Evolution of Viral Proteins Originated De Novo by Overprinting

Sabath, Niv; Wagner, Andreas; Karlin, David

1) The "relative sequence divergence" between pairs of homologous proteins that the genes encode. We define the sequence divergence between two proteins as the proportion of amino acids in which they differ and the "relative" sequence divergence between two protein regions as their sequence divergence normalized (divided) by the sequence divergence of the corresponding ancestral proteins over their entire length. Consider, as a hypothetical example, the protein products of the overlapping genes in taxa T1 and T2 in figure 1b. The relative divergence between the ancestral proteins (red) of taxa T1 and T2 is the divergence between the protein region encoded by the part of the red gene that overlaps with the blue gene in taxa T1 and T2, divided by the divergence between the full-length red proteins of taxa T1 and T2. Analogously, the relative divergence between the de novo proteins of taxa T1-T2 is the divergence between the protein region of the blue gene that overlaps with the red gene in T1 and T2 (in this case the whole blue protein), again divided by the divergence between the full-length red proteins of taxa T1 and T2. The reason why we chose to normalize divergence in this way is to allow comparison between pairs of species that have diverged at different times (e.g., species T1-T2 diverged more recently than T1-T3 in fig. 1b ). We calculated the relative sequence divergence in this way for all homologous pairs of ancestral proteins and for all homologous pairs of de novo proteins in each of our 12 clades containing de novo gene pairs. Note that if the ancestral gene overlaps the de novo gene over its entire length, the relative divergence of the ancestral protein will be 1. This happens in case 6 (umbravirus). 2) The "selective constraint" in the overlapping regions, estimated by the method of Sabath et al. (2008) . This method, developed specifically for overlapping genes, accounts for independent selection pressures acting simultaneously on two overlapping genes by extending the single-gene model of codon evolution (Goldman and Yang 1994) to estimate the nonsynonymous/synonymous rate ratio (dN/dS) for each gene (reading frame) separately. Like the relative divergence, we calculated the selective constraint for pairs of homologous sequences. Specifically, we calculated selective constraint for all ancestral genes and de novo genes in each of our 12 cases. To prevent artifacts from saturation of synonymous substitutions, we restricted the estimation of the selective constraint to pairs in which both ancestral and de novo proteins had less than 50% amino acid divergence (percentage of identity). Because the method is inaccurate at low divergences (Sabath et al. 2008 ), we excluded sequence pairs with less than 1% amino acid divergence.