SiCaSMA: An Alternative Stochastic Description via Concatenation of Markov Processes for a Class of Catalytic Systems

Vincent Wagner and Nicole Erika Radde
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Vincent Wagner: Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, BW, Germany
Nicole Erika Radde: Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, BW, Germany

Mathematics, 2021, vol. 9, issue 10, 1-13

Abstract: The Chemical Master Equation is a standard approach to model biochemical reaction networks. It consists of a system of linear differential equations, in which each state corresponds to a possible configuration of the reaction system, and the solution describes a time-dependent probability distribution over all configurations. The Stochastic Simulation Algorithm (SSA) is a method to simulate sample paths from this stochastic process. Both approaches are only applicable for small systems, characterized by few reactions and small numbers of molecules. For larger systems, the CME is computationally intractable due to a large number of possible configurations, and the SSA suffers from large reaction propensities. In our study, we focus on catalytic reaction systems, in which substrates are converted by catalytic molecules. We present an alternative description of these systems, called SiCaSMA, in which the full system is subdivided into smaller subsystems with one catalyst molecule each. These single catalyst subsystems can be analyzed individually, and their solutions are concatenated to give the solution of the full system. We show the validity of our approach by applying it to two test-bed reaction systems, a reversible switch of a molecule and methyltransferase-mediated DNA methylation.

Keywords: chemical master equation; DNA methylation; catalytic systems; stochastic simulation algorithm; time-continuous Markov process; equivalence of stochastic processes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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