Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling

Qiao, Liang; Nachbar, Robert B.; Kevrekidis, Ioannis G.; Shvartsman, Stanislav Y.

doi:10.1371/journal.pcbi.0030184

Cited by 195 publications

(226 citation statements)

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“…It has also been predicted that they can generate oscillations (6,7,8), amplify weak but attenuate strong signals (9), and give rise to bistability due to enzyme sequestration (10,11). MAPK pathways are, indeed, important for cell signalling, and for this reason they have been studied extensively, both theoretically (2,3,(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and experimentally (2,4,5,7,16,(20)(21)(22). However, with the exceptions of refs.…”

mentioning

confidence: 99%

Spatio-temporal correlations can drastically change the response of a MAPK pathway

Takahashi

Tănase‐Nicola

Wolde

2010

Proc. Natl. Acad. Sci. U.S.A.

254

393

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Multisite covalent modification of proteins is omnipresent in eukaryotic cells. A well-known example is the mitogen-activated protein kinase (MAPK) cascade where, in each layer of the cascade, a protein is phosphorylated at two sites. It has long been known that the response of a MAPK pathway strongly depends on whether the enzymes that modify the protein act processively or distributively. A distributive mechanism, in which the enzyme molecules have to release the substrate molecules in between the modification of the two sites, can generate an ultrasensitive response and lead to hysteresis and bistability. We study by Green's Function Reaction Dynamics (GFRD), a stochastic scheme that makes it possible to simulate biochemical networks at the particle level in time and space, a dual phosphorylation cycle in which the enzymes act according to a distributive mechanism. We find that the response of this network can differ dramatically from that predicted by a mean-field analysis based on the chemical rate equations. In particular, rapid rebindings of the enzyme molecules to the substrate molecules after modification of the first site can markedly speed up the response and lead to loss of ultrasensitivity and bistability. In essence, rapid enzyme-substrate rebindings can turn a distributive mechanism into a processive mechanism. We argue that slow ADP release by the enzymes can protect the system against these rapid rebindings, thus enabling ultrasensitivity and bistability.MAP kinase | Multisite phosphorylation | Reaction diffusion | Simulation M APK cascades are ubiquitous in eukaryotic cells. They are involved in cell differentiation, cell proliferation, and apoptosis (1). MAPK pathways exhibit very rich dynamics. It has been predicted mathematically and shown experimentally that they can generate an ultrasensitive response (2-4) and exhibit bistability via positive feedback (5). It has also been predicted that they can generate oscillations (6,7,8), amplify weak but attenuate strong signals (9), and give rise to bistability due to enzyme sequestration (10, 11). MAPK pathways are, indeed, important for cell signalling, and for this reason they have been studied extensively, both theoretically (2, 3, 6-19) and experimentally (2,4,5,7,16,(20)(21)(22). However, with the exceptions of refs. 7, 9, 11, 15, and 19, the pathway is commonly modeled by using chemical rate equations (2, 3, 6, 8, 10, 12-14, 16, 17). This is a mean-field description, in which it is assumed that the system is well-stirred and that fluctuations can be neglected. Here, we perform particle-based simulations of one layer of the MAPK cascade using our recently developed GFRD algorithm (23, 24). Our simulations reveal that spatio-temporal correlations between the enzyme and substrate molecules that are ignored in the commonly employed mean-field analyses can have a dramatic effect on the nature of the response. They can not only speed up the response, but also lead to loss of ultrasensitivity and bistability.The response time, the sharpness of the ...

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confidence: 99%

Spatio-temporal correlations can drastically change the response of a MAPK pathway

Takahashi

Tănase‐Nicola

Wolde

2010

Proc. Natl. Acad. Sci. U.S.A.

254

393

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“…1), the enzymatic cascade ( modules for various inputs. The reaction rates and initial conditions for the modules used in this study were taken from the range listed in [29]. However, unlike in [29], we assume that all modules are identical, and letĒ, the supremum 165 of the enzymatic input, vary up to the same order of magnitude asM , the maximum of the substrate concentration.…”

Section: Resultsmentioning

confidence: 99%

“…The parameters listed in [29] assume that the phosphatase concentrations are much lower than the proteins they act on. This is also argued in [30].…”

Section: Enzymatic Cascade Modelmentioning

confidence: 99%

“…They discovered that multiple layering generates an ultrasensitive signal-to-response curve, allowing cascades to behave like cooperative enzymes. Qiao et al [29] 75 expanded on this work by sampling a wider range of parameter values and discovered bistability and oscillations in the Huang-Ferrell model. Ventura et al [30] returned to the seminal work of Goldbeter and Koshland…”

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confidence: 95%

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Three level signal transduction cascades lead to reliably timed switches

Armbruster

Nagy

Young

2014

Journal of Theoretical Biology

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Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades.Key words: MAP-kinase network, Michaelis-Menten equations, time-dependent ODEs SignificanceIn MAP-kinase signaling networks, three-level cascades are a very common motif. We try to understand why evolution would favor such a motif by analyzing the set of differential equations describing such signaling cascades. Specifically we study how such multi-level cascades process different time dependent same sigmoidal output signal. Adding additional layers in the cascade does not change the type of output signal but delays its activation time. Introduction 10Biochemical cascades, in which upstream reaction products catalyze downstream reactions, are common patterns in eukaryotic molecular pathways. The mitogen-activated protein kinase (MAPK) system is an ancient, highly conserved example [1]. Functional and evolutionary studies of such cascades tend to emphasize their role as amplifiers of some input signal. Koshland et al. [2] 15 (see also [3]) observe that "amplification" in this context involves at least two distinct notions: amplification of the absolute size of the signal and amplification of the change in signal intensity relative to the signal background intensity, so-called "fold" amplification [4]. Classic examples of the former include bloodclotting [5, 6,7,8] and complement [9,10] among others probably evolved from 20 the same ancestral serine protease cascade [11]. The latter fold-change amplification is characteristic of signal transduction, at least for the MAPK and Wnt, β-catenin pathways [12,13]. In both general cases, amplification is generated by layering in the cascade. Layering can also produce ultrasensitive responses, in which smooth changes in input are converted to a switch-like "off-on" output 25 with a steeper signal-to-response curve than seen with traditional MichaelisMenten dynamics [14, 15,16,2,17,3].The intrinsic blood clotting mechanism of mammals was among the first biochemical cascades studied. 110We then analyze the enzyme cascade using a perturbation analysis which reduces the system to a chain of one parameter modules, allowing us to establish a Michaelis-Menten type equation for open enzymatic systems ...

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“…An activated MAP2K, in turn, phosphorylates a MAPK on its serine and threonine residues. The MAPK cascade is evolutionally preserved in all eukaryotic cells, ranging from yeasts to mammals (see Qiao et al 2007). The MAPK cascade has been implicated in malignant transformations, and in the regulation of cellular growth and proliferation of several tumor types.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of robust tunable oscillators using mitogen activated protein kinase cascades

et al. 2010

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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 L 1 -control theory can be used for a robust synthesis of the oscillator and present the simulation results.

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Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling

Cited by 195 publications

References 44 publications

Spatio-temporal correlations can drastically change the response of a MAPK pathway

Spatio-temporal correlations can drastically change the response of a MAPK pathway

Three level signal transduction cascades lead to reliably timed switches

Synthesis of robust tunable oscillators using mitogen activated protein kinase cascades

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