Violation of the mass-action law in dilute chemical systems

The mass-action law, which predicts the rates of chemical reactions, is widely used for modeling the kinetics of the chemical reactions and their stationary states, also for complex chemical reaction networks. However, violations of the mass-action equations have been reported in various cases: in confined systems with a small number of molecules, in non-ideally-stirred systems, when the reactions are limited by the diffusion, at high concentrations of reactants, or in chemical reaction networks with marginally stable mass-action equations. In this paper, I describe a new mechanism, leading to the violation of the mass-action equations, that takes place at a low concentration of at least one of the reactants; in this limit, the reaction rates can be easily inferred from the chemical reaction network. I propose that this mechanism underlies the replication stability of the hypercycles, a class of chemical reaction networks hypothetically connected with abiogenesis. I provide two simple examples of chemical reaction networks in which the mechanism leading to the violation of the mass-action law is present. I study the two chemical reaction networks by means of a simulation performed with a cellular automaton model. The results have a general validity and represent a limitation of the validity of the mass-action law, which has been overlooked up to now in the studies about the chemical reaction networks.