BIOCHEMICAL SYSTEMS ANALYSIS .1. SOME MATHEMATICAL PROPERTIES OF RATE LAW FOR COMPONENT ENZYMATIC REACTIONS

A mathematical description of component enzymatic reactions is developed as a first step toward a method of analysis for biochemical systems. This serves to emphasize the particular non-linearities encountered in these components. For a broad class of enzymatic mechanisms the general form of the rate law is a ratio of polynomials in the reactant and modifier concentrations. The degree of the numerator is always less than or equal to the degree of the denominator, and all the coefficients are positive real. The rate law, expressed in factored form, is converted into a sum of simple terms by taking the logarithm. In this form, the rate law is formally amenable to a Bode-type of analysis. These properties form the bases for the systems analyses techniques presented in the subsequent papers. The advantages of this approach for the analysis of enzyme kinetic data are also discussed. © 1997 Elsevier Science Ltd. All rights reserved.