Thermodynamics and Fluctuations Far From Equilibrium

Ross, John; Villaverde, Alejandro F.

doi:10.3390/e12102199

Cited by 27 publications

(22 citation statements)

References 62 publications

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“…We can view a Markovian reaction network as a thermodynamic system that absorbs energy, produces entropy, and dissipates heat Gaspard, 2004, 2007;Esposito and van den Broeck, 2010a,b;Gaspard, 2004;Ge, 2009;Ge and Qian, 2010;Oono and Paniconi, 1998;Prigogine, 1978;Qian, 2009Qian, , 2010Ross, 2008;Ross and Villaverde, 2010;Santillán and Qian, 2011;Schmiedl and Seifert, 2007;Schnakenberg, 1976;Zhang et al, 2012). This perspective can provide important insights into functional properties of Markovian reaction networks (such as robustness and stability) and can lead to a better understanding of the relationship between the mesoscopic (unobservable) and macroscopic (observable) behavior of such networks (Gaspard, 2004;Ge et al, 2012;Han and Wang, 2008;Qian, 2009Qian, , 2010Ross, 2008;Ross and Villaverde, 2010;Vellela and Qian, 2009).…”

Section: Macroscopic (Thermodynamic) Behaviormentioning

confidence: 99%

“…This perspective can provide important insights into functional properties of Markovian reaction networks (such as robustness and stability) and can lead to a better understanding of the relationship between the mesoscopic (unobservable) and macroscopic (observable) behavior of such networks (Gaspard, 2004;Ge et al, 2012;Han and Wang, 2008;Qian, 2009Qian, , 2010Ross, 2008;Ross and Villaverde, 2010;Vellela and Qian, 2009).…”

Section: Macroscopic (Thermodynamic) Behaviormentioning

confidence: 99%

“…The first is based on a potential energy landscape perspective (Ao, 2004;Ao et al, 2007;Han and Wang, 2007;Kim and Wang, 2007;Lapidus et al, 2008;Wang et al, 2010aWang et al, , 2008Wang et al, , 2010bWang et al, ,c, 2011Zhou and Qian, 2011) and leads to a powerful approach for conceptualizing and quantifying emergent complex behavior in nonlinear biochemical reaction networks with stochastic dynamics. The second methodology is based on nonequilibrium stochastic thermodynamics Gaspard, 2004, 2007;van den Broeck and Esposito, 2010;Demirel, 2010;Esposito and van den Broeck, 2010b;Ge, 2009;Ge and Qian, 2010;Ge et al, 2012;Han and Wang, 2008;Jiang et al, 2004;Luo et al, 2002;Mou et al, 1986;Puglisi et al, 2010;Qian, 2006Qian, , 2009Qian, , 2010Rao et al, 2011;Ross, 2008;Ross and Villaverde, 2010;Santillán and Qian, 2011;Schlögl, 1980;Schmiedl and Seifert, 2007;Schnakenberg, 1976;Seifert, 2008;Vellela and Qian, 2009;Zhang et al, 2012) and can be effectively used to study the macroscopic behavior of Markovian biochemical reaction networks and, in particular, properties related to their self-organization, functional stability, robustness and evolutionary behavior (Haken, 1975;Han and Wang, ...…”

Section: Introductionmentioning

confidence: 99%

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Markovian dynamics on complex reaction networks

2013

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Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.

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Section: Macroscopic (Thermodynamic) Behaviormentioning

confidence: 99%

Section: Macroscopic (Thermodynamic) Behaviormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Markovian dynamics on complex reaction networks

2013

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“…Due to the interactions between nonlinearity and stochasticity, in nonlinear dynamical systems many phenomena with new regimes can be induced by even weak fluctuations. For the systems far from equilibrium, fluctuation plays an important role in self-organization induced order phenomena [1]. The various fluctuation-induced behaviors, like stochastic resonance [2,3], noise-induced synchronization [4], coherence resonance [5], noise-induced chaos [6], fluctuation-induced escape [7], and noise-induce bifurcation [8] have attracted the attention of a large number of researchers from various fields as central problems in modern nonlinear dynamics theories.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Guo

2017

Entropy

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Abstract:A semi-analytical method is proposed to calculate stochastic quasi-periodic responses of limit cycles in non-equilibrium dynamical systems excited by periodic forces and weak random fluctuations, approximately. First, a kind of 1/N-stroboscopic map is introduced to discretize the quasi-periodic torus into closed curves, which are then approximated by periodic points. Using a stochastic sensitivity function of discrete time systems, the transverse dispersion of these circles can be quantified. Furthermore, combined with the longitudinal distribution of the circles, the probability density function of these closed curves in stroboscopic sections can be determined. The validity of this approach is shown through a van der Pol oscillator and Brusselator.

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“…The kinetic parameters in each of the reactions are related through the equilibrium constants that are dependent on the standard free energy change of the reaction (Cornish-Bowden and Cardenas, 2000;Nelson and Cox, 2005;Beard and Qian, 2008;Ross, 2008). These dependencies imply that the kinetic parameters' space is constrained in a very intricate way, which might reduce the sampling efficiency especially in the case of modeling of large-scale metabolic networks.…”

Section: Introductionmentioning

confidence: 99%

Modeling of uncertainties in biochemical reactions

Mišković

Hatzimanikatis

2010

Biotech & Bioengineering

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Mathematical modeling is an indispensable tool for research and development in biotechnology and bioengineering. The formulation of kinetic models of biochemical networks depends on knowledge of the kinetic properties of the enzymes of the individual reactions. However, kinetic data acquired from experimental observations bring along uncertainties due to various experimental conditions and measurement methods. In this contribution, we propose a novel way to model the uncertainty in the enzyme kinetics and to predict quantitatively the responses of metabolic reactions to the changes in enzyme activities under uncertainty. The proposed methodology accounts explicitly for mechanistic properties of enzymes and physico-chemical and thermodynamic constraints, and is based on formalism from systems theory and metabolic control analysis. We achieve this by observing that kinetic responses of metabolic reactions depend: (i) on the distribution of the enzymes among their free form and all reactive states; (ii) on the equilibrium displacements of the overall reaction and that of the individual enzymatic steps; and (iii) on the net fluxes through the enzyme. Relying on this observation, we develop a novel, efficient Monte Carlo sampling procedure to generate all states within a metabolic reaction that satisfy imposed constrains. Thus we derive the statistics of the expected responses of the metabolic reactions to changes in enzyme levels and activities, in the levels of metabolites, and in the values of the kinetic parameters. We present aspects of the proposed framework through an example of the fundamental three-step reversible enzymatic reaction mechanism. We demonstrate that the equilibrium displacements of the individual enzymatic steps have an important influence on kinetic responses of the enzyme.Furthermore, we derive the conditions that must be satisfied by a reversible threestep enzymatic reaction operating far away from the equilibrium in order to respond to changes in metabolite levels according to the irreversible MichelisMenten kinetics. The efficient sampling procedure allows easy, scalable, A c c e p ted P r e p r i nt implementation of this methodology to modeling of large-scale biochemical networks.

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Thermodynamics and Fluctuations Far From Equilibrium

Cited by 27 publications

References 62 publications

Markovian dynamics on complex reaction networks

Markovian dynamics on complex reaction networks

Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Modeling of uncertainties in biochemical reactions

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