Tài liệu Báo cáo khoa học: Multisite protein phosphorylation – from molecular mechanisms to kinetic models pdf

REVIEW ARTICLE
Multisite protein phosphorylation – from molecular
mechanisms to kinetic models
Carlos Salazar and Thomas Ho
¨
fer
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-associated
tyrosine 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:
T. Ho
¨
fer, 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:
(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, ).
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 2
N
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 (2
2
) 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 2
N
. 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. Ho
¨
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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. Ho
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FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3179
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 G
1
⁄ 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 G
1
phase before binding
to the SCF
Cdc4
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 SCF
Cdc4
binding.
Any combination of six phosphorylated sites is suffi-
cient for Sic1 degradation. While singly phosphory-
lated Sic1 binds to SCF
Cdc4
very weakly, multiply
phosphorylated Sic1 can bind efficiently, presumably
by increasing the local concentration of interaction
sites around the SCF
Cdc4
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 (), Swiss-Prot
( 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 multisite
phosphorylation
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-
Multisite protein phosphorylation C. Salazar and T. Ho
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3180 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS
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.
C. Salazar and T. Ho
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FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3181
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 (2
N
) 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.
Multisite protein phosphorylation C. Salazar and T. Ho
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3182 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS
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
Table 2. Enzyme processivity and order of phospho-site processing for some substrates. ASF/SF2, alternative splicing factor; ATF2, activating transcription factor 2; CDK, cyclin dependent
kinase; MEK, MAPK/ERK kinase; MKP3, mitogen-activated protein kinase phosphatase 3; SRPK, serine-arginine-rich protein kinase.
Substrate
name
Type of
substrate Enzyme name (phosphorylated sites)
Type of
enzyme
Order of phospho-site
processing Enzyme processivity
Other
characteristics Reference
b-catenin Transcription
cofactor
CK1 (Ser45) GSK3 (Thr41,
Ser37, Ser33)

Ser ⁄ Thr kinases Sequential phosphorylation
(dual-kinase)
? – [130,131]
ERK2 MAP kinase MEK (Thr183,Tyr185) Thr ⁄ Tyr kinase Random phosphorylation Distributive phosphorylation – [41,70]
MKP3 (Thr183,Tyr185) Dual specificity
(Thr ⁄ Tyr)
phosphatase
Sequential dephosphorylation Distributive dephosphorylation – [71]
ATF2 Transcription
factor
p38 (Thr69, Thr71) Ser ⁄ Thr kinase Random phosphorylation Distributive phosphorylation – [46]
ASF ⁄ SF2 Splicing factor SRPK1 (10 Ser sites) Clk ⁄ Sty
(20 Ser sites)
Ser kinase Sequential phosphorylation Processive phosphorylation Stable kinase-
substrate complex
[27,64,87]
p130Cas Focal adhesion
protein
Scr (15 repeats of YXXP motif) Tyr kinase Random phosphorylation Processive phosphorylation SH3 domain [7,73]
RNA
polymerase II
– Abl (25–52 repeats of
YSPTSPS motif)
Tyr kinase ? Processive phosphorylation SH2 domain [25,132,133]
Pho4 Transcription
factor
a
Pho80 ⁄ Pho85 (five Ser sites) Ser/Thr kinase Sequential phosphorylation Semi-processive
phosphorylation
– [22,76]

Sic1 CDK inhibitor
a
Cdc28–Cln1,2 (nine Ser ⁄ Thr sites) Ser ⁄ Thr kinase Random phosphorylation Distributive phosphorylation – [18,51]
a
cyclin-CDK complex.
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FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3183
next site before it dissociates is k
cat
⁄ (k
cat
+ k
off
), where
k
off
and k
cat
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
P
processive
¼
k
cat
k

cat
þ k
off

N
ð1Þ
(assuming, for simplicity, that all the sites have the
same k
cat
and are modified sequentially).
Indeed, k
cat
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 k
cat
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 K
d

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].
Multisite protein phosphorylation C. Salazar and T. Ho
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3184 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS
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 multisite
phosphorylation
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
C. Salazar and T. Ho
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FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3185
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 (X
n,0
) or in a complex with the kinase
(X
n,K
) or phosphatase (X
n,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
dX
0;K
dt
¼ d
k
K
L
0
X
0;0
À X
0;K

reversible binding of kinase

À a
1
X
0;K
phosphorylation
ð2Þ
where d
k
and L
0
denote the dissociation rate constant
and equilibrium dissociation constant for the binding
of the kinase, a
1
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
Y
n
= X
n,0
+ X
n,K
+ X
n,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 Y
n
are governed by the algebro-differential
equation system
dY
n
dt
¼ a
n
Y
nÀ1
phosphorylation

of Y
nÀ1
Àða
nþ1
þ b
n
ÞY
n
phosphorylation and
dephosphorylation of Y
n
þ b
nþ1
Y
nþ1
dephosphorylation
of Y
nþ1
;
for 0 n N ð3Þ
with effective rates of phosphorylation and dephos-
phorylation of
a
n
¼ a
n
K=L
nÀ1
1 þ K=L
nÀ1

þ P=Q
nÀ1
and
b
n
¼ b
n
P=Q
n
1 þ K=L
n
þ P=Q
n
; 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 (X
n,0
)
or in a complex with the kinase (X
n,K
) or phosphatase (X
n,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.

Multisite protein phosphorylation C. Salazar and T. Ho
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3186 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS
K
T
¼ K þ
X
N
n¼0
Y
n
K=L
n
1 þ K=L
n
þ P=Q
n
and
P
T
¼ P þ
X
N
n¼0
Y
n
P=Q
n
1 þ K=L

n
þ P=Q
n
ð5Þ
In general, this system is nonlinear with respect to
the Y
n
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 K
d
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 (a
n
= a, b
n
= b, L
n
= L, Q
n
= 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,
Y
n
, are given by the system of Eqns (3–5) with new effec-
tive rate constants of phosphorylation and dephosphor-
ylation, a
ran
and b

ran
, defined as follows:
a
ran
¼ðN À n þ 1Þa and b
ran
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 of
various 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
C. Salazar and T. Ho
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FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3187
providing additional mechanisms for the generation of
activation thresholds. This is particularly true for dis-
tributive kinetics (with multiple binding ⁄ dissociation
events 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.
Multisite protein phosphorylation C. Salazar and T. Ho
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3188 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS
(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
Y

n
Y
total




seq
¼
r
n
ðr À 1Þ
r
Nþ1
À 1
and
Y
n
Y
total




ran
¼
N
n

r

n
ð1 þ rÞ
N
ð7Þ
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 s
1
=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
s
seq
¼

1
b
P
N
i¼1
iðN þ 1 À iÞr
Nþi
P
N
i¼0
r
i
and s
ran
¼
1
a þ b
X
N
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,
P

N
i¼1
1=i).It can be shown that random phos-
phorylation is always faster than sequential phosphory-
lation for otherwise equal parameters (i.e. s
ran
< s
seq
)
[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.
C. Salazar and T. Ho
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FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3189
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. Bru
¨

mmer, C. Salazar,
V. Zinzalla, L. Alberghina and T. Ho
¨
fer, 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 S
N
by the sequential recruit-
ment of proteins X
1
, X
2
, … X
N

. Each protein
recruitment step would increase the mole-
cular noise, resulting in asynchronous forma-
tion of the complex S
N
. (B) Sequential
assembly with sharp triggering step. The
coherence in formation of the complex S
N
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 S
N
(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.
Multisite protein phosphorylation C. Salazar and T. Ho
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3190 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS

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

SCF
Cdc4
ubiquitin ligase [18,43,115,116]. It was
recently proposed that the ultrasensitive binding
observed in the Sic1–SCF
Cdc4
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 K
d
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
(K
d
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 C

0
and initiates a sequence of N phosphoryla-
tions, each with rate constant a, generating the inter-
mediate complexes C
1
, C
2
, … C
N
. Only the fully
phosphorylated state C
N
(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
C
N
S
tot
¼
K
K þ L
equilibrium

binding
a
a þ d

N
kinetic
proofreading
ð9Þ
where S
tot
is the total substrate concentration and
L = d ⁄ b is the equilibrium dissociation constant (K
d
)
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
C. Salazar and T. Ho
¨
fer Multisite protein phosphorylation
FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3191
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.
Multisite protein phosphorylation C. Salazar and T. Ho
¨
fer
3192 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS
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.
C. Salazar and T. Ho
¨
fer Multisite protein phosphorylation
FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS 3193
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, the
HepatoSys 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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