Global stability of a class of futile cycles

Rao, Shodhan

doi:10.1007/s00285-016-1039-8

Cited by 11 publications

(25 citation statements)

References 14 publications

(20 reference statements)

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“…Our main result, which will be proven in Section 5.5, states that the all-encompassing network (10) is globally convergent: Another special case of Theorem 4.1 is Rao's result [17] (recall Remark 3.2). However, our proof differs from his (see Remark 6.2).…”

Section: Main Result: Global Convergence Of All-encompassing Networkmentioning

confidence: 93%

“…Here we introduce a network that encompasses each of the three networks in the Introduction, and also encompasses a network introduced recently by Rao [17]. Accordingly, our new network has m components rather than 2, each with its own enzyme E i and substrate P i .…”

Section: The All-encompassing Networkmentioning

confidence: 99%

“…Remark 3.2. The all-encompassing network (10) generalizes the network analyzed by Rao [17]. To obtain our network from Rao's, each reaction is allowed to be irreversible and the final reaction in each component may be reversible.…”

Section: The All-encompassing Networkmentioning

confidence: 99%

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An all-encompassing global convergence result for processive multisite phosphorylation systems

Eithun

Shiu

2017

Mathematical Biosciences

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Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems, which require an enzyme and substrate to bind several times in order to add multiple phosphate groups, can be bistable. Processive systems, in contrast, require only one binding to add all phosphate groups, and were recently shown to be globally stable. However, this global convergence result was proven only for a specific mechanism of processive phosphorylation/dephosphorylation (namely, all catalytic reactions are reversible). Accordingly, we generalize this result to allow for processive phosphorylation networks in which each reaction may be irreversible, and also to account for possible product inhibition. We accomplish this by first defining an all-encompassing processive network that encapsulates all of these schemes, and then appealing to recent results of Marcondes de Freitas et al. that assert global convergence by way of monotone systems theory and network/graph reductions (corresponding to removing intermediate complexes). Our results form a case study into the question of when global convergence is preserved when reactions and/or intermediate complexes are added to or removed from a network.

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Section: Main Result: Global Convergence Of All-encompassing Networkmentioning

confidence: 93%

Section: The All-encompassing Networkmentioning

confidence: 99%

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An all-encompassing global convergence result for processive multisite phosphorylation systems

Eithun

Shiu

2017

Mathematical Biosciences

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“…The mechanism is called processive since S 1 E, unlike in a distributive mechanism, can only proceed to S 2 +E, and similarly for S 1 F . Processive systems converge to a unique equilibrium and thus do not exhibit oscillations [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Precluding oscillations in Michaelis–Menten approximations of dual-site phosphorylation systems

Tung

2018

Mathematical Biosciences

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Oscillations play a major role in a number of biological systems, from predator-prey models of ecology to circadian clocks. In this paper we focus on the question of whether oscillations exist within dual-site phosphorylation systems. Previously, Wang and Sontag showed, using monotone systems theory, that the Michaelis-Menten (MM) approximation of the distributive and sequential dual-site phosphorylation system lacks oscillations. However, biological systems are generally not purely distributive; there is generally some processive behavior as well. Accordingly, this paper focuses on the MM approximation of a general sequential dual-site phosphorylation system that contains both processive and distributive components, termed the composite system. Expanding on the methods of Bozeman and Morales, we preclude oscillations in the MM approximation of the composite system. This implies the lack of oscillations in the MM approximations of the processive and distributive systems, shown previously, as well as in the MM approximation of the partially processive and partially distributive mixed-mechanism system.

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“…Recent works on dynamical analysis of futile cycles (without allosteric regulation) are presented in [6], [8], [9]. In [6], Zhou Fang is with School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China (e-mail: zhou fang@zju.edu.cn)…”

Section: Introductionmentioning

confidence: 99%

Integral regulation mechanism in phosphorylation cycles

Fang

Jayawardhana

Schaft

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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In this paper, we study integral regulation mechanism in a class of phosphorylation cycles where we consider enzyme regulation by an intermediary metabolite. Using chemical reaction network framework, we prove that the network dynamics is (locally) asymptotically stable for sufficiently small integral gain. Furthermore, we show that the integral regulation ensures the absolute concentration robustness (ACR) property of the network.

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Global stability of a class of futile cycles

Cited by 11 publications

References 14 publications

An all-encompassing global convergence result for processive multisite phosphorylation systems

An all-encompassing global convergence result for processive multisite phosphorylation systems

Precluding oscillations in Michaelis–Menten approximations of dual-site phosphorylation systems

Integral regulation mechanism in phosphorylation cycles

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