Solvable models of neighbor-dependent nucleotide substitution processes

2005/10/03 by Bérard, Jean, Gouéré, Jean-Baptiste, Didier Piau +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #60J25 #92D20 #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Genomics (q-bio.GN) #Origins and Evolution of Life #Probability (math.PR) #RNA and protein synthesis mechanisms

paper · pdf · doi:10.48550/arxiv.math/0510034

openalex publication_date 2005/10/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that a wide class of models of Markov neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotide substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotide frequencies at equilibrium solve explicit finite-size linear systems. Finally, the dynamics of the process and the distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotide sites at distance at least three evolve independently, and the sites, if encoded as purines and pyrimidines, evolve independently.

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