Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade

ABSTRACT: BACKGROUND: The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal. RESULTS: We have built four models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases. CONCLUSIONS: Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design.     

Effects of sequestration on signal transduction cascades

The building blocks of most signal transduction pathways are pairs of enzymes, such as kinases and phosphatases, that control the activity of protein targets by covalent modification. It has previously been shown [Goldbeter A & Koshland DE (1981) Proc Natl Acad Sci USA 78, 6840-6844] that these systems can be highly sensitive to changes in stimuli if their catalysing enzymes are saturated with their target protein substrates. This mechanism, termed zero-order ultrasensitivity, may set thresholds that filter out subthreshold stimuli. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations. Under these conditions a large fraction of the target protein may be sequestrated by the enzymes. This causes a reduction in ultrasensitivity so that the proposed mechanism is unlikely to account for ultrasensitivity under the conditions present in most in vivo signalling cascades. Furthermore, we show that sequestration changes the dynamics of a covalent modification cycle and may account for signal termination and a sign-sensitive delay. Finally, we analyse the effect of sequestration on the dynamics of a complex signal transduction cascade: the mitogen-activated protein kinase (MAPK) cascade with negative feedback. We show that sequestration limits ultrasensitivity in this cascade and may thereby abolish the potential for oscillations induced by negative feedback.     

Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation

There have been a growing number of observations of oscillating protein levels (p53 and NFkB) in eukaryotic signalling pathways. This has resulted in a renewed interest in the mechanism by which such oscillations might occur. Recent computational work has shown that a multisite phosphorylation mechanism such as that found in the MAPK cascade can theoretically exhibit bistability. The bistable behavior was shown to arise from sequestration and saturation mechanisms for the enzymes that catalyse the multisite phosphorylation cycle. These effects generate the positive feedback necessary for bistability. In this paper we describe two kinds of oscillatory dynamics which can occur in a network by which, both use such bistable multisite phosphorylated cycles. In the first example, the fully phosphorylated form of the phosphorylated cycle represses the production of the kinase, which carries out the phosphorylation of the unphosphorylated states of the cycle. The dynamics of this system leads to a relaxation oscillator. In the second example, we consider a cascade of two cycles, in which the fully phosphorylated form of the kinase, in the first cycle, phosphorylates the unphosphorylated forms in the second cycle. A feedback loop, by which the fully phosphorylated form of the second cycle inhibits the kinase step in the first cycle is also present. In this case we obtain a ring oscillator. Both these networks illustrate the versatility of the multisite bistable network.     

Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells

Although epidermal growth factor (EGF) induces transient activation of Ras and the mitogen-activated protein kinase (MAPK) cascade in PC12 cells, whereas nerve growth factor (NGF) stimulates sustained activation, the basis for these contrasting responses is not known. We have developed a computer simulation of EGF-induced MAPK cascade activation, which provides quantitative evidence that feedback inhibition of the MAPK cascade is the most important factor in determining the duration of cascade activation. Hence, we propose that the observed quantitative differences in EGF and NGF signalling can be accounted for by differential feedback regulation of the MAPK cascade.     

Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade

The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.     

Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops

ABSTRACT: BACKGROUND: 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. RESULTS: 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. CONCLUSION: 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.     

Synthesis of robust tunable oscillators using mitogen activated protein kinase cascades

Mitogen activated protein kinase (MAPK) cascade is evolutionally preserved in all eukaryotic cells, and regulates various cellular activities such as gene expression, mitosis, differentiation, and apoptosis. Recently, Bashor et al. have shown that Ste5 scaffold protein can be used to reshape the MAPK cascade through engineered feedback loops, and have used heuristic tuning mechanisms to synthesize the feedback. A problem of interest is to determine whether information regarding the underlying biochemical reactions can be used to synthesize robust feedback that will ensure that the resultant circuit has the desired properties. In this paper, we consider the problem of engineering feedback in MAPK cascade to synthesize an oscillator of the desired frequency. Our approach builds on the MAPK cascade model derived by Chikarmane et al. who have exploited the existence of a Hopf bifurcation point in the Markevich model of the MAPK cascade to synthesize the exciting kinase as a function of the doubly phosphorylated protein. We show how the L₁\mathcal{L}_1-control theory can be used for a robust synthesis of the oscillator and present the simulation results.     

MAPK signaling in equations and embryos

The Extracellularly Regulated Kinase/Mitogen Activated Protein Kinase (ERK/MAPK) signaling pathway is a critical regulator of cellular processes in adult and developing tissues. Depending on the cellular context, MAPK cascade can act as a rheostat, a switch, or an oscillator. The highly conserved structure of the cascade does not imply a rigid function, as was suggested by the early mathematical models of MAPK signaling, and can instead produce a wide range of input-output maps. Given a large number of pathway components and modes of regulation, it is essential to establish experimental systems that will allow both manipulating the MAPK cascade and monitoring its dynamics. The terminal patterning system in the Drosophila embryo appears to be ideally suited for this purpose. Our recent experiments characterized dynamics of the MAPK phosphorylation gradient in the terminal system and proposed that it is regulated by a cascade of diffusion-trapping modules. Here we discuss a biophysical model that can describe the observed dynamics and guide future experiments for exploring the relative importance of multiple layers of MAPK cascade regulation.     

B-Raf is critical for MAPK activation during mitosis and is regulated in an M phase-dependent manner in Xenopus egg extracts

Activation of the MAPK cascade during mitosis is critical for spindle assembly and normal mitotic progression. The underlying regulatory mechanisms that control activation of the MEK/MAPK cascade during mitosis are poorly understood. Here we purified and characterized the MEK kinase activity present in Xenopus M phase-arrested egg extracts. Our results show that B-Raf was the critical MEK kinase required for M phase activation of the MAPK pathway. Consistent with this, B-Raf was activated and underwent hyperphosphorylation in an M phase-dependent manner. Interestingly B-Raf hyperphosphorylation at mitosis occurred, at least in part, as a consequence of a feedback loop involving MAPK-mediated phosphorylation within a conserved C-terminal SPKTP motif. The kinase activity of a B-Raf mutant defective at both phosphorylation sites was substantially greater than its wild type counterpart when incubated in Xenopus M phase egg extracts. Furthermore suppression of MAPK feedback at mitosis enhanced B-Raf activity, whereas constitutive activation of MAPK at mitosis strongly suppressed B-Raf activity. These results suggest that feedback phosphorylation by MAPK negatively regulates B-Raf activity at mitosis. Collectively our data demonstrate for the first time a role for B-Raf at mitosis and provide new insight into understanding the regulation and function of B-Raf during cell proliferation.     

Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.     

A theoretical modeling for frequency modulation of Ca(2+) signal on activation of MAPK cascade

It is known that Ca(2+) signal regulates mitogen-activated protein kinase (MAPK) cascade by a central Ras protein in GTPase-cycle. Therefore, we construct an integrated theoretical model comprising Ca(2+) oscillations, GTPase-cycle and MAPK cascade modules sequentially. Meanwhile, based on multiple feedback regulations in MAPK cascade, three operation modes of this model are introduced. An extended version of this model is further built when spatial heterogeneity is involved. These models allow us to investigate the very interesting and broad question about the effects of Ca(2+) oscillations on the activation of MAPK cascade in both the homogeneous and heterogeneous systems. When the Li-Rinzel model is adopted to simulate endogenous Ca(2+) oscillations, our theoretical results illustrate that the appropriate operation mode of MAPK cascade is required for the negative correlation between a decreasing frequency of Ca(2+) oscillations and activation of MAPK cascade, which was found in the experiment (S. Kupzig et al. PNAS 102 (2005) 7577-7582). While a piecewise function is used to generate Ca(2+) signal to explore much larger range of periods of Ca(2+) oscillations, it is found that the negative correlation feature is independent on the operation mode of MAPK cascade. In this case, different operation modes only influence the strength of negative correlation between activation of MAPK cascade and periods of Ca(2+) oscillations. The quantitative results may be of great use in analyzing interaction of IP3-Ca(2+) and Ras-MAPK signaling pathways, and motivate the further experimental research.     

New analysis technique for multistability detection

Systems with counter-clockwise input-output (I-O) dynamics were recently introduced in order to study the convergence of positive feedback loops (possibly to many different equilibrium states). The author shows how this notion can be used to perform bifurcation analysis and globally predict multistability of a closed-loop feedback interconnection just by using the knowledge of steady-state I-O responses of the systems. To illustrate the theory, this method is then applied to a recently published model of mitogen activated protein kinase (MAPK) cascade. Furthermore, some examples (mainly motivated by molecular biology) of systems that enjoy the property are presented and discussed.     

Optogenetic actuator – ERK biosensor circuits identify MAPK network nodes that shape ERK dynamics

Combining single‐cell measurements of ERK activity dynamics with perturbations provides insights into the MAPK network topology. We built circuits consisting of an optogenetic actuator to activate MAPK signaling and an ERK biosensor to measure single‐cell ERK dynamics. This allowed us to conduct RNAi screens to investigate the role of 50 MAPK proteins in ERK dynamics. We found that the MAPK network is robust against most node perturbations. We observed that the ERK‐RAF and the ERK‐RSK2‐SOS negative feedback operate simultaneously to regulate ERK dynamics. Bypassing the RSK2‐mediated feedback, either by direct optogenetic activation of RAS, or by RSK2 perturbation, sensitized ERK dynamics to further perturbations. Similarly, targeting this feedback in a human ErbB2‐dependent oncogenic signaling model increased the efficiency of a MEK inhibitor. The RSK2‐mediated feedback is thus important for the ability of the MAPK network to produce consistent ERK outputs, and its perturbation can enhance the efficiency of MAPK inhibitors.     

Dynamic studies of scaffold-dependent mating pathway in yeast

The mating pathway in Saccharomyces cerevisiae is one of the best understood signal transduction pathways in eukaryotes. It transmits the mating signal from plasma membrane into the nucleus through the G-protein coupled receptor and the mitogen-activated protein kinase (MAPK) cascade. According to current understanding of the mating pathway, we construct a system of ordinary differential equations to describe the process. Our model is consistent with a wide range of experiments, indicating that it captures some main characteristics of the signal transduction along the pathway. Investigation with the model reveals that the shuttling of the scaffold protein and the dephosphorylation of kinases involved in the MAPK cascade cooperate to regulate the response upon pheromone induction and to help preserve the fidelity of the mating signaling. We explored factors affecting the dose-response curves of this pathway and found that both negative feedback and concentrations of the proteins involved in the MAPK cascade play crucial roles. Contrary to some other MAPK systems where signaling sensitivity is being amplified successively along the cascade, here the mating signal is transmitted through the cascade in an almost linear fashion.     

Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades

Mitogen-activated protein kinase (MAPK) cascades can operate as bistable switches residing in either of two different stable states. MAPK cascades are often embedded in positive feedback loops, which are considered to be a prerequisite for bistable behavior. Here we demonstrate that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation. Importantly, the reported kinetic properties of the kinase (MEK) and phosphatase (MKP3) of extracellular signal-regulated kinase (ERK) fulfill the essential requirements for generating a bistable switch at a single MAPK cascade level. Likewise, a cycle where multisite phosphorylations are performed by different kinases, but dephosphorylation reactions are catalyzed by the same phosphatase, can also exhibit bistability and hysteresis. Hence, bistability induced by multisite covalent modification may be a widespread mechanism of the control of protein activity.     

Computation and analysis of time-dependent sensitivities in Generalized Mass Action systems

Understanding biochemical system dynamics is becoming increasingly important for insights into the functioning of organisms and for biotechnological manipulations, and additional techniques and methods are needed to facilitate investigations of dynamical properties of systems. Extensions to the method of Ingalls and Sauro, addressing time-dependent sensitivity analysis, provide a new tool for executing such investigations. We present here the results of sample analyses using time-dependent sensitivities for three model systems taken from the literature, namely an anaerobic fermentation pathway in yeast, a negative feedback oscillator modeling cell-cycle phenomena, and the Mitogen Activated Protein (MAP) kinase cascade. The power of time-dependent sensitivities is particularly evident in the case of the MAPK cascade. In this example it is possible to identify the emergence of a concentration of MAPKK that provides the best response with respect to rapid and efficient activation of the cascade, while over- and under-expression of MAPKK relative to this concentration have qualitatively different effects on the transient response of the cascade. Also of interest is the quite general observation that phase-plane representations of sensitivities in oscillating systems provide insights into the manner with which perturbations in the envelope of the oscillation result from small changes in initial concentrations of components of the oscillator. In addition to these applied analyses, we present an algorithm for the efficient computation of time-dependent sensitivities for Generalized Mass Action (GMA) systems, the most general of the canonical system representations of Biochemical Systems Theory (BST). The algorithm is shown to be comparable to, or better than, other methods of solution, as exemplified with three biochemical systems taken from the literature.     

Organization and regulation of mitogen-activated protein kinase signaling pathways

Mitogen-activated protein kinases (MAPKs) are components of a three kinase regulatory cascade. There are multiple members of each component family of kinases in the MAPK module. Specificity of regulation is achieved by organization of MAPK modules, in part, by use of scaffolding and anchoring proteins. Scaffold proteins bring together specific kinases for selective activation, sequestration and localization of signaling complexes. The recent elucidation of scaffolding mechanisms for MAPK pathways has begun to solve the puzzle of how specificity in signaling can be achieved for each MAPK pathway in different cell types and in response to different stimuli. As new MAPK members are defined, determining their organization in kinase modules will be critical in understanding their select role in cellular regulation.     

Effect of the MAPK cascade structure, nuclear translocation and regulation of transcription factors on gene expression

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 switch-like 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.     

Involvement of mitogen protein kinase cascade in agonist-mediated human A(3) adenosine receptor regulation

It has been suggested that A(3) adenosine receptors (ARs) play a role in the pathophysiology of cerebral ischemia with dual and opposite neuroprotective and neurodegenerative effects. This could be due to a receptor regulation mediated by rapid phosphorylation and desensitization carried out by intracellular kinases. In this study, we investigated the involvement of extracellular regulated kinase (ERK 1 and 2), members of the mitogen-activated protein kinase (MAPK) family, in A(3) AR phosphorylation. A(3) AR mediated the activation of ERK 1/2 with a typical transient monophasic kinetics (5 min). The activation was not affected by hypertonic sucrose cell pre-treatment, suggesting that this effect occurred independently of receptor internalization. The involvement of MAPK cascade in the A(3) AR regulation process was evaluated using two well-characterized MAPK kinase inhibitors, PD98059 (2-(2'-amino-3'-methoxyphenyl)oxanaphthalen-4-one) and U0126 (1,4-diamino-2,3-dicyano-1,4-bis (aminophenylthio) butadiene). The exposure of cells to PD98059 prevented MAPK activation and inhibited homologous A(3) AR desensitization and internalization, impairing agonist-mediated receptor phosphorylation. PD98059 inhibited the membrane translocation of G protein-coupled receptor kinase (GRK(2)), which is involved in A(3) AR homologous phosphorylation, suggesting this kinase as a target for the MAPK cascade.On the contrary, the chemically unrelated inhibitor of the MAPK cascade, U0126, did not significantly affect GRK(2) membrane translocation or receptor internalization. Nevertheless, the inhibitor induced a significant impairment of receptor phosphorylation and desensitization. These results suggested that the MAPK cascade is involved in A(3) AR regulation by a feedback mechanism which controls GRK(2) activity and probably involves a direct receptor phosphorylation.     

Localized feedback phosphorylation of Ste5p scaffold by associated MAPK cascade

Scaffold proteins play pivotal roles during signal transduction. In Saccharomyces cerevisiae, the Ste5p scaffold protein is required for activation of the mating MAPK cascade in response to mating pheromone and assembles a G protein-MAPK cascade complex at the plasma membrane. To serve this function, Ste5p undergoes a regulated localization event involving nuclear shuttling and recruitment to the cell cortex. Here, we show that Ste5p is also subject to two types of phosphorylation and increases in abundance as a result of MAPK activation. During vegetative growth, Ste5p is basally phosphorylated through a process regulated by the CDK Cdc28p. During mating pheromone signaling, Ste5p undergoes increased phosphorylation by the mating MAPK cascade. Multiple kinases of the mating MAPK cascade contribute to pheromone-induced phosphorylation of Ste5p, with the mating MAPKs contributing the most. Pheromone induction or overexpression of the Ste4p Gbeta subunit increases the abundance of Ste5p at a post-translational step, as long as the mating MAPKs are present. Increasing the level of MAPK activation increases the amount of Ste5p at the cell cortex. Analysis of Ste5p localization mutants reveals a strict requirement for Ste5p recruitment to the plasma membrane for the pheromone-induced phosphorylation. These results suggest that the pool of Ste5p that is recruited to the plasma membrane selectively undergoes feedback phosphorylation by the associated MAPKs, leading to an increased pool of Ste5p at the site of polarized growth. These findings provide evidence of a spatially regulated mechanism for post-activation control of a signaling scaffold that potentiates pathway activation.