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.     

Signal propagation of the MAPK cascade in Xenopus oocytes: role of bistability and ultrasensitivity for a mixed problem

The MAPK signaling cascade is nowadays understood as a network module highly conserved across species. Its main function is to transfer a signal arriving at the plasma membrane to the cellular interior. Current understanding of ‘how’ this is achieved involves the notions of ultrasensitivity and bistability which relate to the nonlinear dynamics of the biochemical network, ignoring spatial aspects. Much less, indeed, is so far known about the propagation of the signal through the cytoplasm. In this work we formulate, starting from a Michaelis–Menten model for the MAPK cascade in Xenopus oocytes, a reaction-diffusion model of the cascade. We study this model in one space dimension. Basing ourselves on previous general results on reaction diffusion models, we particularly study for our model the conditions for signal propagation. We show that the existence of a propagating front depends sensitively on the initial and boundary conditions at the plasma membrane. Possible biological consequences of this finding are discussed.     

Noise propagation in two-step series MAPK cascade

Series MAPK enzymatic cascades, ubiquitously found in signaling networks, act as signal amplifiers and play a key role in processing information during signal transduction in cells. In activated cascades, cell-to-cell variability or noise is bound to occur and thereby strongly affects the cellular response. Commonly used linearization method (LM) applied to Langevin type stochastic model of the MAPK cascade fails to accurately predict intrinsic noise propagation in the cascade. We prove this by using extensive stochastic simulations for various ranges of biochemical parameters. This failure is due to the fact that the LM ignores the nonlinear effects on the noise. However, LM provides a good estimate of the extrinsic noise propagation. We show that the correct estimate of intrinsic noise propagation in signaling networks that contain at least one enzymatic step can be obtained only through stochastic simulations. Noise propagation in the cascade depends on the underlying biochemical parameters which are often unavailable. Based on a combination of global sensitivity analysis (GSA) and stochastic simulations, we developed a systematic methodology to characterize noise propagation in the cascade. GSA predicts that noise propagation in MAPK cascade is sensitive to the total number of upstream enzyme molecules and the total number of molecules of the two substrates involved in the cascade. We argue that the general systematic approach proposed and demonstrated on MAPK cascade must accompany noise propagation studies in biological networks.     

Bifurcations and chaos in the MAPK signaling cascade

The mitogen-activated protein kinase (MAPK) cascade is an important signaling cascade in eukaryotes. We use the approach of generalized modeling to analyze the dynamics of the MAPK cascade and identify key mechanisms of instability. Furthermore, we report sustained multi-mode oscillations and potentially chaotic behavior caused by a sequestration-based feedback mechanism. Finally, we investigate the interplay between sequestration and external feedback loops. Our analysis thereby confirms, extends and generalizes previous results obtained by conventional modeling and points out the diversity of dynamics that sequestration can bring about.     

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.     

A computer-based model for the regulation of mitogen activated protein kinase (MAPK) activation

Computer simulations and mathematical modeling of biological processes are becoming increasingly popular, and yet the complexity of the biochemical systems or the differences between experimental setups make it very difficult to establish a standard formula for these modeling projects. Before we can start using computer-based models for predictions or targeted experiment designs, it is very important to establish a reliable model on which those predictions can be based and experimentally tested. Here we attempt to present a computer model for the mitogen-activated protein kinase (MAPK) signaling cascade which is consistent with previously published experimental results. In this study we have focused our attention to a generic MAPK ERK (extracellular signal-regulated kinase) pathway activated by epidermal growth factor (EGF) in an attempt to understand how receptors may achieve different activation kinetics of the MAPK signaling. We successfully show that the level of receptor expression is one key determinant in this regulation, and that the binding affinity of the active receptor to adaptor proteins can have a small but albeit direct effect on the downstream activation.     

Distinguishing graded and ultrasensitive signalling cascade kinetics by the shape of morphogen gradients in Drosophila

Recently, signalling gradients in cascades of two-state reaction-diffusion systems were described as a model for understanding key biochemical mechanisms that underlie development and differentiation processes in the Drosophila embryo. Diffusion-trapping at the exterior of the cell membrane triggers the mitogen-activated protein kinase (MAPK) cascade to relay an appropriate signal from the membrane to the inner part of the cytosol, whereupon another diffusion-trapping mechanism involving the nucleus reads out this signal to trigger appropriate changes in gene expression. Proposed mathematical models exhibit equilibrium distributions consistent with experimental measurements of key spatial gradients in these processes. A significant property of the formulation is that the signal is assumed to be relayed from one system to the next in a linear fashion. However, the MAPK cascade often exhibits nonlinear dose-response properties and the final remark of Berezhkovskii et al. (2009) is that this assumption remains an important property to be tested experimentally, perhaps via a new quantitative assay across multiple genetic backgrounds. In anticipation of the need to be able to sensibly interpret data from such experiments, here we provide a complementary analysis that recovers existing formulae as a special case but is also capable of handling nonlinear functional forms. Predictions of linear and nonlinear signal relays and, in particular, graded and ultrasensitive MAPK kinetics, are compared.     

Calcium signaling and the MAPK cascade are required for sperm activation in Caenorhabditis elegans

In nematode, sperm activation (or spermiogenesis), a process in which the symmetric and non-motile spermatids transform into polarized and crawling spermatozoa, is critical for sperm cells to acquire fertilizing competence. SPE-8 dependent and SPE-8 independent pathways function redundantly during sperm activation in both males and hermaphrodites of Caenorhabditis elegans. However, the downstream signaling for both pathways remains unclear. Here we show that calcium signaling and the MAPK cascade are required for both SPE-8 dependent and SPE-8 independent sperm activation, implying that both pathways share common downstream signaling components during sperm activation. We demonstrate that activation of the MAPK cascade is sufficient to activate spermatids derived from either wild-type or spe-8 group mutant males and that activation of the MAPK cascade bypasses the requirement of calcium signal to induce sperm activation, indicating that the MAPK cascade functions downstream of or parallel with the calcium signaling during sperm activation. Interestingly, the persistent activation of MAPK in activated spermatozoa inhibits Major Sperm Protein (MSP)-based cytoskeleton dynamics. We demonstrate that MAPK plays dual roles in promoting pseudopod extension during sperm activation but also blocking the MSP-based, amoeboid motility of the spermatozoa. Thus, though nematode sperm are crawling cells, morphologically distinct from flagellated sperm, and the molecular machinery for motility of amoeboid and flagellated sperm is different, both types of sperm might utilize conserved signaling pathways to modulate sperm maturation.     

A Computer‐Based Model for the Regulation of Mitogen Activated Protein Kinase (MAPK) Activation

Abstract

Computer simulations and mathematical modeling of biological processes are becoming increasingly popular, and yet the complexity of the biochemical systems or the differences between experimental setups make it very difficult to establish a standard formula for these modeling projects. Before we can start using computer‐based models for predictions or targeted experiment designs, it is very important to establish a reliable model on which those predictions can be based and experimentally tested. Here we attempt to present a computer model for the mitogen‐activated protein kinase (MAPK) signaling cascade which is consistent with previously published experimental results. In this study we have focused our attention to a generic MAPK ERK (extracellular signal‐regulated kinase) pathway activated by epidermal growth factor (EGF) in an attempt to understand how receptors may achieve different activation kinetics of the MAPK signaling. We successfully show that the level of receptor expression is one key determinant in this regulation, and that the binding affinity of the active receptor to adaptor proteins can have a small but albeit direct effect on the downstream activation.     

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.     

Control and integration of cell signaling pathways during C. Elegans vulval development

Vulval development in the Caenorhabditis elegans hermaphrodite represents a simple, genetically tractable system for studying how cell signaling events control cell fata decisions. Current models suggest that proper specification of vulval cell fates relies on the integration of multiple signaling systems, including one that involves a receptor tyrosine kinase (RTK)→Ras→mitogen activated protein kinase (MAPK) cascade and one that involves a LIN-12/Notch family receptor. In this review, we first discuss how genetic strategies are being used to identify and analyze components that control vulval cell fate decisions. We then describe the different signaling systems that have been elucidated and how they relate to one another. Finally, we highlight several recently characterized genes that encode positive regulators, negative regulators or potential targets of the RTK→Ras→MAPK cascade involved in vulval induction.     

Enhancement of Tunability of MAPK Cascade Due to Coexistence of Processive and Distributive Phosphorylation Mechanisms

The processive phosphorylation mechanism becomes important when there is macromolecular crowding in the cytoplasm. Integrating the processive phosphorylation mechanism with the traditional distributive one, we propose a mixed dual-site phosphorylation (MDP) mechanism in a single-layer phosphorylation cycle. Further, we build a degree model by applying the MDP mechanism to a three-layer mitogen-activated protein kinase (MAPK) cascade. By bifurcation analysis, our study suggests that the crowded-environment-induced pseudoprocessive mechanism can qualitatively change the response of this biological network. By adjusting the degree of processivity in our model, we find that the MAPK cascade is able to switch between the ultrasensitivity, bistability, and oscillatory dynamical states. Sensitivity analysis shows that the theoretical results remain unchanged within a reasonably chosen variation of parameter perturbation. By scaling the reaction rates and also introducing new connections into the kinetic scheme, we further construct a proportion model of the MAPK cascade to validate our findings. Finally, it is illustrated that the spatial propagation of the activated MAPK signal can be improved (or attenuated) by increasing the degree of processivity of kinase (or phosphatase). Our research implies that the MDP mechanism makes the MAPK cascade become a flexible signal module, and the coexistence of processive and distributive phosphorylation mechanisms enhances the tunability of the MAPK cascade.     

Enhancement of Tunability of MAPK Cascade Due to Coexistence of Processive and Distributive Phosphorylation Mechanisms

The processive phosphorylation mechanism becomes important when there is macromolecular crowding in the cytoplasm. Integrating the processive phosphorylation mechanism with the traditional distributive one, we propose a mixed dual-site phosphorylation (MDP) mechanism in a single-layer phosphorylation cycle. Further, we build a degree model by applying the MDP mechanism to a three-layer mitogen-activated protein kinase (MAPK) cascade. By bifurcation analysis, our study suggests that the crowded-environment-induced pseudoprocessive mechanism can qualitatively change the response of this biological network. By adjusting the degree of processivity in our model, we find that the MAPK cascade is able to switch between the ultrasensitivity, bistability, and oscillatory dynamical states. Sensitivity analysis shows that the theoretical results remain unchanged within a reasonably chosen variation of parameter perturbation. By scaling the reaction rates and also introducing new connections into the kinetic scheme, we further construct a proportion model of the MAPK cascade to validate our findings. Finally, it is illustrated that the spatial propagation of the activated MAPK signal can be improved (or attenuated) by increasing the degree of processivity of kinase (or phosphatase). Our research implies that the MDP mechanism makes the MAPK cascade become a flexible signal module, and the coexistence of processive and distributive phosphorylation mechanisms enhances the tunability of the MAPK cascade.     

How quantitative measures unravel design principles in multi-stage phosphorylation cascades

We investigate design principles of linear multi-stage phosphorylation cascades by using quantitative measures for signaling time, signal duration and signal amplitude. We compare alternative pathway structures by varying the number of phosphorylations and the length of the cascade. We show that a model for a weakly activated pathway does not reflect the biological context well, unless it is restricted to certain parameter combinations. Focusing therefore on a more general model, we compare alternative structures with respect to a multivariate optimization criterion. We test the hypothesis that the structure of a linear multi-stage phosphorylation cascade is the result of an optimization process aiming for a fast response, defined by the minimum of the product of signaling time and signal duration. It is then shown that certain pathway structures minimize this criterion. Several popular models of MAPK cascades form the basis of our study. These models represent different levels of approximation, which we compare and discuss with respect to the quantitative measures.     

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.     

The p38 mitogen-activated protein kinase signaling cascade in CD4 T cells

Since the identification of the p38 mitogen-activated protein kinase (MAPK) as a key signal-transducing molecule in the expression of the proinflammatory cytokine tumor necrosis factor (TNF) more than 10 years ago, huge efforts have been made to develop inhibitors of p38 MAPK with the intent to modulate unwanted TNF activity in diseases such as autoimmune diseases or sepsis. However, despite some anti-inflammatory effects in animal models, no p38 MAPK inhibitor has yet demonstrated clinical efficacy in human autoimmune disorders. One possible reason for this paradox might relate to the fact that the p38 MAPK signaling cascade is involved in the functional regulation of several different cell types that all contribute to the complex pathogenesis of human autoimmune diseases. In particular, p38 MAPK has a multifaceted role in CD4 T cells that have been implicated in initiating and driving sustained inflammation in autoimmune diseases, such as rheumatoid arthritis or systemic vasculitis. Here we review recent advances in the understanding of the role of the p38 MAPK signaling cascade in CD4 T cells and the consequences that its inhibition provokes in T cell functions in vitro and in vivo. These new data suggest that p38 MAPK inhibitors may elicit several unwanted effects in human autoimmune diseases but may be useful for the treatment of allergic disorders.     

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.