Discreteness-Induced Criticality in Random Catalytic Reaction Networks

Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the system undergoes a transition from a stationary to an intermittent reaction phase when the flow rate is decreased. In the intermittent reaction phase, two temporal regimes with active and halted reactions alternate. The number frequency of reaction events at each active regime and its duration time are shown to obey a universal power laws with the exponents 4/3 and 3/2, respectively. These power laws are explained by a one-dimensional random walk representation of the number of catalytically active chemicals. Possible relevance of the result to intra-cellular reaction dynamics is also discussed.