A new approach to a century-old problem: Henri-Michaelis-Menten enzyme kinetics

A new approach to Henri-Michaelis-Menten (HMM) enzyme kinetics is presented. In the first part, a simplified but useful description that stresses the cyclic nature of the catalytic process is summarized. In particular, the timedependence of the substrate concentration is obtained in a simple way that dispenses the quasi-steady-state approximation. In the second part an exact one-dimensional formulation of HMM kinetics is presented. The whole problem is condensed in a second-order non-linear autonomous differential equation, and the exact solution of HMM kinetics is given as a set of Maclaurin series. From the same evolution equation, a number of approximate solutions, some known, some new, can be derived in a systematic way. The evolution equation obtained is also well suited for the numerical computation of the concentrations of all species as a function of time for any given combination of parameters.