Expected relationship between the silent substitution rate and the GC content: Implications for the evolution of isochores

The relationship between the silent substitution rate (K-s) and the GC content along the genome is a focal point of the debate about the origin of the isochore structure in vertebrates. Recent estimation of the silent substitution rate showed a positive correlation between K-s and GC content, in contradiction with the predictions of both the regional mutation bias model and the selection or biased gene conversion model. The aim of this paper is to help resolve this contradiction between theoretical studies and data. We analyzed the relationship between K-s and GC content under (1) uniform mutation bias, (2) a regional mutation bias, and (3) mutation bias and selection. We report that an increase in K-s with GC content is expected under mutation bias because of either nonequilibrium of the isochore structure or an increasing mutation rate from AT toward GC nucleotides in GC-richer isochores. We show by simulations that CpG deamination tends to increase the mutation rate with GC content in a regional mutation bias model. We also demonstrate that the relationship between K-s and GC under the selectionist or biased gene conversion model is positive under weak selection if the mutation selection equilibrium GC frequency is less than 0.5.