Genetic code, hamming distance and stochastic matrices
Genetic code, hamming distance and stochastic matrices
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DOI：
10.1016/j.bulm.2004.01.002
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发表时间：
2004-09-01
影响因子：
3.5
通讯作者：
Ricci, PE
中科院分区：
文献类型：
--
作者：
He, MX;Petoukhov, SV;Ricci, PE
在本文中，我们使用遗传密码 C = 00、U = 10、G = 11 和 A = 01（C 与 G 配对，A 与 U 配对）的格雷码表示来生成基于遗传密码的矩阵序列。与这些基于代码的矩阵相关，我们使用汉明距离来生成数值矩阵序列。然后，我们进一步研究数值矩阵的性质，并表明它们是双重随机和对称的。我们确定汉明距离的频率分布、矩阵的构建块、矩阵的分解和迭代。我们根据置换矩阵提出了基于遗传密码的矩阵的显式分解公式，它提供了遗传密码的超立方体表示。还观察到基于遗传密码的超立方体中存在哈密顿循环。 (C) 2004 年数学生物学学会由 Elsevier Ltd 出版。保留所有权利。
In this paper we use the Gray code representation of the genetic code C = 00, U = 10, G = 11 and A = 01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are doubly stochastic and symmetric. We determine the frequency distributions of the Hamming distances, building blocks of the matrices, decomposition and iterations of matrices. We present an explicit decomposition formula for the genetic code-based matrix in terms of permutation matrices, which provides a hypercube representation of the genetic code. It is also observed that there is a Hamiltonian cycle in a genetic code-based hypercube. (C) 2004 Society for Mathematical Biology Published by Elsevier Ltd. All rights reserved.