Approximate Michaelis-Menten kinetics displayed in a stochastic model of cell-mediated cytotoxicity
type: Item
instance of: scholarly article
title: Approximate Michaelis-Menten kinetics displayed in a stochastic model of cell-mediated cytotoxicity
zbMATH Open document ID: 0598.92009
DOI: 10.1016/0025-5564(86)90046-5
author: Stephen J. Merrill
author: S. Sathananthan
published in: Mathematical Biosciences
publication date: 1986-01-01T00:00:00Z
review text: 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 \[ -K_ mE+(C_ T-E)(T_ T-E)+V=0, \] 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 \(\Pi\) 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 \[ f=E(1-e^{-k_ 2t_ f})T_ T^{-1} + \text{Gaussian with mean zero,} \] when \(T_ T\) is large, so that a nonlinear regression procedure is appropriate for the determination of the parameters.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 80A30
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 3965872
zbMATH Keywords: stochastic model of cell-mediated cytotoxicity
zbMATH Keywords: biochemistry
zbMATH Keywords: nonlinear continuous-time Markov chain
zbMATH Keywords: two-step process of cytolytic cells binding
zbMATH Keywords: lysis
zbMATH Keywords: release of label
zbMATH Keywords: enzyme-substrate kinetics
zbMATH Keywords: Michaelis- Menten saturation function
zbMATH Keywords: comparison theorem for the pseudo-steady- state distribution
zbMATH Keywords: nonlinear regression procedure
MaRDI profile type: Publication
full work available at URL: 0025-5564(86)90046-5
OpenAlex ID: W2005776890
cites work: A pseudo-steady state approximation for stochastic chemical kinetics
cites work: Foundations of the use of an enzyme-kinetic analogy in cell-mediated cytotoxicity
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description: scientific article; zbMATH DE number 3965872