A simple stochastic model describing the evolution of genomic GC content in asexually reproducing organisms

Abstract

AbstractA genome’s nucleotide composition can usually be summarized with (G)uanine + (C)ytosine (GC) or (A)denine + (T)hymine (AT) frequencies as GC% = 100% − AT%. Genomic AT/GC content has been linked to environment and selective processes in asexually reproducing organisms. A model is presented relating the evolution of genomic GC content over time to AT $$\rightarrow$$ → GC and GC $$\rightarrow$$ → AT mutation rates. By employing Itô calculus it is shown that if mutation rates are subject to random perturbations, that can vary over time, several implications follow. In particular, an extra Brownian motion term appears influencing genomic nucleotide variability; the greater the random perturbations the more genomic nucleotide variability. This can have several interpretations depending on the context. For instance, reducing the influence of the random perturbations on the AT/GC mutation rates and thus genomic nucleotide variability, to limit fitness decreasing and deleterious mutations, will likely suggest channeling of resources. On the other hand, increased genomic nucleotide diversity may be beneficial in variable environments. In asexually reproducing organisms, the Brownian motion term can be considered to be inversely reflective of the selective pressures an organism is subjected to at the molecular level. The presented model is a generalization of a previous model, limited to microbial symbionts, to all asexually reproducing, non-recombining organisms. Last, a connection between the presented model and the classical Luria–Delbrück mutation model is presented in an Itô calculus setting.