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Systems analysis of MAPK
signal transduction
Nils Blüthgen*‡1,2 and Stefan Legewie†‡1
*Manchester Interdisciplinary Biocentre, School of Chemical
Engineering and Analytical Sciences, The University of Manchester,
131 Princess Street, Manchester M1 7DN, U.K., †Institute for
Theoretical Biology, Humboldt University, Invalidenstraße 43,
10115 Berlin, Germany, and ‡Institute of Pathology, Charité,
Universitätsmedizin Berlin, Charitéplatz 1, D-10117 Berlin, Germany
Abstract
For more than a decade, the MAPK (mitogen-activated protein kinase)
cascade has been studied using mathematical modelling and quantitative
experimentation [1]. The MAPK cascade relays the presence of extracellular
stimuli such as growth hormones to the nucleus and controls the
expression of hundreds of genes. MAPKs control major cell fate decisions
such as proliferation, differentiation and apoptosis, mainly by inducing
alterations in gene expression. In this chapter, we discuss how systems
biology analysis provides insights into the functioning of this cascade. We
show how this pathway assists the cell in responding properly to extracellular
cues by filtering out sub-threshold stimuli, while efficiently transmitting
physiologically relevant inputs. Several different receptors signal through
the MAPK pathway even though they elicit opposite biological responses,
thus raising the question of how specificity is achieved in MAPK signalling.
Experimental studies revealed that specific biological responses are encoded
by quantitative aspects of the MAPK signal such as amplitude or duration.
1Both
authors contributed equally to this chapter.
2To whom correspondence should be addressed (email nils.bluthgen@manchester.
ac.uk).
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We discuss mechanisms that enable the pathway to generate quantitatively
different signals, and also explain how different signals are interpreted by the
downstream gene expression machinery.
Introduction
The three-tiered MAPK (mitogen-activated protein kinase) signal transduction
cascades are activated upon extracellular stimulation and act as intracellular
transducers of environmental signals. Active MAPKs control various
physiological processes and cell fate decisions in all eukaryotic cells, mainly
by regulating gene expression. The classical, most studied MAPK cascade in
higher mammalian cells is the pathway comprising the serine/threonine kinases
Raf, MEK [MAPK/ERK (extracellular-signal-regulated kinase) kinase] and
ERK (Figure 1A). The activity of these three kinases is controlled by their
phosphorylation state. Cascade activation is typically initiated by hormone
binding to cognate transmembrane receptors. The resulting active receptor–
ligand complexes employ various mechanisms to recruit the uppermost cascade
member, Raf, to the plasma membrane, where it is phosphorylated and thereby
activated. Phospho-Raf activates MEK by phosphorylating it at two residues,
and phospho-MEK then in turn acts as an ERK kinase (Figure 1A). Through
double-phosphorylation, ERK is activated and translocates to the nucleus,
where it phosphorylates several nuclear kinases and transcription factors,
which change the expression of approx. 100 genes.
The Raf-MEK-ERK cascade has received much scientific attention since
it plays a central role in various physiological processes such as cell-cycle
MEK
Raf
P
MEK
C
+ Progesterone
Low dose High dose
P
MEK
Xenopus oocytes
P
P
Low ERK
activation
Strong ERK
activation
PC12 cells
+ EGF
ERK*
Raf
B
Transient
Time
ERK
ERK
P
+ NGF
ERK*
Stimulus
A
Sustained
Time
P
ERK P
Response
No maturation
Maturation
Proliferation
Differentiation
Figure 1. MAPK cascade
(A) The MAPK cascades consist of three kinases. The classical MAPK cascade discussed in this
chapter is composed of the three kinases Raf, MEK and ERK. (B) In Xenopus oocytes, ERK activation triggers maturation of the oocytes in a dose-dependent manner. Low doses of stimuli are
filtered out and cause no effect, whereas high doses give rise to maturation. (C) In neuronal
precursor cells (PC12), stimulation with EGF causes only brief ERK activation, whereas NGF triggers prolonged ERK signalling. The stimulus-specific ERK activation profiles (transient compared
with sustained) are thought to determine the fate of PC12. Stimulation with EGF causes cellular
proliferation, whereas stimulation with NGF causes differentiation.
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progression, cell differentiation and cell death. Additionally, cascade activation is dysregulated in many diseases. For example, increased Raf-MEK-ERK
signalling is observed in more than 30% of all cancers, and deregulation is
even more frequent in some specific types of cancer, such as pancreatic cancer
(90%). Finally, the system serves as the best understood paradigm for biological regulation by protein phosphorylation/dephosphorylation cycles. The
human genome encodes approx. 500 kinases and 200 phosphatases, so that
insights into the design principles of the MAPK cascades are expected to be
applicable to cellular regulation in general.
In this chapter we depict, using a few examples, how mathematical modelling and systems biology approaches have helped to gain insights into the
functioning of the mammalian Raf-MEK-ERK module. Readers interested
in MAPK signalling in yeast should consult reference [2] for a review. First,
we focus on how the MAPK cascade ensures reliable cell fate decisions by
amplifying physiologically relevant stimuli, and filtering out background
fluctuations (see Figure 1B). Then, it is discussed how stimulus-specific biological responses arise even though many different hormones signal through
the ubiquitous MAPK cascade. We summarize experimental work, which
reveals that biological responses are encoded in the quantitative aspects of
ERK activity such as amplitude and duration (Figure 1C). Moreover, we
explain how the quantitative characteristics of ERK activity are modulated in a
stimulus-specific manner. Finally, it will be discussed how quantitative features
in ERK activation are interpreted and decoded at the level of gene expression,
and thus give rise to specific cellular responses (see Figure 1C).
Filtering: suppression of background noise and amplification
of relevant signals
Any biochemical signalling network involved in cell fate decisions must be able
to reliably discriminate between physiologically relevant signals and background
fluctuations in order to avoid improper responses. Such filtering is typically
realized by all-or-none, switch-like stimulus–response behaviour. These
stimulus–response relationships are sigmoidal, meaning that sub-threshold
stimuli fail to elicit significant responses, while strong signalling is observed in
response to supra-threshold stimulation. As these sigmoidal curves are highly
sensitive around the threshold, this phenomenon has been often referred to
as ultrasensitivity (compare Figure 2A). Huang and Ferrell [3] observed that
ERK activation in Xenopus oocytes is very sensitive around a threshold input
concentration, with a slight increase in the stimulus having a large effect on the
ERK activity leading ultimately to oocyte maturation. This observation led
them to develop the first mathematical model of the MAPK pathway. Their
model showed that two mechanisms might generate ultrasensitivity in this
pathway, namely multistep ultrasensitivity and zero-order ultrasensitivity.
Multistep ultrasensitivity arises if an input regulates its downstream
effectors at multiple points [4]. In the MAPK cascade, the kinases Raf and
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A
B
Stimulus
Switching on
Switching off
Ultrasensitive
response
ERK activity
ERK activity
Bistable response
Hyperbolic
response
Stimulus
Figure 2. Filtering
(A) Sigmoidal stimulus–response relationships are often termed ultrasensitive, since they are
highly sensitive to changes around a threshold. Ultrasensitive responses efficiently filter out low
signals when compared with a hyperbolic response. (B) A bistable response often occurs when
ultrasensitive behaviour is combined with positive feedbacks. When the response is bistable,
there are two stable states in the system at a certain stimulus range, and whether the system
is in the high- or low- activity state is determined by its history (compare ‘switching on’ and
‘switching off’).
MEK phosphorylate their downstream effectors, MEK and ERK respectively,
at two sites, and thus establish multistep regulation. A relatively simple mathematical calculation illustrates this effect for a case where the phosphorylation
sites are phosphorylated and dephosphorylated in a sequential distributed
manner (i.e. if the enzymes detach after modifying the sites, and if the phosphorylation of one site always precedes the other) [3,4]. If one assumes that
the enzymes are not saturated, the fraction of activated ERK, i.e. ERKPP/
ERKTot, is given by eqn (1):
ERKPP / ERKTot =
(k1 ⋅ MEK / k 2 ⋅ Pase)2
2
1+ k1 ⋅ MEK / k 2 ⋅ Pase + (k1 ⋅ MEK / k 2 ⋅ Pase)
(1)
In eqn (1), MEK and Pase denote the concentrations of MEK and the
phosphatase respectively, and k1 and k2 are their respective first-order rate
constants. A derivation of eqn (1) can be found in [5]. Double phosphorylation
can therefore give rise to quadratic (instead of linear) kinase control over
substrate phosphorylation [6]. Experimental studies revealed that ERK
(de)phosphorylation indeed occurs in a sequential and distributive manner,
thus suggesting that double phosphorylation is an important source for
ultrasensitivity in the MAPK pathway [4,7].
Early theoretical work by Goldbeter and Koshland [8] showed that
phosphorylation cycles can exhibit very strong ultrasensitivity if the catalysing enzymes (i.e. kinase and phosphatase) operate near saturation, i.e.
if the Michaelis–Menten constants (Km values) of the enzymes are much
smaller than the substrate concentration. This phenomenon has been termed
zero-order ultrasensitivity to reflect that the (de)phosphorylation velocities
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are independent of the substrate concentration in the saturated regime. Recent
studies however cast doubt on the physiological relevance of zero-order
ultrasensitivity in mammalian MAPK signalling, as ultrasensitivity is strongly
weakened if the enzyme and substrate concentrations are comparable, i.e.
if the substrate is significantly sequestered on the catalysing enzymes [6,9].
Experimental studies suggest that such substrate sequestration occurs in the
MAPK cascade, so that zero-order ultrasensitivity probably plays only a
minor role in this system.
A third way to generate ultrasensitivity is through stoichiometric
inhibition [4]. Some phosphatases of ERK seem to act as stoichiometric
inhibitors for ERK and not only as catalytic deactivators, as they form stable
complexes with ERK [7,10]. The mechanisms and implications of these phosphatases on ultrasensitivity are discussed elsewhere [11,12].
Switch-like stimulus–response behaviour can be further enhanced if the
basic ultrasensitivity mechanisms described above are embedded into a larger
biochemical network. In particular, signalling cascades such as the MAPK
pathway typically show much stronger and more robust ultrasensitivity than
each level in isolation [3,13,14].
Another way to amplify ultrasensensitivity is positive feedback, as feedback signalling will only start to become significant once the threshold has
been exceeded, thus making the near-threshold response even steeper [15].
An extreme manifestation of feedback amplification is bistability, where the
system switches between two discrete states (on and off) in a true all-or-none
manner. Bistable systems also display hysteresis, meaning that different
stimulus–response curves are obtained depending upon whether the system
began in its off or its on state (see Figure 2B). Thus, the behaviour of the
system is history-dependent, as the positive feedback can act as a memory
device, which maintains high activity even if stimulation strength decreases.
In some cases, the on state is maintained indefinitely after the stimulus is
completely removed, so that the system shows irreversible activation [16].
Bistability is an important mechanism for noise-resistant cell fate decisions,
and it has been proposed that bistability arises in the mammalian MAPK cascade, because ERK activates Raf in a positive feedback loop via PKC (protein
kinase C) [17]. Intriguingly, recent theoretical work indicated that implicit
positive feedbacks and bistability can emerge even in the core Raf-MEK-ERK
module due to enzyme sequestration effects [12,18]. Single-cell measurements
strongly suggest that the Raf-MEK-ERK module is bistable in mammalian
neuronal precursors (PC12 cells), because all-or-none and irreversible ERK
activation was observed in response to extracellular stimulation [19]. However,
this phenomenon appears to be cell-type-specific, as ERK activation at the
single-cell level was gradual but ultrasensitive in fibroblasts [20]. Taken
together, these results suggest that filtering due to ultrasensitivity is a general
property of the mammalian Raf-MEK-ERK module, while bistability appears
to be a context-dependent phenomenon.
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Encoding: stimulus-specific modulation of ERK duration
Different extracellular stimuli frequently engage the same set of intracellular
signalling pathways even though they elicit completely different biological
responses. How can different signals be transmitted by the same pathway?
It seems that stimulus-specific biological information is frequently encoded
by quantitative differences in stimulus-specific activation kinetics. The
Raf-MEK-ERK pathway serves as a paradigm for quantitative encoding
of signalling specificity, as both the amplitude and the duration of ERK
activation are critical determinants for the cell fate. The amplitude of the ERK
signal seems to be important in fibroblasts, where low level of ERK signalling
induces proliferation, while cell-cycle arrest is observed in response to strong
ERK activation [21]. In neuronal precursors (PC12 cells), it seems to be mainly
the ERK signal duration that matters, as these proliferate upon short-term
ERK activation, but differentiate if ERK phosphorylation is sustained [22].
Yet the fate of PC12 cells can be induced in a stimulus-specific manner, as
EGF (epidermal growth factor) stimulation elicits transient ERK activation,
whereas prolonged ERK signalling is observed in response to NGF (nerve
growth factor) (see Figure 1B) [22].
Various mechanisms are thought to contribute to such stimulus-specific
modulation of ERK signal duration. In simple terms, transient ERK activation is observed if the MAPK cascade or upstream pathways are subject to
delayed negative regulation, which ensures efficient signal termination, also
referred to as signal adaptation. In contrast, ERK exhibits sustained activation
if such adaptation mechanisms are absent. Three basic regulatory mechanisms,
depicted in Figures 3(A)–3(C), are known to mediate signal adaptation in
biochemical regulatory networks (sequestration/internalization, incoherent
feed-forward regulation and negative feedback regulation). All of them seem
to be involved in the modulation of MAPK signal duration. Below we discuss
examples of such mechanisms.
Growth factor receptors are taken up into the cell upon ligand binding,
and are deactivated and/or degraded within intracellular vesicles and therefore
the signal is terminated (arrow 1 in Figure 3D). It is known that EGF receptors
internalize more rapidly than NGF receptors, and it has been suggested that
rapid receptor sequestration and degradation accounts for transient ERK signal duration in EGF-treated PC12 cells [23].
Glutamate induces transient ERK activation in neurons, whereas sustained
signalling is observed in response to potassium chloride [24]. Strikingly, the
rapid decline in ERK phosphorylation depends on the ability of glutamate
to specifically activate PTP-STEP [protein tyrosine phosphatase, non-receptor type 5 (striatum-enriched)], an ERK phosphatase (arrow 2 in Figure 3D).
This kind of regulation is known as an incoherent feed-forward loop, because
a common upstream regulator (i.e. glutamate) both activates and inhibits a
downstream effector (i.e. ERK) via two independent branches. Incoherent
feed-forward loops generate transient signals if positive regulation (ERK
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A Sequestration
B Incoherent feed-forward loop
Stimulus
X
X*
Stimulus
Xi*
Intracellular Extracellular
X
Slow
X*
X
X*
Response
Response
Glutamate
NGF
EGF
NMDA receptor
NGF receptor
FRS
Stimulus
Rapid
Response
D
C Negative feedback
Rap
Ras
EGF receptor
5
RasGAP
1
Shc
Grb2
Sos
CrK-L
C3G
Ca2+
Endosome
Raf
2
NGF-specific MEK
positive
feedback
4
ERK
Internalization
pathway
PTP-STEP
3
Lysosome
Figure 3. Duration encoding
(A) Sequestration: signal termination occurs when the activated molecule (X*) is sequestered
into an inactive form (Xi*), e.g. through binding, internalization or degradation. (B) Incoherent
feed-forward loop: the stimulus first activates the molecule through a fast process, and then
terminates signalling through a slow, delayed mechanism. (C) Negative feedback: the activated
molecule inhibits its own production. (D) The signalling network from NGF, glutamate and
EGF stimulation to ERK activation. Various adaptation mechanisms control the duration of
ERK activation in a stimulus-specific manner (see the main text for a full description). Grb2,
growth-factor-receptor-bound protein 2; NMDA, N-methyl-D-aspartate; Sos, Son of sevenless.
phosphorylation) proceeds faster than negative regulation (PTP-STEP activation), as observed in glutamate-induced neuronal MAPK signalling [24].
Early theoretical work indicated that differential feedback control in EGF
compared with NGF signalling may underlie transient, compared with sustained, ERK signalling in PC12 cells [25]. A recent experimental and theoretical study confirmed that stimulus-specific feedback regulation indeed occurs in
PC12 cells [19]. It was shown that EGF specifically induces negative feedback
within the MAPK cascade and thereby induces early termination of ERK
activity (e.g. arrow 3 in Figure 3D). NGF signalling appeared to escape signal
adaptation because strong initial ERK activation (compared with EGF stimulation) specifically triggers a positive feedback that outweighs negative feedback
regulation (arrow 4 in Figure 3D). In particular, this positive feedback was
shown to establish bistable and irreversible ERK activation, thus ensuring
prolonged signalling [19].
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Both theoretical and experimental studies demonstrated that a pathway
consisting of the adaptor protein FRS (fibroblast growth factor receptor substrate) and the small G-protein Rap plays a key role for sustained ERK signalling in NGF-treated PC12 cells [26–28]. Strikingly, this pathway is specifically
engaged by NGF for receptor-mediated Raf activation, but not by EGF [26,28].
Moreover, sustained activation of ERK in response to NGF is abolished if Rap
signalling is blocked [28]. Accordingly, the FRS-Rap pathway shows sustained
activation kinetics, whereas the functionally redundant Shc (Src homology and
collagen homology)-Ras pathway that mediates EGF-induced Raf activation
is only transiently active [26,28]. Various explanations have been proposed
why the duration of Ras and Rap signalling differs: (i) incoherent feed-forward
regulation via Ras-GAP (GTPase-activating protein) limits signal duration
of the Shc-Ras pathway (arrow 5 in Figure 3D), but not that of the FRS-Rap
module [26]; (ii) the Shc-Ras branch is subject to negative feedback control by
ERK (arrow 3 in Figure 3D), whereas no such feedback has been described for
FRS-Rap signalling [25,28]; and (iii) cytosolic adaptor proteins such as Shc are
only functional when recruited to active transmembrane receptors, whereas
signalling via membrane-anchored adaptors like FRS can continue even without
such recruitment. Thus the FRS-Rap pathway is expected to be less susceptible
to signal termination by receptor down-regulation, and should therefore exhibit
more sustained activation [27]. A summary of the network shaping ERK activation upon stimulation with NGF, glutamate and EGF is shown in Figure 3D.
In conclusion, it appears that stimulus-specific upstream regulatory pathways (e.g. receptors, adaptors or small G-proteins) are major determinants of
ERK signal duration, because they exhibit differential susceptibility to negative regulation and thus signal termination. Additionally, the shared MAPK
cascade integrates incoming inputs and generates transient or sustained output
depending on their amplitude.
Decoding: interpretation of ERK amplitude and duration
at the level of gene expression
If the biological information is encoded by quantitative differences in the ERK
signal characteristics, proper biological responses require that the cell is able to
accurately decode the amplitude and the duration of ERK signalling. The mechanisms of decoding are not known at present, but most probably involve those
discussed in the section on filtering above. In particular, multistep regulation
appears to allow for both amplitude and duration decoding as discussed below.
Single-cell measurements revealed that c-Fos, a direct target gene of
ERK signalling (see Figure 4A), is induced in an all-or-none manner in
response to different doses of extracellular stimulation [20]. This suggests
that amplitude decoding occurs at the level of ERK-induced transcriptional
induction. Although the molecular mechanism of decoding remains to be
established, we will explain how ultrasensitivity could arise in ERK-induced
transcription-factor regulation.
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A
B
FosRna
ERK
OutputRna
0.3
NGF
0.2
4.0×
0.1
0
0
EGF
2
4
6
8
P
Output
OutputRna
0.4
NGF
0.3
3.57×
0.2
EGF
0.1
0
0
2
4
6
8
h
d
FosRna(t) = k1ERK(t) – d1 FosRna(t)
dt
d
Fos(t) = k2FosRna – d2 Fos(t) – k3 Fos(t) ERK(t)
dt
10
2
NGF
1
6.5×
EGF
0
0
10
0.5
P
P
Fos
FosRna
Output
Target expression
P
0.4
Target expression
Fos
Fos expression
Fos
Fos expression
ERK
C
0.5
P
P
5
10
15
20
2
NGF
3.9×
1
EGF
0
0
5
10
h
15
20
d
FosP(t) = k3 Fos(t) ERK(t) – d3 Fos(t)
dt
d
Output(t) = k4 (Fos(t) + FosP(t))
dt
Figure 4. Duration decoding
(A) Feed-forward mechanism by which c-Fos decodes ERK duration. ERK induces c-Fos transcription, and also stabilizes c-Fos protein by phosphorylation. (B) c-Fos time series for short
and long ERK activation shown in solid blue and broken black lines respectively. The model
input, i.e. ERK activation pulses of different lengths, is indicated by blue and black backgrounds
respectively. The maximal amount of c-Fos produced depends linearly on the input duration,
and thus does not allow for duration decoding. (C) Output gene expression shown for the two
stimuli. The feed-forward loop significantly changes the difference in the amount of output genes
produced by the long compared with short stimulation, and thus mediates duration decoding.
(Parameters for simulation: d1=4 h−1, d2=2 h−1, d3=0.25 h−1 and k3=10 h−1; all other parameters
are set to 1.)
Upstream regulatory signals (such as ERK activity) usually enhance gene
expression by phosphorylation of transcription factors, which in turn induces
transcription factor binding to target promoter sites. Transcriptional initiation
typically requires simultaneous binding of multiple transcription factors to
individual promoters. This requirement for simultaneous transcription-factor
binding establishes multistep regulation, because ERK needs to phosphorylate
both transcription factors in order to allow for gene expression. It is relatively
easy to understand why ultrasensitivity arises in this system due to multistep
regulation (see also the section on filtering above). Suppose that A and B are
the active pools of two ERK-regulated transcription factors both of which
bind to the same promoter. For each promoter site, the probability that the site
is occupied is given by eqns (2) and (3):
P(A binds) =
A
A + K1
(2)
P(B binds) =
B
B + K2
(3)
and
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Keeping in mind that both A and B are functions of ERK activity, the joint
probability that both sites are occupied can be written as eqn 4:
P(A∧B bind) = P(A binds) ⋅ P(B binds) =
A ⋅B
(A + K1) (B + K 2)
f (ERK) ⋅ g (ERK)
=
⎡⎣f (ERK) + K1⎤⎦ ⎡⎣g (ERK) + K 2⎤⎦
(4)
Eqn (4) is in a similar form as that describing double-phosphorylation (eqn 1),
and thus confirms the occurrence of ultrasensitivity with respect to ERK. Cooperativity between the sites, i.e. when the occupation of one site promotes the
binding to the second site, will even enhance decoding of the ERK amplitude.
Several transcription factors remain constitutively bound to DNA, regardless of their activation state. These constitutive binders often act as transcriptional repressors in the inactive state, while being transcriptional activators
in the active state. Swillen et al. [29] have theoretically analysed this case of
ambivalent transcription factor action and concluded that repressor–activator switching allows for highly ultrasensitive stimulus–response behaviour.
In conclusion, it seems that recurrent regulatory motifs in transcription factor networks exhibit ultrasensitive responses and thus might mediate ERK
amplitude decoding.
Multistep regulation is known to allow for duration decoding in biochemical signalling networks as previously discussed for transcriptional feed-forward
loops [30] and for multisite phosphorylation [31]. An example for multistep
regulation that has been implicated in the decoding of ERK signal duration
is the induction and stabilization of the transcription factor c-Fos (see Figure
4A) [32,33]. The transcription of c-Fos is induced by ERK. After translation,
the protein is very unstable (half-life t1/2=15 min) unless it is stabilized by
ERK-mediated phosphorylation (t1/2=4 h). Such a mechanism, where ERK
positively regulates c-Fos at two levels (transcription and protein stability), is
known as coherent feed-forward loop [30].
Coherent feed-forward regulation of c-Fos is thought to allow for selective
c-Fos accumulation upon sustained ERK activation, because short ERK signals
vanish before they are able to stabilize the slowly rising c-Fos protein pool.
We translated this mechanism into a simple mathematical model with physiologically relevant parameter values (Figure 4). We simulated c-Fos expression
for two stimuli of different lengths, 30 min and 2 h. The maximum expression
level of c-Fos protein is 4-fold higher for the longer stimulus (Figure 4B, top
panel). Thus the stimulus length seems to be linearly translated into maximal
protein levels. Such linear translation into activated c-Fos is similar to a simpler
model, where c-Fos is immediately stable without the need for feed-forward
control (Figure 4B, bottom panel). This might lead to the conclusion that this
feed-forward regulation of c-Fos does not allow for efficient duration decoding.
However, duration decoding at the level of c-Fos might not be necessary,
because c-Fos protein solely acts as an intermediary transcription factor, which
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in turn controls the expression of physiologically relevant output genes such
as those involved in cell-cycle control. Thus it might be more important that
these output genes are differentially expressed depending on the duration of
ERK activity. In fact, Figure 4(C) shows that the expression level of output
protein increases by 6.5-fold upon a 4-fold increase in ERK signal duration.
The ability to decode ERK signal duration at the level of output gene expression increases even further if one introduces a delay in transcription and translation of c-Fos (results not shown).
Why does the output gene decode the duration of ERK? The expression of a long-lived output gene integrates the time-course of c-Fos activity.
For brief ERK activation, most c-Fos remains unphosphorylated (i.e. unstable), and therefore decays relatively quickly once ERK is inactivated. On the
other hand, long-lasting stimuli result in most c-Fos being in the phosphorylated state, which decays less quickly. Thus the output gene expression,
which integrates c-Fos protein levels over time, can differ more than 4-fold.
Taken together, our simulations suggest that the integral output (but not the
amplitude) of the c-Fos feed-forward loop can efficiently decode duration if
physiologically relevant parameters are assumed.
Conclusions
In this chapter, we have summarized experimental and theoretical evidence
that suggests that the quantitative characteristics of ERK activation are crucial
determinants for the cellular fate. Different stimuli are encoded into different lengths and amplitude of the signal by mechanisms such as sequestration,
incoherent feed-forward regulation and negative feedback regulation. They are
interpreted at the level of gene expression, for example through the regulated
proteolysis of c-Fos. One important quantitative aspect of MAPK signalling,
which deserves further systems biological analysis, is the balance of the ERK
cascade with other cellular signalling pathways. For example, it was shown
that single PC12 cells subjected to oxidative stress activate pro-survival ERK
signalling or pro-death p53 signalling in a mutually exclusive manner, and thus
perform an accurate all-or-none cell fate decision based on inhibitory signalling cross-talk [34]. Therefore we expect that in the near future mathematical
modelling of the interactions and cross-talk between the major signalling pathways will boost our understanding of how cells make their decisions based on
their environments.
Summary
•
•
The MAPK signalling pathway has been subject to mathematical
modelling and quantitative experimentation for more than a decade.
The MAPK signalling pathway filters sub-threshold stimuli, with
multi-site phosphorylation and positive feedback loops as major
filtering mechanisms.
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•
•
Essays in Biochemistry volume 45 2008
Different feedback/feed-forward loops shape quantitative aspects of
the signal in a stimulus-dependent manner, allowing for different
signals through one pathway.
Information can be encoded by signal duration and can be decoded by
a feed-forward loop such as the induction and stabilization of the transcription factor c-Fos.
S.L. is supported by the German Research Foundation [DFG (Deutsche
Forschungsgemeinschaft)] through the SFB (Sonderforschungbereich) Theoretical
Biology.
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