Fundamental limits and achievable performance in biomolecular control

Understanding how a biomolecular system achieves various control objectives via chemical reactions is of crucial importance in cell biology. However, unlike typical control problems where full information about the system is assumed to be known, typically, only a small portion of the entire biomolecular system can be characterized with certainty. In order to gain insights in these situations, we use control and information theory to derive the performance bounds when chemical species implement feedback control via the production rate or the degradation rate of chemical species. We expand the approach of the pioneering work of Lestas et al. to treat more general scenarios and derive explicit lower bounds on the achievable Fano factor of the controlled species. Our results suggest that control and sensing via the degradation rates, compared with those via the production rates, benefit from the additional design freedom to choose degradation efficiencies, in addition to previously considered signal rate, which helps to lower the Fano factor of the controlled species. We compare our lower bounds with achievable performance via simulation of chemical master equations.