Matthew, He Double helical sequences and doubly stochastic matrices. (English) Zbl 1089.92012 Symmetry Cult. Sci. 12, No. 3-4, 307-330 (2001). Summary: We establish a relation between the genetic code and a stochastic matrix based on hydrogen bonds of DNA. Using fundamental properties of the stochastic matrices, we determine explicity the decomposition formula of genetic code-based biperiodic tables. By iterating the stochastic matrix, we demonstrate the symmetrical relations between the entries of the matrix and DNA molar concentration accumulation. The evolution matrices based on the genetic code were derived by using hydrogen bonds based \(2\times 2\) symmetric stochastic matrices as primary building blocks. The fractal structure of the genetic code and stochastic matrices were illustrated in the process of matrix decomposition, iteration and expansion in correspondence to the fractal structure of the biperiodic table discovered by Petoukhov. MSC: 92C40 Biochemistry, molecular biology 15B51 Stochastic matrices 92D10 Genetics and epigenetics Keywords:genetic code; codons; tripeptide; doubly stochastic matrix; fractal structure; molecular evolution PDFBibTeX XMLCite \textit{H. Matthew}, Symmetry Cult. Sci. 12, No. 3--4, 307--330 (2001; Zbl 1089.92012)