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