Confidence Bands for Rational Rate Equations

The standard Michaelis-Menten expression for the rate of an enzyme-catalysed reaction (v) can be extended using the ratio of two polynomials in the substrate concentration (s). Such rational functions are nonlinear and their behaviour can vary considerably. Comparisons of two such functions requires more than a simple consideration of a particular coefficient, especially given the coefficients do not necessarily have any mechanistic significance. A second issue is the identification of particular coefficients that contribute significantly to the overall error of the estimate of v at a given s. As the number of coefficients rises this becomes increasingly difficult. To address the first of these issues we provide a general expression for the estimated confidence band of an arbitrary rational function of this type. We employ sensitivity analysis to address the second issue and provide general expressions for the coefficient elasticities. We apply these in the analysis of the kinetics of chymotrypsin and muscle lactate dehydrogenase.