Non-equilibrium thermodynamics of biological signal transduction predicts conservation of entropy production rate

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using M atlab . A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

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Non-Equilibrium Thermodynamics and Stochastic Dynamics of a Bistable Catalytic Surface Reaction

Entropy ◽

10.3390/e20110811 ◽

2018 ◽

Vol 20 (11) ◽

pp. 811 ◽

Cited By ~ 1

Author(s):

Miguel Pineda ◽

Michail Stamatakis

Keyword(s):

Steady State ◽

Entropy Production ◽

Production Rate ◽

Surface Reaction ◽

Stochastic Dynamics ◽

Reaction System ◽

Entropy Production Rate ◽

Minimum Entropy ◽

Catalytic Surface ◽

Non Equilibrium

Catalytic surface reaction networks exhibit nonlinear dissipative phenomena, such as bistability. Macroscopic rate law descriptions predict that the reaction system resides on one of the two steady-state branches of the bistable region for an indefinite period of time. However, the smaller the catalytic surface, the greater the influence of coverage fluctuations, given that their amplitude normally scales as the square root of the system size. Thus, one can observe fluctuation-induced transitions between the steady-states. In this work, a model for the bistable catalytic CO oxidation on small surfaces is studied. After a brief introduction of the average stochastic modelling framework and its corresponding deterministic limit, we discuss the non-equilibrium conditions necessary for bistability. The entropy production rate, an important thermodynamic quantity measuring dissipation in a system, is compared across the two approaches. We conclude that, in our catalytic model, the most favorable non-equilibrium steady state is not necessary the state with the maximum or minimum entropy production rate.

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Entropy Production Rate of Non-equilibrium Systems from the Fokker-Planck Equation

Brazilian Journal of Physics ◽

10.1007/s13538-014-0234-6 ◽

2014 ◽

Vol 44 (4) ◽

pp. 410-414 ◽

Cited By ~ 2

Author(s):

Yu Haitao ◽

Du Jiulin

Keyword(s):

Entropy Production ◽

Production Rate ◽

Planck Equation ◽

Entropy Production Rate ◽

Fokker Planck Equation ◽

Non Equilibrium ◽

Fokker Planck

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An information thermodynamic approach quantifying MAPK-related signaling cascades by average entropy production rate

10.1101/431676 ◽

2018 ◽

Author(s):

Tatsuaki Tsuruyama

Keyword(s):

Signal Transduction ◽

Entropy Production ◽

Production Rate ◽

Integrated Analysis ◽

Entropy Production Rate ◽

List Type ◽

Signal Molecule ◽

Phosphorylation Reaction ◽

Mitogen Activated Protein ◽

Novel Method

ABSTRACTInformation thermodynamics has recently greatly developed the application for analysis of biological phenomenon. During the signal transduction, entropy production from phosphorylation of signal molecule is produced at individual step production. Using this value, average entropy production rate (AEPR) is computable.In the current study, AEPR in each signal step was analyzed using experimental data from previously reported studies of the mitogen-activated protein kinases (MAPK) cascade. The result revealed that the differences of AEPR is smaller when using ligands, suggesting that AEPR is one of the attributes of the given cascade and useful for quantitative analysis. This consistency of AEPR suggests that the number of signal events is maximized, in other words, signaling efficiency is maximized. In conclusion, the current information theoretical approach provides not only a quantitative means for comparison of responses to a specified extracellular stimulation, but also a method for evaluation of active cascades.SynopsisA variety of methods for quantifying intracellular signal transduction have been proposed. Herein, a novel method of quantification by integrated analysis consisting of kinetics, non-equilibrium thermodynamics, fluctuation theorem and graph theory was attempted.Signal transduction can be computed by entropy production amount from the fluctuation in the phosphorylation reaction of signaling molecules.By Bayesian analysis of the entropy production rates of individual steps, they are consistent through the signal cascade.

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Estimating time-dependent entropy production from non-equilibrium trajectories

Communications Physics ◽

10.1038/s42005-021-00787-x ◽

2022 ◽

Vol 5 (1) ◽

Author(s):

Shun Otsubo ◽

Sreekanth K. Manikandan ◽

Takahiro Sagawa ◽

Supriya Krishnamurthy

Keyword(s):

Time Series ◽

Entropy Production ◽

Production Rate ◽

Time Series Data ◽

Quantitative Measure ◽

Machine Learning Techniques ◽

Series Data ◽

Entropy Production Rate ◽

Relevant Parameter ◽

Non Equilibrium

AbstractThe rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary dynamics, some of which are based on a variational characterization of the entropy production rate. However, the issue of obtaining it in the case of non-stationary dynamics remains largely unexplored. Here, we solve this open problem by demonstrating that the variational approaches can be generalized to give the exact value of the entropy production rate even for non-stationary dynamics. On the basis of this result, we develop an efficient algorithm that estimates the entropy production rate continuously in time by using machine learning techniques and validate our numerical estimates using analytically tractable Langevin models in experimentally relevant parameter regimes. Our method only requires time-series data for the system of interest without any prior knowledge of the system’s parameters.

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