Optimal Control in Gene Mutation

OF THE DISSERTATION Optimal Control in Gene Mutation by Juanyi Yu Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, 2011 Research Advisor: Professor Tzyh-Jong Tarn, Professor Jr-Shin Li Gene mutations are the radical causes of many diseases, including inheritance diseases and cancers. Current medical treatments usually focus on changing the concentrations of related chemicals or mRNAs at the cellular level to stop protein productions or cell duplications, which can only control the diseases under certain circumstances but cannot cure them. Little research work has been done at the molecular level, the fundamental of inheritance, to search possible ways to cure those severe diseases. In this dissertation, we propose a molecular level control system view of the gene mutations in DNA replication from the finite field concept. By treating DNA sequences as state variables, chemical mutagens and radiation as control inputs, one cell cycle as a step increment, and the measurements of the resulting DNA sequence as outputs, we derive system equations for both deterministic and stochastic discrete-time, finite-state systems of different scales. Defining the cost function as a summation of the costs of applying mutagens and the off-trajectory penalty, we solve the deterministic and stochastic optimal control problems by dynamic programming algorithm. In