APPROXIMATE MICHAELIS-MENTEN KINETICS DISPLAYED IN A STOCHASTIC-MODEL OF CELL-MEDIATED CYTOTOXICITY

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 PI is constructed to enable examination of that distribution whose expected value E and variance V satisfy minus K//mE plus (C//T minus E)(T//T minus E) plus V equals 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 PI 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 equals E(l minus e** minus **K//2**t//f)/T//T plus Gaussian with mean zero when T//T is large, so that a nonlinear regression procedure is appropriate for the determination of the parameters.