Towards realistic codon models: among site variability and dependency of synonymous and non-synonymous rates

Codon evolutionary models are widely used to infer the selection forces acting on a protein. The non-synonymous to synonymous rate ratio (denoted by Ka/Ks) is used to infer specific positions that are under purifying or positive selection. Current evolutionary models usually assume that only the non-synonymous rates vary among sites while the synonymous substitution rates are constant. This assumption ignores the possibility of selection forces acting at the DNA or mRNA levels. Towards a more realistic description of sequence evolution, we present a model that accounts for among-site-variation of both synonymous and non-synonymous substitution rates. Furthermore, we alleviate the widespread assumption that positions evolve independently of each other. Thus, possible sources of bias caused by random fluctuations in either the synonymous or non-synonymous rate estimations at a single site is removed. Our model is based on two hidden Markov models that operate on the spatial dimension: one describes the dependency between adjacent non-synonymous rates while the other describes the dependency between adjacent synonymous rates. The presented model is applied to study the selection pressure across the HIV-1 genome. The new model better describes the evolution of all HIV-1 genes, as compared to current codon models. Using both simulations and real data analyses, we illustrate that accounting for synonymous rate variability and dependency greatly increases the accuracy of Ka/Ks estimation and in particular of positively selected sites. Finally, we discuss the applicability of the developed model to infer the selection forces in regulatory and overlapping regions of the HIV-1 genome.