Estimation of the error implicit in modelling multisubstrate biochemical reactions as lumped-substrate systems

The necessary and sufficient condition associated with the maximum absolute error arising from the simulation of a biochemical reaction occurring in a batch multi-substrate system as if it were equivalent to a system with a pseudo single substrate is presented. The kinetics of the reaction catalyzed by the soluble enzyme is assumed to be described by a Michaëlis-Menten rate equation in the absence of enzyme deactivation, whereas the batch system is assumed to be perfectly mixed. The relevance of the analysis is due to the fact that monitoring the concentration of multiple species in a reaction system (as, in principle, required for controlling purposes) is often technically and/or economically unfeasible especially on the industrial scale. Hence, the strategy reported is useful during the pre-design steps of enzymatic batch reactors as an aid for the decision of whether or not to use complex analytical equipment. According to the analysis described, the appropriateness of the lumped substrate approach needs evaluation at a single point using an algorithm which is of straightforward implementation.