Approximate Michaelis-Menten kinetics displayed in a stochastic model of cell-mediated cytotoxicity

Abstract

A nonlinear continuous-time Markov chain describing a two-step process of cytolytic cells binding to target and the subsequent lysis and release of label is shown to have kinetics which resemble standard enzyme-substrate kinetics. The Michaelis-Menten saturation function is found as a special case resulting when the target population is in excess. A comparison theorem for the pseudo-steady-state distribution Π is constructed to enable examination of that distribution whose expected value E and variance V satisfy −KmE+(CT−E)(TT−E)+V=0 , where K m is the Michaelis half-saturation constant and C T and T T are the initial populations of the two cell types. Using Π as an initial condition, the release of label process is examined. The main result is that the fraction of specific release, f, has the approximate form f=E1−e−k2tfTT+Gaussian with mean zero, when T t is large, so that a nonlinear regression procedure is appropriate for the determination of the parameters.