Instantaneous and overall indicators for determination of bottleneck ranking in metabolic reaction networks

A dynamic logarithmic gain expresses the percentage change in a dependent variable or metabolite concentration in response to an infinitesimal percentage change in an independent variable or enzyme activity. This article discusses the usefulness of several bottleneck ranking (BR) indicators that are functions of the logarithmic gain, to determine the most likely bottleneck enzyme in a dynamic metabolic reaction system. Mathematical models for penicillin V and ethanol fermentations are considered as case studies. The calculated results reveal that the instantaneous BR indicator, which is a product of the dynamic logarithmic gain and the metabolite concentration, is an effective measure for instantaneous bottleneck enzyme ranking changed during the fermentation period, whereas the overall BR indicator, which is a time-averaged value of the instantaneous BR indicator, is an effective measure for bottleneck enzyme ranking throughout the entire fermentation period.