Optimal control in molecular-level gene manipulation

The sequential information stored in DNA determines the appearance and inheritance of different life forms and individuals. Precision control of DNA sequences at the molecular level is crucial to maintain the fidelity of genes and to ensure the accuracy of gene expression. In this paper, we propose state-space control models at the molecular level by converting character-based DNA sequences into state vectors and incorporating on/off controls for mutagens into DNA replication systems in different scales. Subsequently, we compute the optimal control sequence for minimizing the risk of applying mutagens and the off-trajectory penalty using dynamic programming algorithm. By the brute force method and simulation results, we conclude that the global optimum can always be achieved within a finite number of steps of deterministic DNA replication systems. The upper limit of steps to reach the global optimum depends on the length of the DNA sequence.