Abstract
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accelerated stochastic simulation algorithms. Numerical experiments compare the new methods with the established stochastic simulation algorithm and the tau-leaping method.
Highlights
In many biological systems the small number of participating molecules make the chemical reactions inherently stochastic
This study proposes new numerical solvers for stochastic simulations of chemical kinetics
The proposed approach exploits the linearity of the chemical master equation (CME) and the exponential form of its exact solution
Summary
In many biological systems the small number of participating molecules make the chemical reactions inherently stochastic. Gillespie proposed the Stochastic Simulation Algorithm (SSA), a Monte Carlo approach that samples from CME [8]. SSA simulates one reaction and is inefficient for most realistic problems This motivated the quest for approximate sampling techniques to enhance the efficiency. The first approximate acceleration technique is the tau-leaping method [9] which is able to simulate multiple chemical reactions appearing in a pre-selected time step of length τ. Explicit tau-leaping method is numerically unstable for stiff systems [5]. The approach explains the explicit tau-leap method as an exact sampling procedure from an approximate solution of the CME. Numerical experiments are performed with two different chemical systems to assess the accuracy and stability of each of the algorithms.
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