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.     

Tunable signal processing in synthetic MAP kinase cascades

The flexibility of MAPK cascade responses enables regulation of a vast array of cell fate decisions, but elucidating the mechanisms underlying this plasticity is difficult in endogenous signaling networks. We constructed insulated mammalian MAPK cascades in yeast to explore how intrinsic and extrinsic perturbations affect the flexibility of these synthetic signaling modules. Contrary to biphasic dependence on scaffold concentration, we observe monotonic decreases in signal strength as scaffold concentration increases. We find that augmenting the concentration of sequential kinases can enhance ultrasensitivity and lower the activation threshold. Further, integrating negative regulation and concentration variation can decouple ultrasensitivity and threshold from the strength of the response. Computational analyses show that cascading can generate ultrasensitivity and that natural cascades with different kinase concentrations are innately biased toward their distinct activation profiles. This work demonstrates that tunable signal processing is inherent to minimal MAPK modules and elucidates principles for rational design of synthetic signaling systems.     

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.     

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 robust are switches in intracellular signaling cascades?

Since all-or-none decisions of the cell are controlled by extracellular signals, cells have biochemical switches within their intracellular signaling networks. Central elements of these switches are multisite phosphorylation, enzymic saturation, and amplification by cascades. Moreover, positive feedback can contribute to switch-like behavior termed also ultrasensitivity. Here we analyse the robustness of these mechanisms exemplified by models of the three-molecule MAPK-cascade and the single-molecule Goldbeter-Koshland switch. We show that the ultrasensitivity in the MAPK-cascades is more robust against changes of the kinetic parameters than the Goldbeter-Koshland switch. If multiple parameters are changed randomly, the effects of parameter changes can compensate each other in the cascade leading to a remarkable robustness of the switch-like behavior. The different degrees of robustness can be traced back to the different mechanisms of generating ultrasensitivity. While in the Goldbeter-Koshland switch the saturation of the enzymes are crucial, in the MAPK-cascade the adjustment of working ranges determines the ultrasensitivity. Our results indicate that amplification of ultrasensitivity in cascades and multisite phosphorylation might be a design principle to achieve robust switches.     

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.     

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.     

Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements

Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero-order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.     

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.     

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.     

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.     

植物MAPK级联途径参与调控ABA信号转导

促分裂原活化蛋白激酶(MAPK)级联途径信号通路在真核生物细胞信号的转换和放大过程中起重要作用。MAPK级联途径由三个成员组成,分别是MAPK、MAPKK及MAPKKK,此三个信号组分按照MAPKKK-MAPKK-MAPK的方式依次磷酸化将外源信号级联放大向下传递。大量研究表明,植物MAPK级联途径参与调控脱落酸(ABA)信号转导。因此,该文就ABA和MAPK的生物学功能、ABA信号转导中的磷酸化与去磷酸化以及MAPK级联途径与ABA信号转导之间的关系等方面的研究进展进行综述,以便进一步认识MAPK和ABA信号转导的分子机制。     

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.     

Using chemical reaction network theory to discard a kinetic mechanism hypothesis

Feinberg's chemical reaction network theory (CRNT) connects the structure of a biochemical reaction network to qualitative properties of the corresponding system of ordinary differential equations. No information about parameter values is needed. As such, it seems to be well suited for application in systems biology, where parameter uncertainty is predominant. However, its application in this area is rare. To demonstrate the potential benefits from its application, different reaction networks representing a single layer of the well-studied mitogen-activated protein kinase (MAPK) cascade are analysed. Recent results from Markevich et al. (2004) show that, unexpectedly, multilayered protein kinase cascades can exhibit multistationarity, even on a single cascade level. Using CRNT, we show that their assumption of a distributive mechanism for double phosphorylation and dephosphorylation is crucial for multistationarity on the single cascade level.     

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.     

Effect of positive feedback loops on the robustness of oscillations in the network of cyclin-dependent kinases driving the mammalian cell cycle

The transitions between the G(1) , S, G(2) and M phases of the mammalian cell cycle are driven by a network of cyclin-dependent kinases (Cdks), whose sequential activation is regulated by intertwined negative and positive feedback loops. We previously proposed a detailed computational model for the Cdk network, and showed that this network is capable of temporal self-organization in the form of sustained oscillations, which govern ordered progression through the successive phases of the cell cycle [Gérard and Goldbeter (2009) Proc Natl Acad Sci USA106, 21643-21648]. We subsequently proposed a skeleton model for the cell cycle that retains the core regulatory mechanisms of the detailed model [Gérard and Goldbeter (2011) Interface Focus1, 24-35]. Here we extend this skeleton model by incorporating Cdk regulation through phosphorylation/dephosphorylation and by including the positive feedback loops that underlie the dynamics of the G(1) /S and G(2) /M transitions via phosphatase Cdc25 and via phosphatase Cdc25 and kinase Wee1, respectively. We determine the effects of these positive feedback loops and ultrasensitivity in phosphorylation/dephosphorylation on the dynamics of the Cdk network. The multiplicity of positive feedback loops as well as the existence of ultrasensitivity promote the occurrence of bistability and increase the amplitude of the oscillations in the various cyclin/Cdk complexes. By resorting to stochastic simulations, we further show that the presence of multiple, redundant positive feedback loops in the G(2) /M transition of the cell cycle markedly enhances the robustness of the Cdk oscillations with respect to molecular noise.