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Title: The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation

Abstract

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of thesemore » external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the “plasticity property” of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.« less

Authors:
; ; ;  [1]
  1. Physics and Astronomy Department, Bologna University and INFN Sezione di Bologna (Italy)
Publication Date:
OSTI Identifier:
22420043
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CHAIN REACTIONS; MOLECULES; NUMERICAL ANALYSIS; PLASTICITY; RELAXATION TIME

Citation Formats

Oliveira, Luciana Renata de, Bazzani, Armando, Giampieri, Enrico, and Castellani, Gastone C., E-mail: Gastone.Castellani@unibo.it. The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation. United States: N. p., 2014. Web. doi:10.1063/1.4891515.
Oliveira, Luciana Renata de, Bazzani, Armando, Giampieri, Enrico, & Castellani, Gastone C., E-mail: Gastone.Castellani@unibo.it. The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation. United States. doi:10.1063/1.4891515.
Oliveira, Luciana Renata de, Bazzani, Armando, Giampieri, Enrico, and Castellani, Gastone C., E-mail: Gastone.Castellani@unibo.it. Thu . "The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation". United States. doi:10.1063/1.4891515.
@article{osti_22420043,
title = {The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation},
author = {Oliveira, Luciana Renata de and Bazzani, Armando and Giampieri, Enrico and Castellani, Gastone C., E-mail: Gastone.Castellani@unibo.it},
abstractNote = {We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the “plasticity property” of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.},
doi = {10.1063/1.4891515},
journal = {Journal of Chemical Physics},
number = 6,
volume = 141,
place = {United States},
year = {Thu Aug 14 00:00:00 EDT 2014},
month = {Thu Aug 14 00:00:00 EDT 2014}
}
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