Emergence of Oscillations in a Mixed-Mechanism Phosphorylation System

Conradi, Carsten; Mincheva, Maya; Shiu, Anne

doi:10.1007/s11538-019-00580-6

Cited by 24 publications

(36 citation statements)

References 40 publications

(66 reference statements)

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“…A related topic -mentioned earlier -is the question of how dynamical properties arise in phosphorylation systems. Several works have examined this problem at the level of parameters, focusing on the question of which rate constants and/or initial conditions give rise to oscillations [12] or bistability [10,11]. Our perspective is slightly different; instead of allowing parameter values to change, we modify the network itself.…”

Section: Erkmentioning

confidence: 99%

“…Such parametrizations have been shown in recent years to be indispensable for analyzing multistationarity (multiple steady states, which are necessary for bistability) and oscillations [22,31,45]. Indeed, here we build on results in [10,12,17]. Specifically, following [12], we investigate oscillations by employing a steady-state parametrization together with a criterion of Yang [47] that characterizes Hopf bifurcations in terms of determinants of Hurwitz matrices.…”

Section: Erkmentioning

confidence: 99%

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Oscillations and bistability in a model of ERK regulation

et al. 2019

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This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and dephosphorylation of extracellular signal-regulated kinase (ERK). We prove that oscillations persist even as the model is greatly simplified (reactions are made irreversible and intermediates are removed). Bistability, however, is much less robust -this property is lost when intermediates are removed or even when all reactions are made irreversible. Moreover, bistability is characterized by the presence of two reversible, catalytic reactions: as other reactions are made irreversible, bistability persists as long as one or both of the specified reactions is preserved. Finally, we investigate the maximum number of steady states, aided by a network's "mixed volume" (a concept from convex geometry). Taken together, our results shed light on the question of how oscillations and bistability emerge from a limiting network of the ERK network -namely, the fully processive dual-site network -which is known to be globally stable and therefore lack both oscillations and bistability. Our proofs are enabled by a Hopf bifurcation criterion due to Yang, analyses of Newton polytopes arising from Hurwitz determinants, and recent characterizations of multistationarity for networks having a steady-state parametrization.

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Section: Erkmentioning

confidence: 99%

Section: Erkmentioning

confidence: 99%

Oscillations and bistability in a model of ERK regulation

et al. 2019

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“…This strategy has been used in numerous recent works with chemical reaction network theory, e.g. [3,5,19], and we refer the reader to [3] for an expository account.…”

Section: Sign-sensitivitiesmentioning

confidence: 99%

Sign-sensitivities for reaction networks: an algebraic approach

Feliu

2019

Mathematical Biosciences and Engineering

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This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small perturbation on the parameter vector. We provide a closed formula for the derivatives that accommodates common perturbations, and illustrate its form with numerous examples. We argue that, mathematically, the study of the response to the system with respect to changes in total amounts is not well posed, and that one should rather consider perturbations with respect to the initial conditions. We find a sign-based criterion to determine, without computing the sensitivities, whether the sign depends on the steady state and parameters of the system. This is based on earlier results of so-called injective networks. Finally, we address systems with multiple steady states and the restriction to stable steady states.

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“…In contrast purely processive phosphorylation cycles have a unique stable steady state [10], while the mixed cycles depicted in Fig. 1b and 1c have a unique steady state that might not be stable, and admit oscillations [9,28]. Distributive steps therefore seem to be involved with Figure 1.…”

Section: Introductionmentioning

confidence: 95%

“…In this paper we work towards solving the problem of existence or non-existence of Hopf bifurcations for the double phosphorylation network. We follow the strategy outlined in [9] and as in [14] we use convex parameters (see Section 3.2). As in [14] we consider simplifications of the mass action model derived from Figure 1a.…”

Section: Introductionmentioning

confidence: 99%

On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

Conradi

Feliu

Mincheva

2020

Mathematical Biosciences and Engineering

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Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and dephosphorylation is distributive admit oscillations (for some value of the rate constants and total concentrations) it is not known whether or not this is the case if both phosphorylation and dephosphorylation are distributive. We study simplified mass action models of sequential and distributive phosphorylation and show that for each of those there do not exist rate constants and total concentrations where a Hopf bifurcation occurs. To arrive at this result we use convex parameters to parametrize the steady state and Hurwitz matrices.

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Emergence of Oscillations in a Mixed-Mechanism Phosphorylation System

Cited by 24 publications

References 40 publications

Oscillations and bistability in a model of ERK regulation

Oscillations and bistability in a model of ERK regulation

Sign-sensitivities for reaction networks: an algebraic approach

On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

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