Yu Juanyi, Li Jr-Shin, Tarn Tzyh-Jong
Department of Electrical and Systems Engineering, Washington University in St. Louis, Green Hall, Campus Box 1042, One Brookings Drive, St. Louis, MO 63130, USA.
J Biomed Biotechnol. 2012;2012:743172. doi: 10.1155/2012/743172. Epub 2012 Jan 22.
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.
我们从有限域概念出发，提出了一种关于DNA复制中基因突变的分子水平控制系统观点。将DNA序列视为状态变量，化学诱变剂和辐射视为控制输入，一个细胞周期作为步长增量，将所得DNA序列的测量结果视为输出，我们推导了不同尺度的确定性和随机离散时间、有限状态系统的系统方程。将成本函数定义为应用诱变剂的成本与偏离轨迹惩罚的总和，我们通过动态规划算法解决了确定性和随机最优控制问题。此外，鉴于该系统是完全可控的，我们发现逐碱基和逐密码子确定性突变的全局最优解总能在有限步数内实现。
