Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions

Conradi, Carsten; Shiu, Anne

doi:10.1016/j.bpj.2017.11.3787

Cited by 57 publications

(68 citation statements)

References 75 publications

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“…, h c,a,12 in (12), each nonconstant coefficient is, up to sign, one of the a i 's. Hence, theā i 's in (14) are effective parameters, and the function in (12) is an effective steady-state function. Finally, the fact that φ is a positive parametrization with respect to (12) (as in Definition 2.2) follows directly from comparing equations (12) and (13).…”

Section: Irreversible Versions Of the Erk Networkmentioning

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: Irreversible Versions Of the Erk Networkmentioning

confidence: 99%

“…In recent years, significant attention has been devoted to the question of how bistability and oscillations emerge in biological networks involving multisite phosphorylation [14]. Such networks are of great biological importance [9].…”

Section: Introductionmentioning

confidence: 99%

Oscillations and bistability in a model of ERK regulation

et al. 2019

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“…Runtimes (in minutes) on benchmark problems Chemical Reaction System The following system of ODEs corresponds to a chemical reaction network[4, Eq. 3.4], which is a reduced fully processive, n-site phosphorylation network.…”

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confidence: 99%

SIAN: software for structural identifiability analysis of ODE models

et al. 2019

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Biological processes are often modeled by ordinary differential equations with unknown parameters. The unknown parameters are usually estimated from experimental data. In some cases, due to the structure of the model, this estimation problem does not have a unique solution even in the case of continuous noise-free data. It is therefore desirable to check the uniqueness a priori before carrying out actual experiment. We present a new software SIAN (Structural Identifiability ANalyser) that does this. Our software can tackle problems that could not be tackled by previously developed packages. * All the results presented in the rest of the section are computed with probability of correctness p = 0.99.

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“…the emergence of oscillations, in particular as in more involved combinations of distributive and processive steps, oscillations have been reported as well [11,24].…”

Section: Introductionmentioning

confidence: 96%

“…Mathematical models of both processive and distributive phosphorylation have been extensively studied and it is known that they admit complex dynamics (see e.g. [11,20,27,30] and the many references therein). The mass action model of the sequential and distributive phosphorylation cycle depicted in Fig.…”

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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Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions

Cited by 57 publications

References 75 publications

Oscillations and bistability in a model of ERK regulation

Oscillations and bistability in a model of ERK regulation

SIAN: software for structural identifiability analysis of ODE models

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

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