When is optimal experimental design advantageous for the analysis of Michaelis–Menten kinetics?

A systematic analysis is performed for the estimation of parameters for the Michaelis–Menten kinetic using the dynamic mechanistic model. As quality measure the Cramer–Rao lower bond (CRLB) is used. Depending on three different optimization criteria, two different measurement errors, the process operation mode (batch and fed-batch) as well as the error of the rough estimates of the parameters used for optimal experimental design the CRLB is calculated. These values are used to decide, if optimal experimental design is favourable compared to equidistant measurement points. It will be demonstrated, that optimization criteria A and E are just slightly more favourable than criteria D. The considered measurement errors give different results, but will not change the design and the precision of the parameters significant. The fed-batch process operation gives always a significant higher precision of the parameters compared to the batch mode. If the rough estimated parameter values, with which the optimal experimental design is carried out, are just known with low accuracy equidistant measurement points are in favour to model-based optimal experimental design. Using a batch process the error of the rough value of k2 (=vmax/Etot) must be smaller than 17% and of Km smaller than 40% so an optimal experimental design is worth for the parameter estimation. For fed-batch the errors of the rough estimates can be even bigger (up to 40% for k2 and 68% for Km).