Method for determination of the main bottleneck enzyme in a metabolic reaction network by dynamic sensitivity analysis

In fermentation processes, it is important to identify the bottleneck enzyme in a given metabolic reaction network, because increasing its activity would lead to an enhancement in the productivity of a desired metabolite. To efficiently identify the bottleneck enzyme, the present work discusses a systematic approach using dynamic logarithmic gains, i.e., percentage changes in the concentration of the desired metabolite in the response to an infinitesimal percentage change in enzyme activities, as an indicator. A penicillin V fedbatch fermentation model proposed by other researchers was used as an example of application. The calculated results showed that not only the time courses of the dynamic logarithmic gains but also the ranking of the magnitudes of their values is changed with time, implying that the bottleneck enzyme is changed with time in this fermentation process. To determine the bottleneck enzyme from such time-transient behaviors, the dynamic logarithmic gains were integrated over the entire fermentation period and divided by the total process time. The time-averaged dynamic logarithmic gains thus calculated were then ranked according to the magnitudes of their values. However, this ranking, corresponding to the ranking of candidate bottleneck enzymes, was not identical to that obtained with regard to the total amount of the desired metabolite produced as a result of finite change in each enzyme activity. This is because the concentration of the substrate for the reaction catalyzed by the relevant enzyme displays a decreasing behavior, so that the degree of increase in the corresponding flux was smaller for the finite increase of the enzyme activity and the total amount of the desired metabolite did not proportionally increase. When the concentration of the substrate for the reaction catalyzed by the most likely bottleneck enzyme displays a decreasing behavior, therefore, it is necessary to check not only the ranking of the time-average dynamic logarithmic gains but also whether the total amount of the desired metabolite is ranked first when the relevant enzyme activity is finitely changed.