A comparison of stochastic and deterministic models for cell membrane transport.

This paper describes several models for enzyme mediated transport across a cell membrane. A standard Michaelis-Menten model (based on empirical descriptions) is compared to a deterministic model (based on the idealization of the plasma membrane as a tri-Iamellar structure) and to a stochastic model (having the additional assumption of compartmentation of the tri-Iamellar membrane). Lineweaver-Burke plots for each model are compared using two different sets of parameter values. These plots suggest, and analytic investigations of the models show, that the deterministic formulations yield different transport kinetics than does the stochastic formulation. The effect of the application of the concept of compartmentation to some stochastic models of in vivo systems is briefly discussed. Research partially supported North Carolina State University at Raleigh. by a N.I.G.M.S. Training Grant No. 5TI GM 678. 2 I University of North Carolina at Chapel Hill. Research partially supported by the Air Force Office of Scientific Research under Contract No. AFOSR-68-1415.