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Journal of Biomedicine and Biotechnology
Volume 2012, Article ID 743172, 26 pages
Research Article

Optimal Control of Gene Mutation in DNA Replication

Department of Electrical and Systems Engineering, Washington University in St. Louis, Green Hall, Campus Box 1042, One Brookings Drive, St. Louis, MO 63130, USA

Received 30 June 2011; Accepted 3 September 2011

Academic Editor: T. Akutsu

Copyright © 2012 Juanyi Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.