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

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-

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

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-

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.

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

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-

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

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.
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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-

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)

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

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-

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].
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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

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

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
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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

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

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

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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

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

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
¨

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.
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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
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

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

However, random versus sequential phosphorylation
can also make a significant difference in timing.
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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
¨

. 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
¨
fer
3190 FEBS Journal 276 (2009) 3177–3198 ª 2009 The Authors Journal compilation ª 2009 FEBS

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

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

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

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-

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-

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