Michaëlis–menten kinetics: explicit dependence of substrate concentration on reaction time

The nonlinear dependence of the rate expressions associated with enzymecatalysed reactions on the concentration of substrate implies that the corresponding integrated form of the substrate mass balance in a batch reactor cannot be expressed as an explicit function of time..This paper addresses this problem for the classical case of Michaelis–Menten kinetics by providing a self-pacing exploration of the characteristics of a Taylor expansion of the substrate concentration on time. The accuracy of such an approximation is discussed. The procedure presented is appropriate to model situations of technological and practical interest.