- Research article
- Open Access
Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops
© Sarma and Ghosh; licensee BioMed Central Ltd. 2012
- Received: 14 December 2011
- Accepted: 30 April 2012
- Published: 13 June 2012
Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs.
We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case.
The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.
- Positive Feedback
- Mitogen Activate Protein Kinase
- Negative Feedback Loop
- Incoming Signal
- Target Module
Coordinated actions of coupled positive and negative feedback loops have been reported earlier for biochemical systems with different architectural designs. In cyclin-dependent kinase 1 (CDK1) pathway, coupled positive and negative feedback loops leads to robust oscillations where time periods of oscillations can be changed without compromising the amplitude of oscillations. In another study, it was found that during calcium spike regulation, positive feedback loops constituting IP3R and RYR and a negative feedback loop constituting SERCA ATPases triggers and regulates the Ca2++ oscillations. Similarly the cell cycle oscillations are essentially built from coupled positive and negative feedback loops between Cdc2 and APC system that gives reliable cell cycle oscillations. The p53 pathway which is another oscillatory pathway is also densely wired in positive and negative feedback loops. A recent experimental study shows that a negative feedback from the phosphorylated ERK (MK**) to its upstream activator SOS and a coupled positive feedback from MK** to M3K* (by phosphorylation mediated dissociation of M3K* complex from its inhibitor RKIP) results in robust system-level oscillations, suggesting for the first time that the MAPK pathway can employ coupled positive and negative feedback loops for generating its oscillations.
Schematics of positive and negative feedback loops operational in MAPK cascade
Feedback interaction of kinases
Sub module 1
Sub module 2
Sub module 3
Sub module 4
Also during long duration signaling, MK and its phosphorylated forms (MK* and MK**), traverses between cytoplasm and nucleus[10–12]. Inside the nucleus, MK** induces expression of its phosphatase (MKP-1) that subsequently carries out MK** dephosphorylation in the nucleus itself[4, 10]. It is not known how nuclear-cytoplasmic shuttling of the terminal layer kinase of MAPK cascade and the subsequent transcriptional induction of phosphatase such as MKP-1 would affect the oscillations triggered by PN-I and PN-II.
Here we built two oscillating models of MAPK cascade where oscillations in one model were triggered by PN-I and the oscillations in the other model were triggered by PN-II. We found that in both the cases, the amplitude, frequency and nature (digital/analogous) of oscillations were uniquely shaped by the coupled positive and negative feedback loops embedded in the cascade. Our simulations show that the MAPK cascade embedded in PN-II exhibited remarkable robustness in generating oscillations with identical frequency and amplitude while subjected to a wide range of input stimuli, whereas, the cascade embedded in PN-I was less robust in maintaining its frequency and amplitude when subjected to input signal of different strengths. We also found that a positive feedback emerging from an oscillating MAPK cascade and functional in a different pathway or signaling module could lead to both signal amplification and oscillations in the external module. Further we investigated the fate of oscillations of the MAPK cascade considering the nuclear and cytoplasmic shuttling. Our analysis revealed that the oscillations of the MAPK cascade embedded in PN-I were not affected by such shuttling of the cascade components and induction of its nuclear phosphatase, whereas oscillations triggered by PN-II were completely abolished when induction of nuclear phosphatase was considered. Sensitivity analysis for small perturbations in parameters of the oscillating models were carried out which showed that the organization of the feedbacks (PN-I or PN-II) also distinctly determines the most sensitive kinetic parameters in the oscillating systems. Biological significance of our findings is discussed.
I. Model building
In the phosphorylation reaction, the ‘Signal’ could be an upstream kinase or other activators that triggers M3K phosphorylation[3, 10]. The phosphorylation-dephosphorylation cycles follow in the M2K and MK layers and the cascade delivers its final output MK**.
Where , k1 and k2 are the catalytic rates associated with the phosphorylation and dephosphorylation processes respectively. K1 and K2 are the Km values of the reactions. Phosphorylation-dephosphorylation reactions for the M2K and MK layer takes place in two steps and the equations could be derived accordingly assuming steady state conditions[14, 15].
In MAPK cascade, both positive and negative feedback loops emerge from MK** and are functional in either of the two upstream layers, M2K and M3K (Table1). Thus the flux equations will be modified in presence of these feedback loops.
In equation (3), ‘KI’ captures the strength of negative feedback of MK** on M3K phosphorylation. The negative feedback is assumed as a hyperbolic modifier, which is non competitive in nature and ‘n1’ is the associated Hill coefficient. The subscript ‘neg’ associated with v1 in equation (3) represents phosphorylation in presence of negative feedback.
In equation (4), A and Ka are the kinetic constants associated with the positive feedback from MK** to the M3K layer phosphorylation. The subscript ‘pos’ associated with v1 in equation (4) represents phosphorylation in presence of positive feedback. In equation (4) the exponent n1 is the Hill coefficient which indicates that the positive feedback is a hyperbolic modifier of the M3K phosphorylation. The positive feedback was assumed as a hyperbolic modifier in all the model equations involving the positive feedback.
Flux of signal flow in cytoplasmic MAPK cascades ‘S1’ and ‘S2’
Flux equations in model S1
Flux equations in model S2
2] M3K*→ M3K
5] M2K**→ M2K*
6] M2K*→ M2K
7] MK→ MK*
8] MK*→ MK**
9] MK** → MK*
10] MK* → MK
As the total concentration of a kinase is known, M3K, M2K and MK can be calculated from the above mass conservation equations and the differential equations.
Models S1 and S2
Modification of the models S1 and S2 to incorporate nuclear-cytoplasmic shuttling
Nuclear-cytoplasmic shuttling of the MK layer components (MK, MK* and MK**) of the MAPK cascade takes place[10–12] where MK** triggers various transcription factors in the nucleus, aiming to activate target genes[10, 17]. We updated the models S1 and S2 to S1n and S2n respectively, to incorporate the nuclear-cytoplasmic translocation of the MK layer components of the cascade.
After addition of the nuclear components, ‘S1’ and ‘S2’ were renamed as ‘S1n’ and ‘S2n’ respectively
Reaction number in models S1n and S2n
MK** ↔ MK**-n
k11f.MK** - k11b.MK**-n
k11f = 10.34 sec-1
k11b = 2.86 sec-1
P3-n gene → PreP3mRNA
V12 = 29.24 nmol/sec
K12 = 169 nmol/ml
n12 = 3.97
k13 = 0.022 sec-1
P3mRNA → ɸ
k14 = 0.0078 sec-1
P3mRNA → P3-c
k15 = 0.0012 sec-1
P3-c ↔ P3-n
k16f.P3-c - k16b.P3-n
k16f = 22.56 sec-1
k16b = 15.4 sec-1
P3-c → ɸ
k17 = 0.00025 sec-1
P3-n → ɸ
k18 = 0.00025 sec-1
MK ↔ MK-n
k19f.MK - k19b.MK-n
k19f = 10.34 sec-1
k19b = 2.86 sec-1
MK* ↔ MK*-n
k20f.MK* - k20b.MK*-n
k20f = 10.34 sec-1
k20b = 2.86 sec-1
MK**-n → MK*-n
k21 = 0.68 sec-1
K21 = 10300 nmol/ml
K22 = 87 nmol/ml
MK*-n → MK-n
k22 = 0.31 sec-1
K21 = 10300 nmol/ml
K22 = 87 nmol/ml
II. Model assumptions
In substantiation with the previous studies[14, 15], it was assumed that a steady state in the enzyme-substrate complexes is achieved during the signal propagation, for all the reactions in both S1 and S2. For the sake of simplicity we assumed that no degradation and production of the cascade components (kinases and phosphatases) of S1 and S2 takes place during the course of signal propagation and hence their concentrations remain constant. However, following experimental guidelines, the models S1n and S2n were built with certain degradation and phosphatase (P3-n) production steps, as shown in Table3. In models S1 and S2 we also assumed that each layer of the cascade is phosphorylated by one phosphatase specific to each layer[3, 14], except, in the models S1n and S2n, where dephosphorylation of the third layer MK was carried out by two phosphatases, P3 and transcriptionally induced P3-n. The model presented here represents a three layer MAPK cascade that is evolutionarily conserved from yeast to mammal. Although differences in the rewiring of the kinases-phosphatases interaction are observed in some eukaryotic systems[13–15, 18], the kinases-phosphatases interaction shown here represents the most generalized structure of the cascade known till now[1–3]. The simplifications also included ignoring various intra modular crosstalks which involve MAPK cascade and other signaling modules. While building the flux equations for positive and negative feedback loops we assumed that both the feedback types are hyperbolic modifiers, which is in corroboration with earlier studies[14, 16].
III. Model parameters and concentrations
The kcat and Km values for S1, S2, S1n and S2n were chosen in biochemically observed ranges[3, 14–16, 18]. Additional file2: Table S1 describes the reactions capturing signal flow in the three layer MAPK cascade and their kinetic parameter values, which are common in all the four models S1, S2, S1n and S2n. Additional file2: Table S2 describes the concentration of kinases and phosphatases used in S1, S2, S1n and S2n. Table3 shows the additional reaction parameters corresponding to the modified fraction of the models S1n and S2n. Parameters for the additional reactions in the model S1n and S2n were adopted from a recent study.
IV. Sensitivity analysis for small perturbations in the model parameters
Sensitivity studies reveal the relative importance of kinetic parameters associated with the model. We performed sensitivity analysis of all the four models by applying small perturbations to the kinetic parameters of the models and measuring the sensitivity of MK** in each of the model to such perturbations.
Upon normalization, the sensitivity coefficient Sij is given as:
In the above equation, we calculated Sij with ∆pj = 0.001*pj for any perturbed parameter pj. The variation of ∆pj in the range of 0.0001*pj-0.1*pj didn’t alter Sij. The perturbations were applied locally, which means parameters were perturbed one at a time and Sij for each of the parameter’s perturbation on the output MK** of the models was calculated.
V. Software used and model simulations
For performing the simulations SBML models were initially constructed using Complex pathway simulator (COpasi). The time course simulations were carried out in COpasi. Sensitivity analysis was performed using SBML_SAT, a MATLAB toolbox for sensitivity analysis. Bifurcation analysis to inspect oscillation in S2n was carried out using Bifurcation Discovery tool. The model files are given as additional files.
We constructed two models S1 and S2 of the MAPK cascade, one embedded in PN-I and the other embedded in PN-II respectively, such that oscillations in both the models were triggered by coupled positive and negative feedback loops. We investigated the fate of MAPK oscillations in S1 and S2, when signal strength was varied in wide ranges. Our simulations also revealed that MAPK cascade can utilize its positive feedback to trigger oscillations in an external signal processing module. Next we examined the fate of oscillations triggered by PN-I and PN-II when nuclear–cytoplasmic shuttling of the components of terminal layer MK of the MAPK cascade takes place followed by the induction of a nuclear phosphatase by MK**. Results show that oscillations triggered by PN-II exists only in the cytoplasm and induction of the P3-n completely abolished the oscillations, whereas oscillations triggered by PN-I are not affected by the nuclear translocation of MK layer and subsequent induction of nuclear phosphatase. Various in-silico knock out studies were carried out to elucidate the importance of cytoplasmic and nuclear phosphatases in both S1 and S2. Also, when the parameters of S1, S1n, S2 and S2n were subjected to small perturbations, we found that PN-I and PN-II differentially regulates the cascades’ output sensitivity to these perturbations.
Oscillations in models S1 and S2
Previous studies show that negative feedback from MK** to M3K layer (Sub module 2, Table1), or negative feedbacks from MK** to M2K layer (Sub module 4, Table1), triggers sustained oscillations in the MAPK cascade. Positive feedback from MK** to M3K phosphorylation (Sub module 1 Table1) results in all-or-none behavior in production of MK**[4, 25, 26]. Positive feedback from MK** to M2K phosphorylation step (Sub module 3, Table1) was found to facilitate propagation of long range phosphorylation waves of MK** in the developing neurons. Earlier computational investigations revealed that a negative feedback from MK** to M3K layer is a prerequisite in triggering MAPK oscillations, but later it was found that for certain parameter combinations, the three layer MAPK cascade can trigger its oscillations in absence of the explicit negative feedback loop from MK** to M3K.
But a recent experiment exposed that MAPK oscillations are triggered by coupled positive and negative feedback loops. This experimental finding necessitated an investigation on the significance of differential designs of coupled positive and negative feedback loops that can plausibly trigger oscillations in the cascade and the characteristics of oscillations triggered by each of the design. The MAPK cascades embedded in the two designs of coupled positive and negative feedback loops, PN-I and PN-II are shown in Figure2A and2B.
Oscillations in S1
Introduction of the positive feedback loop from MK** to M2K layer in the cascade with negative feedback from MK** to M3K layer first resulted in enhancement of the amplitude of M2K** followed by enhancement in MK** amplitude. Since both positive and negative feedbacks emerges from MK**, enhanced MK** amplitude results in stronger inhibition in the M3K* layer and stronger activation in the M2K layer. However as M3K lies upstream to M2K, decrease in M3K* concentration beyond a certain threshold results in attenuation of M2K layer phosphorylation, even in the presence of the positive feedback loop. With inhibition of M2K** amplitude, phosphorylation of MK layer gets inhibited. With decrease in MK layer phosphorylation, attenuation of the strengths of both positive and negative feedback loops follow. As MK** amplitude reaches its lowest amplitude, one cycle of oscillation is completed (Figure3C). As the input signal is available for M3K phosphorylation, M3K* starts building up in absence of the negative feedback and the next cycle of oscillation is triggered. The process continues until the external signal is available to phosphorylate M3K. Coupling of inhibitory and activating effects of the PN-I, triggered oscillations (Figure3C) in all the three kinases of the MAPK cascade S1.
Oscillations in S2
Oscillations in S2 emerged due to positive feedback mediated enhancement of M3K* amplitude coupled to the negative feedback mediated inhibition of M2K**. Upon stimulation of the cascade by external signal, positive feedback from MK** to M3K enhanced the M3K* amplitude. This subsequently enhances M2K layer phosphorylation (in presence of the negative feedback from MK** to the M2K layer), ultimately resulting in amplification of MK** amplitude. Amplified MK** subsequently enhances the strengths of both positive and negative feedback loops. When MK** reaches its maximum phosphorylation amplitude (Figure3F), negative feedback mediated inhibition of M2K layer phosphorylation surmounts the positive feedback mediated enhancement of M2K layer phosphorylation by M3K*. With progressive attenuation of M2K** amplitude, MK layer phosphorylation gets inhibited until it reaches its lowest phosphorylation amplitude (Figure3F). The whole process completes one cycle of oscillation. The next cycle of oscillation starts when the external signal triggers phosphorylation of M3K in absence of the negative feedback from MK**. It could be noted that the negative feedback in S2 inhibits MK** production in two ways, firstly by directly inhibiting the M2K** amplitude and secondly by indirectly inhibiting the M2K** by attenuating the strength of positive feedback loop from MK** to the M3K layer. The study additionally uncovered that positive feedback not only enhanced M3K* amplitude but it also triggered oscillations in M3K* (Figure3F).
Nature of oscillations in S1 and S2
In S1, where the incoming signal encounters the negative feedback first and then the positive feedback, output oscillations (MK**) are digital in nature (Figure3C). In S2, the signal encounters positive feedback first followed by its encounter with the negative feedback, which resulted in sinusoidal oscillations (Figure3F). In the MAPK cascade, it is known that positive feedback stabilizes[25, 28] and negative feedback destabilizes[14, 24] the output (MK**) amplitude. Here we showed that the interplay between such stabilizing and destabilizing effect differentially determines the nature of oscillations which ultimately depends on the designs of coupled feedback loops. The digital oscillations in S1 exhibited sharp switch like characteristics of a positive feedback in the rise and fall of the phosphorylation waves (Figure3C) and the analogous oscillations in S2 exhibited characteristics of a negative feedback mediated oscillations observed earlier. The study suggests that output characteristics of an oscillating MAPK cascade is based on the feedback type encountered by the incoming signal at the M2K layer.
Next we examined how oscillations in the MAPK cascade embedded in PN-I and PN-II are affected when both S1 and S2 are activated by input signal of different strengths.
Oscillations in S1 and S2 subjected to a wide range of input stimuli
Signal strength varies widely in the in-vivo conditions. The strength of the incoming signal is governed by the concentration of the signal as well as the proximity of the signal source to the target receptor that activates a signaling pathway[3, 5, 30, 31]. However biological systems are built to maintain their output characteristics in the face of perturbations. Thus we examined the relative robustness of S1 and S2 in triggering their characteristic oscillations when both the systems were subjected to a spectrum of input signals.
I. Model S1
II. Model S2
The model S2 was subjected to signals of variable strengths. Beyond a certain threshold (Sig ~ 5 nM) that triggered oscillations in the cascade, oscillations were observed for signals of any given strength (we tested the Sig range in 5 nM – 5000000 nM) of incoming signal. Figure4B shows MK** oscillations in S2 for the signal strength 5-500 nM. S2 also exhibited sustained oscillations with equal frequency and amplitude for all the strengths of applied signal above the threshold strength. The causality behind emergence of such robust oscillations could emerge from the design of the coupled feedback loops. In S2, positive feedback enhances M3K* amplitude and thus for a relatively smaller signal dose M3K* reaches its maximum amplitude and saturates. Hence when the signal strength is increased further, no additional changes will be observed in the M3K layer. Since the strengths of the feedback loops becomes unresponsive to the further increases in signal strength, MK** oscillations with robustly conserved amplitude and frequency could be generated for a very wide range of input signals.
As shown earlier for the system S2, positive feedback led to oscillations in the M3K* amplitude in addition to the amplification in its phosphorylation (Figure3F). We next investigated whether the positive feedback component of S2 (and also S1) is capable of transferring oscillations to external signal transduction modules in general.
Positive feedback transfers oscillations from an oscillating MAPK cascade to other signaling modules
Results shown in Figure3F opens up a possibility that positive feedback loop emerging from an oscillating MAPK cascade could trigger oscillations in its place of action in addition to the signal amplification in the target site. Experimentally such positive feedback loop is observed from the output MK** (from p38MAPK cascade) to the p53 phosphorylation step. Similarly positive feedback from the output MK** (from ERK cascade) leads to modification of Lck kinase as observed in the T lymphocytes. We investigated how the positive feedback from oscillating MAPK cascades such as S1 or S2 would affect the phosphorylation in an external signal transduction module, by building a hypothetical phosphorylation-dephosphorylation cycle with a kinase X and its phosphorylated form X-P. The model used for simulation of the positive feedback from S2 to X is provided as an additional SBML model file.
We built a model where MK** of system S2 provides a positive feedback to the phosphorylation of a kinase X (X is a hypothetical kinase phosphorylated by a different signal). Kinase X was assumed to be activated by phosphorylation like most of the kinases in the signaling networks. Also we assumed that a cellular phosphatase dephosphorylates phosphorylated X (X-P) back to its unphosphorylated form. This simple one step covalent modification cycle represents the most fundamental module of signal transduction and is a building block of nearly all the signal processing modules[35, 36].
Next we investigated the fate of oscillations triggered by PN-I and PN-II when nuclear cytoplasmic shuttling of the MK layer takes place. The analysis was performed to investigate the fate of oscillations triggered by PN-I and PN-II when the oscillations in the cascade output (MK**) are triggered in the cytoplasm but its nuclear translocation takes place subsequently.
Fate of MAPK oscillations in S1 and S2 upon nuclear translocation of the MK layer followed by induction of its own nuclear phosphatase
I. Oscillations in S1n
II. Oscillations in S2n
Simulations were carried out in S2n after incorporation of the transcriptional components (nuclear cytoplasmic shuttling and induction of P3-n) in the MAPK cascade. Similar to the model S1n, the model S2n was also built upon the existing model S2. Similar to S1n, the parameters for transcriptional processes were kept identical to the experimentally reported values.
We also searched the parameter space (in the range of 0.01-100 times their reference values as given in Table3) of model S2n for combinations of parameters that could possibly trigger sustained oscillations in S2n. The parameters were varied using Bifurcation discovery tool where we searched specific combinations of parameters that could trigger oscillations in S2n in presence of both P3 and P3-n. The analysis provided a parameter set that triggered transient oscillations (data not shown), but to trigger such oscillations, values of several of the parameters were largely shifted from their experimentally observed values. Thus applying changes in those parameter values would perhaps not represent the realistic scenario anymore and we restricted ourselves from applying such changes in S2n. Our analysis thus suggests that in a MAPK cascade embedded in feedback design such as PN-II, sustained oscillations could only be triggered in absence of its nuclear phosphatase P3-n.
PN-I and PN-II differentially shapes the MAPK cascades’ output sensitivity to small perturbations in parameter values
In signaling networks with multiple parameters, perturbation in only a few parameters pivotally decides the output fate of the systems and changes in majority of the parameters doesn’t alter the output characteristics. Knowledge of the crucial and less-crucial parameter values improves the understanding on the regulatory principles and helps in finding suitable drug targets[39, 40]. We subjected the kinetic parameters of S1, S2, S1n and S2n to small perturbations and the sensitivities of the outputs MK** (in S1 and S2) and MK**-n (in S1n and S2n) were calculated. Thus a model parameter ‘p’ was subjected to perturbation where = 0.001*p. Such small perturbations in the parameter values didn’t affect the sustained nature of oscillations, but revealed the relative sensitivity of the output to the perturbations.
The differential sensitivity profile of MK** in the two models could be mechanistically understood as follows. The MAPK cascade being a ultrasensitive cascade and signal amplifier[3, 25], any small changes in the input layer gets amplified as it propagates downstream and results in significantly larger changes in the output of the system. Usually negative feedback is a noise suppressor and small fluctuations in the values of signal/parameters are filtered by the negative feedback[41, 42]. But as the positive feedbacks are coupled to the system as well they further amplify the effect of small changes/perturbations, and subsequently alter the phosphorylation of the MK**. Thus in S1 and S1n (Figure9A and9C), changes in the M3K layer due to small fluctuations in the parameter values were amplified at the M2K layer owing to the positive feedback. Thus coupling of the effect of the positive feedback together with the MAPK cascade’s inherent ability for signal amplification (due to multisite phosphorylation and multi layer organization[3, 4]) resulted in maximum sensitivity of MK** to small perturbations in kinetic parameters in M3K layer. On the contrary, in S2 (Figure9B) the incoming signal encounters the positive feedback before negative feedback. Here the changes in the M3K layer are suppressed at the M2K layer by the negative feedback but as small changes in the MK** can affect the strength of the positive feedback at the M3K layer, the output MK** exhibited maximum relative sensitivity to small changes in the MK layer itself (Figure9B). S2n having identical architecture of feedback loops as S2 also exhibited maximum sensitivity to changes in the MK layer and the layers below MK specifically to the shuttling rate of MK** between the nucleus and cytoplasm (k11f and k11b in Figure9D).
Computationally it was predicted more than a decade earlier that MAPK cascade can exhibit oscillations embracing one negative feedback loop from MK** to suppress M3K phosphorylation, much earlier than the experimental report on biochemical oscillations of the MAPK cascade[11, 43]. Experiments have now shown that phosphorylation dynamics of MAPK exhibit oscillatory behavior from yeast to mammal[11, 17, 43]. Here we have studied the significance of differential designs of coupled positive and negative feedback loops in triggering MAPK oscillations. We have also investigated how MAPK cascades embedded in designs such as PN-I and PN-II can shape their oscillation and the effect of nuclear-cytoplasmic shuttling of the cascade components triggered by each of the design.
Oscillations in MAPK cascade due to PN-I and PN-II designs
Although a single negative feedback is the minimal requirement for triggering MAPK oscillations, a growing number of studies indicates that oscillations in various cellular signaling systems[6, 8] including the MAPK cascade, are triggered by coupled positive and negative feedback loops. These experimental reports led us to investigate the roles of negative and positive feedback loops operative in a three-layer MAPK cascade (Table1). Based on literature, we found that two possible designs of coupled positive and negative feedback loops can exist in a three layer MAPK cascade (S1 and S2 in Figure2), namely PN-I and PN-II. Our simulations show that both PN-I and PN-II can trigger oscillations in the cascade. In S1, the cascades output exhibited digital oscillations, whereas in S2 analogous oscillations were observed. These results show that the nature of the MK** output is determined by the type of the feedback loop functional in the M2K layer. From the context of information processing by a MAPK cascade, the ability to utilize two distinct designs of coupled positive and negative feedback loops would enable it to deliver unique oscillatory output while responding to input signal of similar strengths. We show that two MAPK cascades with identical concentrations of their respective kinases and phosphatases can trigger digital or analogous oscillations based on the design of coupled positive and negative feedback loop embedded in it.
Information processing systems such as the signal transduction networks are usually activated by a spectrum of signals and strength of an incoming signal may not remain constant[41, 44]. Thus in the living systems a signaling pathway needs to respond to signals of various strengths and subsequently deliver the desired output. We examined whether the models S1 and S2 can deliver oscillatory output when subjected to a wide range of signal strengths. It was found that both S1 and S2 can exhibit their characteristic oscillations when subjected to a range of input signal, although the system S2 was extremely robust to increase in signal strength above a threshold. The system S1 exhibited equal amplitude oscillations whose oscillation frequencies were reciprocally dependent on the strength of the input signal (Figure4A). However, S2 with feedback design PN-II exhibited equal amplitude and equal frequency oscillations for virtually any strength of input signal, beyond threshold signal strength (Figure4B). As the MAPK cascade is present in almost all the living systems, it is conceivable that the cascade is subjected to signal strengths varying in orders of magnitudes. We uncovered a remarkable ability of the cascade to trigger and maintain its oscillations with unchanged amplitudes and frequencies when subjected to varying signal strengths. A recent experimental report on epithelial cells stimulated with EGF also shows that the MAPK (ERK1) cascade conserves the frequency of oscillation of MK** when subjected to perturbations[27, 28]. Our analysis reveals a plausible design of coupled positive and negative feedback loops that the cascade can adopt to deliver such constant frequency oscillations. We additionally show that together with conservation of amplitude, the cascade is also capable of preserving its oscillation frequencies in response to large fluctuations in incoming signals.
Positive feedback emerging from an oscillating MAPK cascade triggers oscillations in its external target module.
Literature of intra-modular crosstalk involving MAPK pathways is abundant. In T cell receptor triggered signaling pathways, MK** is the origin of 92% of the feedback loops (both positive and negative), which implies that using the positive and negative feedback loops, the MAPK cascade determines fate of multiple pathways in the large scale network. Here we showed that oscillating MAPK cascade such as S1 or S2 can use their respective positive feedback loops to trigger oscillations in any external signal transduction module. The extent of oscillation in the target module would be determined by the ratio of rates of phosphorylation and dephosphorylation in the target module. When the parametric conditions were satisfied in the target module (phosphorylation rate < dephosphorylation rate), oscillations were triggered (Figure5C). Oscillations in the target module spanning from zero to its maximum phosphorylation amplitude were observed when phosphorylation rate was very much less than dephosphorylation rate. (Figure5D). The ability to induce oscillations in the target modules depending on the ratio of kinetic parameters in the target module itself can be extremely useful from the cellular context. This is because a plethora of target modules, each with unique ratios of phosphorylation-dephosphorylation will differentially deliver their oscillatory outputs (Figure5A-D).
The result also exposes a multifaceted regulatory aspect of positive feedback loops which was not specifically addressed before. Positive feedbacks hallmark characteristics is signal amplification and promoting switch like behavior to its target[25, 33]. The feedbacks ability to trigger oscillations in its target (Figure5A) reveals this novel regulatory aspect of the positive feedback.
Fate of oscillations triggered by PN-I and PN-II upon nuclear cytoplasmic shuttling of MK layer and induction of its nuclear phosphatase
Nuclear cytoplasmic shuttling of the MAPK cascade’s MK layer components takes place and MK** induces various transcription factors including its own phosphatases. The models S1 and S2 exhibited oscillations which are specific to cytoplasm but as MK layer of the cascade shuttles between the nucleus and cytoplasm, fate of the oscillations under such conditions is worth analyzing. We modified the oscillating systems where the modified systems were built with both cytoplasmic and nuclear components (S1 becomes S1n and S2 becomes S2n). The nuclear reactions comprised shuttling of MK, MK* and MK** between cytoplasm and nucleus, P3-n induction followed by dephosphorylation of MK**-n and MK*-n in the nucleus by P3-n. As the oscillations were triggered by the two different designs of feedback, PN-I and PN-II, we investigated how nuclear-cytoplasmic shuttling and transcriptional induction of P3-n affect the oscillations of S1n and S2n. Simulations show that oscillations triggered by the feedback design PN-I in S1n remains unaffected by the shuttling process and P3-n mediated dephopshorylation in the nucleus (Figure7A-D). However oscillations in S2n were abolished when nuclear phosphatase P3-n was transcribed in the nucleus (Figure8A-D). Hence we show for the first time that fate of oscillations in a MAPK cascade is determined by the design of coupled positive and negative feedback loops that trigger such oscillations especially when compartmentalization of the cascade components take place. The study exposed probable cellular strategies underlying generation and maintenance of robust MAPK oscillations for a longer duration, as long duration signal processing involves such nuclear cytoplasmic shuttling and activation of various transcription factors.
The feedback designs PN- and PN-II differentially determines the MAPK cascade’s sensitivity to small perturbations in the model kinetic parameters
Local sensitivity analysis was performed to understand the responses of the outputs MK** (S1 and S2) and MK**-n (S1n and S2n) to small perturbations in their kinetic parameters (Figure9A-D). Sensitivity analysis exposed the most sensitive parameters in the models embedded in the designs PN-I and PN-II. We found that sensitivity of MK** and MK**-n exhibits differential sensitivity profiles in S1 (S1n) and S2 (S2n), implying that the outputs sensitivity were determined by the design of the embedded feedback loops in the MAPK cascades. Sensitivity analysis results are useful for designing drugs. For example, for a system S1/S1n the most suitable strategy to suppress MK**/MK**-n will be to inhibit the strength of input stimuli (Sig) or enhance the flux of M3K* dephopshorylation. However if a drug needs to be designed for a MAPK cascade S2/S2n, MK**/MK**-n will be altered most effectively by altering the dephosphorylation flux of the MK layer (for S2) or by altering the MK layer shuffling rates (for S2n).
Proposed experimental verification of the model propositions
The prediction made based on the simulation of the models S1, S2, S1n and S2n could be tested experimentally using different approaches. In the first approach mammalian cells such as COS-1 cells can be chosen to verify model type such S1. Experiments with COS-1 show that MK** such as ERK** gives positive feedback to M2K (MEK) phosphorylation step by inhibiting its competitive inhibitor RKIP. At the same time ERK** gives negative feedback to M3K (Raf) phosphorylation by inhibiting the upstream signal that triggers Raf phosphorylation. The design resembles the system design PN-I (S1) which also exhibited oscillations, as observed experimentally. Hence considering COS-1 cells as experimental system one could subject them with various perturbation conditions as described in the models. For example it is predicted from the simulations that S1 can deliver oscillations with conserved amplitudes whose frequencies will vary according to the strength of incoming signal. Western blot analysis could subsequently be performed where kinetics of ERK phosphorylation for various strengths of input stimuli can be compared, which would then verify the model predictions. Further the model predicts that S1n (with design PN-I) should retain its oscillations upon nuclear-cytoplasmic shuttling and induction of phosphatase such as MKP-1 should not affect the ERK oscillations. This can be tested by subjecting the COS-1 cells to prolonged stimuli and subsequently capturing the phosphorylation kinetics of ERK**, which should exhibit oscillations, as predicted by the simulations. Presence of oscillations during the nuclear cytoplasmic compartmentalization of the ERK cascade can be experimentally tested in the same lines as explained elsewhere.
The system design S2 where positive and negative feedbacks are coupled as design PN-II are not reported in one single study as yet. But a recent study shows that three layer MAPK cascade can be synthetically built. Such synthetic systems will be ideal for testing hypothesis. One could design the system S2 as a synthetic system. Mass spectrometry data suggest that ERK** provides positive feedback to Raf (M3K) by phosphorylating it in certain residues which enhances specificity of Raf phosphorylation by many fold. Coupled to that a negative feedback from ERK to Raf can be considered in which ERK hyperphosphorylates and desensitizes Raf. The overall design would resemble the system design PN-II. Here the positive feedback is in the form of enhanced Raf phosphorylation in response to the incoming signal which is followed by the negative feedback in the form of desensitization of phosphorylated Raf (M3K*) that will consequently inhibit MEK (M2K) phosphorylation. Such synthetic cascades with positive and negative feedback resembling design PN-II could be subjected to signals of variable strengths and the oscillatory amplitudes of the cascade output can be captured in the form of western blots. The simulations proposed that the system S2 subjected to a very wide range of input signal should exhibit oscillations with conserved amplitude and frequencies which could be verified building the synthetic MAPK cascade.
Biological significance of MAPK oscillations and proposed implications of this study
Exact biological message encoded in the oscillatory waves of the MAPK cascade is not yet understood well, though it is argued that the oscillatory MK** fulfils some requirement for triggering transcription of certain cyclic genes. The current archetype states that, signaling system in general encodes messages either in amplitude or in frequency (or may be in both) of the oscillatory signals, for triggering transcription of a plethora of genes[11, 12, 24, 48]. Here, through our study we demonstrated various ways in which unique oscillatory message could be transmitted by the MAPK cascade embedded in coupled positive and negative feedback loops to its nuclear targets.
The feedback design PN-I can trigger oscillations of equal amplitudes but of variable frequencies. This type of cascade could be utilized by the cell for activating a subset of cyclic target genes, all of which require identical amplitude of MK** as their activation threshold but the interval of expression of each target gene is determined by the frequency of oscillations. The feedback design PN-II can be utilized to deliver oscillations with near identical frequency and amplitude in response to widely varying signal strengths. This type of feedback design would be suitable for a MAPK cascade involved in robustly inducing specific sets of genes whose expressions are critically dependent on the amplitude and/or frequencies of the MK**.
We demonstrated how oscillations could be maintained during a long duration signaling when signal processing involves nuclear-cytoplasmic shuttling of the MK layer of the cascade, followed by transcriptionally inducing the phosphatases that interact with the cascade itself. We showed that it is not always possible to maintain oscillations in the face of obvious biological perturbations, such as interaction with the transcriptionally induced phosphatases and thus the cascade has to adopt certain feedback designs (such as PN-I) to endure such perturbations to exhibit prolonged oscillations.
The MAPK cascade can utilize architecturally distinct organizations of coupled positive and negative feedback loops to trigger its oscillations. We uncovered that the signaling pathways such as the MAPK pathway can uniquely process wide range of signals by utilizing its feedback loops. It is intriguing how adoption of specific design (PN-II) of coupled feedback loops can trigger oscillations with extremely robust frequency and amplitude, specifically when such robustness in the oscillations are desired in an environment where the external signal strength fluctuates in several orders of magnitudes. Subsequently we show the trade off associated with such feedback designs (PN-II) during the nuclear cytoplasmic compartmentalization of the cascade, where oscillations triggered by PN-II couldn’t sustain such compartmentalization effect. However oscillations triggered by PN-I were robustly maintained during the compartmentalization of the MAPK cascade components. Thus it can be argued based on our analysis that MAPK cascade embedded in PN-II can be used by specific cell types to exhibit short duration oscillations in response to extremely noisy signal, where frequency and amplitude needs to be robustly maintained. The oscillations triggered by PN-II will be of short duration as longer duration in signaling implies nuclear compartmentalization of the MAPK cascade, which leads to attenuation of PN-II triggered oscillations. On the contrary the design PN-I can trigger long duration oscillations (involving nuclear cytoplasmic compartmentalization), when the cascade embedded in such design is exposed to a relatively less noisy input signal.
We additionally found a completely unexpected regulatory behavior of the positive feedback component of a coupled positive and negative feedback loop used for triggering MAPK oscillations. We show that positive feedback emerging from an oscillating MAPK cascade can generate a spectrum of unique oscillatory information to various external target modules. The amplitude of oscillations thus triggered would depend on the ratio of phosphorylation and dephosphorylation in each of the target modules, which means, each target can attain differential oscillatory fates by adjusting such ratios.
US would like to thank Department of Biotechnology, Govt. of India for providing fellowship during the period of study. IG would like to thank Department of Biotechnology, Govt. of India and Ministry of Information Technology, Govt. of India, for supporting the study.
- Widemann C, Gibson S, Jarpe BM, Lohson LG: Mitogen-activated protein kinase: conservation of a three-kinase module from yeast to human. Physiol Rev. 1999, 79 (1): 143-180.Google Scholar
- Davis JR: The Mitogen-activated protein kinase signal transduction pathway. J Biol Chem. 1993, 268 (20): 14553-14556.PubMedGoogle Scholar
- Huang CYF, Ferrell JE: Ultrasensitivity in the mitogen-activated protein kinase cascade. PNAS. 1996, 93 (19): 10078-10083. 10.1073/pnas.93.19.10078.PubMedPubMed CentralView ArticleGoogle Scholar
- Bhalla US, Ram PT, Iyengar R: MAP Kinase phosphatase as a locus of flexibility in a mitogen-activated protein kinase signaling network. Science. 2002, 297 (5583): 1018-1023. 10.1126/science.1068873.PubMedView ArticleGoogle Scholar
- Sung-Young Shin SY, Oliver Rath O, Choo SM, Fee F, McFerran B, Kolch W, Cho HK: Positive- and negative-feedback regulations coordinate the dynamic behavior of the Ras-Raf-MEK-ERK signal transduction pathway. J Cell Science. 2009, 122 (Pt 3): 425-435.PubMedView ArticleGoogle Scholar
- Tsai TYC, Choi YS, Ma W, Pomerening JR, Tang C, Ferrell JE: Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science. 2008, 321 (5885): 126-129. 10.1126/science.1156951.PubMedPubMed CentralView ArticleGoogle Scholar
- Keizer J, Li YX, Stojilkovic S, Rinzel J: InsP3-induced Ca2++excitability of the endoplasmic reticulum. Mol Biol Cell. 1995, 6 (8): 945-951.PubMedPubMed CentralView ArticleGoogle Scholar
- Pomerening JR, Kim SY, Ferrell JE: Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations. Cell. 2005, 122 (4): 565-578. 10.1016/j.cell.2005.06.016.PubMedView ArticleGoogle Scholar
- Harris SL, Levine1 AJ: The p53 pathway: positive and negative feedback loops. Oncogene. 2005, 24 (17): 2899-2908. 10.1038/sj.onc.1208615.PubMedView ArticleGoogle Scholar
- Nakakuki T, Birtwistle MR, Saeki Y, Yumoto N, Ide K, Nagashima T, Brusch L, Ogunnaike BA, Okada-Hatakeyama M, Kholodenko BN: Ligand-specific c-Fos expression emerges from the spatiotemporal control of ErbB network dynamics. Cell. 2010, 141 (5): 884-896. 10.1016/j.cell.2010.03.054.PubMedPubMed CentralView ArticleGoogle Scholar
- Shankaran H, Ippolito DL, Chrisler WB, Resat H, Bollinger N, Opresko LK, Wiley HS: Rapid and sustained nuclear–cytoplasmic ERK oscillations induced by epidermal growth factor. Mol Syst Biol. 2009, 5: 332-PubMedPubMed CentralView ArticleGoogle Scholar
- Shankaran H, Wiley HS: Oscillatory dynamics of the extracellular signal-regulated kinase pathway. Curr Opin Genet Dev. 2010, 20 (6): 650-655. 10.1016/j.gde.2010.08.002.PubMedView ArticleGoogle Scholar
- Bhalla US, Iyengar R: Emergent properties of networks of biological signaling pathways. Science. 1999, 283 (5400): 381-387. 10.1126/science.283.5400.381.PubMedView ArticleGoogle Scholar
- Kholodenko BN: Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur J Biochem. 2000, 267 (6): 1583-1588. 10.1046/j.1432-1327.2000.01197.x.PubMedView ArticleGoogle Scholar
- Atakeyama M, Kimura S, Takashi N, Kawasaki T, Yumoto N, Ichikawa M, Kim JH, Saito K, Saeki M, Shirouzu M, Yokoyama S, Konagaya A: A computational model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signalling. Biochem J. 2003, 373 (Pt 2): 451-463.View ArticleGoogle Scholar
- Mrkevich NI, Tsyganov MA, Hoek JB, Kholodenko BN: Long-range signaling by phosphoprotein waves arising from bistability in protein kinase cascades. Mol Syst Biol. 2006, 2: 61-Google Scholar
- Hilioti H, Sabbagh W, Paliwal S, Bergmann S, Goncalves MD, Bardwell L, Levchenko A: Oscillatory phosphorylation of yeast Fus3 MAP kinase controls periodic gene expression and morphogenesis. Curr Biol. 2008, 18 (21): 1700-1706. 10.1016/j.cub.2008.09.027.PubMedPubMed CentralView ArticleGoogle Scholar
- Chaudhri VK, Kumar D, Misra M, Dua R, Rao KV: Integration of a phosphatase cascade with the mitogen-activated protein kinase pathway provides for a novel signal processing function. J Biol Chem. 2010, 285 (2): 1296-1310. 10.1074/jbc.M109.055863.PubMedPubMed CentralView ArticleGoogle Scholar
- Saez-Rodriguez J, Simeoni L, Lindquist JA, Hemenway R, Bommhardt U, Arndt B, Haus UU, Weismantel R, Gilles ED, Klamt S, Schraven B: A logical model provides insights into T cell receptor signaling. PLoS Comput Biol. 2007, 3: e163-10.1371/journal.pcbi.0030163.PubMedPubMed CentralView ArticleGoogle Scholar
- Zi Z, Cho KH, Sung MH, Xia X, Zheng J, Sun Z: In silico identification of the key components and steps in IFN-gamma induced JAK-STAT signaling pathway. FEBS Lett. 2005, 579 (5): 1101-1108. 10.1016/j.febslet.2005.01.009.PubMedView ArticleGoogle Scholar
- Zi Z, Zheng Y, Rundell AE, Klipp E: SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool. BMC Bioinforma. 2008, 9: 342-10.1186/1471-2105-9-342.View ArticleGoogle Scholar
- Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U: COPASI–a COmplex PAthway Simulator. Oxford Bioinformatics. 2006, 22 (24): 3067-3074.View ArticleGoogle Scholar
- Chickarmane V, Paladugu SR, Bergmann F, Sauro HM: Bifurcation discovery tool. Bioinformatics. 2005, 21 (18): 3688-3690. 10.1093/bioinformatics/bti603.PubMedView ArticleGoogle Scholar
- Chickarmanea V, Kholodenko BN, Sauro HM: Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation. J Theor Biol. 2007, 244 (1): 68-76. 10.1016/j.jtbi.2006.05.013.View ArticleGoogle Scholar
- Bagowski CP, Ferrell JE: Bistability in the JNK cascade. Current Biol. 2001, 11 (15): 1176-1182. 10.1016/S0960-9822(01)00330-X.View ArticleGoogle Scholar
- Kholodenko BN: Cell signaling dynamics in time and space. Nat Rev Mol Cell Biol. 2006, 7 (3): 165-176. 10.1038/nrm1838.PubMedPubMed CentralView ArticleGoogle Scholar
- Qiao L, Nachbar RB, Kevrekidis IG, Shvartsman SY: Bistability and oscillations in the Huang-Ferrell model of MAPK signaling. PLoS Comput Biol. 2007, 3 (9): 1819-1826.PubMedView ArticleGoogle Scholar
- Xiong W, Ferrell JE: A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision. Nature. 2003, 426 (6965): 464-472.View ArticleGoogle Scholar
- Altan-Bonnet G, Germain RN: Modeling T cell antigen discrimination based on feedback control of digital ERK responses. PLoS Biol. 2005, 3 (11): e356-10.1371/journal.pbio.0030356.PubMedPubMed CentralView ArticleGoogle Scholar
- Sasagawa S, Ozaki Y, Fujita K, Kuroda S: Prediction and validation of the distinct dynamics of transient and sustained ERK activation. Nat Cell Biol. 2005, 7 (4): 365-373. 10.1038/ncb1233.PubMedView ArticleGoogle Scholar
- Heit B, Tavener S, Raharjo E, Kubes P: An intracellular signaling hierarchy determines direction of migration in opposing chemotactic gradients. J Cell Biol. 2002, 159 (1): 91-102. 10.1083/jcb.200202114.PubMedPubMed CentralView ArticleGoogle Scholar
- Stelling J, Sauer U, Szallasi Z, Doyle FJ, Doyle J: Robustness of cellular functions. Cell. 2004, 118 (6): 675-685. 10.1016/j.cell.2004.09.008.PubMedView ArticleGoogle Scholar
- Stefanová I, Hemmer B, Vergelli M, Martin R, Biddison WE, Germain RN: TCR ligand discrimination is enforced by competing ERK positive and SHP-1 negative feedback pathways. Nat Immunol. 2003, 4 (3): 248-254. 10.1038/ni895.PubMedView ArticleGoogle Scholar
- Goldbeter A, Koshland DE: An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci. 1981, 78 (11): 6840-6844. 10.1073/pnas.78.11.6840.PubMedPubMed CentralView ArticleGoogle Scholar
- Samaga R, Saez-Rodriguez J, Alexopoulos LG, Sorger PK, Klamt S: The logic of EGFR/ErbB signaling: theoretical properties and analysis of high-throughput data. PLoS Comput Biol. 2009, 5 (8): e1000438-10.1371/journal.pcbi.1000438.PubMedPubMed CentralView ArticleGoogle Scholar
- Raza S, Robertson KA, Lacaze PA, Page D, Enright AJ, Ghazal P, Freeman TC: A logic-based diagram of signalling pathways central to macrophage activation. BMC Syst Bio. 2008, 23 (2): 36-View ArticleGoogle Scholar
- Srivastava N, Sudan R, Saha B: CD40-modulated dual-specificity phosphatases MAPK phosphatase (MKP)-1 and MKP-3 reciprocally regulate Leishmania major infection. J Immunol. 2011, 186 (10): 5863-5872. 10.4049/jimmunol.1003957.PubMedView ArticleGoogle Scholar
- Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP: Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol. 2007, 3: 1871-1878.PubMedView ArticleGoogle Scholar
- Kitano HA: Robustness-based approach to systems-oriented drug design. Nat Rev Drug Discov. 2007, 6 (3): 202-210. 10.1038/nrd2195.PubMedView ArticleGoogle Scholar
- Hopkins AL: Network pharmacology: the next paradigm in drug discovery. Nat Chem Biol. 2008, 4 (11): 682-690. 10.1038/nchembio.118.PubMedView ArticleGoogle Scholar
- Fritsche-Guenther R, Witzel F, Sieber A, Herr R, Schmidt N, Braun S, Brummer T, Sers C, Blüthgen N: Strong negative feedback from Erk to Raf confers robustness to MAPK signalling. Mol Syst Biol. 2011, 7: 489-PubMedPubMed CentralView ArticleGoogle Scholar
- Nevozhay D, Adams RM, Murphy KF, Josic K, Balázsi G: Negative autoregulation linearizes the dose–response and suppresses the heterogeneity of gene expression. Proc Natl Acad Sci. 2009, 106 (13): 5123-5128. 10.1073/pnas.0809901106.PubMedPubMed CentralView ArticleGoogle Scholar
- Nakayama K, Satoh T, Igari A, Kageyama R, Nishida E: FGF induces oscillations of Hes1 expression and Ras/ERK activation. Curr Biol. 2008, 18: R332-R334. 10.1016/j.cub.2008.03.013.PubMedView ArticleGoogle Scholar
- O'Shaughnessy EC, Palani S, Collins JJ, Sarkar CA: Tunable signal processing in synthetic MAP kinase cascades. Cell. 2011, 144 (1): 119-131. 10.1016/j.cell.2010.12.014.PubMedPubMed CentralView ArticleGoogle Scholar
- Yeung K, Janosch P, McFerran B, Rose DW, Mischak H, Sedivy JM, Kolch W: Mechanism of suppression of the Raf/MEK/extracellular signal-regulated kinase pathway by the raf kinase inhibitor protein. Mol Cell Biol. 2000, 20 (9): 3079-3085. 10.1128/MCB.20.9.3079-3085.2000.PubMedPubMed CentralView ArticleGoogle Scholar
- Balan V, Leicht DT, Zhu J, Balan K, Kaplun A, Singh-Gupta V, Qin J, Ruan H, Comb MJ, Tzivion G: Identification of novel in vivo Raf-1 phosphorylation sites mediating positive feedback Raf-1 regulation by extracellular signal-regulated kinase. Mol Biol Cell. 2006, 17 (3): 1141-1153.PubMedPubMed CentralView ArticleGoogle Scholar
- Dougherty MK, Müller J, Ritt DA, Zhou M, Zhou XZ, Copeland TD, Conrads TP, Veenstra TD, Lu KP, Morrison DK: Regulation of Raf-1 by direct feedback phosphorylation. Mol Cell. 2005, 17 (2): 215-224. 10.1016/j.molcel.2004.11.055.PubMedView ArticleGoogle Scholar
- Cheong R, Levchenko A: Oscillatory signaling processes: the how, the why and the where. Curr Opin Genet Dev. 2010, 20: 665-669. 10.1016/j.gde.2010.08.007.PubMedPubMed CentralView ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.