2003/06/09 by Emmanuel Tannenbaum, Eugene I. Shakhnovich · 1 citation
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Mathematical and Theoretical Epidemiology and Ecology Models #cond-mat.stat-mech #q-bio
paper · pdf · doi:10.1103/physreve.69.011902
14 pages, 3 figures. Submitted to Physical Review E
arxiv created 2003/06/09 · openalex publication_date 2004/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops a two-gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by sigma(via), yields a viable organism with first-order growth rate constant k>1 if it is equal to some target "master" sequence sigma(via,0). The second gene, denoted by sigma(rep), yields an organism capable of genetic repair if it is equal to some target "master" sequence sigma(rep,0). This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on micro identical with Lepsilon, the product of sequence length and per base pair replication error probability, and epsilon(r), the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of the three possible "phases." In the first phase, the population is localized about the viability and repairing master sequences. As epsilon(r) exceeds the fraction of deleterious mutations, the population undergoes a "repair" catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when micro exceeds ln k/epsilon(r), while above the repair catastrophe, the distribution undergoes the error catastrophe when micro exceeds ln k/f(del), where f(del) denotes the fraction of deleterious mutations.