Experimental design for optimal parameter estimation of an enzyme kinetic process based on the analysis of the Fisher information matrix

The investigation of enzyme kinetics is increasingly important, especially for finding active substances and understanding intracellular behaviors. Therefore, the determination of an enzymeʹs kinetic parameters is crucial. For this a systematic experimental design procedure is necessary to avoid wasting time and resources. The parameter estimation error of a Michaelis–Menten enzyme kinetic process is analysed analytically to reduce the search area as well as numerically to specify the optimum for parameter estimation. From analytical analysis of the Fisher information matrix the fact is obtained, that an enzyme feed will not improve the estimation process, but substrate feeding is favorable with small volume flow. Unconstrained and constrained process conditions are considered. If substrate fed-batch process design is used instead of pure batch experiments the improvements of the Cramer–Rao lower bound of the variance of parameter estimation error reduces to 82% for μmax and to 60% for Km of the batch values in average.