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.     

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.     

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.     

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.     

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.     

Membrane localization of scaffold proteins promotes graded signaling in the yeast MAP kinase cascade

BACKGROUND: Signaling through mitogen-activated protein kinase (MAPK) cascade pathways can show various input-output behaviors, including either switch-like or graded responses to increasing levels of stimulus. Prior studies suggest that switch-like behavior is promoted by positive feedback loops and nonprocessive phosphorylation reactions, but it is unclear whether graded signaling is a default behavior or whether it must be enforced by separate mechanisms. It has been hypothesized that scaffold proteins promote graded behavior. RESULTS: Here, we experimentally probe the determinants of graded signaling in the yeast mating MAPK pathway. We find that graded behavior is robust in that it resists perturbation by loss of several negative-feedback regulators. However, the pathway becomes switch-like when activated by a crosstalk stimulus that bypasses multiple upstream components. To dissect the contributing factors, we developed a method for gradually varying the signal input at different pathway steps in vivo. Input at the beginning of the kinase cascade produced a sharp, threshold-like response. Surprisingly, the scaffold protein Ste5 increased this threshold behavior when limited to the cytosol. However, signaling remained graded whenever Ste5 was allowed to function at the plasma membrane. CONCLUSIONS: The results suggest that the MAPK cascade module is inherently ultrasensitive but is converted to a graded system by the pathway-specific activation mechanism. Scaffold-mediated assembly of signaling complexes at the plasma membrane allows faithful propagation of weak signals, which consequently reduces pathway ultrasensitivity. These properties help shape the input-output properties of the system to fit the physiological context.     

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.     

MAPK cascade possesses decoupled controllability of signal amplification and duration

The three important characteristics of the output signal of mitogen activated protein kinase (MAPK) cascade are time delay between stimulus and response, amplitude gain, and duration of the output signal. In this study, we performed a sensitivity analysis on the computational model of epidermal growth factor receptor (EGFR) activated MAPK cascade developed by Schoeberl and co-workers (1) to identify the sensitive steps of the pathway affecting these characteristics. We show that the signaling network is sensitive in a decoupled manner, which provides the ability to control its output amplitude and duration one at a time. Signal duration is found sensitive only to the phosphatase reactions at the MEK level. In contrast, signal amplitude is found most sensitive to the phosphatase reactions at the ERK level. Time delay is found to be a robust characteristic of the system.     

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.     

Genome-wide exploration of the molecular evolution and regulatory network of mitogen-activated protein kinase cascades upon multiple stresses in Brachypodium distachyon

Background

Brachypodium distachyon is emerging as a widely recognized model plant that has very close relations with several economically important Poaceae species. MAPK cascade is known to be an evolutionarily conserved signaling module involved in multiple stresses. Although the gene sequences of MAPK and MAPKK family have been fully identified in B. distachyon, the information related to the upstream MAPKKK gene family especially the regulatory network among MAPKs, MAPKKs and MAPKKKs upon multiple stresses remains to be understood.

Results

In this study, we have identified MAPKKKs which belong to the biggest gene family of MAPK cascade kinases. We have systematically investigated the evolution of whole MAPK cascade kinase gene family in terms of gene structures, protein structural organization, chromosomal localization, orthologs construction and gene duplication analysis. Our results showed that most BdMAPK cascade kinases were located at the low-CpG-density region, and the clustered members in each group shared similar structures of the genes and proteins. Synteny analysis showed that 62 or 21 pairs of duplicated orthologs were present between B. distachyon and Oryza sativa, or between B. distachyon and Arabidopsis thaliana respectively. Gene expression data revealed that BdMAPK cascade kinases were rapidly regulated by stresses and phytohormones. Importantly, we have constructed a regulation network based on co-expression patterns of the expression profiles upon multiple stresses performed in this study.

Conclusions

BdMAPK cascade kinases were involved in the signaling pathways of multiple stresses in B. distachyon. The network of co-expression regulation showed the most of duplicated BdMAPK cascade kinase gene orthologs demonstrated their convergent function, whereas few of them developed divergent function in the evolutionary process. The molecular evolution analysis of identified MAPK family genes and the constructed MAPK cascade regulation network under multiple stresses provide valuable information for further investigation of the functions of BdMAPK cascade kinase genes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1452-1) contains supplementary material, which is available to authorized users.     

Activation of the MAPK module from different spatial locations generates distinct system outputs

The Ras/Raf/MEK/ERK (MAPK) pathway directs multiple cell fate decisions within a single cell. How different system outputs are generated is unknown. Here we explore whether activating the MAPK module from different membrane environments can rewire system output. We identify two classes of nanoscale environment within the plasma membrane. The first, which corresponds to nanoclusters occupied by GTP-loaded H-, N- or K-Ras, supports Raf activation and amplifies low Raf kinase input to generate a digital ERKpp output. The second class, which corresponds to nanoclusters occupied by GDP-loaded Ras, cannot activate Raf and therefore does not activate the MAPK module, illustrating how lateral segregation on plasma membrane influences signal output. The MAPK module is activated at the Golgi, but in striking contrast to the plasma membrane, ERKpp output is analog. Different modes of Raf activation precisely correlate with these different ERKpp system outputs. Intriguingly, the Golgi contains two distinct membrane environments that generate ERKpp, but only one is competent to drive PC12 cell differentiation. The MAPK module is not activated from the ER. Taken together these data clearly demonstrate that the different nanoscale environments available to Ras generate distinct circuit configurations for the MAPK module, bestowing cells with a simple mechanism to generate multiple system outputs from a single cascade.     

Eisosomes Regulate Phosphatidylinositol 4,5-Bisphosphate (PI(4,5)P2) Cortical Clusters and Mitogen-activated Protein (MAP) Kinase Signaling upon Osmotic Stress

Eisosomes are multiprotein structures that generate linear invaginations at the plasma membrane of yeast cells. The core component of eisosomes, the BAR domain protein Pil1, generates these invaginations through direct binding to lipids including phosphoinositides. Eisosomes promote hydrolysis of phosphatidylinositol 4,5 bisphosphate (PI(4,5)P₂) by functioning with synaptojanin, but the cellular processes regulated by this pathway have been unknown. Here, we found that PI(4,5)P₂ regulation by eisosomes inhibits the cell integrity pathway, a conserved MAPK signal transduction cascade. This pathway is activated by multiple environmental conditions including osmotic stress in the fission yeast Schizosaccharomyces pombe. Activation of the MAPK Pmk1 was impaired by mutations in the phosphatidylinositol (PI) 5-kinase Its3, but this defect was suppressed by removal of eisosomes. Using fluorescent biosensors, we found that osmotic stress induced the formation of PI(4,5)P₂ clusters that were spatially organized by eisosomes in both fission yeast and budding yeast cells. These cortical clusters contained the PI 5-kinase Its3 and did not assemble in the its3-1 mutant. The GTPase Rho2, an upstream activator of Pmk1, also co-localized with PI(4,5)P₂ clusters under osmotic stress, providing a molecular link between these novel clusters and MAPK activation. Our findings have revealed that eisosomes regulate activation of MAPK signal transduction through the organization of cortical lipid-based microdomains.     

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.     

Activation of mitogen-activated protein kinase by membrane-targeted Raf chimeras is independent of raft localization.

Binding of proteins to the plasma membrane can be achieved with various membrane targeting motifs, including combinations of fatty acids, isoprenoids, and basic domains. In this study, we investigate whether attachment of different membrane targeting motifs influences the signaling capacity of membrane-bound signal transduction proteins by directing the proteins to different membrane microdomains. We used c-Raf-1 as a model for a signaling protein that is activated when membrane-bound. Three different membrane targeting motifs from K-Ras, Fyn, and Src proteins were fused to the N or C terminus of Raf-1. The ability of the modified Rafs to initiate MAPK signaling was then investigated. All three modified Raf-1 constructs activated MAPK to nearly equivalent levels. The extent of localization of the Raf-1 constructs to membrane microdomains known as rafts did not correlate with the level of MAPK activation. Moreover, treatment of cells with the raft disrupting drug methyl-beta-cyclodextrin (MbetaCD) caused activation of MAPK to levels equivalent to those achieved with membrane-targeted Raf constructs. The use of pharmacological agents as well as dominant negative mutants revealed that MAPK activation by MbetaCD proceeds via a phosphoinositide 3-kinase-dependent mechanism that is Ras/Raf-independent. We conclude that cholesterol depletion from the plasma membrane by MbetaCD constitutes an alternative pathway for activating MAPK.     

Plasticity of the MAPK Signaling Network in Response to Mechanical Stress

Cells display versatile responses to mechanical inputs and recent studies have identified the mitogen-activated protein kinase (MAPK) cascades mediating the biological effects observed upon mechanical stimulation. Although, MAPK pathways can act insulated from each other, several mechanisms facilitate the crosstalk between the components of these cascades. Yet, the combinatorial complexity of potential molecular interactions between these elements have prevented the understanding of their concerted functions. To analyze the plasticity of the MAPK signaling network in response to mechanical stress we performed a non-saturating epistatic screen in resting and stretched conditions employing as readout a JNK responsive dJun-FRET biosensor. By knocking down MAPKs, and JNK pathway regulators, singly or in pairs in Drosophila S2R+ cells, we have uncovered unexpected regulatory links between JNK cascade kinases, Rho GTPases, MAPKs and the JNK phosphatase Puc. These relationships have been integrated in a system network model at equilibrium accounting for all experimentally validated interactions. This model allows predicting the global reaction of the network to its modulation in response to mechanical stress. It also highlights its context-dependent sensitivity.     

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.     

Bistability and oscillations in the Huang-Ferrell model of MAPK signaling

Physicochemical models of signaling pathways are characterized by high levels of structural and parametric uncertainty, reflecting both incomplete knowledge about signal transduction and the intrinsic variability of cellular processes. As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes. Based on the combination of random parameter search and continuation algorithms, we developed a methodology for the statistical analysis of mechanistic signaling models. In applying it to the well-studied MAPK cascade model, we discovered a large region of oscillations and explained their emergence from single-stage bistability. The surprising abundance of strongly nonlinear (oscillatory and bistable) input/output maps revealed by our analysis may be one of the reasons why the MAPK cascade in vivo is embedded in more complex regulatory structures. We argue that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics.     

Involvement of plasma membrane proteins in plant defense responses. Analysis of the cryptogein signal transduction in tobacco.

Cryptogein, a 98 amino acid protein secreted by the fungus Phytophthora cryptogea, induces a hypersensitive response and systemic acquired resistance in tobacco plants (Nicotiana tabacum var Xanthi). The mode of action of cryptogein has been studied using tobacco cell suspensions. The recognition of this elicitor by a plasma membrane receptor leads to a cascade of events including protein phosphorylation, calcium influx, potassium and chloride effluxes, plasma membrane depolarization, activation of a NADPH oxidase responsible for active oxygen species (AOS) production and cytosol acidification, activation of the pentose phosphate pathway, and activation of two mitogen-activated protein kinase (MAPK) homologues. The organization of the cryptogein responses reveals that the earliest steps of the signal transduction pathway involve plasma membrane activities. Their activation generates a complex network of second messengers which triggers the specific physiological responses. This study may contribute to our understanding of plant signaling processes because elicitors and a variety of signals including hormones, Nod factors, light, gravity and stresses share some common transduction elements and pathways.