  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
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 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 latter. 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.
