Effect of the MAPK cascade structure, nuclear translocation and
regulation of transcription factors on gene expression
Vivek K. Mutalik, K.V. Venkatesh ∗
Department of Chemical Engineering and School of Biosciences and Bioengineering, Indian Institute of Technology,
Bombay, Powai, Mumbai 400076, India
Abstract
The mitogen activated protein kinase (MAP kinase) cascade system represents a highly conserved prototype of signal transduction
by enzyme cascades. One of the best-studied properties of the MAPK system is its ability to convert graded input stimulus to switchlike all-or-none responses. Previous theoretical studies have centered on quantifying dual phosphorylated MAPK as a final output
response and have not incorporated its influence on the regulation of gene expression. The main objective of the current work
is to understand the regulatory effect of positive feedback loop embedded in the MAPK cascade, nuclear translocation of active
MAPK, phosphorylation and activation of nuclear target proteins on the regulation of specific gene expression. To achieve this
objective, we have simulated the MAPK cascade system, which resembles Hog1p activation pathway in yeast, at steady state. Thus,
the input signal to the MAPK system is correlated with gene expression as a final system-level output response. The steady state
simulation results suggest that other than regulating the signal propagation through cascades, the nuclear translocation of activated
MAPK and subsequent regulation of gene expression represent one of the key modes to control the threshold level of response. This
work proposes that, it is essential to consider the compartmental distributions of signaling species and the corresponding regulatory
mechanisms of gene expression to study the system-level performance of signaling modules such as the MAPK cascade. Such
an analysis will relate the extracellular cues to the final phenotypic response by capturing the mechanistic details of the signaling
pathway.
Keywords: MAPK cascade; Switch-like response; Ultrasensitivity; Systems biology; Theoretical modeling; Regulatory design principles
Cellular signal transduction networks continuously
sense extracellular cues and transduce signals from the
cell surface to interior of the cell. The cell responds to
this signal through change in protein activity and gene
expression to yield a specific phenotype. In eukaryotic
cells, the MAPK cascade system represents a highly conserved regulatory element mediating the transduction of
signals from the cell surface to the nucleus (Widmann
et al., 1999; Pearson et al., 2001). MAPK cascades
are known to be activated by a wide array of signals
ranging from growth factors, hormones, stress signals,
cytokines and neurotransmitters perceived by different
types of receptors (Schaeffer and Weber, 1999; Widmann
et al., 1999; Pearson et al., 2001; Kyriakis and Avruch,
2002). MAPK cascades have been shown to regulate
numerous cellular processes including cell differentiation, movement, division and cell death. Because of
its highly conserved architecture and biological significance, the MAPK cascade system has been a prototype
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of signal transduction by enzyme cascades and is a
very well studied biological system (Gustin et al., 1998;
Banuett, 1998; Schaeffer and Weber, 1999; Lengeler et
al., 2000; Pearson et al., 2001; Kyriakis and Avruch,
2002; Hohmann, 2002).
The basic assembly of MAPK system consists
of three sequentially activating enzyme cascades of
phosphorylation–dephosphorylation reaction such that
an active MAPK kinase kinase (MAPKKK, e.g., Raf,
mos) activates MAPK kinase (MAPKK, e.g., Mek,
MKK), which further activates a specific MAPK (e.g.,
ERK, JNK, P38, P42). The terminal MAPK acts as an
effector of a unique pathway, by regulating the gene
expression and protein activity to elicit an appropriate physiological response. MAPKK and MAPK are
activated by double phosphorylation on conserved serine/threonine and tyrosine residues and are inactivated
by dephosphorylation reaction catalyzed by specific
phosphatases (Widmann et al., 1999; Pearson et al.,
2001). Some of the intriguing aspects of the MAPK
cascade system that have made both experimental and
theoretical biologists to take a keen interest in the MAPK
cascade signaling are, its highly conserved three tier regulatory architecture, retaining specificity even when cascade components are shared between different pathways,
ability of a particular pathway structure to elicit diverse
responses depending on the type and/or amplitude of
input signal, the possibility of signal and sensitivity
amplification and the intricate feedback loops embedded in the signaling pathway (Madhani and Fink, 1998;
Ferrell and Machleder, 1998; Schaeffer and Weber, 1999;
Widmann et al., 1999; Pearson et al., 2001; Breitkreutz
and Tyers, 2002).
One of the best-studied properties of signal transduction through the MAPK system is its ability to
convert the graded input stimulus to switch-like all-ornone responses (Ferrell, 1996, 1997, 1998, 2002; Ferrell
and Machleder, 1998). Such ultrasensitive switch-like
responses display steeply sigmoidal stimulus–response
curves. Mutisite phosphorylation, zero order effects and
cascade structure appear to contribute to such molecular
switch phenomenon (Ferrell, 1996, 1997). The presence
of positive feedback loops or double negative feedback
loops further impart extreme ultrasensitivity to the system in which signaling species switch between two stable states without settling in an unstable intermediate
state (bistable response). However, these system-level
responses appear to be specific to a cell type or are
dependent on a particular signaling milieu. For example,
the switch-like performance of the MAPK cascade has
been shown in Xenopus oocytes (Ferrell and Machleder,
1998), whereas it has been implicated to display a graded
output response in mammalian cells (Whitehurst et al.,
2004; MacKeigan et al., 2005) and budding yeast mating pheromone pathway (Poritz et al., 2001) at the level
of individual cells. Thus, in such cases graded output
of the MAPK cascade system displays rheostat like performance and may be the all-or-none regulatory phenomenon is imposed somewhere downstream of the
MAPK cascade such as nuclear translocation or regulatory mechanisms of gene expression (Ferrell, 2002).
Studies have indicated that, sub-cellular translocation
of proteins can also exhibit switch-like outputs (Ferrell,
1998; Teruel and Meyer, 2002). It can be argued that,
such all-or-none responses may not be always required,
for example, when the target protein has to sense wide
range of change in the input signal (Poritz et al., 2001;
Sauro and Kholodenko, 2004). Typically, there are several target proteins of active MAPK in the cytoplasm and
in the nucleus. This action of MAPK is dependent on
many other aspects such as phosphatase activity, interaction with adaptors and scaffold proteins and nuclear
translocation of active MAPK.
Several theoretical models of the MAPK cascade system are available which have focused on its different regulatory facets (reviewed in Sauro and Kholodenko, 2004;
Kolch et al., 2005; Orton et al., 2005). Most of the previous theoretical studies have centered on uncovering the
design features of MAPK cascades with dual phosphorylated MAPK as a final output response and have not been
studied in the context of gene expression (Huang and
Ferrell, 1996; Brightman and Fell, 2000; Kholodenko,
2000; Asthagiri and Lauffenburger, 2001; Bhalla et al.,
2002; Schoeberl et al., 2002; Harakeyama et al., 2003;
Chapman and Asthagiri, 2004; Nakabayashi and Sasaki,
2005). Recently, Hazzalin and Mahadevan (2002) proposed that, the MAPK activation and its nuclear translocation may yield a continuously variable switch at the
level of gene expression. They related each cycle of
transcriptional initiation to a single event of phosphorylation and dephosphorylation. Thus, as transcription
factors shuttle between phosphorylated and dephosphorylated states, the genes switch on and off in a periodic
way rather than a stable on and off state (Hazzalin and
Mahadevan, 2002).
The main objective of the present work is to understand the regulatory effect of nuclear translocation of
active MAPK, phosphorylation and activation of nuclear
target proteins leading to regulation of specific gene
expression. To achieve this objective, we have simulated a MAPK cascade system, which resembles Hog1p
activation pathway in yeast, at steady state. The MAPK
pathway was quantified at system-level by incorporating the regulatory mechanisms such as, activation and
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nuclear translocation of MAPK, activation of transcription factors and regulation of gene expression. Thus, the
input signal to the MAPK system is correlated with gene
expression as a final system-level output response. The
effect of positive feedback on the MAPK translocation
and gene activation is also analyzed. The steady state
simulation results suggest that, other than regulating the
signal propagation through cascades, nuclear translocation of activated MAPK and subsequent regulation of
gene expression represent one of the key modes of regulation by means of controlling the threshold level of
activation. This work proposes that, it is essential to
consider the compartmental distributions of signaling
species and the corresponding regulatory mechanisms of
gene expression to study the system-level performance
of signaling modules such as the MAPK cascade system.
1. Materials and methods
The modeling framework considered for the MAPK cascade system, nuclear translocation of activated MAPK, activation and dimerization of transcription factors and subsequent gene expression is schematically shown in Fig. 1.
The concentration of metabolites ATP, UTP and PPi are
considered to be invariant. The framework of Goldbeter
and Koshland (1981) was used to model the system at
steady state and accordingly an equivalent rate constant and
Michaelis-Menten constant nomenclature scheme for each
phosphorylation–dephosphorylation cycle is applied. The forward and reverse covalent modification–demodification reactions are considered to be at steady state, and all protein–protein
and protein–DNA interactions are assumed to be at equilibrium. The mass balance equations for total species in each
module are taken into account while simulating the network.
The reaction scheme shown in Fig. 1 was represented in
the form of a set of steady state algebraic equations instead of
writing ordinary differential equations for each species of the
signaling pathway. This set of steady state algebraic equations
and molar balances for each species was written by neglecting
Michaelis-Menten complexes (details given in Appendix A).
These equations were then numerically solved to estimate the
output response of the system for a given input stimuli. Four
different cases were considered for the analysis.
(1) The MAPK cascade system without the effect of feedback
loop.
(2) The MAPK cascade system with positive feedback loop.
(3) The MAPK cascade system with nuclear translocation of
active MAPK and subsequent regulation of gene expression in absence of feedback loop.
(4) The effect of positive feedback loop in the MAPK cascade
system on the overall regulation of gene expression.
In the MAPK cascade system, an input signal (a kinase)
activates MAPKKK and which further phosphorylates down-
stream MAPKK. The activated MAPKK phosphorylates terminal MAPK. The input signal is then related to the fractional
activation of MAPKKK, MAPKK and MAPK. The fractional
activation of cascade components is given by,
f1 =
MAPKKKp
MAPKKKtotal
(1)
f2 =
MAPKKpp
MAPKKtotal
(2)
f3 =
MAPKpp
MAPKtotal
(3)
where subscript p and total indicate the number of phosphorylations and total concentration of that kinase, respectively. f1 , f2
and f3 represent the fractional phosphorylation of MAPKKK,
MAPKK and MAPK, respectively.
The input stimulus to the MAPK cascade in absence of positive feedback loop is defined as, total concentration of kinase
at a fixed concentration of phosphatase of MAPKKK cycle.
In presence of positive feedback loop, it is assumed that the
dual phosphorylated MAPK activates the phosphorylation of
MAPKKK. Thus, in presence of positive feedback loop, the
input stimulus to MAPKKK is defined as,
input = E1t + v
MAPKnppH
nH
MAPKnppH + K0.5
(4)
where E1t is total concentration of primary kinase, i.e., input
stimulus at a fixed concentration of corresponding phosphatase,
v the strength of feedback loop, K0.5 the half saturation constant
and nH is Hill coefficient quantifying the steepness of MAPK
dual phosphorylation against concentration of input stimulus
in absence of feedback loop. Here it is assumed that, the dual
phosphorylation (activation) of MAPKK and MAPK occurs by
the two-step distributive mechanism (Ferrell and Bhatt, 1997).
To simulate the effect of activation of MAPK on its nuclear
translocation and gene expression, a simple modular steady
state approach was used. The MAPK cascade system with or
without feedback loop was considered as one module, whereas,
the activation of transcription factor, its dimerization and gene
expression are considered as another module. The output of the
MAPK cascade module (i.e., the dual phosphorylated MAPK)
is fed as an input to the gene expression module. By connecting these modules, the input signal to the MAPK cascade is
related to the output of gene expression module. Here, the regulatory structure of Hog1p activation and nuclear translocation
in yeast is taken as an example. It is assumed that, dual phosphorylated MAPK translocates into the nucleus and activates
phosphorylation of two different transcription factors (TF1 and
TF2 ). The nuclear translocation of MAPK is considered to be
in equilibrium and is defined as,
Kt =
MAPKpp nucleus
MAPKpp cytoplasmic
(5)
where Kt is the translocation constant defining the ratio of
nuclear to cytoplasmic active MAPK. Phosphorylation and
dephosphorylation cycles of both transcription factors are
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Fig. 1. Schematic of MAPK signaling network considered in the present work: number of phosphorylations are indicated by the letter p. Enzyme
E1 (a kinase) catalyzes the forward reaction of first cycle, and E2 , E3 and E4 are phosphatases of first, second and third cycle of MAPK system,
respectively. E5 , and E6 are phosphatases of transcription factor-1 and -2, respectively. Kmi , Kd and ki are Michaelis constant, dissociation constants
and rates of the reaction, respectively (subscript i indicate numbers from 1 to 10) as shown in the figure. Output of MAPK cascade system is assumed
to be the dualphosphorylated MAPK. Dual phosphorylated MAPK translocates into the nucleus and phosphorylates transcription factor-1 (TF1 ) and
TF2 . Activated TF1 and TF2 get dimerized and bind to enhancer sites. Dimerized active form of TF1 activates the expression of gene D1, whereas
dimerized active form of TF2 represses the expression of gene D2. The input to this system is the total input kinase concentration of MAPKKK
cascade and final output response is the fractional gene expression.
assumed to operate with different properties. Activation of TF1
is considered to operate under zero order effects and that of
TF2 is assumed to operate away from zero order. Here the zero
order effect is defined as the operation of converter enzymes
(kinase/phosphatase) in a region of saturation with respect to
their substrates (target proteins). Thus, the cascade parameters are chosen such that, the dose–response curve of TF1 and
TF2 are sigmoidal and hyperbolic to input signal, respectively.
TF2 is therefore sensitive to broad change in the concentration
of nuclear MAPK, whereas TF1 is highly sensitive to levels
of nuclear MAPK. The fractional phosphorylation of TF1 and
TF2 is given as,
f4 =
TF1p
TF1total
(6)
f5 =
TF2p
TF2total
(7)
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Fig. 2. Predicted dose–response curves for MAPK system: (A) steady state fractional modification of MAPKKK (curve a, Hill coefficient 1),
MAPKK (curve b, Hill coefficient 1.65) and MAPK (curve c, Hill coefficient 4.8) in MAPK cascade at various concentration of the input E1t on
semi-logarithmic plots. (B) Predicted dose–response curves for MAPK system in presence of positive feedback. Dashed line connecting the data
points (shown as symbol star) indicates the discrete response curves and switching between stable states. The curve nomenclature is same as in (A).
Feedback strength was 10−5 , Hill coefficient of feedback loop was 5 and half saturation constant is 10−5 ␮M.
where TF1p and TF2p are concentration of phosphorylated TF1
and TF2 , and the subscript total represents the total concentration of transcription factors. The phosphorylated TF1 and TF2
further dimerize and regulate the expression of two separate
genes D1 and D2 , respectively. The phosphorylated TF1 stimulates the expression of gene D1 , whereas phosphorylated TF2
represses the gene D2 . Thus, the fractional expression of genes
D1 and D2 is given as,
f6 =
D1 TF1p2
D1total
(8)
f7 =
D2free
D2total
(9)
where D1total and D2total are total enhancer sites for binding of
TF1 and TF2 , respectively. D1 TF1p2 represent complex between
active dimer TF1p and corresponding enhancer site D1 , whereas
D2free represent free enhancer site D2 .
The steady state equations for covalent modification cycles,
equilibrium relationships for allosteric interactions and mass
balance equations for total species are listed in Appendix
A. These algebraic equations were solved numerically using
fsolve program of Matlab (The MathWorks Inc., USA). The
accuracy of the simulation was verified at each stage by numerically checking the mass balance of all species of pathway.
The simulations were carried out for estimating the fractions
of phosphorylated MAPKKK, MAPKK, MAPK (cytoplasmic
and nuclear), TF1 , TF2 and gene expression. The steepness of
the dose–response curves was approximated by the apparent
Hill coefficient. The set of parameters and concentrations used
in the simulations were taken from literature. These simulation
parameters and the solution strategy employed to analyze the
system are given in Appendix A.
2. Results
The steady state model was used to obtain the
dose–response curves of fractional activation of MAPK,
its nuclear translocation, activation of transcription fac-
tors and gene expression in absence and presence of
positive feedback loop. To analyze the effect of positive
feedback on the output response of the MAPK cascade
system, simulations were performed in presence and
absence of positive feedback. Fig. 2A shows the effect
of input signal on the fractional activation of each of
MAPK cascade component in absence of feedback loop.
Results indicate that the steepness of the dose–response
curve for MAPKKK is hyperbolic with Hill coefficient
of one, whereas the predicted response curves for the
activation of MAPKK and MAPK are sigmoidal with
Hill coefficient of 1.65 and 4.8, respectively. The predicted response curves indicate that, as signal propagates
down the MAPK cascade, it gets amplified requiring very
less input concentration to activate the terminal kinase.
These results are in agreement with that of Huang and
Ferrell (1996) and validate the methodology adopted in
the present work.
Fig. 2B shows the dose–response curves of MAPK
cascade system components in presence of a positive
feedback loop at various input concentrations. Results
indicate that, the output response of MAPK cascade (i.e.,
dual phosphorylated MAPK) is of all-or-none nature
with discrete dose–response curve. This is a characteristic of a binary response seen in presence of positive feedback loop, in which signaling molecules switch between
two stable states without settling in an intermediate
unstable state. For the set of parameters used, activation of MAPKK also exhibits partial binary response. By
comparing Fig. 2A and B, it is clear that, presence of positive feedback effects not only imparts binary characteristics to the entire system, but also illustrates significant
amplification of the input signal. It was observed that,
this binary response in MAPK cascade is strongly dependent on the strength of feedback loop defined by the term
v (Eq. (4)). To analyze its effect on the overall output
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Fig. 3. Predicated dose–response curves of MAPK cascade components in presence of positive feedback loop. (A–C) The effect of
feedback strength on the response curves for MAPKKK, MAPKK and
MAPK modifications. The different feedback strengths are indicated
as, curve (a) no feedback, (b) 10−6 , (c) 10−5 , (d) 10−3 and (e) 1. Simulation was carried out with a Hill coefficient of 5 and half saturation
constant of 10−5 ␮M. Binary response of MAPK is more sensitive than
MAPKK and MAPKKK to feedback strength. Dashed lines indicate
the discrete response of cascade components between stable states.
response of MAPK cascade, simulations were done with
different values of feedback strengths. Fig. 3 shows the
effect of different feedback strengths on the steady state
response of MAPKKK, MAPKK and MAPK phosphorylation.
The dose–response curves in Fig. 3 demonstrate
that, as the feedback strength is increased the fractional
phosphorylation of all three kinases exhibit true switch
(binary) characteristics. The transition of MAPK phosphorylation from monostable to binary behavior requires
much lower feedback strength as compared to that for
MAPKK and MAPKKK modification (curve b in Fig. 3).
It can be noted that, as feedback strength is increased, the
signal propagates down the cascade with high amplification. This signal amplification and binary characteristic
are not much affected by changes in the nonlinearity embedded in the (quantified as Hill coefficient) of
feedback loop in Eq. (4). The basic characteristics of
the response remain same, even if the feedback loop
is defined with Hill coefficient one. However, changes
in the Hill coefficient do affect the threshold of the
response.
Once MAPK is activated in response to a particular stimulus, it phosphorylates several target proteins
with in the cytoplasm as well as in the nucleus. Most
of the nuclear target proteins are transcription factors,
which either activate a particular gene expression or regulate it by repression (Widmann et al., 1999; Pearson
et al., 2001). In the present work, it was assumed that,
active MAPK translocates into the nucleus and phosphorylates two different transcription factors. One of
these transcription factors (TF1 ) activates the expression of gene D1 and the other TF (TF2 ) represses the
expression of gene D2. By solving the set of equations,
it was observed that, the threshold stimulus to activate
or repress a particular gene expression depends on the
translocation constant of active MAPK. Fig. 4 shows
the effect of MAPK translocation constant (in absence
of feedback) on the activation of transcription factors
and the corresponding gene expressions. The simulated
results reveal that, as the translocation constant Kt is
increased, the threshold input stimulus for activation or
repression of gene expression decreases indicating signal amplification as MAPK translocates from cytoplasm
to nucleus. Even though, the nuclear concentration of
MAPK is very less at low Kt (curve a in Fig. 4A and B),
it is capable of activating and repressing gene D1 and D2
expression, respectively (curve c in Fig. 4A and B). As Kt
increases, the nuclear concentration of MAPK increases
and which in-turn amplifies the performance of TF1 and
TF2 (curve b in Fig. 4). Since, the reversible phosphorylation of transcription factors is assumed to operate
under zero order and first order conditions, respectively,
the response curves of transcription factor activation and
the expression of gene D1 and D2 show distinct steepness with respect to input stimulus. Thus, at low Kt
values even though the MAPK concentration in nucleus
150
Fig. 4. Simulated dose–response curves for gene expression in the case nuclear translocation of active MAPK and effect of translocation constant on
the output response: the effect of translocation constant (Kt ) on the fractional concentration of nuclear MAPK (curve a), activation of transcription
factor (TF, curve b) and fractional expression of genes (curve c). The analysis was performed in absence of positive feedback loop. Three different
translocation constants were used in the study, Kt = 0.01 (A and B), Kt = 1 (C and D) and Kt = 100 (E and F). Simulated graphs in (A), (C) and (D)
represent the performance of TF1 and corresponding gene D1 expression, whereas, graphs in (B), (D) and (F) represent the performance of TF2 and
repression of gene D2. As the translocation constant increases, the signal propagation responds with amplification. The Hill coefficient of curve a in
(E) and (F) is about 4–5. The Hill coefficient of curve b in (A), (C) and (E) is about 10 and curve b in (D) and (F) is about 4–5. The Hill coefficient
of curve c in (A), (C) and (E) is about 7–7.2, and curve c in (B), (D) and (F) is about 6.2–6.5.
is negligible, it is sufficient for full activation of TF1 ,
whereas TF2 display partial activation (curve b in Fig. 4A
and B). At high Kt values both TF1 and TF2 display full
activation (curve b in Fig. 4E and F) with Hill coefficient of 10 and 4.5, respectively. It can be noted that
as Kt increases the threshold response of transcription
factor activation and gene expression display potential
signal amplification (curve c in Fig. 4) without affecting
the steepness of response.
A separate set of conditions was chosen, to analyze
the effect of ultrasensitivity arising out of MAPK cascade on the activation of TF and gene expression (see
Appendix A) such that the output response of MAPK
cascade (fractional phosphorylation of MAPK to input
stimulus) is hyperbolic with a Hill coefficient of one.
Fig. 5A and B shows that, when MAPK activation is
graded function of the input stimulus, the activation of
TF1 and TF2 display characteristic performance of ultrasensitive and graded output response, respectively. TF1
activation is ultrasensitive (with Hill coefficient of 11)
due to its operation in the zero order region, whereas,
TF2 activation is almost graded (with Hill coefficient of
1) due to its operation in the first order region. The transfer of signal from the active TF1 to expression of genes
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Fig. 5. Effect of hyperbolic output of MAPK cascade on the dose–response curves of fractional concentration nuclear MAPK, activation of
transcription factor and fractional gene expression in absence of feedback loop. (A) The performance response in the case of TF-1 and (B) activation
of TF-2. Curve a represents fractional concentration of nuclear MAPK, curve b for TF activation and curve c for fractional gene expression. Input
concentration refers to the input applied to MAPK cascade. The Hill coefficient of curves a–c in (A) are about 1, 11 and 7, whereas the Hill coefficient
of curves b and c in (B) are about 1 and 6. The translocation constant Kt = 100 and other parameters used for the simulations are given in Appendix
A.
appears to be attenuated since the steepness of fractional
gene expression is less ultrasensitive (Hill coefficient of
7) than transcriptional factor activation (Hill coefficient
of 11). The fractional expression of gene D2 displays
ultrasensitivity to graded output of TF2 activation and
this is primarily due to the inherent nonlinearity embedded in dimerization of TF and high association constant
of enhancer sites with dimerized TF.
Fig. 6 shows the effect of positive feedback on
the nuclear translocation of MAPK, activation of
Fig. 6. Effect of positive feedback loop embedded in MAPK cascade on activation of transcription factor and gene expression: two representative
cases are analyzed for showing the effect of translocation constant on the overall response. (A and C) The performance of the TF1 system (for
Kt = 0.01 and 100, respectively), whereas (B and D) the output response in the case of TF2 (for Kt = 0.01 and 100, respectively). Curve a represents
fractional concentration of nuclear MAPK, curve b for TF activation and curve c for fractional gene expression. Input concentration refers to the
input applied to MAPK cascade. Dashed line indicates the discrete responses and the dots represent the stable states between which the signaling
components switch depending upon the threshold input concentration. For simulating the feedback effects following parameters were used: feedback
strength of 10−3 , Hill coefficient of 5 and half saturation constant of 10−5 ␮M.
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transcription factors and regulation of gene expression
at two different translocation constants. From our earlier simulations (Fig. 2B) it is clear that the final output
response of MAPK cascade displays binary characteristics. Fig. 6 shows that nuclear translocation, activation of transcription factor and gene expression can also
exhibit binary on–off characteristics in presence of the
MAPK cascade embedded with positive feedback loop.
The threshold input stimulus required for the activation
displays amplification of the signal due to presence of
positive feedback loop, even though the activation levels
of both transcription factors depended on their cascade
parameters.
3. Discussion
Signaling pathways are made up of intricate network
of enzyme cascades, allosteric interactions and multiple feedback/feedforward loops. The molecular connectivity within and across these signaling networks
are responsible for mounting appropriate input–output
dose–response relationships. In the present work, we
demonstrate through steady state modeling that, the
system-level performance of a signaling pathway is
dependent on the numerous operational conditions and
on the multiple levels of regulatory mechanisms in the
pathway. Our results indicate that, in the case of signaling pathways with common signaling modules like
the MAPK cascade, the nuclear translocation, nuclear
retention of active signaling molecules, modulation and
operatibility of transcription factors control the differential regulation of gene expression. The steady state
simulation further shows that, in the presence of positive feedback loop with appropriate feedback strength
and translocation constant of communicating species
across the compartments modify the threshold level
of output response. The translocation constant primarily regulates the signal amplification, while the properties of reversible modification cycles influence the
response sensitivity. The positive feedback loop embedded in MAPK cascade system imparts binary or digital
characteristic to the cascade output and other downstream signaling components to an applied input stimulus. The binary output response in this case is characterized by the discontinuous dose–response curves
and not by the hysteresis feature commonly observed in
bistable responses. Since, the fractional modified pathway species were estimated by numerically solving a
set of algebraic equations and not by solving the ordinary differential equations at steady states, we obtained
only the switching-on property of the response curves.
The results indicate that, the modification of terminal
kinase MAPK is highly sensitive to the applied feedback strength than that of upstream kinases MAPKK
and MAPKKK.
Our analysis show that, the regulation of gene expression can demonstrate switch-like outputs even in absence
of ultrasensitivity at the level of upstream MAPK cascade. That is, even though the dose–response curve of
activation of MAPK may still be hyperbolic, the downstream components may show distinct response sensitivity. This emergence of ultrasensitivity at the level of
gene expression to graded input stimuli can be attributed
to the nuclear translocation, activation and oligomerization of transcription factors and other regulatory mechanisms of gene expression. Our results indicate that,
this regulatory machinery can also cause attenuation
of terminal response sensitivity. This can be clearly
seen in Fig. 5A in which the fractional phosphorylation of TF1 is ultrasensitive with apparent Hill coefficient of 11, where as the fractional gene expression
shows an apparent Hill coefficient of 7. This sensitivity attenuation appears to be due to the dimerization of active transcription factor and its affinity with
the enhancer cites. Thus, these results indicate that,
the upstream ultrasensitivity in TF activation is not
entirely transmitted down to the gene expression level
and may represent an important feature of the cellular
regulation.
Our results are in agreement with recent experimental analysis, which demonstrated that graded
MAPK activity is preceded with switch-like induction of immediate early genes and cell cycle progression in mammalian cells (MacKeigan et al., 2005).
Similar analysis in primary human cells demonstrated
that, the activation of MAPK is graded in mammalian cells (Whitehurst et al., 2004) whereas it is
reported to be bistable in progesterone-induced Xenopus oocytes (Ferrell and Machleder, 1998). Then the
question arises as to what may the significance of such
variability in response sensitivity of signaling modules, which share a common regulatory architecture.
This may indicate the context or cell type specific
responses displayed by the signaling modules underpinning the importance of regulatory design principles
behind the system-level output responses. Such variability in response sensitivity may represent the advantage for a specific case in terms of flexibility and
adaptability to different environmental cues. Our analysis suggests that, the differential sensitivity of signaling modules can facilitate in regulating numerous
other target proteins across compartments, thus avoiding excessive signal amplification or higher response
sensitivity.
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Most often, the biological responses are highly nonlinear with respect to input signal displaying sigmoidal
dose–response characteristics (Koshland et al., 1982;
Koshland, 1987, 1998). In an extreme nonlinearity, the
dose–response curves approach a step function, in which
a very small increment in the input concentration (signal) above the threshold level, the system switches
from off-state to on-state. The biological reaction networks, which demonstrate such sigmoidal dependence
on an input signal, are known as molecular/regulatory
switches (Koshland, 1987; Ferrell, 1996, 2002). These
molecular switches typically exhibit a threshold phenomenon in which the concentration of input stimulus
just below the threshold are unable to exhibit output
response, while concentration just above the threshold
can induce stronger responses (Mutalik et al., 2003,
2004; Tyson et al., 2003; Wolf and Arkin, 2003).
The regulatory switches are known to control a wide
range of biological processes, from stress/starvation
responses and chemotaxis to more complex cellular
development and cell fate decisions (Ferrell, 1996, 2002;
Anderson et al., 2002). In such systems the nonlinearity resides either at the level of signal transmitting
receptor and enzyme cascades or at the response executing gene expression level. Depending upon the regulatory design, these switches can elicit monostable
ultrasensitive responses or bistable discrete all-or-none
responses.
The system-level approaches in experimental and theoretical studies have shown that, bistability is one of the
recurring themes in regulatory circuits across all living
systems (Ferrell, 2002). At the level of individual cell,
the gene expression appears to be regulated essentially
in an all-or-none binary response with either a gene is
maximally expressed or is not expressed at all (Smolen
et al., 1998; Rossi et al., 2000; Biggar and Crabtree,
2001; Becskei et al., 2001; Louis and Becskei, 2002).
The digital output response of transcriptional process is
mainly attributed to several design features of regulatory circuits. Positive feedback loops or double negative
feedback loops with embedded nonlinearity are known
to be essential to display binary responses, which switch
between two stable on–off states (Ferrell and Xiong,
2001; Ferrell, 2002; Angeli et al., 2004; Giri et al.,
2004).
Recently it was shown that, under certain conditions
the dual phosphorylation itself could exhibit bistable
response (Markevich et al., 2004). Thus, MAPK cascade system in presence of feedback loops may exhibit
multistable output response (Markevich et al., 2004).
Such multistable response at the cascade level and
multiple regulatory points at the level of translocation
and gene expression may yield a highly nonlinear system. These features may be difficult to demonstrate
solely through experiments. It is essential to quantify the regulatory architecture of smaller subsystems
and further connect them to each other to uncover
the regulatory design principles present at the modular level to predict the system-level regulation. In one
such attempt, the present work proposes that it is essential to quantify the compartmental distribution of signaling species for system-level analysis of signaling
modules.
Appendix A
A.1. Steady state model used for analyzing MAPK
cascade system (Fig. A.1)
For convenience, following nomenclature is used:
A, MAPKKK; AP, MAPKKKp ; B, MAPKK; BP,
MAPKKp ; BPP, MAPKKpp ; C, MAPK; CP, MAPKp ;
CPP, MAPKpp .
Mass balances
Rate expressions
At = A + AP
Bt = B + BP + BPP
Ct = C + CP + CPP
E1t = E1 + E1 A
E2t = E2 + E2 AP
E3t = E3 + E3 BP + E3 BPP
E4t = E4 + E4 CP + E4 CPP
k1 AE1 = k2 APE2
k3 BAP = k4 BPE3
k3 BPAP = k4 BPPE3
k5 CBPP = k6 CPE4
k5 CPBPP = k6 CPPE4
BPP CPP
Estimated: AP
At ; Bt ; Ct
Complexes
1)
AE1 = (A)(E
; APE2 =
K
(AP)(E2 )
Km2 ;
m1
(B)(AP)
BAP = K
; BPAP = (BP)(AP)
Km3 ;
m3
(BPP)(E3 )
3)
BPE3 = (B)(E
;
BPPE
=
3
Km4
Km4 ;
(C)(BPP)
; CPBPP = (CP)(BPP)
CBPP = K
Km5 ;
m5
(CPP)(E4 )
4)
CPE4 = (CP)(E
;
CPPE
=
4
Km6
Km6
The parameters used for the analysis were:
Analysis of MAPKKK cascade was performed
using Goldbeter and Koshland equation and was
connected to MAPKK and MAPK analysis, which
in-turn was done using following parameters on
fsolve program of Matlab (The MathWorks Inc.) software. The solution strategy is shown in Fig. A.1.
Parameter set referred from Huang and Ferrell
(1996). See figure legends in the text for nomenclature. The total enzyme concentrations: At (total
MAPKKK) = 0.003 ␮M, Bt (total MAPKK) = 1.2 ␮M,
Ct (total MAPK) = 1.2 ␮M; phosphatase concentration: E2t = E3t = 0.0003 ␮M, E4t = 0.12 ␮M; reaction rates: k1 –k6 = 150 min−1 , Michaelis constants:
154
Fig. A.1. Solution strategy for analyzing MAPK cascade system at steady state (results shown in Figs. 2–3 in text).
Km1 –Km6 = 0.3 ␮M.
To obtain a hyperbolic MAPK response, following
parameter set was used:
The total enzyme concentrations: At (total
MPKKK) = 0.2 ␮M, Bt (total MPKK) = 0.18 ␮M, Ct
(total MPK) = 0.036 ␮M; phosphatase concentration:
E2t = E3t = 0.224 ␮M, E4t = 0.0032 ␮M; reaction rates
(min−1 ): k1 = 24, k2 = 6, k3 = 60, k4 = 60, k5 = 9, k6 = 60;
Michaelis constants (␮M): Km1 = 66.6, Km2 = 15.65,
Km3 = 0.159, Km4 = 65, Km5 = 0.46, Km6 = 0.75.
Positive feedback effects:
To incorporate the positive feedback of active MAPK
on upstream kinase, following modified input relationship was used:
E1t = E1t + v
CPPnH
n
H + CPPnH
K0.5
E1t is the total input kinase, v the feedback strength, nH
the Hill coefficient and K0.5 is the half saturation constant. The feedback parameters are given in the figure
legends.
155
Fig. A.2. Solution strategy for analyzing MAPK cascade system, nuclear translocation of active MAPK, transcription factor activation, dimerization
and gene expression at steady state (results shown in Figs. 4–6 in text).
156
A.2. Steady state model used for analyzing MAPK activation, nuclear translocation, activation of transcription
factors and regulation of gene expression (Fig. A.2)
The mass balance equations and equilibrium relationships for MAPK cascade components are same as given in
Section A1. The following equations are for gene expression module.
Mass balances
Complexes
TF1 activation
CPPnt = CPP + CPPTF1
TF1 CPPn =
k7 TF1 CPPn = k8 TF1p E5
TF1p E5 =
(TF1 )(CPPn )
Km7
(TF1p )(E5 )
Km8
Translocation constant: Kt =
TF2 CPPn =
k9 TF2 CPPn = k10 TF2p E6
TF2p E6 =
(TF2 )(CPPn )
Km9
(TF2p )(E6 )
Km10
Translocation constant: Kt =
TF1t = TF1 + TF1p
E5t = E5 + TF1p E5
TF2 activation
CPPnt = CPP + CPPTF2
TF2t = TF2 + TF2p
E6t = E6 + TF2p E6
gene D1 expression
D1t = D1 + D1 TF1p2
Equilibrium relationships
TF1pt = TF1p + 2TF1p2 + 2D1 TF1p2
fgene1 =
(TF1p )(TF1p )
;
Kd1
D1 TF1p2
D1t
gene D2 expression
D2t = D2 + D2 TF2p2
TF2pt = TF2p + 2TF2p2 + 2D2 TF2p2
TF2p2 =
fgene2 =
(TF2p )(TF2p )
;
Kd3
D2
D2t
TF1p2 =
A.3. The parameters used for the analysis were
MAPK cascade parameters are same as above.
The nuclear translocated MAPK, CPPn (calculated
in presence or absence of feedback) was taken as an
input to the gene expression module. The modification
of transcription factors (TF’s, TF1 and TF2 ) was
calculated using Goldbeter and Koshland equation. The
regulation of gene expression module was solved by
using fsolve program of Matlab (see solution strategy
in Fig. A.2). The parameters used for the simulation
are: total concentration of TF’s (␮M)—TF1t = 2,
TF2t = 0.002; phosphatase concentration (␮M)—E5t =
0.003, E6t = 0.02; reaction rates (min−1 )—k7 = k8 =
150, k9 = 40, k10 = 360; Michaelis constants (␮M)—
Km7 = 0.03, Km8 = 0.3, Km9 = 20, Km10 = 150; total
enhancer sites (␮M)—D1t = D2t = 1d-6; dissociation
constants (␮M)—Kd1 = 0.1, Kd2 = 0.0001, Kd3 = 1,
Kd4 = 0.001. The translocation constant values are
given in Figs. 4 and 6. The final output response is
fractional expression of gene D1 and D2 and is defined
as fgene1 = (D1 TF1 /D1t ); fgene2 = (D2 /D2t ).
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