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The Journal of Cell Biology, Volume 164, Number 3, February 2, 2004 353–359
http://www.jcb.org/cgi/doi/10.1083/jcb.200308060 353
Report
Signaling switches and bistability arising from
multisite phosphorylation in protein kinase cascades
Nick I. Markevich, Jan B. Hoek, and Boris N. Kholodenko
Department of Pathology, Anatomy, and Cell Biology, Thomas Jefferson University, Philadelphia, PA 19107
itogen-activated protein kinase (MAPK) cascades
can operate as bistable switches residing in either
of two different stable states. MAPK cascades are
often embedded in positive feedback loops, which are
considered to be a prerequisite for bistable behavior. Here
we demonstrate that in the absence of any imposed feedback
regulation, bistability and hysteresis can arise solely from a
distributive kinetic mechanism of the two-site MAPK phosphorylation
and dephosphorylation. Importantly, the reported
kinetic properties of the kinase (MEK) and phosphatase
M
(MKP3) of extracellular signal–regulated kinase (ERK) fulfill
the essential requirements for generating a bistable switch
at a single MAPK cascade level. Likewise, a cycle where
multisite phosphorylations are performed by different kinases,
but dephosphorylation reactions are catalyzed by the same
phosphatase, can also exhibit bistability and hysteresis.
Hence, bistability induced by multisite covalent modification
may be a widespread mechanism of the control of
protein activity.
Introduction
Cellular pathways often display switch-like behavior in
response to a transient or graded stimulus. Such responses
can be either ultrasensitive, resembling the responses of
cooperative enzymes, or true switches between alternate
states of a bistable system. A system is termed bistable if it
can switch between two distinct stable steady states but
cannot rest in intermediate states. A bistable system always
displays hysteresis, meaning that the stimulus must exceed a
threshold to switch the system to another steady state, at
which it may remain, when the stimulus decreases. Recently,
there has been emerging interest in bistability as a ubiquitous
and unifying principle of cellular regulation. Under proper
condition, bistability can arise from substrate inhibition or
product activation in metabolic pathways (Sel’kov, 1975)
or from a double-negative feedback or positive feedback in
artificial genetic circuits in Escherichia coli and Saccharomyces
cerevisiae (Gardner et al., 2000; Becskei et al., 2001). Hysteresis
was documented in responses of signaling systems
involving positive feedback loops, such as MAPK cascades and
a cell cycle mitotic trigger (Bhalla et al., 2002; Pomerening
et al., 2003; Sha et al., 2003).
Signaling through MAPK pathways is critical for cellular
decisions to proliferate, differentiate, or undergo apoptosis
(Chang and Karin, 2001). MAPK cascades are evolutionarily
conserved and consist of several (usually three) levels, where
the activated kinase at each level phosphorylates the kinase at
the next level down the cascade. A three-tier cascade comprises
a MAPK, a MAPK kinase (MAPKK), and a MAPKK kinase.
An important feature of each individual level is a two-site
phosphorylation required for full activation and, consequently,
a two-site dephosphorylation by protein phosphatases. For
instance, all MAPKs require phosphorylation on conserved
threonine (T) and tyrosine (Y) residues in a TXY motif.
Dual specificity phosphatases, the MAP kinase phosphatases
(MKPs), dephosphorylate both residues on MAPK.
In a variety of cells, MAPK cascades are tightly controlled
by multiple feedback regulations. For instance, in Xenopus
oocytes, the p42 MAPK cascade and the c-Jun NH2-terminal
kinase cascade appear to be embedded in positive feedback
loops (Ferrell and Machleder, 1998; Bagowski and Ferrell,
2001). In mammalian cells, extracellular signal–regulated
kinase (ERK) activates phospholipase-A2 and phosphorylates
SOS, creating positive and negative feedback circuits (Langlois
et al., 1995; Bhalla et al., 2002). Although the basic structure
of all MAPK cascades is the same, differences in feedback
control enable them to generate a plethora of biological
The online version of this article includes supplemental material.
Address correspondence to Boris N. Kholodenko, Department of Pathology,
Anatomy, and Cell Biology, Thomas Jefferson University, 1020
Locust St., Philadelphia, PA 19107. Tel.: (215) 503-1614. Fax: (215)
923-2218. email: Boris.Kholodenko@jefferson.edu
Key words: covalent protein modification; multisite phosphorylation;
mitogen-activated protein kinase cascades; bistable biological switch
Abbreviations used in this paper: ERK, extracellular signal–regulated
kinase; MAPKK, MAPK kinase; MEK, ERK kinase; MKP, MAP kinase
phosphatase.
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Supplemental Material can be found at:
354 The Journal of Cell Biology | Volume 164, Number 3, 2004
responses, including oscillations, gradual and ultrasensitive responses,
and discontinuous bistable switches (Huang and Ferrell,
1996; Kholodenko et al., 1997; Kholodenko, 2000;
Bhalla et al., 2002; Heinrich et al., 2002).
A positive or double-negative feedback regulation is generally
considered to be a prerequisite for bistability in accordance
with Thomas’s conjecture that a “positive” circuit
is a necessary structural condition for multistationarity
(Thomas et al., 1976). In fact, all known bistable signaling
systems contain activating molecular interactions or even
numbers of inhibitory interactions within a feedback loop.
For instance, in the MAPK cascades in Xenopus oocytes, bistability
is thought to arise from activation of the upstream
kinases by p42 MAPK and c-Jun NH2-terminal kinase
(Ferrell and Machleder, 1998; Bagowski and Ferrell, 2001).
At first glance, bistability cannot arise at an individual
MAPK level, unless there is an allosteric activation or inhibition
of a converter enzyme (kinase or phosphatase) by its
product or substrate, respectively, creating a positive circuit
required for bistability.
The present paper demonstrates that this conclusion is incorrect.
We report that a dual phosphorylation–dephosphorylation
cycle (a two-site covalent-modification cycle)
with a nonprocessive, distributive mechanism for the kinase
and phosphatase already possesses all the required ingredients
to display bistable behavior. The key attributes include
substrate saturation of at least one of the two converter enzymes
and competitive inhibition of the second covalentmodification
step by the substrate of the first step. Importantly,
in the absence of any allosteric interaction, the
required feedback emerges at the systems level as a consequence
of competitive inhibition and saturation. Both the
ERK kinase (MEK) and phosphatase (MKP3) satisfy these
conditions (Ferrell and Bhatt, 1997; Zhao and Zhang,
2001). We conclude that bistability and hysteresis are inherent
properties of multistep phosphorylation–dephosphorylation
cycles, such as the ERK cycle. This feature by itself may
cause a MAPK cascade to exhibit bistable behavior even in
the absence of feedback loops.
Results and discussion
Kinetic analysis background: description of a dual
phosphorylation–dephosphorylation cycle
For a generic MAPK, the activation–deactivation cycle can
include four distinct forms: the dephosphorylated MAPK
(M), the form phosphorylated on tyrosine alone (MpY), the
form phosphorylated on threonine alone (MpT), and
MAPK phosphorylated on both residues (Mpp). A kinetic
mechanism for a dual phosphorylation or dephosphorylation
might be either processive or distributive. In a processive
catalysis, after binding the substrate, the kinase or
phosphatase carries out two phosphorylations or dephosphorylations
before releasing the final product. In contrast,
in a nonprocessive, distributive mechanism, the enzyme releases
the intermediate monophosphorylated product, and a
new collision is required for the conversion of this intermediate
into the final product.
Recent data demonstrated that both dual phosphorylation
and dephosphorylation of MAPK occur through a distributive,
two-collision mechanism (Burack and Sturgill, 1997;
Ferrell and Bhatt, 1997; Zhao and Zhang, 2001). This kinetic
mechanism makes MAPK activation responses “ultrasensitive”
(Goldbeter and Koshland, 1981; Huang and Ferrell,
1996; Kholodenko et al., 1998) and, as we will show,
may also cause hysteresis and bistability.
Initially, we will consider a simple four-step cycle in which
both MAPKK and MKP follow a strictly ordered mechanism
with the same intermediate (Mp), Fig. 1. In this cycle,
the number of different MAPK forms reduces to three (M,
Mp, and Mpp). The total concentration (Mtot) of these
forms remains constant, and the system dynamics is described
by the following equations:
(1)
Rate expressions. Scheme 1 illustrates a distributive, ordered
mechanism of dual phosphorylation of MAPK by
MAPKK.
Scheme 1
At constant ATP/ADP and under steady-state assumptions
for the intermediate protein–protein complexes in Scheme
1, the following Michaelis-Menten expressions describe the
rates v1 and v2 (Fig. 1):
(2)
where [MAPKK]tot is the total MAPKK concentration, and
the kinetic parameters k1
cat
, k2
cat
, Km1, and Km2 relate to the
d M[ ] dt⁄ v4 v1,–=
d Mpp[ ] dt⁄ v2 v3,–=
Mp[ ] Mtot M[ ]– Mpp[ ].–=
M MAPKK M–MAPKK Mp MAPKK
k1 k2
kϪ1
+→↔+
Mp MAPKK Mp–MAPKK Mpp MAPKK
k3
kϪ3
k4
+→↔+
v1
k1
cat
MAPKK[ ]tot M[ ] Km1⁄⋅ ⋅
1 M[ ] Km1⁄ Mp[ ] Km2⁄+ +( )
--------------------------------------------------------------------------=
v2
k2
cat
MAPKK[ ]tot Mp[ ] Km2⁄⋅ ⋅
1 M[ ] Km1⁄ Mp[ ] Km2⁄+ +( )
-----------------------------------------------------------------------------,=
Figure 1. Dual phosphorylation–dephosphorylation cycle of MAPK,
in which both MAPKK and MKP follow distributive ordered kinetic
mechanisms. M, Mp, and Mpp stand for the unphosphorylated,
monophosphorylated, and bisphosphorylated forms of MAPK.
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Bistability arising from multisite phosphorylation | Markevich et al. 355
elementary rate constants as follows: k1
cat
ϭ k2; k2
cat
ϭ k4;
Km1 ϭ (kϪ1 ϩ k2)/k1; and Km2 ϭ (kϪ3 ϩ k4)/k3.
ERK dephosphorylation by the phosphatase MKP3 was
reported to follow a distributive, ordered mechanism in
which the phosphotyrosine residue is dephosphorylated first
and MpT dissociates from the enzyme (Scheme 2, where
Mp stands for MpT) (Zhao and Zhang, 2001). Subsequently,
MpT binds to another MKP3 molecule, yielding
the complex Mp–MKP3*, and the phosphothreonine residue
is dephosphorylated.
Scheme 2
Based on Scheme 2, the following Michaelis-Menten expressions
are derived for the rates v3 and v4 (Fig. 1):
(3)
Scheme 2 explicitly considers both the dephosphorylation
step and the product release step, whereas in Scheme 1, the
catalysis and product dissociation are lumped into a single
step. The presence of an additional step does not alter the
form of the Michaelis-Menten equation, changing only the
expressions for the Michaelis and catalytic constants in terms
of the elementary rate constants. However in Scheme 2, a reversible
release of the product leads to an additional term in
the denominator of the rate equation due to the sequestration
of the phosphatase by its product (as opposed to the kinetically
irreversible product release for the kinase). As we
will see below, this sequestration decreases the parameter domain
where the MAPK cycle exhibits bistability.
A description of the MAPK cycle of Fig. 1 at the elementary
step level involves all reactions shown in Schemes 1 and
2. The differential equations, rate expressions and kinetic
constants are given in Table S1 (available at http://www.
jcb.org/cgi/content/full/jcb.200308060/DC1).
A more complex kinetic mechanism of the ERK cycle.
Dual phosphorylation of Xenopus p42 MAPK and rat p42
ERK by MEK occurs through a distributive, random mechanism,
Scheme 3 (Ferrell and Bhatt, 1997). The first phosphorylation
of p42 ERK (M) is predominantly on tyrosine
residue, yielding MpY, whereas the yield of the form phosphorylated
on threonine (MpT) is ‫ف‬9% of the total monophosphorylated
ERK.
Mpp MKP3 Mpp–MKP3 Mp–MKP3 Mp MKP3
h1
hϪ1
h2 h3
hϪ3
+↔→↔+
Mp MKP3 Mp–MKP3* M–MKP3 M MKP3
h4 h5 h6
hϪ4 hϪ6
+↔→↔+
v3
k3
cat
MKP3[ ]tot Mpp[ ] Km3⁄⋅ ⋅
1 Mpp[ ] Km3⁄ Mp[ ] Km4⁄ M[ ] Km5⁄+ + +( )
--------------------------------------------------------------------------------------------------------------,=
v4
k4
cat
MKP3[ ]tot Mp[ ] Km4⁄⋅ ⋅
1 Mpp[ ] Km3⁄ Mp[ ] Km4⁄ M[ ] Km5⁄+ + +( )
--------------------------------------------------------------------------------------------------------------;=
k3
cat
h2 1 h2 h3⁄+( )⁄ ;=
k4
cat
h5 1 h5 h6⁄ hϪ3 hϪ4 h5+( ) h3 h4⋅( )⁄⋅+ +[ ]
Ϫ1
;⋅=
Km3 hϪ1 h2+( ) h1 h1 h2 h3⁄⋅+( )⁄ ;=
Km4 hϪ4 h5+( ) h4 1 h5 h6⁄ hϪ3 hϪ4 h5+( ) h3 h4⋅( )⁄⋅+ +[ ]⋅{ }
Ϫ1
;⋅=
Km5 h6 hϪ6⁄( ).=
Scheme 3
Kinetic constants for the MEK-catalyzed reaction were
calculated from the data on the time course of MpY and
MpT accumulation (Burack and Sturgill, 1997; Ferrell
and Bhatt, 1997), using NLSQ minimization implemented
in the software package Dbsolve (Goryanin et al.,
1999) (Fig. S1, available at http://www.jcb.org/cgi/content/
full/jcb.200308060/DC1).
The random mechanism makes the dual phosphorylation–dephosphorylation
cycle of ERK more complex than
shown in Fig. 1. The kinetic scheme in Fig. 2 shows how
ERK (M) is activated via MpY and MpT to yield Mpp and
also takes into account that the phosphatase MKP3 can
dephosphorylate both forms MpY and MpT (Zhao and
Zhang, 2001). The kinetic equations for both elementary
step and Michaelian descriptions of the ERK cycle are given
in Tables S2 and S3 (available at http://www.jcb.org/cgi/
content/full/jcb.200308060/DC1).
Regulatory properties of a dual phosphorylation–
dephosphorylation cycle responsible for bistability
To explain how bistability arises in a two-site phosphorylation–dephosphorylation
cycle of MAPK (Fig. 1), we will
first impose only one of the two steady-state conditions, e.g.,
for the unphosphorylated MAPK (M), d[M]/dt ϭ v1 Ϫ
v4 ϭ 0. Because of the conservation relationship, the monophosphorylated
MAPK (Mp) can be expressed in terms of M
and Mpp (Eq. 1), and the stationary condition v1 ϭ v4 relates
changes in [M] and [Mp] to changes in [Mpp] (i.e.,
[M] and [Mp] are implicit functions of [Mpp]). Assuming
that both the kinase and phosphatase are saturated by their
M MEK M–MEK MpY MEK
k1 k2
kϪ1
+→↔+
MpY MEK MpY–MEK Mpp MEK
k3 k4
kϪ3
+→↔+
M MEK M–MEK* MpT MEK
k5 k6
kϪ5
+→↔+
MpT MEK MpT–MEK Mpp MEK
k7 k8
kϪ7
+→↔+
Figure 2. Dual phosphorylation–dephosphorylation cycle of ERK.
The ERK kinase (MEK) follows a distributive random mechanism.
The ERK phosphatase (MKP3) obeys an ordered mechanism with
MpT as an intermediate, but is also capable of dephosphorylating
MpY (step 7).
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356 The Journal of Cell Biology | Volume 164, Number 3, 2004
respective substrates, M and Mpp, we will analyze how [M]
and [Mp] change with increasing [Mpp] (below we show
that it is sufficient for only one enzyme to be saturated). As
Mp competes with Mpp for access to the phosphatase, its
saturation by Mpp implies that the rate v4 is inhibited by
Mpp (Eq. 3). In addition, v4 is competitively inhibited by its
product M. The rate v1 does not depend on Mpp and is inhibited
by Mp because Mp competes with M (Eq. 2).
Therefore, an increase in [Mpp] should be compensated by
either a decrease in [M] or by an increase in [Mp] or both to
maintain the balance of v4 ϭ v1.
Now, all steady states of the MAPK cycle can be found
by adding the second stationary condition, d[Mpp]/dt ϭ
v2 Ϫ v3 ϭ 0. A convenient way of doing so is to analyze the
dependence of the rates of Mpp production (v2) and consumption
(v3) on [Mpp] under the stationary condition
v4 ϭ v1 (“stationary” production/consumption rates). As
M competes with Mp for access to MAPK, and an increase
in [Mpp] is accompanied by decreasing [M] and increasing
[Mp], as explained above, the stationary rate v2 will increase
with increasing [Mpp], which is equivalent to apparent
product activation or positive feedback. The term
apparent emphasizes that there is no direct molecular activation
of MAPK by Mpp, and this activation is a systemslevel
effect.
The stationary Mpp consumption rate (v3) depends hyperbolically
on its substrate Mpp. Fig. 3 illustrates that as
functions of Mpp, the rates v2 and v3 potentially have three
points of intersection, meaning that the equation v2 ϭ v3 determines
three distinct steady states (within the bistability
parameter range, the stationary rates v1 and v2 generically do
not assume the same values). The steady states S1 and S3,
which correspond to low and high concentrations of Mpp,
are stable, whereas the intermediate state S2 is unstable. Note
that if the stationary condition for Mpp (v2 ϭ v3) is considered
first, the stationary rate v4 of M supply displays apparent
product activation by M, and the same three steady
states are obtained.
Parameter and concentration domain, where the system
exhibits bistability
The key properties of a two-step protein modification cycle
giving rise to bistability include substrate saturation of the
first modification step and competitive inhibition of a second
reaction by the substrate of the first step. In terms of the
Michaelis constants and concentrations, these conditions require
that the Km for the substrate of the first step (Km1 or
Km3 for the kinase or phosphatase) should be considerably
lower than the total concentration of the target protein, Mtot.
In addition, the competitive inhibition should be strong,
implying that the Km for the substrate of the second step
should be greater than the Km for the substrate of the first
step. For the kinase (Eq. 2), this results in Km1 Ͻ Km2 and
Km1 Ͻ Mtot.
This intuitive consideration can be formalized by analyzing
the saddle-node bifurcation, where an unstable steady state
merges with a stable state, leaving the system with a single
steady state. In biological terms, at the bifurcation point, the
bistable response becomes merely ultrasensitive, or vice versa.
As shown in Fig. 3 B, if the catalytic activity of the first dephosphorylation
decreases, the rate v3 descends (dashed line)
and the two steady states S1 and S2 approach each other until
both merge and then disappear, leaving a single state S3. By
calculating critical parameter values at which the bifurcation
appears, we obtain a bifurcation diagram that determines the
bistability domain. Fig. 4 illustrates this domain in the plane
of the Michaelis constants for the kinase reaction, Km1 and
Km2. The bifurcation diagram confirms these considerations
and shows that bistable responses emerge even if only one enzyme
is saturated, although the bistability domain becomes
much smaller (Fig. 4, domain 3).
The bistability domain also depends on the catalytic constants
of the converter enzymes. For instance, the k1
cat
/k2
cat
ratio regulates the extent to which the stationary Mpp proFigure
3. Hysteresis and bistability in a dual phosphorylation cycle.
Three steady states, S1, S2, and S3 (panel A), correspond (panel B) to
the three intersection points of the dependencies of stationary rates
of Mpp production v2 and consumption v3 on [Mpp]. The parameter
values are as follows: Km1 ϭ 50, Km2 ϭ 500, Km3 ϭ 22, Km4 ϭ 18
(values in nM); k1
cat
ϭ 0.01, k2
cat
ϭ 15, k3
cat
ϭ 0.084, k4
cat
ϭ 0.06 (sϪ1
);
Mtot ϭ 500, [MKP3]tot ϭ 100 (nM). (B) [MAPKK]tot ϭ 50 nM. k3
cat
ϭ
0.061 sϪ1
, dashed line.
Figure 4. Bifurcation diagram in the Km1 Km2 plane. Bistability domains
calculated for different models correspond to the closed regions
bounded by solid (1), dash-dot (2), and dash (3) lines. Bistability
domain 1 is calculated for Michaelis-Menten equations (Eqs. 2 and 3),
the parameters are given in the legend to Fig. 3. Domain 2 is calculated
for the elementary step model (the equations and rate constants
are given in Table S1, available at http://www.jcb.org/cgi/content/full/
jcb.200308060/DC1). Domain 3 corresponds to an “unsaturated”
phosphatase, v3 ϭ 0.084 и [Mpp], v4 ϭ 0.06 и [Mp]. Mtot ϭ 500,
[MAPKK]tot ϭ 100, [MPK3]tot ϭ 100 (nM) for all calculations.
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Bistability arising from multisite phosphorylation | Markevich et al. 357
duction rate v2 is activated by Mpp. For considerable product
activation, k1
cat
should be much smaller than k2
cat
, as
shown in the bifurcation diagram in the k1
cat
, k2
cat
plane
(Fig. S2, available at http://www.jcb.org/cgi/content/full/
jcb.200308060/DC1).
Sequestration effects: when Michaelis-Menten
equations should be substituted by an elementary
step description
A steady-state approximation for the enzyme–substrate complexes
gives rise to the Michaelis-Menten equation, substituting
a (micro)description of each elementary step. This approximation
holds well when the substrate concentration
greatly exceeds that of the enzyme or when only steady states
of an “open” reaction system are considered. It may at first
appear that because the stationary behavior of the MAPK cycle
is considered, the Michaelis-Menten equations are applicable
even when the relative abundances of MAPK, its kinase,
and phosphatase are similar. However, this argument
overlooks the fact that the total MAPK concentration is conserved,
and the concentrations of the MAPK complexes with
the converter enzymes cannot be neglected in the total
MAPK balance. In fact, it has been shown that for systems
with conserved moieties, the difference between steady-state
description at the macro level versus micro level becomes important
(Kholodenko and Westerhoff, 1995). Fig. 4 illustrates
a marked deviation of the bistability domain calculated
for the Michaelis-Menten (macro)description (line 1) from
the domain calculated for the elementary step model (2).
Bistability and hysteresis in the ERK activation
Random phosphorylation of ERK by MEK on either threonine
or tyrosine results in two branches of ERK (M) activation
either through MpY or MpT, Fig. 2. The appearance of
two branches in the ERK cycle does not change the premises
that give rise to bistability. Similarly to a cycle with an ordered
mechanism, bistability is brought about by an emerging
positive feedback from Mpp under the stationary condition
for M and one of the monophosphorylated forms, MpT
or MpY. Moreover, if along two different branches, the corresponding
steps had the same rate constants, the ERK cycle
would exhibit hysteresis under practically the same conditions
as the simple cycle of Fig. 1. In the general case, the bistability
domain depends on the rate constants of the elementary
steps and on the relative abundances of ERK,
MEK, and MKP3.
Our computational model of the ERK cycle takes into account
all available kinetic information and demonstrates
that bistability and hysteresis exist for realistic parameter values
retrieved from experimental data. Fig. 5 illustrates the
bistability domain in the plane of the total MEK and MKP3
concentrations. The two insets show hysteresis in the
response of the bisphosphorylated ERK to changes in
[MEK]tot and [MKP3]tot. Note that the threshold values for
rising and descending transitions are equal to the boundary
values of the bistability domain. Beyond the bistability domain,
hysteresis is not observed, but the ERK cycle can still
behave as an ultrasensitive switch.
Proposed experimental verification and conclusions
Our finding of potential bistability in the cyclic two-step
phosphorylation–dephosphorylation of ERK is awaiting direct
experimental verification. A feasible experimental design
for in vitro test is suggested by Fig. 5, which shows that adding
or removing active MEK (or MKP3) leads to different
ERK activities at the same MEK (or MKP3) level, depending
on whether experimental manipulations have begun in
the ERK “off” or “on” state. If initially ERK is in its off
state, adding [MEK] causes a gradual increase in the ERK
activity, and only after [MEK] increases over a threshold,
ERK switches to its on state (Fig. 5, Going up). When starting
with the on state of ERK (Fig. 5, Coming down),
[MEK] can decrease to below the threshold, yet the activity
of ERK exceeds by more than twofold its activity obtained
Figure 5. Bifurcation diagram for the ERK
cycle in the plane of the total concentrations
of MEK and MKP3. The “off” and “on” states of
the ERK activation correspond to the area above
(1) and below (3) the bistability domain (2). The
dependences of the [ERK-pYpT] on [MEK]tot at
constant [MKP3]tot ϭ 180 nM and on [MKP3]tot
at constant [MEK]tot ϭ 400 nM are shown as
insets. The differential equations and the elementary
rate constants are given in Table S2
(available at http://www.jcb.org/cgi/content/full/
jcb.200308060/DC1). [ERK]tot ϭ 1,000 nM.
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358 The Journal of Cell Biology | Volume 164, Number 3, 2004
for the same [MEK] when beginning with the off state of
ERK. Experimentally, the level of the active MEK or MKP3
can be controlled, e.g., by using degradable proteins or enzymes
attached to beads that can be rapidly removed. A similar
approach has been recently used to demonstrate hysteresis
in the activation of Cdc2 by cyclin B in Xenopus egg
extracts (Pomerening et al., 2003; Sha et al., 2003).
Bifurcation analysis helps assess the parameter range
where bistability exists. Emerging product activation feedback
is a key premise for bistability in the ERK cycle. We
can approximate this activation by a Hill-type expression,
and estimate the parameters involved. For 200 nM
[MEK]tot, 100 nM [MKP3]tot, and [ERK]tot in the range of
250 to 1000 nM, the best fit values for A, Ka, and n are 15–
30, 700–2,000 nM, and 1.1–2.4, respectively (both the stationary
rate of Mpp production and Hill-type approximation
are depicted in Fig. S3, available at http://www.jcb.org/
cgi/content/full/jcb.200308060/DC1). The estimated values
for Ka imply that a strong positive feedback appears only
for sufficiently high [ERK]tot (Ͼ250–300 nM), and increasing
the abundance of ERK enhances the bistability range
(Figs. S4 and S5, available at http://www.jcb.org/cgi/
content/full/jcb.200308060/DC1). ERK sequestration by
MKP3 decreases that range. These estimates may help test
the theoretical prediction of bistability in the ERK cycle.
Bistability and zero-order ultrasensitivity appear to be inherent
“stoichiometric” properties of a dual phosphorylation
cycle. Hysteresis can be observed for any mechanism of distributive
catalysis, e.g., ordered for both converter enzymes
(Fig. 3), ordered and random (Fig. 5), or random for both
(Figs. S6, S7 and Table S4, available at http://www.jcb.org/
cgi/content/full/jcb.200308060/DC1). Bistable behavior displayed
by single cascade cycles may lead to multistability in
the whole pathway regardless of the presence of feedback
loops between different cascade levels. Fig. S8 (available at
http://www.jcb.org/cgi/content/full/jcb.200308060/DC1) illustrates
potential multiple steady states for a MAPK pathway
in the absence of any imposed feedback regulation (the kinetic
model used for simulations is similar to models reported previously;
Huang and Ferrell, 1996; Kholodenko et al., 2002).
Multisite phosphorylation is a recurrent theme in a plethora
of signaling systems, including the cell cycle (Tyson et al.,
2001). Signaling proteins are phosphorylated by specific kinases
at multiple residues, resulting in precise dynamic tuning
of the signaling potential. Protein phosphatases often have
much broader substrate specificity than protein kinases. Dephosphorylation
within diverse motifs can be performed by
the same phosphatase, such as the protein phosphatase 2A. Remarkably,
hysteresis continues to be an inherent property of a
cycle, where successive phosphorylations are performed by different
kinases, as long as dephosphorylations are catalyzed by a
single phosphatase (Fig. S9, available at http://www.jcb.org/
cgi/content/full/jcb.200308060/DC1). Cell fate decisions may
depend on bistable behavior of signaling cascades. Bistable responses
at individual cascade levels increase the robustness of
such bistable switches with positive feedback regulation and
expand the bistability domain in the parameter space.
1 A Mpp Ka⁄⋅+( )
n
1 Mpp Ka⁄+( )
n
------------------------------------------------,
In a cell cycle oscillator, bistability arises from positive and
double-negative feedback loops in the reactions, where Cdc2
activates its activator (the phosphatase Cdc25) and inactivates
its inhibitor (the kinases Wee1 and Myt1). Cdc25 and
Wee1 themselves can be phosphorylated on multiple sites
and therefore can potentially exhibit hysteresis, implying
that the Cdc2/cyclin system can display multiple steady
states, and not only bistability. In summary, switch-like behavior
at the level of a single protein controlled by a multisite
phosphorylation may be a widespread regulatory feature
of biological systems.
Materials and methods
Software used for numerical analysis
Numerical calculations of stationary rates and concentrations, the stability
analysis of steady states, and the bifurcation analysis were performed using
Dbsolve (Goryanin et al., 1999). Dbsolve 5 is freely available at http://
biosim.genebee.msu.su/index_en.htm.
Online supplemental material
The online supplemental material (Tables S1–S4 and Figs. S1–S9) is
available at http://www.jcb.org/cgi/content/full/jcb.200308060/DC1. A description
of the MAPK cycle at the elementary step level is presented in Table
S1. A description of the ERK cycle at the elementary step level is presented
in Table S2. The Michaelis-Menten rate equations and parameter
values for the ERK phosphorylation-dephosphorylation cycle are presented
in Table S3. Table S4 contains kinetic equations and rate constants of elementary
steps for distributive random mechanisms of MAPK kinase and
phosphatase. Fig. S1 shows a simulation of the time course of tyrosine and
threonine phosphorylation of p42 MAPK by MAPKK. Fig. S2 is a bifurcation
diagram for the elementary steps description of MAPK phosphorylation–dephosphorylation
cycle on the k1
cat
, k2
cat
plane. Fig. S3 shows the
Hill-type approximation of emerging product activation in the ERK cycle.
Fig. S4 shows bifurcation diagrams for the elementary step description of
the ERK cycle in the plane of the total concentrations of MEK and MKP3 at
different total ERK concentrations. Fig. S5 shows steady-state responses of
bisphosphorylated ERK to total MEK concentration. Fig. S6 shows the dual
phosphorylation–dephosphorylation cycle of MAPK (M), in which both
MAPKK and MKP follow distributive random kinetic mechanisms. Fig. S7
shows a bifurcation diagram for the MAPK phosphorylation cycle in the
plane of the activities (total concentrations) of the kinase and phosphatase.
Fig. S8 shows hysteresis and multistability in the MAPK cascade arising
from the bistable behavior of individual cycles of dual phosphorylation
and dephosphorylation. Fig. S9 shows bistability in a cycle where MAPK
(M) is phosphorylated by two different kinases (MAPKK1 and MAPKK2)
and dephosphorylated by a single phosphatase.
This work was supported by the National Institutes of Health grant
GM59570.
Submitted: 11 August 2003
Accepted: 19 December 2003
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