A simple stochastic model to describe the evolution over time of core genome SNP GC content in prokaryotes

Abstract

Genomes in living organisms consist of the nucleotides adenine (A), guanine (G), cytosine (C) and thymine (T). All prokaryotes have genomes consisting of double-stranded DNA, where the A's and G's (purines) of one strand bind respectively to the T's and C's (pyrimidines) of the other. As such, the number of A's on one strand nearly equals the number of T's on the other, and the same is true of one strand's G's and the other's C's. Globally, this relationship is formalized as Chargaff's first parity rule; its strandwise equivalent is Chargaff's second parity rule. Therefore, the GC content of any double-stranded DNA genome can be expressed as %GC=100%-%AT. Variation in prokaryotic GC content can be substantial between taxa but is generally small within microbial genomes. This variation has been found to correlate with both phylogeny and environmental factors. Since novel single-nucleotide polymorphisms (SNPs) within genomes are at least partially linked to the environment, SNP GC content can be considered a compound measure of an organism's environmental influences, lifestyle and phylogeny. We present a mathematical model that describes how SNP GC content in microbial genomes evolves over time as a function of the AT->GC and GC->AT mutation rates with Gaussian white noise disturbances. The model suggests that, in non-recombining bacteria, mutations can first accumulate unnoticeably and then abruptly fluctuate out of control. Thus, minuscule variations in mutation rates can suddenly become unsustainable, ultimately driving a species to extinction if not counteracted early enough. This model, which is suited specifically to symbiotic prokaryotes, conforms to scenarios predicted by Muller's ratchet and may suggest that this is not always a gradual, degrading process.