Most biological reactions occur on 2D surfaces, where the peculiarities of diffusion lead to nontrivial concentration dependence of the reaction rates. However, usually, it is assumed that the reaction rates are concentration independent constants, which is at the heart of the so-called Law of Mass Action of reaction kinetics. It remains unclear whether such discrepancies lead to any nontrivial consequences or not, and this is the question we sought to understand in this paper.
We find that the concentration-dependence indeed has a profound impact on the behavior of the systems studied. For example, we find that oscillations that are predicted to be stable by the law of mass action, becomes unstable. These results will allow us to create better model of the biological processes and lead to better understanding of the microscopic world. In particular, our multiscale method allowed us to formulate an empirical law that quantifies the concentration dependence. Using this empirical law, we analytically calculated the stability of the steady states of well-known chemical oscillators, such as the Lotka-Volterra predator-prey model. We found that robust oscillation, the hallmark of the this model, becomes fine-tuned to the parameter values in the presence of concentration dependent rates.
Our empirical law agrees with prior efforts to quantify the concentration dependence. In addition, we provide testable predictions of its consequences that can be verified easily by simple experiments. Importantly, our results offer a way to accurately model reactions on spatially heterogeneous surfaces, which will be broadly useful to model biophysical systems.