Kinetics of single-enzyme reactions on vesicles: Role of substrate aggregation

Enzymatic reactions occurring in vivo on lipid membranes can be influenced by various factors including macromolecular crowding in general and substrate aggregation in particular. In academic studies, the role of these factors can experimentally be clarified by tracking single-enzyme kinetics occurring on individual lipid vesicles. To extend the conceptual basis for such experiments, we analyze herein the corresponding kinetics mathematically with emphasis on the role of substrate aggregation. In general, the aggregation may occur on different length scales. Small aggregates may e.g. contain a few proteins or peptides while large aggregates may be mesoscopic as in the case of lipid domains which can be formed in the membranes composed of different lipids. We present a kinetic model describing comprehensively the effect of aggregation of the former type on the dependence of the reaction rate on substrate membrane concentration. The results obtained with physically reasonable parameters indicate that the aggregation-related deviations from the conventional Michaelis-Menten kinetics may be appreciable. Special Issue Comments: This theoretical article is focused on single-enzyme reactions occurring in parallel with substrate aggregation on individual vesicles. This subject is related to a few Special Issue articles concerning enzyme dynamics and function and mathematical aspects of stochastic kinetics