Monte Carlo simulations of single- and multistep enzyme-catalyzed reaction sequences: effects of diffusion, cell size, enzyme fluctuations, colocalization, and segregation.

Following the discovery of slow fluctuations in the catalytic activity of an enzyme in single-molecule experiments, it has been shown that the classical Michaelis-Menten (MM) equation relating the average enzymatic velocity and the substrate concentration may hold even for slowly fluctuating enzymes. In many cases, the average velocity is that given by the MM equation with time-averaged values of the fluctuating rate constants and the effect of enzyme fluctuations is simply averaged out. The situation is quite different for a sequence of reactions. For colocalization of a pair of enzymes in a sequence to be effective in promoting reaction, the second must be active when the first is active or soon after. If the enzymes are slowly varying and only rarely active, the product of the first reaction may diffuse away before the second enzyme is active, and colocalization may have little value. Even for single-step reactions the interplay of reaction and diffusion with enzyme fluctuations leads to added complexities, but for multistep reactions the interplay of reaction and diffusion, cell size, compartmentalization, enzyme fluctuations, colocalization, and segregation is far more complex than for single-step reactions. In this paper, we report the use of stochastic simulations at the level of whole cells to explore, understand, and predict the behavior of single- and multistep enzyme-catalyzed reaction systems exhibiting some of these complexities. Results for single-step reactions confirm several earlier observations by others. The MM relationship, with altered constants, is found to hold for single-step reactions slowed by diffusion. For single-step reactions, the distribution of enzymes in a regular grid is slightly more effective than a random distribution. Fluctuations of enzyme activity, with average activity fixed, have no observed effects for simple single-step reactions slowed by diffusion. Two-step sequential reactions are seen to be slowed by segregation of the enzymes for each step, and results of the calculations suggest limits for cell size. Colocalization of enzymes for a two-step sequence is seen to promote reaction, and rates fall rapidly with increasing distance between enzymes. Low frequency fluctuations of the activities of colocalized enzymes, with average activities fixed, can greatly reduce reaction rates for sequential reactions.