Current trends in the estimation of Michaelis-Menten parameters

Abstract

This review is about two aspects of the design and analysis of steady state kinetic experiments: (i) how one decides whether an enzymic reaction conforms to the Michaelis-Menten equation; and (ii) given that it does, how one then estimates the characteristic parameters ( K m , K i , V etc.). 1 1 Abbreviations used: K m , Michaelis constant (single-substrate reaction); K A , K B , Michaelis constants (two-substrate reaction); K i , inhibitor dissociation constant of enzyme-inhibitor, and K i , inhibitor dissociation constant of enzyme-substrate-inhibitor complexes; V, maximum velocity of reaction; v, initial velocity of reaction; e, concentration of enzyme; i, concentration of inhibitor; p, concentration of product; s, concentration of substrate (single-substrate reaction); A, B, concentrations of substrate (two-substrate reaction); t, time; var, variance; w, weighing factor. The answers to these problems depend on several factors, of which perhaps the most important is the reason for doing the experiment in the first place. There are many examples in the biochemical literature of investigations in which kinetic data are used simply to give an indication of an enzyme's properties. In these instances graphical analysis with little or no computational backup is the usual choice, and is perfectly satisfactory. On the other hand, the subjectivity of graphical methods precludes their use when the experiment has more precise objectives, such as (i) the determination of the mechanism of action of the enzyme; (ii) the derivation of rate constants; and (iii) the detection of kinetic variants. In these cases some form of statistical analysis is required. Fortunately, the advent of computers means that the tedious but necessary computations are easily done; it has also stimulated a search for reliable statistical techniques and (to a lesser extent) for efficient experimental designs. As a result, one can now calculate better estimates of kinetic parameters than was possible 20 years ago. (A good estimate in this context is one that is both accurate, i.e., free from bias, and precise, i.e., having a small coefficient of variation.)