A site-specific measure for rate difference after gene duplication or speciation.

Abstract

Gene family proliferation by gene (genome) duplication has provided the raw materials for functional innovations (Ohno 1970; Lundin 1993; Holland et al. 1994; Henikoff et al. 1997; Golding and Dean 1998). Several models were proposed for functional divergence among member genes (e.g., Li 1983; Clark 1994; Hughes 1994; Fryxell 1996; Nei, Gu, and Sitnikova 1997; Force et al. 1999), but the details remain largely unknown. Gu (1999) developed a statistical method for testing type I functional divergence, i.e., changes in protein function between two gene clusters result in changes in selective constraints (and therefore shifted evolutionary rates) at some residues. It stands in contrast to type II functional divergence, i.e., changes in protein function between two gene clusters do not alter the level of selective constraints. Amino acid residues with rate shifts are the sites that have either gained or lost importance as a consequence of the change of function during evolution, as proposed by the hypothesis of type I functional divergence (Gu 1999). Moreover, type I functional divergence provides a biological basis for the covarion theory of molecular evolution (Fitch and Markowitz 1970). If a statistical testing shows a significant rate difference between two gene clusters, it is of great interest to predict important amino acid residues, which can be further verified by available functional-structural evidence (Dermitzakis and Clark 2001; Gaucher, Miyamoto, and Benner 2001; Wang and Gu 2001). The posterior probability of each site is suitable to develop a statistically sound profile for selecting critical amino acid residues (Gu 1999), but little information is provided about how much rate difference is generated at these sites after gene duplication. In this article, we report a new site-specific profile for the rate difference, which is useful for studying the pattern of protein sequence evolution. Consider two gene clusters generated by gene duplication (or speciation), e.g., see figure 1, the bone morphogenetic proteins (BMP) gene family tree. In each cluster, a site can be in either of two states: (1) F0, which means no altered functional constraint after gene duplication, and (2) F1, which means altered functional constraint at this site after gene duplication. As a result, there are four combined states in the case of two gene clusters: (1) F0 in both clusters, denoted by S0 5 (F0, F0), resulting in no rate difference between clusters; and