TY - JOUR

T1 - Evaluation of the multiplane method for efficient simulations of reaction networks

AU - Barzel, Baruch

AU - Biham, Ofer

AU - Kupferman, Raz

PY - 2007/8/17

Y1 - 2007/8/17

N2 - 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. 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.

AB - 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. 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.

UR - http://www.scopus.com/inward/record.url?scp=34548141755&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.026703

DO - 10.1103/PhysRevE.76.026703

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C2 - 17930170

AN - SCOPUS:34548141755

SN - 1539-3755

VL - 76

JO - Physical Review E

JF - Physical Review E

IS - 2

M1 - 026703

ER -