Abstract
The hybrid stochastic simulation algorithm, proposed by Haseltine and Rawlings, can significantly improve the simulation efficiency for multiscale biochemical networks. However, the population of some species might be driven negative under certain situations. This paper investigates the negativity problem of the hybrid method based on the second slow reaction firing time. Our analysis and tests on several models demonstrate that usually the error caused by negative populations is negligible compared with approximation errors of the method itself. But for systems involving nonlinear reactions or highly sensitive species, the system stability will be influenced and may lead to system failure. The proposed Zero-Reaction rule is recommended considering its efficiency and simplicity.
Highlights
The stochastic simulation algorithm (SSA) [3], widely used in simulating stochastic effects in biochemical networks, is computationally intensive and inefficient for systems with fast reactions or large populations
Negative populations may appear in stochastic simulations of reaction-diffusion systems, especially when low-density species are distributed in a well-meshed space
We further extend that work and study the second slow reaction firing time (SSRFT), which reflects the influence of a negative population on the firing of slow reactions
Summary
In the HR hybrid method framework, populations of some reactant species may become negative if they are involved in both deterministic and stochastic systems. If reaction rate constants satisfy f1 ≫ kc and b1 ≫ kc , the system can be divided into a fast reaction group and a slow reaction group, containing the reversible and irreversible reactions, respectively. Assume that this system has two S1 molecules at the beginning, and the system parameters are f1 = 1, b1 = 9, kc = 0.01. Negative populations may appear in stochastic simulations of reaction-diffusion systems, especially when low-density species are distributed in a well-meshed space
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