Multisite protein phosphorylation - from molecular mechanisms to kinetic models

REVIEW ARTICLE

Multisite protein phosphorylation – from molecularmechanisms to kinetic modelsCarlos Salazar and Thomas Hofer

Research Group Modeling of Biological Systems (B086), German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, Heidelberg,

Germany

Introduction

Signal transduction networks are formed, in large part,

by interacting protein kinases and phosphatases.

Phosphorylation of proteins by kinases (or dephosphor-

ylation by phosphatases) provides docking sites for

interaction partners or triggers conformational changes

that alter a protein’s enzymatic activity or its

interactions with other proteins or DNA. These altered

enzymatic and ⁄or interaction properties may transmit

signals in various ways. For example, protein kinases

activated by phosphorylation can themselves phosphor-

ylate target proteins (e.g. receptor ⁄ receptor-associatedtyrosine kinases, mitogen-activated protein (MAP)

kinase cascades). Phosphorylation status can deter-

mine the subcellular localization of a protein (e.g. by

Keywords

enzyme processivity; kinetic proofreading;

mathematical models; order of phospho-site

processing; ultrasensitivity

Correspondence

C. Salazar, Research Group Modeling of

Biological Systems (B086), German Cancer

Research Center (DKFZ), Im Neuenheimer

Feld 280, 69120 Heidelberg, Germany

Fax: +49 6221 54 51487

Tel: +49 6221 54 51383

E-mail: [email protected]

T. Hofer, Research Group Modeling of

Biological Systems (B086), German Cancer

Research Center (DKFZ), Im Neuenheimer

Feld 280, 69120 Heidelberg, Germany

Fax: +49 6221 54 51487

Tel: +49 6221 54 51380

E-mail: [email protected]

(Received 15 January 2009, revised 4 March

2009, accepted 27 March 2009)

doi:10.1111/j.1742-4658.2009.07027.x

Multisite phosphorylation is an important mechanism for fine-tuned regula-

tion of protein function. Mathematical models developed over recent years

have contributed to elucidation of the functional consequences of a variety

of molecular mechanisms involved in processing of the phosphorylation

sites. Here we review the results of such models, together with salient

experimental findings on multisite protein phosphorylation. We discuss

how molecular mechanisms that can be distinguished with respect to the

order and processivity of phosphorylation, as well as other factors, regulate

changes in the sensitivity and kinetics of the response, the synchronization

of molecular events, signalling specificity, and other functional

implications.

Abbreviations

ASF ⁄ SF2, alternative splicing factor; BAD, Bcl-XL ⁄ Bcl-2-associated death promoter; CDK, cyclin dependent kinase; DYRK, dual-specificity

tyrosine-regulated kinase; EGF, epidermal growth factor; ERK, extracellular signal-regulated protein kinase; ITAM, immunoreceptor tyrosine-

based activation; MAP kinase, mitogen-activated protein kinase; MEK, MAPK ⁄ ERK kinase; N-WASP, neuronal Wiskott–Aldrich syndrome

protein; NES, nuclear export signal; NFAT, nuclear factor of activated T cells; NLS, nuclear localization signal; PDE3B, cyclic nucleotide

phosphodiesterase 3B; RS, arginine-serine repeats; SH2 domain, Src homology 2 domain; SP, serine–proline repeat; SRPK, serine-arginine-

rich protein kinase; SRR, serine-rich regions; TCR, T-cell receptor; ZAP-70, zeta-chain-associated protein kinase 70.

FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3177

controlling nuclear import ⁄ export in Janus kinase/

signal transducer and activator of transcription (Jak/

Stat) and nuclear factor jB (NFjB) pathways). In tran-

scriptional regulation, phosphorylation events control

the binding of specific transcription factors to their regu-

latory sequence elements, as well as the action of RNA

polymerase. Proteins can also be targeted for degrada-

tion through multisite phosphorylation (e.g. the yeast

cell-cycle regulator Sic1).

Phosphorylation affects a very large number of intra-

cellular proteins, and is arguably the most widely stud-

ied post-translational modification [1]. An important

(and as yet not fully resolved) question in this regard is

how many of the observed protein phosphorylation sites

are specifically regulated and serve a regulatory function

[2]. Given that there are approximately 500 protein

kinases in the human genome [3], which are themselves

regulated by and have in all likelihood at least one spe-

cific target, the number of regulatory phosphorylation

sites must be in the thousands or even higher. It is thus

not surprising that abnormal protein phosphorylation

events have been observed in many human diseases,

including cancer, diabetes, hypertension, heart attacks

and rheumatoid arthritis [1].

Phosphorylation ⁄dephosphorylation has been con-

sidered as a fundamental on ⁄off switch for protein

function. In the last decade, however, it has become

clear that many proteins harbour multiple phosphory-

lation sites, and this can considerably expand the

repertoire for combinatorial regulation or fine-tuning

of switch properties [4–6]. Phosphoproteome analyses

have shown that most phosphoproteins in eukaryotic

cells contain more than one phosphorylatable site [7]

(Phospho.ELM database, http://phospho.elm.eu.org).

Several proteins with 10, 20 or even more (regulatory)

phosphorylation sites are known [6,8]. Multiply phos-

phorylated proteins are found in a great variety of

cellular processes; they include membrane receptors

(e.g. growth-factor receptors [9] and the T-cell receptor

complex [10]), ion channels (e.g. the Kv2.1 potassium

channel in mammalian neurons [11]), protein kinases

(e.g. MAP kinases [12,13] and Src family kinases [14]),

adaptor proteins (e.g. SH2-domain containing leuko-

cyte protein of 76 kDa [15], Vav [16] and LAT linker

of activated T cells [17] in hematopoetic cells), cell-

cycle regulators (e.g. Sic1 [18], Cdc25 [19] and Sld2

[20] in budding yeast), circadian clock proteins (e.g.

frequency protein, FRQ [21] in the bread mold Neuro-

spora), transcription factors (e.g. Pho-4 in budding

yeast [22] and nuclear factor of activated T cells

(NFAT) in mammalian cells [23]), transcriptional coac-

tivators (e.g. PC4 [24]), RNA polymerase II [25],

histones [26], splicing factors [27], and others. Overall,

serine phosphorylations are the most abundant

(approximately 86% of all phosphorylation sites in

HeLa cells), followed by threonine (12%) and tyrosine

phosphorylations (2%) [7]. With respect to kinetics,

tyrosine phosphorylations generally occur faster during

cell signalling than serine ⁄ threonine phosphorylations.

For example, upon addition of epidermal growth

factor (EGF) to HeLa cells, most tyrosines become

phosphorylated within 1 min, while threonine and

serine phosphorylations require up to 10 min [7].

Compared to phosphorylation of a single residue,

multisite phosphorylation increases the possibilities for

regulating protein function very considerably. A protein

with N phosphorylation sites can exist in 2N phosphory-

lation states. Each such state may have a different func-

tional characteristic. For example, the Src family

kinases have at least two regulatory Tyr phosphoryla-

tion sites, one activating and the other inhibitory, so

that there are four (22) different phosphorylation states

of these residues. Accordingly, Src kinases may exist in

several distinct states of enzymatic activity (additionally

depending on protein–protein interactions, some of

which are also governed by phosphorylation) [14]. On

the other hand, for larger N, the number of possible

states becomes so high that it is unlikely that each one

has specific functional properties (e.g. for N = 10, there

are 1024 phosphorylation states). The reduction of such

high-dimensional phosphorylation state spaces to a

smaller number of functional states may occur on two

levels. First, the molecular mechanisms of phosphoryla-

tion may realise only a subset of the possible states. For

example, for a strictly sequential phosphorylation mech-

anism (and reverse-order dephosphorylation), there are

only N + 1 phosphorylation states instead of 2N. Sec-

ond, several individual phosphorylation sites may coop-

erate in effecting a functional outcome (e.g. through a

conformational change), such that it is primarily the

number of phosphorylated sites that counts rather than

their specific location. Both types of dimensionality-

reduction mechanisms do indeed occur in protein

phosphorylation, as detailed below. Nevertheless the

occurrence of many phosphorylation states (especially

in random phosphorylation ⁄dephosphorylation mecha-

nisms) is an important factor shaping both dose–

response curves and kinetics.

These rather basic considerations already make it

clear that in-depth analysis of the mechanisms and

functions of multisite protein phosphorylation requires

mathematical modelling. Both general mathematical

analyses of multisite phosphorylation [28–36] and

models of specific systems [12,13,37–46] have bee pub-

lished in recent years. Here we review these theoretical

developments within the context of salient experi-

Multisite protein phosphorylation C. Salazar and T. Hofer

3178 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS

mental findings on the molecular mechanisms of protein

regulation by phosphorylation. This comparison high-

lights several questions for further modelling as well as

experiments required for progress in the quantitative

understanding of multisite protein phosphorylation.

Biological model systems

To provide a background for the theoretical section,

we briefly introduce three experimental model systems

that highlight various mechanistic and functional

aspects of multisite phosphorylation.

Recruitment and activation of signalling proteins

at plasma membrane receptors

In response to extracellular stimuli, many plasma

membrane receptors are phosphorylated at multiple

tyrosine residues that provide docking sites for signal-

ling proteins. A particularly intriguing example is

signalling through the T-cell receptor (TCR) complex.

The subunits of the TCR together contain 20 regula-

tory tyrosine residues located pairwise in ten immuno-

receptor tyrosine-based activation (ITAM) motifs [10].

Following binding of a cognate ligand (an antigen–

major histocompatibility complex), these tyrosine resi-

dues become phosphorylated by the Src kinase Lck,

and in turn another tyrosine kinase, zeta-chain-asso-

ciated protein kinase 70 (ZAP-70), binds strongly to

ITAMs containing two phosphotyrosines (Fig. 1A).

The recruited ZAP-70 adopts an open conformation,

and becomes activated by several tyrosine phosphory-

lations (catalysed by Lck and by ZAP-70 trans-auto-

phosphorylation). These events form the beginning of

a cascade of phosphorylation events that are thought

to be critical for a T cell’s ability to discriminate

between a cognate antigen (triggering an immune

response) and self-peptides (for which a response

would be detrimental) [10,47].

Nuclear transport and DNA binding of

transcription factors

Multisite phosphorylation regulates the activity of tran-

scription factors at several levels, such as subcellular

localization, DNA binding affinity and transcriptional

activity (reviewed in Ref. [6]). An example of such multi-

level regulation is provided by the transcription factors

of the NFAT family, NFAT1–4, which reside in the

cytoplasm of unstimulated cells in a highly phosphory-

lated state (Fig. 1B) [48,49]. In response to calcium-

mobilizing stimuli, several conserved serine residues (13

in NFAT1), located in serine-rich regions (SRR) and

serine–proline repeats (SP), are dephosphorylated by

calcineurin [23]. In NFAT1, dephosphorylation of the

SRR1 motif (and possibly also of the SP2 and SP3

motifs) induces exposure of a nuclear localization

sequence (NLS), promoting nuclear import of NFAT.

Full dephosphorylation is needed for maximal DNA

binding of NFAT. Dephosphorylation of NFAT by cal-

cineurin is counteracted by several kinases, among them

CK1, GSK3 and dual-specificity tyrosine-regulated

kinases (DYRKs). Experiments suggest the existence of

a preferential order of phosphorylation and dephos-

phorylation. DYRKs phosphorylate the SP3 motif, thus

Fig. 1. Prototypical examples of multisite phosphorylation in signal

transduction and cell-cycle regulation. (A) Receptor proteins. Bind-

ing of a high-affinity ligand to the T-cell receptor (TCR) leads to

phosphorylation of ITAM motifs at two tyrosine sites, to which the

kinase ZAP-70 binds via its tandem Src homology 2 (SH2) domains.

(B) Transcription factors. Dephosphorylation of the transcription fac-

tor NFAT (nuclear factor of activated T cells) by calcineurin (CaN) at

several Ser residues induces a conformational change that exposes

a nuclear localization signal (NLS), leading to nuclear localization of

NFAT, its binding to DNA, and maximal transcriptional activity.

NES, nuclear export signal. (C) Cell-cycle inhibitors. The cell-cycle

inhibitor Sic1 requires phosphorylation by the cyclin-dependent

kinase Cdc28 on at least six sites before it can be ubiquitinated by

the Cdc4 ⁄ SCF complex and degraded by the 26S proteasome.

C. Salazar and T. Hofer Multisite protein phosphorylation


priming further phosphorylation of the SP2 and SRR1

motifs by GSK3 and CK1, respectively [50]. Dephos-

phorylation of the SRR1 motif appears to increase the

accessibility of the SP motifs to calcineurin [23]. NFAT

kinases are activated by distinct signalling pathways,

and may be differentially regulated in the cytoplasmic

and nuclear compartments.

Cell-cycle regulation

Multisite phosphorylation is prominent in regulation

of the cell cycle, in particular at the G1 ⁄S transition.

In yeast, the cyclin kinase inhibitor Sic1 must be phos-

phorylated on at least six of nine Ser ⁄Thr residues by

a cyclin-CDK complex during G1 phase before binding

to the SCFCdc4 ubiquitin ligase [18,51,52]. This, in

turn, leads to ubiquitination of Sic1, its degradation

by the proteasome, release of the S-phase cyclin-depen-

dent kinase from inhibition, and, finally, the onset of

DNA synthesis (Fig. 1C). The number of phosphory-

lated sites appears to be more important than the iden-

tities of the individual residues for SCFCdc4 binding.

Any combination of six phosphorylated sites is suffi-

cient for Sic1 degradation. While singly phosphory-

lated Sic1 binds to SCFCdc4 very weakly, multiply

phosphorylated Sic1 can bind efficiently, presumably

by increasing the local concentration of interaction

sites around the SCFCdc4 binding surface. It has been

suggested that multisite phosphorylation can act as a

counting mechanism that ensures the proper timing of

critical cell-cycle transitions [51]. Interestingly, another

multiple protein modification, multi-ubiquitination,

also plays a central role in the cell cycle [53].

Quantitative data

Experimental data on the dynamics of key phosphory-

lation events in signal transduction and other cellular

processes are essential for the development of accurate

quantitative models and therefore for a mechanistic

understanding of cellular behaviour. Biochemical

approaches, such as immunoblotting with phospho-

specific antibodies, are routinely used for monitoring

(previously identified) phosphorylation sites, and many

studies based on this technique have yielded valuable

mechanistic insight (e.g. [54]). Mathematical modelling

frequently requires quantitative information (e.g. what

fraction of a given protein is phosphorylated) that is

cumbersome to obtain in this way. Higher throughput

can be achieved with antibody microarrays [55], while

flow cytometric analysis of intracellular phosphopro-

teins provides single-cell resolution and high sensitivity

that cannot be achieved with immunoblotting [56].

However, all these methods require appropriate anti-

bodies to known phosphorylation sites. Radionucleo-

tide incorporation experiments may also provide

accurate information about phosphorylation kinetics

[27], but are time-consuming to perform. Mass spec-

trometry allows both large-scale analysis and the

identification of novel phosphorylation sites and phos-

phoproteins not previously known to be involved in

cellular signalling [7,8,57]. Information about phos-

phorylation sites obtained in large-scale screens has

been incorporated into searchable databases such as

Phosphosite (http://www.phosphosite.org), Swiss-Prot

(http://us.expasy.org/sprot) and Phospho.ELM (http://

phospho.elm.eu.org). Mass spectrometric data for

protein phosphorylation may be very useful for kinetic

analysis and modelling, although rather few applica-

tions exist to date (e.g. [7, 23]). Time-resolved high-

resolution NMR spectroscopy has been used recently

to study mechanistic questions regarding multisite pro-

tein phosphorylation [58,59]. We discuss below which

type of data are required to establish kinetic models.

Molecular mechanisms of multisitephosphorylation

The presence of multiple phosphorylation sites raises

new mechanistic questions compared to the case of sin-

gle phosphorylation. These pertain to (a) the order in

which individual sites are phosphorylated and (b) the

number of enzyme binding events required. A third

mechanistic aspect, which is relevant both for

single- and multisite phosphorylation, is whether the

counteracting kinase(s) and phosphatase(s) compete

for binding to the target protein. We also discuss how

cooperativity can arise in multiply phosphorylated

proteins, and the role played by subcellular compart-

mentalization.

Order of phospho-site processing

The order in which phosphorylation sites in a protein

are acted on by kinases and phosphatases determines

the possible phosphorylation states (Fig. 2A).

Although it has generally been difficult to obtain such

information experimentally at the required resolution,

inferences have been drawn regarding the order of

phospho-site processing in several cases. Sequential

phosphorylation has been suggested for several kinas-

es, especially Ser ⁄Thr kinases [60–68]. When dephos-

phorylation also follows a fixed order, strictly

sequential or cyclic mechanisms of phosphorylation

arise, depending on whether the last site to be phos-

phorylated is the first, or the last, to be dephosphoryl-



ated. Both types of mechanism have been proposed,

one for NFAT and the other for rhodopsin [38,69].

Alternatively, a particular site may be modified irre-

spective of the phosphorylation state of the other sites,

giving rise to essentially random phosphorylation and

dephosphorylation.

Combinations of random and sequential mechanisms

are possible. For example, it is conceivable that phos-

phorylation of a protein is random while dephosphory-

lation is sequential, e.g. for the MAP kinase ERK2

[41,70,71]. A particularly interesting mixed case has

been suggested for the yeast cell-cycle regulator Sld2,

Fig. 2. Mechanistic aspects of multisite phosphorylation. (A) Order of phospho-site processing. Phosphorylation sites can be modified fol-

lowing a strict order. The last site to be phosphorylated may be the first (sequential mechanism) or the last (cyclic mechanism) to become

dephosphorylated. Alternatively, the sites can be modified in a completely random manner. In some cases, multiple sites must be randomly

phosphorylated before a site with a specific function becomes accessible to the kinase (hierarchical mechanism). (B) Enzyme processivity.

The enzyme can modify all the sites without intermediate dissociation from the substrate (processive kinetics), or, conversely, must bind

and dissociate repeatedly before all residues become phosphorylated (distributive kinetics). (C) Competition effects. At low enzyme concen-

trations, the distinct phosphorylation forms of the substrate may compete for binding the enzyme, while counteracting enzymes may

compete for binding the substrate at low substrate concentrations. (D) Conformational changes and cooperativity. The dynamic equilibrium

between distinct functional conformations may be affected by the phosphorylation state of the protein. In the example shown, phosphoryla-

tion of each site increases the probability of a closed conformation with a higher affinity for the kinase, which accelerates the remaining

phosphorylation steps (cooperative kinetics). (E) Compartmentalization. Phosphorylation sites exerting distinct functions can be modified by

kinases localized in distinct subcellular compartments. In the example shown, the subcellular localization of a substrate is regulated by

cytoplasmic and nuclear kinases.



for which random phosphorylation of multiple

Ser ⁄Thr residues appears to allow the eventual phos-

phorylation of a critical threonine, possibly through a

conformational change (hierarchical mechanism) [20].

The various mechanisms differ considerably in the

number of phosphorylation states they generate.

Sequential mechanisms have a linear dependence on

the number (N) of phosphorylation sites (strictly

sequential: N + 1; cyclic: 2N), while the number of

states grows exponentially (2N) for random mecha-

nisms. The difference is considerable: for 13 regulatory

sites (as in NFAT1 [23]), there would be 8192 possible

phosphorylation states in the case of a random mecha-

nism but only 14 states for a strictly sequential mecha-

nism. Below we analyse the consequences of such

differences for the regulatory properties of the protein.

The amino acid sequence can determine the order of

phosphorylation (see Table 1). In particular, a consen-

sus sequence for a kinase may occur repetitively, thus

establishing a hierarchy in the phosphorylation. For

example, yeast kinase SRPK family kinases, which are

implicated in RNA processing, sequentially phosphory-

late Ser residues in consecutive arginine-serine (RS)

dipeptide repeats [63,64]. Moreover, the substrate spec-

ificity of certain kinases may depend on (or be

enhanced by) nearby residues phosphorylated by

another kinase (priming kinase). Phosphorylation of

the serine S or threonine T in the (S/T)XXX(Sp ⁄Tp)motif by the kinase GSK3 requires priming by another

kinase that phosphorylates the Sp ⁄Tp site [60–62]. In a

sequence of appropriately spaced serines, only the first

may need to be primed, while the remaining are then

sequentially phosphorylated by GSK3. Priming

phosphorylation facilitates the binding of a second

kinase either by creating specific docking sites, chang-

ing the substrate conformation, or dislodging the sub-

strate from the cell membrane [65–69]. An interesting

example of such a dual-enzyme mechanism is found in

the canonical Wnt ⁄ b-catenin pathway, where sequen-

tial phosphorylations of the Wnt co-receptor lipo-

protein receptor-related protein 6 (LRP6) and the

transcriptional cofactor b-catenin by the kinases GSK3

and CK1 mirror each other. Sequential phosphoryla-

tion of b-catenin by CK1 and cytosolic GSK3 anta-

Table 1. Consensus sequences and docking motifs for some kinases and phosphatases. PP1, protein phosphatase; PTP1B, protein tyrosine

phosphatase 1B; SHP2, Src homology domain-containing protein tyrosine phosphatase 2.

Enzyme Consensus sequences Docking motifs Other characteristics

Ser ⁄ Thr kinases

Calmodulin-dependent

protein kinase II (CaMKII)

RXX(S ⁄ T) – –

Casein kinase 1 (CK1) (Sp/Tp)XX(S ⁄ T) – Primed substrate

(D ⁄ E)XX(S ⁄ T) – –

Casein kinase 2 (CK2) (S ⁄ T)XX(Sp ⁄ Tp) – Primed substrate

(S ⁄ T)XX(D/E) – –

Glycogen synthase kinase 3 (GSK3) (S/T)XXX(Sp ⁄ Tp) – Primed substrate

Protein kinase B (PKB ⁄ Akt) RXRXX(S ⁄ T) – –

Protein kinase C (PKC) (S ⁄ T)X(K ⁄ R) – –

Tyr kinases

EGF receptor kinase X(D ⁄ E)YX – –

Abl tyrosine kinase (I ⁄ V ⁄ L)YXX(P ⁄ F) – SH2 domain

Ser ⁄ Thr phosphatases

Dual-specificity protein

phosphatase 6 (DUSP6)

TpXYp – –

PP1 – RVXF

FXXRXR

–

PP2A, PP2C RRA(Sp ⁄ Tp)VA – –

Calcineurin (PP2B) – PXIXIT –

Tyr phosphatases

PTP1B E(Y ⁄ F ⁄ D)Yp

RDXYXTDYYpR

– –

SHP2 YpASI

YpIDL

– SH2 domain

Amino acids are indicated by the one-letter code; X indicates any amino acid; Sp, Tp and Yp indicate phosphoserine, phosphothreonine and

phosphotyrosine, respectively. Interchangeable residues at a given position are grouped within parentheses, and separated by forward

slashes. The target residues are in bold.



gonizes Wnt ⁄ b-catenin signalling, whereas plasma mem-

brane-associated GSK3 primes further LRP6 phos-

phorylation by CK1 in response to Wnt stimulation

and activates Wnt ⁄ b-catenin signalling [65].

To achieve high specificity, many protein kinases

and phosphatases recognize their targets through inter-

actions that occur outside of the active site [72]. Tyro-

sine kinases and phosphatases often utilize dedicated

interaction domains, such as SH2 and SH3 domains,

that are distinct from the catalytic domain [14,73,74].

Specific docking interactions may also occur in the cat-

alytic domain but outside of the catalytic site, as found

for many serine ⁄ threonine kinases and phosphatases

[72]. These mechanisms appear to contribute in some

cases to sequential processing of the phosphorylation

sites.

The three-dimensional structure of the substrate

may also affect the order of (de)phosphorylation.

Random phosphorylation may be linked to the

adoption of a flexible or unfolded structure by the

target protein so that several residues become equally

accessible to the kinase. In some cases, the order of

phosphorylation is not determined by structural

factors but rather by the activation kinetics of the

participating kinases. For example, Ser ⁄Thr phos-

phorylation of the EGF receptor by several down-

stream kinases such as the MAP kinases ERK1/2

and p38 shows delayed kinetics compared to auto-

phosphorylation of the EGF receptor on multiple

tyrosine residues [7].

Processivity of phosphorylation

Kinases (or phosphatases) may differ in the number of

binding events required to phosphorylate (or dephos-

phorylate) all target sites on a protein (reviewed in

Ref. [75]). A kinase may bind to the substrate and

phosphorylate all the sites while staying bound (pro-

cessive mechanism) (Fig. 2B). Conversely, the kinase

may bind, phosphorylate one residue and dissociate, so

that next phosphorylation first requires re-binding of a

kinase molecule (distributive mechanism).

Although some proteins clearly follow one of these

two models (see Table 2), the processive and distribu-

tive mechanisms are the extremes of a continuous

spectrum. For example, the cyclin-CDK complex

Pho80 ⁄Pho85 phosphorylates the yeast transcription

factor Pho4 on five serines, with a mean of approxi-

mately two phosphorylation events per enzyme–sub-

strate binding [76]. The degree of processivity depends

on the relative time scales of enzyme dissociation and

catalytic reaction [77], and can be quantified as follows:

the probability that an enzyme proceeds to modify the Tab

le2.

Enzy

me

pro

cessiv

ity

and

ord

er

of

phospho-s

ite

pro

cessin

gfo

rsom

esubstr

ate

s.

AS

F/S

F2,

altern

ative

splic

ing

facto

r;A

TF2,

activating

transcription

facto

r2;

CD

K,

cyclin

dependent

kin

ase;

ME

K,

MA

PK

/ER

Kkin

ase;

MK

P3,

mitogen-a

ctivate

dpro

tein

kin

ase

phosphata

se

3;

SR

PK

,serine-a

rgin

ine-r

ich

pro

tein

kin

ase.

Substr

ate

nam

e

Type

of

substr

ate

Enzy

me

nam

e(p

hosphory

late

dsites)

Type

of

enzy

me

Ord

er

of

phospho-s

ite

pro

cessin

gE

nzy

me

pro

cessiv

ity

Oth

er

chara

cte

ristics

Refe

rence

b-c

ate

nin

Tra

nscription

cofa

cto

r

CK

1(S

er4

5)

GS

K3

(Thr4

1,

Ser3

7,

Ser3

3)

Ser

⁄Thr

kin

ases

Sequentialphosphory

lation

(dual-kin

ase)

?–

[130,1

31]

ER

K2

MA

Pkin

ase

ME

K(T

hr1

83,T

yr1

85)

Thr

⁄Tyr

kin

ase

Random

phosphory

lation

Dis

trib

utive

phosphory

lation

–[4

1,7

0]

MK

P3

(Thr1

83,T

yr1

85)

Dualspecifi

city

(Thr

⁄Tyr)

phosphata

se

Sequentialdephosphory

lation

Dis

trib

utive

dephosphory

lation

–[7

1]

ATF2

Tra

nscription

facto

r

p38

(Thr6

9,

Thr7

1)

Ser

⁄Thr

kin

ase

Random

phosphory

lation

Dis

trib

utive

phosphory

lation

–[4

6]

AS

F⁄S

F2

Splic

ing

facto

rS

RP

K1

(10

Ser

sites)

Clk

⁄Sty

(20

Ser

sites)

Ser

kin

ase

Sequentialphosphory

lation

Pro

cessiv

ephosphory

lation

Sta

ble

kin

ase-

substr

ate

com

ple

x

[27,6

4,8

7]

p130C

as

Focaladhesio

n

pro

tein

Scr

(15

repeats

of

YX

XP

motif)

Tyr

kin

ase

Random

phosphory

lation

Pro

cessiv

ephosphory

lation

SH

3dom

ain

[7,7

3]

RN

A

poly

mera

se

II

–A

bl(2

5–52

repeats

of

YS

PTS

PS

motif)

Tyr

kin

ase

?P

rocessiv

ephosphory

lation

SH

2dom

ain

[25,1

32,1

33]

Pho4

Tra

nscription

facto

r

aP

ho80

⁄Pho85

(five

Ser

sites)

Ser/

Thr

kin

ase

Sequentialphosphory

lation

Sem

i-pro

cessiv

e

phosphory

lation

–[2

2,7

6]

Sic

1C

DK

inhib

itor

aC

dc28–C

ln1,2

(nin

eS

er

⁄Thr

sites)

Ser

⁄Thr

kin

ase

Random

phosphory

lation

Dis

trib

utive

phosphory

lation

–[1

8,5

1]

acyclin

-CD

Kcom

ple

x.



next site before it dissociates is kcat ⁄ (kcat + koff), where

koff and kcat are the dissociation rate constant and the

catalytic rate constant, respectively, of a substrate-

bound enzyme molecule. The probability of a fully

processive modification of N sites is then

Pprocessive ¼kcat

kcat þ koff

� �N

ð1Þ

(assuming, for simplicity, that all the sites have the

same kcat and are modified sequentially).

Indeed, kcat values as fast as 10Æs)1 have been

reported for protein kinases, while dissociation rate

constants may be much lower (0.01Æs)1 and below).

However, phosphorylation rates in the minute range

have been reported for a processive substrate, indicat-

ing that kcat can also be much lower [78], as required

for distributive phosphorylation mechanisms. For

example, the splicing factor ASF ⁄SF2 is fully phos-

phorylated during a single encounter with its kinase

SRPK1 due to the high-affinity interaction between

the proteins (equilibrium dissociation constant Kd

approximately 50 nm) [27]. By contrast, the dissocia-

tion rate of the MEK:pERK2 complex is at least five

times as fast as the phosphorylation rate of the second

site in ERK2 [77]. Enzyme processivity may be

enhanced by the presence of protein–protein interac-

tion domains such as SH2 and SH3 that recognize

newly phosphorylated products, allowing repositioning

of the enzyme and substrate [73,74]. Tethering a sub-

strate to its modifying enzymes through a scaffold pro-

tein can also increase the degree of processivity [79].

Two biochemical methods have mainly been

employed to determine the processivity of substrate

phosphorylation. In the ‘start-trap’ strategy, ATP is

added to the enzyme–substrate complex, together with

an inhibitor that can trap the free enzyme [27]. In a

distributive mechanism, the inhibitor traps the free

enzyme, stopping the reaction before full phosphoryla-

tion is achieved. By contrast, in a processive mecha-

nism, the inhibitor does not influence the rate or

extent of phosphorylation. A second strategy consists

of measuring the phosphorylation rate at various con-

centrations of substrate (or enzyme) [73]. For a distrib-

utive mechanism, the partially phosphorylated forms

can act as competitive inhibitors of phosphorylation,

so that increases in substrate concentration result in a

decreased formation rate of the fully phosphorylated

substrate. Recently, time-resolved high-resolution

NMR spectroscopy has been used to identify the pres-

ence of free partially phosphorylated forms of the

substrate and the existence of a defined order of phos-

phorylation [58].

Processive enzymes can catalyse sequential phos-

phorylation, while distributive enzymes may process

the phosphorylation sites in a random manner. For

example, the intermolecular autophosphorylation of

several Tyr residues in the fibroblast growth factor

receptor 1 kinase apparently proceeds in a sequential

and processive manner [80]. Dual phosphorylation of

extracellular regulated kinase (ERK) by MEK in the

MAP kinase cascade was reported to occur via a ran-

dom and distributive mechanism [41,70]. However, a

processive kinase can also catalyse random phosphory-

lations, as recently proposed for phosphorylation of

the focal adhesion protein p130Cas by Scr kinase [81].

Conversely, sequential DUSP6 dephosphorylation of

ERK2 at Thr and Tyr was shown to occur distribu-

tively [71]. Thus there appears to be no strict link

between the degree of processivity of a kinase and

random or sequential phosphorylation of its multiple

target sites. The phosphorylation order and enzyme

processivity of some relevant proteins are listed in

Table 2.

Competition mechanisms

The interactions between the target protein and its

modifying enzymes can lead to two distinct types of

competition effects (Fig. 2C). The binding affinities of

kinases and phosphatases may change with the phos-

phorylation state of the target protein. For example,

the fully phosphorylated target may lose (or retain) its

affinity for the kinase. Such affinity changes may lead

to interesting effects when the concentration of the

kinase is much smaller than that of the target protein

[28–30,82,83]. In this case, target proteins of various

phosphorylation states compete for the kinase (or,

equally, for the phosphatase). When the kinase

remains associated with the higher or fully phosphory-

lated forms of its target protein, product inhibition will

result, because the bound kinase is not available to act

on unphosphorylated target molecules.

Conversely, when the concentrations of the modify-

ing enzymes [kinase(s) and phosphatase(s)] are large

compared to their target protein, as may be the case in

signal transduction, the enzymes can compete for bind-

ing to the target. Phosphorylation is then inhibited by

the phosphatase and dephosphorylation by the kinase.

In particular, when the kinase has a high affinity for

the phosphorylated target, the latter is sequestered and

is not available for dephosphorylation. The structural

basis for such competition may involve overlapping

binding sites for kinases and phosphatases on the tar-

get, such that they are unable to bind to the target at

the same time [84].



The phosphorylation of a particular residue can also

compete with other covalent modifications. For exam-

ple, in addition to phosphorylation, Ser and Thr resi-

dues are also targets for glycoxylation, while the

hydroxyl group of Tyr residues can be phosphorylated

or sulfated [4]. Intermolecular competition can occur

between substrates of similar affinity for the same

enzyme; a substrate with a lower affinity will be

phosphorylated once the preferred targets have been

saturated with the enzyme [30].

Conformational changes and cooperativity

For some proteins, phosphorylation controls their

function by creating or eliminating docking sites for

the recruitment of specific binding partners. In other

cases, phosphorylation alters the local environment of

a catalytic center or a binding site. For proteins with a

large number of regulatory phosphorylation sites,

phosphorylation sites distant from such functional

motifs may regulate protein activity by inducing

changes in its global conformation [23,85] (Fig. 2D).

For example, extensive charge modifications caused by

multiple phosphorylations on NFAT have been pre-

dicted to alter its tertiary structure [85].

As a plausible model for the control of protein con-

formation by multisite phosphorylation, it has been

proposed that individual phosphorylation events shift

the equilibrium between two or more pre-existing con-

formations of the protein [23,38,86]. For instance, the

nucleo-cytoplasmic transport of NFAT can be

accounted for by a conformational switch model, with

an active conformation that is transported from the

cytoplasm to the nucleus and an inactive conformation

that is exported back to the cytoplasm. The probability

of attaining the active conformation increases with

each dephosphorylation step [23,38]. Somewhat more

complicated models with four conformation states

have also been proposed [39].

The conformation of the target protein can also

affect the binding of kinases or phosphatases, and the

kinetics of the (de)phosphorylations. This can induce

cooperativity among the phosphorylation states. For

example, in the case of NFAT, dephosphorylation of

the SRR1 region enhances dephosphorylation of the

SP2 and SP3 motifs by calcineurin [23].

Compartmentalization

Phosphorylation sites can be modified by two or more

kinases (or phosphatases) that are localized in distinct

subcellular compartments (Fig. 2E). An example is the

interplay between the cytoplasmic kinase SRPK1 and

the nuclear kinase Clk ⁄Sty in phosphorylation of the

splicing factor ASF ⁄SF2 [27,87,88]. A docking motif in

ASF ⁄SF2 restricts its phosphorylation by SRPK1 to the

N-terminal half (approximately 10 sites) of the RS

domain, mediating nuclear import of ASF ⁄SF2 and

localization in nuclear speckles [87]. Clk ⁄Sty, however,can phosphorylate the entire RS domain (approximately

20 sites), causing release of ASF ⁄SF2 from speckles.

The subcellular localization of kinases and phospha-

tases is an important issue in signalling from the

plasma membrane to the nucleus. For example, in rest-

ing cells, the NFAT phosphatase calcineurin resides

predominantly in the cytoplasm, but upon cell stimula-

tion may be imported into the nucleus together with

NFAT to maintain NFAT dephosphorylation and

nuclear localization [89,90]. The NFAT kinases GSK3

and CK1, which phosphorylate the SP2 and SRR1

motifs, respectively, are present in both subcellular

compartments. However, DYRK2 and DYRK1A,

which phosphorylate the SP3 motif, are cytoplasmic

and nuclear, respectively [50]. DYRK2 probably helps

to maintain the phosphorylated state of cytoplasmic

NFAT in resting cells, whereas DYRK1A re-phospho-

rylates nuclear NFAT and promotes its export from

the nucleus. Such compartmentalization of kinases or

phosphatases confers different functions, and, in turn,

may expand the repertoire for regulating signal trans-

duction networks.

Kinetic modelling of multisitephosphorylation

General framework

Kinetic models of multisite protein phosphorylation

are quite distinct from those of traditional enzyme

kinetics [91,92] for several reasons. First, the number

of molecular states to be accounted for is usually

larger (including partially phosphorylated states, both

enzyme-bound and free, and, where appropriate, vari-

ous conformations of the protein due to its phosphory-

lation state). Second, and more importantly, the

simultaneous presence of kinases and phosphatases

needs to be considered in a physiological context, so

that there are at least two counteracting enzymes in

the system (although consideration of a single enzyme

acting on the target may be relevant for in vitro experi-

ments). Indeed, we show below that, in general, no

explicit enzymatic rate laws can be derived for phos-

phorylation and dephosphorylation reactions. Third,

there are usually no strict concentration hierarchies in

phosphorylation modules [i.e. target protein, kinase(s)

and phosphatase(s)], so that enzymes and their



subtrates may have similar concentrations. The low

enzyme concentration is the chief condition for deriva-

tion of Michaelis–Menten-type enzymatic rate laws,

although this can be relaxed in certain cases [93–95].

However, as a rule of thumb, explicit enzymatic rate

laws (Michaelis–Menten or other) can generally not be

derived when the concentrations of the various

enzyme–substrate complexes are appreciable compared

to the free concentrations of substrate and product.

This situation is probably common in protein phos-

phorylation networks.

For these reason, Michaelis–Menten kinetics are not

an appropriate starting point for studying the kinetic

behaviour of (multisite) phosphorylation modules

[29,82,95], although some authors have used them [32].

Instead, a mathematical description based on elemen-

tary steps of enzyme–substrate binding and catalysis is

appropriate [29,33,82]. As an example of how this for-

malism works, Fig. 3 (upper box) shows the strictly

sequential mechanism of phosphorylation [29]. For

each phosphorylation state, the substrate can occur in

a free form (Xn,0) or in a complex with the kinase

(Xn,K) or phosphatase (Xn,P), where n = 0, … N is the

number of phosphorylated residues (simultaneous

binding of kinases and phosphatases to the target pro-

tein has not been considered here but may also occur).

The dynamic behaviour of all possible complexes and

phosphorylation states can be described by a set of

kinetic equations. For example, the balance for the

unphosphorylated substrate in a binary complex with

the kinase is

dX0;K

dt¼ dk

K

L0X0;0 � X0;K

� �

reversible binding of kinase

� a1X0;Kphosphorylation

ð2Þ

where dk and L0 denote the dissociation rate constant

and equilibrium dissociation constant for the binding

of the kinase, a1 is the phosphorylation rate constant

of the first phosphorylation site, and K is the concen-

tration of free kinase. A model of this type can easily

be solved numerically, but contains a rather large

number of parameters that need to be specified

(6N + 4 when the kinase and phosphatase are

assumed to have different binding, dissociation and

catalytic rate constants for each phosphorylation

state).

The model can be simplified by exploiting time-scale

hierarchies. Perhaps the simplest assumption is that

enzyme–target binding interactions occur more rapidly

than the addition and cleavage of phosphoryl groups,

and thus a rapid-equilibrium approximation for kinase

and phosphatase binding can be applied [29,82]. This

approximation models a distributive mechanism of

(de)phosphorylation whereby the enzymes have to bind

and dissociate many times before the target protein is

fully (de)phosphorylated. The system dynamics can be

formulated in terms of the total concentration

Yn = Xn,0 + Xn,K + Xn,P attained by the various

phosphorylated forms. Moreover, the number of

parameters is reduced considerably as only the equilib-

rium dissociation constants (and no longer the binding

and dissociation rate constants) are needed (Fig. 3,

lower box). The total concentrations of the phospho-

forms Yn are governed by the algebro-differential

equation system

dYn

dt¼ anYn�1

phosphorylationofYn�1

� ðanþ1 þ bnÞYnphosphorylation and

dephosphorylation ofYn

þ bnþ1Ynþ1dephosphorylation

ofYnþ1

;

for 0 � n � N ð3Þ

with effective rates of phosphorylation and dephos-

phorylation of

an ¼ anK=Ln�1

1þ K=Ln�1 þ P=Qn�1and

bn ¼ bnP=Qn

1þ K=Ln þ P=Qn; ð4Þ

respectively, and the conservation conditions

Fig. 3. Reaction scheme for a multisite protein phosphorylation

module. A model based on elementary steps for the sequential

mechanism of phosphorylation is shown in the upper box. In each

phosphorylation state, the substrate can occur in a free form (Xn,0)

or in a complex with the kinase (Xn,K) or phosphatase (Xn,P).

Because protein–protein interactions generally occur more rapidly

than catalytic steps, the model can be simplified and the number of

parameters considerably reduced (lower box). See text for more

details.



KT ¼ K þXN

n¼0

YnK=Ln

1þ K=Ln þ P=Qnand

PT ¼ P þXN

n¼0

YnP=Qn

1þ K=Ln þ P=Qnð5Þ

In general, this system is nonlinear with respect to

the Yn variables and has no explicit solution except for

special cases [29,82].

Thus comprehensive kinetic models of multisite phos-

phorylation require knowledge of protein concentra-

tions (kinases, phosphatases and substrate) and the

binding and dissociation rate constants for the enzymes

(or at least the Kd values), as well as the rate constants

of phosphorylation and dephosphorylation reactions.

Large-scale measurements of cellular protein concentra-

tions have been performed (e.g. in budding yeast [96]),

and binding affinities (or dissociation constants) have

been determined in some cases [27]. Viscosity and fast-

mixing kinetic methods have recently been applied to

dissect the individual steps in substrate phosphorylation

such as substrate binding, product release and catalytic

steps [27,97]. One way to address this difficulty may be

to design kinetic experiments that allow simultaneous

fitting of several kinetic parameters (e.g. by determining

the time course of substrate phosphorylation forms

combined with dose–response curves, and possibly also

mutations of individual phosphorylation sites).

Sequential versus random phoshorylation order

Analysis of the random mechanism is, in principle,

more complex due to the larger number of phosphory-

lation states, but the same formalism as given for the

sequential scheme applies. However, there is an inter-

esting connection with regard to the kinetic description

of random and sequential phosphorylation mecha-

nisms. In the special case that the parameters do not

depend on the phosphorylation state of the target pro-

tein (an = a, bn = b, Ln = L, Qn = Q), the random

mechanism can be mapped exactly onto a sequential

one by grouping all n-times phosphorylated target mol-

ecules into a single class regardless of the position of

the phosphorylated residues [29]. The concentrations of

these new grouped variables for the random scheme,

Yn, are given by the system of Eqns (3–5) with new effec-

tive rate constants of phosphorylation and dephosphor-

ylation, aran and bran, defined as follows:

aran ¼ ðN � nþ 1Þa and bran ¼ nb; ð6Þ

where a and b are as given in Eqn (5). Equation (6)

expresses the fact that the effective phosphorylation

rate decreases as the target becomes increasingly

phosphorylated because fewer residues remain avail-

able for phosphorylation. This is exactly the opposite

for dephosphorylation, and as a result of this rapid

phosphorylation of the unphosphorylated target and

rapid dephosphorylation of the phosphorylated

target, the random mechanism has a tendency to

produce partially phosphorylated forms of the target

protein.

Kinetic and functional implications ofvarious phosphorylation mechanisms

Multisite phosphorylation has been associated with

signal integration, threshold responses, signalling

specificity, precise timing, and other properties. Based

on the results of mathematical models, we discuss

how these functional implications are related to the

mechanisms of multisite phosphorylation presented

above.

Graded, switch-like and bi-stable responses

Phosphorylation modules may exhibit a wide variety

of stimulus–response relationships, whereby the stimu-

lus is usually translated into activity of a kinase (or

phosphatase, e.g. for the calcineurin ⁄NFAT pathway).

Several studies have identified important parameters

that shape the stimulus–response relationship includ-

ing: (a) the concentrations of the modifying enzymes

relative to the substrate, (b) the affinities of the modi-

fying enzymes for the various phosphorylation states

of the target and (c) the (cooperative or non-coopera-

tive) kinetics of the catalytic steps [28,29,33,82,83].

Even when a single phosphorylatable site is involved,

changes in these parameters can produce diverse

responses such as graded (or hyperbolic), ultrasensitive

(or sigmoidal), and even dual thresholds [82]. In partic-

ular, when the substrate concentration is so large that

the enzymes operate near saturation and the kinase

readily dissociates from the phosphorylated target

(and, likewise, the phosphatase from the unphosphory-

lated target), a steep threshold response, or ‘switch’, is

obtained. This phenomenon has been termed zero-

order ultrasensitivity [98], and has been experimentally

observed for the phosphorylation of phosphorylase

and isocitrate dehydrogenase [99,100]. However, ultra-

sensitivity does not occur if the kinase (or phospha-

tase) remains sequestered by the phosphorylated

(dephosphorylated) substrate [28,82,101].

Compared to a single-site target, multisite phosphor-

ylation expands the possibilities for protein–protein

interactions and the phosphorylation sequence, thus



providing additional mechanisms for the generation of

activation thresholds. This is particularly true for dis-

tributive kinetics (with multiple binding ⁄dissociationevents for kinase or phosphatase), whereas a multisite

phosphorylation module with processive kinetics of

kinase and phosphatase behaves much like a single-site

module with regard to the response curve. In particu-

lar, when phosphorylation of the first residues acceler-

ates the remaining phosphorylation steps (i.e. positive

cooperativity), ultrasensitivity of the response can be

observed (Fig. 4A). In that case, the effective Hill coef-

ficient that quantifies the overall steepness of the

response curve can be nearly as large as the number of

phosphorylation sites [38]. Ultrasensitive responses can

be used in signal transduction to filter out noise signals

while amplifying strong inputs.

Multisite phosphorylation, however, is not sufficient

to generate a switch-like response. In the absence of

cooperative kinetics or zero-order ultrasensitivity, dis-

tributive multisite phosphorylation gives rise to an

activation threshold but does not produce a sharp

switch (Fig. 4A) [33]. In such a case, the response coef-

ficient, defined as the fractional change in the concen-

tration of the fully phosphorylated substrate upon a

fractional change of the kinase concentration, seems to

be more appropriate than the effective Hill coefficient

to measure the sensitivity of the response [102]. When

the conditions for zero-order ultrasensitivity (i.e. very

low enzyme concentration and negative cooperativity

of enzyme binding) are combined with positive cooper-

ativity of catalytic steps, the system can be bi-stable,

and a ‘perfect switch’ can be obtained [12,29,31]

Fig. 4. Mechanistic effects of multisite phosphorylation on the dose–response curves and phosphorylation kinetics. (A–C) Dose–response

curves. (A) Enzyme processivity and cooperativity. Processivity leads to a hyperbolic dose–response curve, while distributive kinetics gener-

ates an activation threshold. In addition to distributive phosphorylation, cooperativity is required for a switch-like response. (B) Bi-stability.

Depending on the initial conditions (kinase activity), the substrate can attain one of the two stable steady states (with different levels of

phosphorylation). (C) Order of phospho-site processing. A sequential mechanism produces steeper dose–response curves than a random

one. (D,E) Phosphorylation kinetics. (D) Transition time. Upon kinase activation, a target protein, initially dephosphorylated (blue curve), can

be phosphorylated at multiple residues, attaining a highly phosphorylated state (red curve) after a certain time. (E) Order of phospho-site

processing. Multisite phosphorylation is achieved much faster by a random mechanism due to the various ways to phosphorylate the target

protein.



(Fig. 4B). Such bi-stability has been proposed for the

doubly phosphorylated MAP kinase [12]. Recent stud-

ies have demonstrated that the maximal number of

possible steady states increases with the number of

phosphorylation sites, and that multi-stable responses

can arise under certain conditions [34].

Importantly, the stimulus–response curve depends

strongly on the order in which the phosphorylation

sites are modified by the enzyme [29]. For sequential

and random distributive mechanisms, the steady-state

fractions of the n-times phosphorylated target protein

are

Yn

Ytotal

��seq

¼ rnðr� 1ÞrNþ1 � 1

andYn

Ytotal

��ran

¼ Nn

� �rn

ð1þ rÞNð7Þ

where r = a ⁄ b is the stimulus strength [ratio of kinase

to phosphatase activities as defined in Eqn (4)] The

sequential mechanism generates steeper response

curves than the random mechanism, with the latter

favouring intermediate phosphorylation states of the

target (Fig. 4C). The number of intermediate phos-

phorylation states grows exponentially with the ran-

dom mechanism and only linearly with the sequential

mechanism. Thus, the difference in the steepness of the

response curve between random and sequential mecha-

nisms becomes more pronounced when the number of

phosphorylation sites is large.

In addition to these intramolecular mechanisms,

competition between several substrates for access to

the same enzyme can also be a source of ultrasensitivi-

ty. A preferred target can act as a stoichiometric inhib-

itor and produce a threshold for the activation of a

low-affinity substrate. The response of the low-affinity

substrate becomes less ultrasensitive when the

preferred target decreases in concentration [30].

As a rule of thumb, distributive sequential phos-

phorylation and dephosphorylation kinetics with posi-

tive cooperativity favour threshold responses, whereas

more processive and ⁄or random kinetics without

cooperativity result in smooth response curves.

Phosphorylation kinetics

Diverse cellular processes such as cell-cycle progression

and circadian oscillations need to be precisely timed,

and multisite phosphorylation has been implicated in

this [18,45,51,103–105]. As a result of a change in

kinase or phosphatase activities, the target protein

reaches a new phosphorylation state after a certain

transition time (Fig. 4D). To illustrate how the transi-

tion times of multisite phosphorylation modules

behave, we consider the special case that the free kinase

and phosphatase concentrations remain (approxi-

mately) constant over the course of the reaction (this is

valid when the target affinity to the enzymes is indepen-

dent of the phosphorylation state). For a single-site

target, the transition time is s1 = 1 ⁄ (a + b) [see

Eqn (4)] [29,82]. Kinase and phosphatase activity have

equal effects on the time of transition to the new steady

state, and the transition time decreases monotonically

with either parameter. Note that this is different for

short, transient signals, the duration of which is

essentially controlled by phosphatases [106].

For a multisite target, however, the transition time

depends critically on the order of (de)phosphorylation.

For sequential and random (distributive) multisite

phosphorylation, the transitions times for full phos-

phorylation of the target are

sseq¼1

b

PNi¼1

iðNþ1� iÞrNþi

PNi¼0

ri

and sran¼1

aþb

XN

i¼1

1

i; ð8Þ

respectively. Thus the kinetics of random multisite

phosphorylation show essentially the same dependence

on the enzyme activities as a single-phosphorylation

module; there is only an additional factor accounting

for the number of sites (the so-called Nth harmonic

number,PN

i¼1 1=i).It can be shown that random phos-

phorylation is always faster than sequential phosphory-

lation for otherwise equal parameters (i.e. sran < sseq)[29]. Moreover, the transition time for sequential phos-

phorylation exhibits a maximum when the kinase and

phosphatase activities balance (Fig. 4E). In the sequen-

tial mechanism, an intermediate site is targeted by the

kinase only after all the preceding sites have been

modified. For the random mechanism, however, there

are many more phosphorylation routes (namely N!

shortest routes) available for complete phosphorylation

of the target, hence the faster kinetics. For example, for

the protein Wee1 with five CDK phosphorylation sites,

there are 120 possible phosphorylation routes, on the

assumption of a completely random mechanism [30].

Phosphorylation kinetics is also affected by the

substrate saturation of the enzymes and the kinetics of

protein–protein interactions. Phosphorylation cycles

involving saturated enzymes are usually slower than

those with unsaturated enzymes [29]. Multisite phos-

phorylation can be very slow if the kinase must re-bind

several times in order to phosphorylate the substrate

fully and the binding step itself is slow [27]. Conversely,

processive phosphorylation can be much faster.

However, random versus sequential phosphorylation

can also make a significant difference in timing.



Precise timing of molecular events

Multisite phosphorylation may function as a precise

timing device, allowing synchronization of molecular

events. In eukaryotes, a complex molecular machinery

involving multiply phosphorylated proteins allows

DNA replication to start simultaneously from multiple

origins of replication [20,107–110]. We have shown

recently in a model of replication initiation in budding

yeast that synchrony of activation of replication ori-

gins depends on the kinetics of two branches that

eventually converge at the origins: (a) the distributive

multisite phosphorylation of the protein Sld2 by the

cyclin-CDK complex during the S phase of the cell

cycle [20,109], leading to formation of an activator

complex outside the origins and (b) a series of protein

recruitments forming a pre-initiation multiprotein com-

plex at the origins. The distributive multisite phosphor-

ylation of Sld2 generates a switch-like response to the

S-CDK level, and provides the time delay required to

make S-CDK input rate-limiting for origin activation.

This results in robust synchronous activation of the

replication origins that is decoupled from the specific

S-CDK activation kinetics (A. Brummer, C. Salazar,

V. Zinzalla, L. Alberghina and T. Hofer, unpublished

results).

If sequential recruitment of proteins to the origins is

completed before the activator complex (containing

multiply phosphorylated Sld2) is available, the molecu-

lar noise of these preceding steps becomes irrelevant

(Fig. 5B, solid line). The synchrony in origin activation

is then determined by a sharp triggering step: forma-

tion of the activator complex, which in turn is

controlled by the multisite phosphorylation of Sld2. By

contrast, in the absence of such a triggering reaction,

each protein recruitment step would increase the noise,

leading to asynchronous activation of the replication

origins (Fig. 5A). The timing of the triggering step

controlled by multisite phosphorylation is crucial for

Fig. 5. Coherence and timing of molecular

events. (A) Sequential assembly design. The

scheme shows the assembly of a multipro-

tein complex SN by the sequential recruit-

ment of proteins X1, X2, … XN. Each protein

recruitment step would increase the mole-

cular noise, resulting in asynchronous forma-

tion of the complex SN. (B) Sequential

assembly with sharp triggering step. The

coherence in formation of the complex SN

can be considerably enhanced when a late

triggering step (provided by distributive mul-

tisite phosphorylation events) is introduced

(solid green line). The noise in the preceding

protein recruitment steps becomes irrele-

vant (solid red line). However, proper timing

of the triggering step is required; premature

triggering (dashed green line) would cause

asynchronous formation of the complex SN

(dashed red line).

Fig. 6. Phosphorylation-induced protein interactions. (A) Entropic

mechanism. Each phosphorylation event imposes a local structural

order that nonlinearly reduces the number of conformations avail-

able to the ligand. (B) Electrostatic mechanism. Each phosphoryla-

tion event adds negative charges on the ligand increasing the

electrostatic interactions with its binding partner.



synchronous activation of the replication origins. If

formation of the pre-initiation complex is not com-

pleted before the activator complex is available, activa-

tion of replication origins becomes strongly

desynchronized (Fig. 5B, dashed line).

Switch-like and graded modulation of protein

interactions

Most eukaryotic proteins involved in cell signalling

have large disordered regions, which in some cases

adopt a stable structure upon binding to their part-

ners [111–113]. Phosphorylation events may be

involved in modulating protein interactions by locally

increasing structural order and changing protein con-

formations. A recent theoretical paper has suggested

that multisite phosphorylation can favour binding by

reducing the conformational entropy of a disordered

ligand [42] (Fig. 6A). Accordingly, each phosphoryla-

tion event could increase local structural order,

resulting in a nonlinear decrease in the number of

conformations available to the ligand, and leading to

a sigmoidal change in the fraction of bound ligand

as a function of its phosphorylation state. Effective

binding of the ligand would only occur when the

protein is phosphorylated a critical number of times

or more.

In other systems, however, multisite phosphorylation

does not substantially increase the conformational

order of the ligand, which appears to remain largely

disordered even when bound to its partner [112,114].

One example is binding of the CDK inhibitor Sic1 to

SCFCdc4 ubiquitin ligase [18,43,115,116]. It was

recently proposed that the ultrasensitive binding

observed in the Sic1–SCFCdc4 system might rely on

polyelectrostatic interactions between a positively

charged receptor protein and a disordered ligand phos-

phorylated at multiple sites (Fig. 6B) [43,115,116].

Each phosphorylation event adds two negative charges

to the ligand, increasing the electrostatic interactions

between the binding partners.

Multisite phosphorylation can also regulate the

binding of disordered proteins to their partners in a

graded manner [117,118]. For example, phosphoryla-

tion of an unstructured region of the transcription acti-

vator Ets-1 results in graded binding to DNA rather

than a switch [117]. In such a case, only three sites reg-

ulate the binding to DNA, and each phosphorylation

decreases the binding energy by about 0.4 kcal mol)1

(the dissociation constant Kd is increased by a factor

of 2) [117]. However, in another case, regulation by

eight phosphorylation sites results in ultrasensitive

recruitment of the MAP kinase scaffold protein Ste5

to the bc G-protein subunit at the plasma membrane,

where it was assumed that each phosphorylation

decreased the binding energy by 1.4 kcal mol)1 (Kd is

increased by a factor of 10) [116]. Generally, the

degree of ultrasensitivity depends both on the number

of phosphorylation sites and the change in binding

affinity with each phosphorylation. Ultrasensitive bind-

ing is observed when each phosphorylation signifi-

cantly changes the binding affinity and a large number

of phosphorylation sites are involved.

Specificity and sensitivity of cell signalling

The high substrate specificity of many enzymes is due

to the complementary molecular structure of the sub-

strate and its binding site in the enzyme. Therefore, an

enzyme may not readily distinguish between targets of

very similar chemical structure. For some reactions, it

can be crucial that only a single substrate is accepted.

To ensure accurate cell activation, membrane receptors

must distinguish between extracellular ligands of simi-

lar affinity. Multi-step mechanisms such as multisite

phosphorylation may improve selection of the correct

substrate (or ligand) by a process known as kinetic

proofreading [37,119,120].

In the variant of the kinetic proofreading model

originally proposed by McKeithan and inspired by

T-cell receptor signalling [37] (Fig. 7A), binding of the

substrate S to the kinase K forms the kinase–substrate

complex C0 and initiates a sequence of N phosphoryla-

tions, each with rate constant a, generating the inter-

mediate complexes C1, C2, … CN. Only the fully

phosphorylated state CN (or at least a highly phos-

phorylated form) is able to convey a downstream

signal. At every step, the kinase–substrate complex

may dissociate with rate d, and, due to the assumed

rapid action of phosphatases, the substrate rapidly

returns to its unphosphorylated state. (Note that the

proofreading scheme originally proposed by Hopfield

also relies on phosphorylation but invokes different

molecular mechanisms [121]). The fraction of active

N-times phosphorylated substrate is

CN

Stot¼ K

K þ Lequilibriumbinding

a

aþ d

� �N

kineticproofreading

ð9Þ

where Stot is the total substrate concentration and

L = d ⁄ b is the equilibrium dissociation constant (Kd)

of the substrate–kinase complex. Thus the usual equi-

librium binding factor is modified by a proofreading

factor that equals to the probability that N phosphory-

lations occur before the kinase dissociates. Thus the



stability of the substrate–kinase complex is tested

(expressed by the dissociation rate constant d) at the

expense of metabolic energy. The specificity increases

with the number of proofreading steps N, but, at the

same time, the sensitivity decreases because of more

abortive phosphorylation attempts [47] (Fig. 7B, C).

Differences in the processivity of multisite phosphor-

ylation can be exploited by the cell to establish a tem-

Fig. 7. Specificity of cell signalling and

kinetic proofreading. (A) Kinetic proofreading

model. An enzyme-bound substrate must

complete a series of modifications (e.g.

phosphorylations) for a cellular response

(e.g. cell signalling) to occur. If the enzyme

dissociates before the full set of modifica-

tions is completed, the substrate return to

its basal state, and signalling is aborted. See

text for more details. (B) Signalling specific-

ity. The degree of discrimination between

substrates of similar affinity for the same

kinase increases with the number of phos-

phorylation steps. (C) Signalling sensitivity.

The fraction of fully phosphorylated sub-

strate decreases with the number of phos-

phorylation steps. (D) Enzyme processivity

establishes a temporal ordering of substrate

phosphorylation. Distributive substrates are

more susceptible to dephosphorylation by

phosphatases and to competition by more

processive substrates.

Fig. 8. Integration of signalling events by multisite phosphorylation. (A) Redundance. Phosphorylation at any site is sufficient for protein acti-

vation. (B) Summation. Phosphorylation of each site has an additive effect on the protein activity. (C) Synergy. Phosphorylation of both sites

is required for protein activation. (D) Antagonism. One phosphorylation may enhance and another inhibit the protein activity.



poral order of substrate activation or deactivation

(Fig. 7D). The more distributive the phosphorylation

of a substrate, the more likely it is that it will undergo

proofreading before reaching the active state [36,53].

Distributive substrates are more susceptible to dephos-

phorylation and compete less efficiently than proces-

sive substrates for kinase. These mechanisms appear to

explain the ordering of substrate degradation in the

cell cycle [53]. The more processive the multiubiquiti-

nation of a substrate by the ubiquitin ligase anaphase-

promoting complex, the earlier it is degraded relative

to the other substrates.

Integration of signalling events

Individual phosphorylation sites on a protein can be

regulated by different kinases and phosphatases, sug-

gesting that multisite phosphorylation can mediate the

integration of distinct signalling events [122]. In some

cases, phosphorylation at any site is sufficient to pro-

voke a functional change (Fig. 8A). For example, the

apoptosis regulator Bcl-XL/Bcl-2-associated death

promoter (BAD) is phosphorylated at different serine

sites by kinases activated by the MAP kinase cascade,

the phosphoinositol-3-kinase ⁄Akt pathway and the

cAMP pathway. Any phosphorylation is enough to

trigger dissociation of BAD from the anti-apoptotic

protein Bcl-XL, inhibiting the pro-apoptotic activity

of BAD [123]. In other cases, the effect of multisite

phosphorylation on the protein activity is additive

(Fig. 8B). For instance, phosphorylation of two dis-

tinct sites in cyclic nucleotide phosphodiesterase 3B

(PDE3B) by the kinases PKA and PKB is required for

full activity of PDE3B [124]. PDE3B is partially acti-

vated if only one of the two sites becomes phosphory-

lated. Some signalling molecules act as ‘coincidence

detectors’, and are activated only when two incoming

signals occur within a limited time window (Fig. 8C).

For example, cAMP and calcium pathways act cooper-

atively to induce dephosphorylation of the transcrip-

tional co-activator target of rapamycin 2 at distinct

sites by inhibiting the associated kinase salt-inducible

kinase 2 and simultaneously stimulating the phospha-

tase PP2B [125].

Phosphorylation of distinct residues may also have

antagonistic effects on the protein activity (Fig. 8D).

One phosphorylation may enhance and another inhibit

the activity of the same protein. For example, the

ability of the actin-binding protein cortactin to

activate neuronal Wiskott–Aldrich syndrome protein

(N-WASP) via its SH3 domain is promoted by ERK

and inhibited by Src [126]. ERK phosphorylates

Ser405 and Ser418, rendering the SH3 domain of cort-

actin fully accessible for binding N-WASP, whereas

Src phosphorylates Tyr466 and Tyr482, which are

located immediately upstream of the SH3 domain,

abolishing the effect of ERK phosphorylation. In

another example, phosphorylation of Bim on Thr112

by c-Jun-N-terminal kinase increases its apoptotic

activity, while ERK-mediated phosphorylation on

Ser55 ⁄ 65 ⁄ 73 causes rapid proteasomal degradation of

Bim [127].

Multisite phosphorylation can also elicit combinato-

rial effects. A distinct function may be activated

when, in addition to the phosphorylation of a certain

residue, a second residue is also phosphorylated. For

example, phosphorylation of histone H3 at Ser10 is

associated with gene activation, whereas phosphoryla-

tion of both Ser10 and Ser28 marks condensed

chromatin [26].

Regulation of individual phosphorylation sites

Individual phosphorylation sites may control different

functions of the target protein, such as nuclear import,

export, binding to DNA or interactions with other

proteins, thereby requiring precise regulation. As seen

before, this can be achieved when each residue is phos-

phorylated by a distinct kinase. However, individual

control of multiple sites by the same kinase is also

feasible, whereby particular sites are phosphorylated at

specific kinase activities while others are dephosphoryl-

ated. Cyclic phosphorylation mechanisms (see Fig. 2A)

may lend themselves to this type of regulation [29].

For example, for a protein with two phosphorylation

sites A and B, if site A is phosphorylated more rapidly

than site B, and site B is dephosphorylated more

rapidly than site A, the two partially phosphorylated

forms ApB and ABp will occur at distinct kinase

activities.

An interesting example of individual regulation of

phosphorylation sites by the same kinase was recently

described for autophosphorylation of the protein KaiC

at two sites (Ser431 and Thr432) in the cyanobacterial

circadian clock [128]. The amount of phosphorylated

KaiC oscillates with the circadian period, and, interest-

ingly, its four phosphorylation forms predominate at

different time points in the cycle. The protein KaiC au-

tophosphorylates and autodephosphorylates at both

Ser431 and Thr432; the autophosphorylation is

enhanced by the protein KaiA, whereas KaiB antago-

nizes the activity of KaiA. Such negative feedback

ensures that the amount of phosphorylated KaiC oscil-

lates with the circadian period, and, in particular, that

the four distinct phosphorylation forms predominate

at different time points in a cycle.



Concluding remarks

Notwithstanding the interesting developments in

recent years reviewed here, the kinetic analysis and

accompanying mathematical modelling of multisite

protein phosphorylation is still in its infancy. More-

over, phosphorylation is only one of several types of

reversible covalent protein modification. Acetylation,

methylation, ubiquitination and sumoylation are pro-

tein modifications that are of great current interest

(and have been intensely studied for histones [129],

for example). The modeling concepts introduced here

may also be applicable to these other kinds of protein

modification. Future experimentally based mathemati-

cal modelling should help to elucidate the function of

multisite protein modifications in such important pro-

cesses as the timing of cell-cycle events, the control of

circadian rhythms, and antigen recognition in the

immune system. High-throughput quantitative tech-

niques hold enormous promise for the mechanistic

understanding of phosphorylation (and other protein

modification) networks in the cell. They will surely

pose new challenges and present new opportunities

for mathematical modelling and simulation to obtain

predictive models for the dynamics of cellular regula-

tory networks.

Acknowledgements

The work was supported by the Initiative and Net-

working Fund of the Helmholtz Association within the

Helmholtz Alliance on Systems Biology ⁄SBCancer, theHepatoSys program of the German Federal Ministry

for Education and Research (BMBF), and the EU-FP7

Network Systems Biology of T-cell Activation (SYB-

ILLA).

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Multisite protein phosphorylation - from molecular mechanisms to kinetic models

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