Singularly Perturbed Initial Value Problems

Abstract

Readers should refer to Murray (1977) and to earlier chemical engineering literature [especially Bowen et al. (1963) and Heinekin et al. (1967)] for experts’ explanations of the significance of the pseudo-steady-state hypothesis in biochemistry. The theory of Michaelis and Menton (1913) and Briggs and Haldane (1925) concerns a substrate S being converted irreversibly by a single enzyme E into a product P. There is also an intermediate substrate-enzyme complex SE. Since the back reaction is negligible, we shall systematically write

$$S + E\begin{array}{*{20}{c}} {{{k}_{1}}} \\ \to \\ \leftarrow \\ {{{k}_{{ - 1}}}} \\ \end{array} SE\xrightarrow{{{{k}_{2}}}}P + E. $$