Biological System Control

Constructing control algorithms using biological interactions is one of the interests in synthetic biology. Synthetic biology provides new biomolecular parts, functions, and systems. We show how to construct an approximate proportional integral (PI) controller for an enzyme–substrate interaction network using only elementary molecular interactions. The performance of the approximated PI controller is compared to that of the true PI controller. Another set of elementary molecular interactions calculates the error between the desired and current product, which is the input to the controller. We highlight the incapability of expressing negative numbers using only positive numbers expressed by molecular concentration, which indicates the lack of capability to adjust the current product overshooting the desired. An additional degradation interaction introduced reduces the current amount of the product molecules to overcome the limitation. The robustness of designed biological circuits is performed using $\mu$‐analysis. The basic concept of $\mu$‐analysis is introduced, and an advanced numerical method using a geometrical approach is presented to calculate $\mu$‐bounds for non‐linear parametric uncertainties.