On balance relations for irreversible chemical reaction networks

Levien, Ethan; Bressloff, Paul C.

doi:10.1088/1751-8121/aa91de

Cited by 6 publications

(8 citation statements)

References 31 publications

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“…(Hoessly and Mazza 2019, § 3)) and with Z Γ the normalising constant. Some other results on the stochastic behavior of CRN beyond complex balance are in (Bibbona et al 2020) or (Levien and Bressloff 2017).…”

Section: Known Results On Stationary Distributionsmentioning

confidence: 99%

Stationary distributions via decomposition of stochastic reaction networks

Hoessly

2021

J. Math. Biol.

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We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of the Markov processes and calculations of stationary distributions. Since the class of processes expressible through such networks is big and only few assumptions are made, the principle also applies to other stochastic models. We give examples of interest from CRN theory to highlight the decomposition.

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Section: Known Results On Stationary Distributionsmentioning

confidence: 99%

Stationary distributions via decomposition of stochastic reaction networks

Hoessly

2021

J. Math. Biol.

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“…The stochastic modelling of a chemical reaction network, dating back to Delbrück [7], is based upon the idea that molecular concentrations are subject to statistical fluctuation. Rather than treat the molecular counts as continuous quantities that evolve deterministically in time, the stochastic representation follows the time-evolution of the probability distributions of discrete states of a stochastic process [1,3] where the collections of states is the set of all permissible combinations of molecular counts of the chemical species in the reaction network at a time t ≥ 0 [4,8,9].…”

Section: S + Ementioning

confidence: 99%

“…Specifically, we are interested in this distribution for networks that reach an equilibrium in the Markov sense (as opposed to a chemical equilibrium) where the joint distribution has converged to a fixed stationary distribution that is no longer changing in time. A sufficient condition for a stationary distribution to exist is that the reaction rates satisfy constraints known as circuit conditions [14,20] or that the network has deficiency zero [4,9,21].…”

Section: Modelling a Two-species Network As A Birth-and-death Processmentioning

confidence: 99%

Coupling from the Past for the Stochastic Simulation of Chemical Reaction Networks

Mueller¹,

Corcoran²

2021

Preprint

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Chemical reaction networks (CRNs) are fundamental computational models used to study the behavior of chemical reactions in well-mixed solutions. They have been used extensively to model a broad range of biological systems, and are primarily used when the more traditional model of deterministic continuous mass action kinetics is invalid due to small molecular counts. We present a perfect sampling algorithm to draw error-free samples from the stationary distributions of stochastic models for coupled, linear chemical reaction networks. The state spaces of such networks are given by all permissible combinations of molecular counts for each chemical species, and thereby grow exponentially with the numbers of species in the network. To avoid simulations involving large numbers of states, we propose a subset of chemical species such that coupling of paths started from these states guarantee coupling of paths started from all states in the state space and we show for the well-known Reversible Michaelis-Menten model that the subset does in fact guarantee perfect draws from the stationary distribution of interest. We compare solutions computed in two ways with this algorithm to those found analytically using the chemical master equation and we compare the distribution of coupling times for the two simulation approaches.

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“…[14, § 3]) and with Z Γ the normalising constant. Some other results on the stochastic behavior of CRN beyond complex balance are in [16].…”

Section: 4mentioning

confidence: 99%

Stationary distributions via decomposition of stochastic reaction networks

Hoessly

2019

Preprint

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Despite their importance, stationary distributions of stochastic reaction networks (CRNs) are only known in few cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of CRNs and calculations of stationary distributions, generalizing the underlying principle of [14]. We give examples of interest from CRN theory to highlight the decomposition.

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On balance relations for irreversible chemical reaction networks

Abstract: View the article online for updates and enhancements.

Cited by 6 publications

References 31 publications

Stationary distributions via decomposition of stochastic reaction networks

Stationary distributions via decomposition of stochastic reaction networks

Coupling from the Past for the Stochastic Simulation of Chemical Reaction Networks

Stationary distributions via decomposition of stochastic reaction networks

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