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The stochastic thermodynamics of a rotating Brownian particle in a gradient flow.

ABSTRACT: We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism.

SUBMITTER: Lan Y

PROVIDER: S-EPMC4508657 | biostudies-literature | 2015 Jul

REPOSITORIES: biostudies-literature

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The stochastic thermodynamics of a rotating Brownian particle in a gradient flow.

Lan Yueheng Y Aurell Erik E

Scientific reports 20150721

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are based on the fluctuation relatio ...[more]

PMID: 26194015

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Project description:BackgroundStochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.ResultsWe propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models.ConclusionsThe SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sgd.

Dataset Information

The stochastic thermodynamics of a rotating Brownian particle in a gradient flow.

Publications

The stochastic thermodynamics of a rotating Brownian particle in a gradient flow.

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