Optimal regulatory programs for the control of metabolic pathways: The case of feedback inhibition

In this work we investigate the influence of feedback regulation on optimal programs of pathway control by means of advanced dynamic optimization techniques. The problem is formulated using a general dynamic optimization framework and solved using a control vector parametrization approach together with a suitable global optimization method. We consider the case of a linear pathway and we compare the resulting pathway regulation strategies with the introduction of feedback-inhibition at different positions in the pathway. Our results show that feedback inhibition is an important component of pathway control that allows to reduce the number of transcriptional regulatory interactions that are required to control the flux through a metabolic pathway. In particular, the presence of a feedback of the product of a pathway on the first enzyme can reduce the total number of transcriptional regulatory interactions (that are required to control the flux) to a single regulatory interaction. Moreover, we find that there is an optimal strength of the feedback inhibition. If inhibition is too strong, there is a large increase in protein cost to maintain the pathway flux. In contrast, if the inhibition is too weak, it does not exert any significant regulatory effect. Overall, these results demonstrate that dynamic optimization is an important tool that allows us to elucidate and understand design principles of biological networks.