growth conditions.

B. 4. Ex t ended geno typ ic transition

As shown in fig. 14, the tip-splitting growth that evolved f rom the chiral g rowth had the same appearance as that which evolved f rom the tip-splitting growth . First we though t that bo th transit ions were due to phenotyp ic changes , and it was simply an example of p h e n o c o p y ( two different genotypes with

similar phenotypes) . The surprise was that indeed it is a p h e n o c o p y , but reverse than expected. The tip-splitting growth turned into geno type C and the


Table VI Source plate d17.

Plate 3 4 5

p19 C T C 0.4g/l p20 C T C growth within 3-4 days

q19 C T C 2g/I q20 C T C growth within 2-3 days

u19 C T C 5g/l u20 C T C growth within 1-2 days

chiral growth into geno type T. O n e example is shown in table VI, where po in t

3 is the i nne r par t of the chiral growth, and points 4 and 5 are the ou te r

regimes of the chiral and t ip-spli t t ing growth, respectively. As the t rans i t ions

were ex t ended (figs. 13-14) , it means that we have observed s imul t aneous and

e x t e n d e d genotypic t ransi t ions .

Note added in proof

Afte r the submiss ion of this manuscr ip t for publ ica t ion , we lea rned abou t the

fol lowing references: J .A. Shapiro , G e n o m e s as smart systems, Gene t i ca 84

(1991); Na tura l genet ic eng inee r ing in evolu t ion , Gene t i ca (1992), in press.

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