Non-Markovian effects on protein sequence evolution due to site dependent substitution rates

Abstract

BackgroundMany models of protein sequence evolution, in particular those based on Point Accepted Mutation (PAM) matrices, assume that its dynamics is Markovian. Nevertheless, it has been observed that evolution seems to proceed differently at different time scales, questioning this assumption. In 2011 Kosiol and Goldman proved that, if evolution is Markovian at the codon level, it can not be Markovian at the amino acid level. However, it remains unclear up to which point the Markov assumption is verified at the codon level.ResultsHere we show how also the among-site variability of substitution rates makes the process of full protein sequence evolution effectively not Markovian even at the codon level. This may be the theoretical explanation behind the well known systematic underestimation of evolutionary distances observed when omitting rate variability. If the substitution rate variability is neglected the average amino acid and codon replacement probabilities are affected by systematic errors and those with the largest mismatches are the substitutions involving more than one nucleotide at a time. On the other hand, the instantaneous substitution matrices estimated from alignments with the Markov assumption tend to overestimate double and triple substitutions, even when learned from alignments at high sequence identity.ConclusionsThese results discourage the use of simple Markov models to describe full protein sequence evolution and encourage to employ, whenever possible, models that account for rate variability by construction (such as hidden Markov models or mixture models) or substitution models of the type of Le and Gascuel (2008) that account for it explicitly.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1135-1) contains supplementary material, which is available to authorized users.

Predicting Amino Acid Substitution Probabilities Using Single Nucleotide Polymorphisms

“…A possible interpretation of these results is that standard models are learned from alignments at medium sequence identity. Then, the instantaneous rate matrices of these models are consistent with an effective Markovian dynamics, in which the effects of the degeneration of the genetic code (Kosiol and Goldman 2011) and of the rate variability (Rizzato et al 2016) are averaged out. Instead, the Q matrix obtained from the SNPs describes evolution at extremely short evolutionary times.…”

“…An important result of our analysis is that substitution frequencies learned from SNPs can be used to predict amino acid substitution probabilities only if rate variability is taken into account (Rizzato et al 2016). Indeed, the performance obtained by a SNP-based model in which this effect is not included is very bad (see Figure 4).…”

“…The diagonal entries of Q SNP are, instead, defined as Q SNP c;c ¼ 2 P c96 ¼c Q SNP c;c9 : By construction, P c;c9 ðf c Q SNP c;c9 Þ ¼ 1: Therefore, the evolutionary time is measured in units of expected substitutions per site. From Q SNP ; or any other generic Q matrix on codons or amino acids, we compute the transition probability from c to c9 after a time t by following Rizzato et al (2016):…”

“…This may seem counterintuitive, since it is well known that the G-correction tends to improve phylogenetic estimations with all these models. However, the G distribution is only included on average, without associating a specific rate to each site (Miyazawa 2011a;Rizzato et al 2016).…”

“…We select from the dbSNP database (Sherry et al 2001) only the human polymorphisms characterized by no known clinical significance, and which are present in at least 1% of the population, having therefore a high probability of being nearly neutral. We demonstrate that a protein evolution model based on a substitution matrix inferred from this subset of SNPs, and taking into account substitution rate variability (Miyazawa 2011a;Rizzato et al 2016), can be used to predict the transition probabilities between amino acids observed in alignments. The accuracy of this model in the range of 85-100% of sequence identity is better than that achieved using any other substitution matrix we are aware of, including LG (Le and Gascuel 2008), WAG (Whelan and Goldman 2001), JTT (Jones et al 1992) and BLOSUM90 (Henikoff and Henikoff 1992) for amino acid models or ECM (Kosiol et al 2007) for codon models.…”