Results on stochastic reaction networks with non-mass action kinetics
نویسندگان
چکیده
In 2010, Anderson, Craciun, and Kurtz showed that if a deterministically modeled reaction network is complex balanced, then the associated stochastic model admits a stationary distribution that is a product of Poissons [5]. That work spurred a number of followup analyses. In 2015, Anderson, Craciun, Gopalkrishnan, and Wiuf considered a particular scaling limit of the stationary distribution detailed in [5], and proved it is a well known Lyapunov function [4]. In 2016, Cappelletti and Wiuf showed the converse of the main result in [5]: if a reaction network with stochastic mass action kinetics admits a stationary distribution that is a product of Poissons, then the deterministic model is complex balanced [8]. In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered in [5] are non-explosive (so the stationary distribution characterizes the limiting behavior). In this paper, we generalize each of the three followup results detailed above to the case when the stochastic model has a particular form of non-mass action kinetics.
منابع مشابه
Exploration of cellular reaction systems
We discuss and review different ways to map cellular components and their temporal interaction with other such components to different non-spatially explicit mathematical models. The essential choices made in the literature are between discrete and continuous state spaces, between rule and event-based state updates and between deterministic and stochastic series of such updates. The temporal mo...
متن کاملA detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balanced
Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN. We will refer to this property as reaction network de...
متن کاملQuantum techniques for studying equilibrium in reaction networks
Anderson, Craciun, and Kurtz have proved that a stochastically modelled chemical reaction system with mass-action kinetics admits a stationary distribution when the deterministic model of the same system with mass-action kinetics admits an equilibrium solution obeying a certain ‘complex balance’ condition. Here we present a proof of their theorem using tools from the theory of second quantizati...
متن کاملAccuracy of the Michaelis-Menten approximation when analysing e↵ects of molecular noise
Quantitative biology relies on the construction of accurate mathematical models, yet the e↵ectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, due to the ubiq...
متن کاملNonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations with mass action kinetics. Our most general framework considers open networks driven by time-dependent chemostats. The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced...
متن کامل