Mathematical analysis of models for reaction kinetics in intracellular environments

Two models that have been proposed in the literature for description of kinetics in intracellular environments characterized by macromolecular crowding and inhomogeneities, are mathematically analyzed and discussed. The models are first derived by using phenomenological arguments that lead to generalizations of the law of mass action. The prediction of these models in the case of bimolecular binding reaction is then analyzed. It is mathematically proved that the models may predict qualitatively different behavior of progress curves. In particular, they also predict asymptotic steady state concentrations that cannot be reconciled. In this paper we propose and discuss generalizations of these models which under specified conditions lead to qualitatively similar behavior of reaction progress curves. We believe that these generalized models are better suited for data analysis.