2018 **Abstract:** Deterministic and stochastic models of chemical reaction kinetics can give starkly different results when the deterministic model exhibits more than one stable solution. For example, in the stochastic Schlögl model, the bimodal stationary probability distribution collapses to a unimodal distribution when the system size increases, even for kinetic constant values that result in two distinct stable solutions in the deterministic Schlögl model. Using zero-information (ZI) closure scheme, an algorithm for solving…

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“…The estimation of the higher moments in this way is denoted by the superscript S, that means that the MEP has been used, this closure scheme is known as the zero-information (ZI) closure, and has been recently used by Vlysidis and Kaznessis, using factorial moments for the Slogi chemical reaction network [ 60 ]. It does not matter to use one polynomial basis or the factorial moment basis because both polynomial and factorial basis are related by a transformation matrix.…”

confidence: 99%

“…The estimation of the higher moments in this way is denoted by the superscript S, that means that the MEP has been used, this closure scheme is known as the zero-information (ZI) closure, and has been recently used by Vlysidis and Kaznessis, using factorial moments for the Slogi chemical reaction network [ 60 ]. It does not matter to use one polynomial basis or the factorial moment basis because both polynomial and factorial basis are related by a transformation matrix.…”

confidence: 99%

“…As a final note on the future extensions of this work, we would like to emphasise that, when dealing with non-equilibrium mesoscopic systems, we need to make a proper distinction between the predictions of the stochastic approach and those of the ODEs based on the traditional law of mass action kinetics. For example, it has been recognised that the size of the system, which does not appear in the ODEs, is an important bifurcation parameter [ 50 , 51 ]. In the context of catalytic surface reactions, a work along these lines was presented in [ 52 ].…”

confidence: 99%

“…However, several assumptions underlying the original model were purposefully modified what changed the underlying interaction network, such as the dissociation of EGFR dimers when phosphorylated or bound to other molecules. In addition to contrasting rules to reactions, another intensively studied aspect, finalised with positive conclusions, was whether stochastic simulation can reveal new properties of a system previously modelled as deterministic one (Vlysidis and Kaznessis, 2018; Hahl and Kremling, 2016; Bustos et al, 2018). As simplistic as it may sound, none of the comparisons mentioned were intended to painstakingly disassemble reaction using the rules of a relatively medium-sized model and compare simulation results.…”

confidence: 99%