A suitable parameterization of the Michaelis-Menten enzyme reaction.
It is shown here that a suitable form for estimation and inference using the Michaelis-Menten [(1913) Biochem Z. 49, 333-369] model for simple enzymic reactions is one in which the two parameters appear in the denominator of the equation. In this form, convergence to the least-squares estimates using the Gauss-Newton method [see Kennedy & Gentle (1980) Statistical Computing, Marcel Dekker, New York] is virtually ensured, or, as the model in this form is a member of the class of 'generalized linear models', it may be fitted by packages such as those of Rothamsted Experimental Station [(1977) GENSTAT (A General Statistical Program), Rothamsted Experimental Station, Harpenden] and the Numerical Algorithms Group [(1978) GLIM (Generalised Linear Interactive Modeling), Numerical Algorithms Group, Oxford]. Furthermore, the parameters-in-denominator principle is readily extended to more complicated catalytic models. With all parameters in the denominator, the least-squares estimators are close to being unbiased and normally distributed, whereas severe bias and non-normality may result from use of the standard formulations.
D002384:Catalysis; D004798:Enzymes / Q000378:metabolism*; D007700:Kinetics; D008956:Models, Chemical
D004798:Enzymes