Statistical physics approaches to subnetwork dynamics in biochemical systems

Bravi, Barbara; Sollich, Peter

doi:10.1088/1478-3975/aa7363

Cited by 19 publications

(60 citation statements)

References 60 publications

(122 reference statements)

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“…Uhl et al [20] have considered the fluctuations of an apparent entropy production in bipartite systems, finding many cases where an effective affinity restores the FR. For chemical networks where only some molecular species can be monitored experimentally, Bravi and Sollich [21] derived systematic models for subsystem dynamics that can help with the inference problem of estimating properties of the environment from observed sub-network dynamics. Another situation where the observer does not have access to all of the thermodynamic currents are stochastic models of so-called "Maxwell demons", systems composed of an engine and a memory that operates a feedback control on the engine.…”

Section: Figmentioning

confidence: 99%

Effective Fluctuation and Response Theory

Polettini

Esposito

2019

J Stat Phys

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The response of thermodynamic systems slightly perturbed out of an equilibrium steady-state is described by two milestones of early nonequilibrium statistical mechanics: the reciprocal and the fluctuation-dissipation relations. At the turn of this century, the so-called fluctuation theorems extended the study of fluctuations far beyond equilibrium. All these results rely on the crucial assumption that the observer has complete information about the system: there is no hidden leakage to the environment, and every process is assigned its due thermodynamic cost. Such a precise control is difficult to attain, hence the following questions are compelling: Will an observer who has marginal information be able to perform an effective thermodynamic analysis? Given that such observer will only be able to establish local equilibrium amidst the whirling of hidden degrees of freedom, by perturbing the stalling currents will he/she observe equilibrium-like fluctuations nevertheless? We address these two fundamental problems, providing a broad theory of the statistical behavior of some out of many currents that flow across a thermodynamic system.We model the dynamics of open systems as Markov jump processes on finite networks. Configurationspace currents count the net number of transitions between pairs of configurations; conjugate forces quantify their thermodynamic cost. Phenomenological currents are linear combinations of configuration currents, and only ensue when affinities enjoy appropriate symmetries, granting thermodynamic consistency. A complete thermodynamic description is achieved when the set of currents under consideration covers all cycles in the network, otherwise the set is marginal.Within this formalism, we establish that: 1) While marginal currents do not obey a full-fledged fluctuation relation, there exist effective affinities for which an integral fluctuation relation holds; 2) Under reasonable assumptions on the parametrization of the rates, effective and "real" affinities only differ by a constant; 3) At stalling, i.e. where the marginal currents vanish, a symmetrized fluctuation-dissipation relation holds while reciprocity does not; 4) There exists a notion of marginal time-reversal that plays a role akin to that played by time-reversal for complete systems, which restores the fluctuation relation and reciprocity; 5) The effective affinity is the putative affinity of an observer who only has marginal information about a system and formulates a minimal model accounting for his/her steady-state observations; 6) There exist fluctuation relations across different levels in the hierarchy of more and more "complete" theories. The above results hold for configurationspace currents, and for phenomenological currents provided that certain symmetries of the effective affinities are respected -a condition that we call marginal thermodynamic consistency, which is stricter thermodynamic consistency and whose range of validity we deem the most interesting question left open to future inquiry. Our results are construc...

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Section: Figmentioning

confidence: 99%

Effective Fluctuation and Response Theory

Polettini

Esposito

2019

J Stat Phys

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“…An interesting question for future investigation is the theoretical analysis of approximations of the filtering equation more accurate than the product-Poisson ansatz or the product-Bernoulli ansatz. In particular, approximations based on first-and second-order moments might allow one to compare the marginal process framework to other marginalization approaches published previously [12][13][14]. For this purpose, a variant of the marginal process framework for subnet and environment both modeled by stochastic differential equations would be of interest.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the Lotka-Volterra system (37) satisfies this condition. This will put the marginal process framework in a form more similar to other approaches for obtaining reduced models that have recently been investigated [12][13][14].…”

Section: B Explicit Representation Of Marginal Ratesmentioning

confidence: 99%

Marginal process framework: A model reduction tool for Markov jump processes

Bronstein

Koeppl

2018

Phys. Rev. E

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Markov jump process models have many applications across science. Often these models are defined on a state space of product form and only one of the components of the process is of direct interest. In this paper we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation, which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operations applied to the full master equation so that we obtain a principled model reduction framework. We demonstrate the resulting reduced description on the totally asymmetric exclusion process. An important class of Markov jump processes are stochastic reaction networks, which have applications in chemical and biomolecular kinetics, ecological models, and models of social networks. We obtain a particularly simple instantiation of the marginal process framework for mass-action systems by using product Poisson distributions for the approximate solution of the filtering equation. We investigate the resulting approximate marginal process analytically and numerically.

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“…We mention in passing that by using the differential equations (14) for the parameters of (18), the computationally expensive explicit minimization of the relative entropy 16 does not have to be performed 15 .…”

Section: Zero-information Moment Closurementioning

confidence: 99%

A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

Bronstein

Koeppl

2018

The Journal of Chemical Physics

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Approximate solutions of the chemical master equation and the chemical FokkerPlanck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the momentclosure approach used to obtain such approximations, calling it an ad-hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable. a)

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Statistical physics approaches to subnetwork dynamics in biochemical systems

Cited by 19 publications

References 60 publications

Effective Fluctuation and Response Theory

Effective Fluctuation and Response Theory

Marginal process framework: A model reduction tool for Markov jump processes

A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

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