Optimal evolutionary control for artificial selection on molecular phenotypes

Controlling an evolving population is an important task in modern molecular genetics, including in directed evolution to improve the activity of molecules, in breeding experiments, and in devising public health strategies to suppress pathogens. An optimal intervention should be designed by considering its impact over an entire evolutionary trajectory that follows. As a result, a seemingly suboptimal intervention at a given time can be globally optimal as it can open opportunities for desirable actions. Here, we propose a feedback control formalism to devise globally optimal artificial selection protocol to direct evolution of molecular phenotypes. We show that artificial selection should counter evolutionary tradeoffs among multi-variate phenotypes to avoid undesirable outcomes in one phenotype by imposing selection on another. Control by artificial selection is challenged by our ability to predict evolution. We develop an information theoretical framework and show that molecular time-scales for evolution under natural selection can inform how to monitor a population to acquire sufficient predictive information for an effective intervention. Our formalism opens a new avenue for devising optimal artificial selection for directed evolution of molecular functions.