2007/08/17 by Baruch Barzel, Ofer Biham, Raz Kupferman +3 · 1 citation
Arts and Humanities · Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · Social Sciences · #Archaeology and Cultural Heritage #Bioinformatics and Genomic Networks #Gene Regulatory Network Analysis #Historical Studies of Medieval Iberia #Medieval Architecture and Archaeology #Molecular Communication and Nanonetworks #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.76.026703
published as Phys. Rev. E 76, 026703 (2007)
arxiv created 2007/10/11 · arxiv updated 2009/12/01 · openalex publication_date 2011/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11
Reaction networks in the bulk and on surfaces are widespread in physical, chemical, and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations. However, many physical systems are partitioned into microscopic domains, where the number of molecules in each domain is small and fluctuations are strong. Under these conditions, the simulation of reaction networks requires stochastic methods such as direct integration of the master equation. However, direct integration of the master equation is infeasible for complex networks, because the number of equations proliferates as the number of reactive species increases. Recently, the multiplane method, which provides a dramatic reduction in the number of equations, was introduced [Lipshtat and Biham, Phys. Rev. Lett. 93, 170601 (2004)]. The reduction is achieved by breaking the network into a set of maximal fully connected subnetworks (maximal cliques). Lower-dimensional master equations are constructed for the marginal probability distributions associated with the cliques, with suitable couplings between them. In this paper, we test the multiplane method and examine its applicability. We show that the method is accurate in the limit of small domains, where fluctuations are strong. It thus provides an efficient framework for the stochastic simulation of complex reaction networks with strong fluctuations, for which rate equations fail and direct integration of the master equation is infeasible. The method also applies in the case of large domains, where it converges to the rate equation results.