Hybrid Method for Simulating Small-Number Molecular Systems

Abstract

Computational devices such as the toggle switch or the oscillator have recently been used in artificial or biological cells in which the number of molecular species is very small. To simulate their behavior, the stochastic simulation algorithm by Gillespie and the “τ-leap” method, also proposed by Gillespie to reduce simulation time, are widely used. In this paper, we discuss groups of cells that interact with the environment by exchanging molecules through their membranes. The stochastic simulation algorithm or even the “τ-leap” method requires a large amount of computation time because all the cells in the group and the environment need to be stochastically simulated. In this paper, we propose a hybrid simulation method in which molecular species in the environment are treated based on their concentration, and their time evolution is obtained by solving ordinary differential equations. The behavior of the cell group is then estimated by stochastically simulating some sampled cells. If the state of cells influences the environment, the whole simulation process is iterated until the time evolution of the environment becomes invariant. If the simulation ends after a few iterations, then the overall simulation time greatly decreases.