Mathematics Faculty Articles
Genetic Code, Hamming Distance and Stochastic Matrices
Document Type
Article
Publication Date
9-1-2004
Publication Title
Bulletin of Mathematical Biology
ISSN
0092-8240
Volume
66
Issue/No.
5
First Page
1405
Last Page
1421
Abstract
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.
NSUWorks Citation
He, Matthew; Petoukhov, Sergei V.; and Ricci, Paolo E., "Genetic Code, Hamming Distance and Stochastic Matrices" (2004). Mathematics Faculty Articles. 166.
https://nsuworks.nova.edu/math_facarticles/166
DOI
10.1016/j.bulm.2004.01.002