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The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the CME have been proposed. In this work we focus on one such model, the Linear Noise Approximation. Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced order LNA converges to the full order model in the mean square sense. Using this as motivation we derive a network structure preserving reduction algorithm based on structured projections. We present convex optimisation algorithms that describe how such projections can be computed and we discuss when structured solutions exits. We also show that for a certain class of systems, structured projections can be found using basic linear algebra and no optimisation is necessary. The algorithms are then applied to a linearised stochastic LNA model of the yeast glycolysis pathway.
In this paper, we consider the problem of model order reduction of stochastic biochemical networks. In particular, we reduce the order of (the number of equations in) the Linear Noise Approximation of the Chemical Master Equation, which is often used
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these properties should b
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic
Leaping methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue usi
This paper presents a model reduction method for the class of linear quantum stochastic systems often encountered in quantum optics and their related fields. The approach is proposed on the basis of an interpolatory projection ensuring that specific