Multisubstrate Michaëlis-Menten kinetics: Explicit dependence of substrate concentration on time for batch reactors

The problem of expressing the concentration of each of a set of substrates in a batch reactor as an explicit function of time in the case the multisubstrate system is described by Michaelis-Menten kinetics is tackled in dimensionless form via expansion as a Taylor series. The general analytical form for the coefficients of this expansion is obtained and estimates of the average quadratic error associated with increasing number of terms of the expansion is calculated. Considering the situation where the concentration of all substrates varies in a similar fashion, one concludes that use of four terms yields errors well within the range acceptable for predesign steps. In addition to other applications, the reasoning developed here finds applications in the statistical design and analysis of experiments aiming at the nonlinear fitting of kinetic parameters to actual data