A New Approach to the Estimation of the Parameters of the Michaelis-Menten Equation

Abstract

A stochastic model of an enzymic reaction is considered. Using statistical methods, formulas are derived for calculating the coefficients contained in this model. In particular, estimators of the parameters of the Michaelis-Menten equation are obtained. The numerical examples are also considered. In the investigation of the enzymic reaction kinetics, an important role is played by various forms of aMichaelis- Menten type equation which establish the relation between the substrate concentration and the initial velocity of an enzymic reaction. These equations also contain two unknown parameters - a maximal velocity of reaction and the so-called Michaelis-Menten constant. These constants can be defined in each concrete case by means of the available heuristic and statistical methods Dawes (1) and Dochviri, Nadaraya, Sokhadze & Tkemaladze (2). We denote by u(t; S) the optical density of the suspension (velocity of reaction) at a moment of time t. Note that the values of V and K are naturally time-dependent: V = V (t), K = K(t). In other words, u(t; S) describes the reaction course, i.e. the evolution of optical density in time. Using this notation, the expression in the right-hand part of (1) will take the form