Behaviors of Chemical Reactions with Small Number of Molecules

Living systems are composed of biochemical reactions and many of them involves a small number of molecules. We investigate the behaviors of chemical reactions of the Lotka-Volterra model with small number of molecules by using Abstract Rewriting System on Multisets, ARMS; ARMS is a stochastic method of simulating chemical reactions and it is based on the reaction rate equation. We confirmed that the magnitude of fluctuations on periodicity of oscillations becomes large, as the number of involved molecules is getting smaller and the dynamical characteristics is changed. We investigate the coarse grained state space of ARMS and show that the mechanism of fluctuations occur in the chemical reactions involved a small number of molecules.