  A different view of Henri-Michaelis-Menten (HMM) enzyme kinetics is
presented. In the first part of the paper, a simplified but useful description
that stresses the cyclic nature of the catalytic process is introduced. The
time-dependence of the substrate concentration after the initial transient
phase is derived in a simple way that dispenses the mathematical technique
known as quasi-steady-state approximation. In the second part of the paper an
exact one-dimensional formulation of HMM kinetics is obtained. The whole
problem is condensed in a single one-variable evolution equation that is a
second-order non-linear differential equation, and the control parameters are
reduced to three dimensionless quantities: enzyme efficiency, substrate reduced
initial concentration, and enzyme reduced initial concentration. The exact
solution of HMM kinetics is obtained as a set of Maclaurin series. From the
same equation, a number of approximate solutions, some known, some new, are
derived in a systematic way that allows a precise evaluation of the respective
level of approximation and conditions of validity. The evolution equation
derived is also shown to be well suited for the numerical computation of the
concentrations of all species as a function of time for any given combination
of parameters.
