Discreteness-induced transition in catalytic reaction networks.

Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a state is observed with the decrease in the total molecule number N , characterized by (i) large fluctuations in chemical concentrations as a result of intermittent switching over several states with extinction of some molecule species and (ii) strong deviation of time averaged distribution of chemical concentrations from that expected in the continuum limit, i.e., N-->infinity. The origin of transition is explained by the deficiency of the molecule leading to termination of some reactions. The critical number of molecules for the transition is obtained as a function of the number of molecule species M and that of reaction paths K, while total reaction rates, scaled properly, are shown to follow a universal form as a function of NK/M.