Author's School

School of Engineering & Applied Science

Author's Department/Program

Electrical and Systems Engineering


English (en)

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Tyzh-Jong Tarn


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 addition, given that the system is completely controllable, we find that the global optimum of both base-to-base and codon-to-codon deterministic mutations can always be achieved within a finite number of steps.


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