Concentration Dependence of Diffusion-Limited Reaction Rates and Its Consequences

Abstract

Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional surfaces, such as the cell membrane. The peculiarities of diffusion on two-dimensional surfaces may lead to nontrivial reaction kinetics, such as a concentration-dependent rate of association between two molecules. However, traditionally, the kinetics of biomolecular association reactions has been modeled using the law of mass action, which assumes that the rate of reaction is a concentration-independent constant. In this paper, using multiscale molecular simulation, we investigate the concentration dependence of diffusion-limited association reactions on 2D surfaces. In particular, we quantify the influence of short-ranged pair interactions on the concentration dependence of the reaction rates and codify it in an empirical law. Using this law in a chemical kinetic model, we find that the steady-state behaviors of simple chemical systems are drastically modified by the presence of concentration-dependent rates. In particular, we find that it leads to suppression of intrinsic noise in dimerization reaction and destabilizes robust oscillation in Lotka-Volterra predator-prey systems. In fact, we see a transition from robust to fine-tuned behavior in the steady-state oscillations. In addition, we show that concentration-dependent reaction rates arise naturally in stochastic predator-prey systems due to intrinsic noise. We comment on the consequences of these results and discuss their implications in the modeling of complex chemical and biological systems. In particular, we comment on the range of validity of the law of mass action, which is a staple in all theoretical modeling of these systems.