Selective constraints on amino acids estimated by a mechanistic codon substitution model with multiple nucleotide changes

Abstract

Background: Empirical substitution matrices represent the average tendencies of substitutions over various protein families by sacrificing gene-level resolution. We develop a codon-based model, in which mutational tendencies of codon, a genetic code, and the strength of selective constraints against amino acid replacements can be tailored to a given gene. First, selective constraints averaged over proteins are estimated by maximizing the likelihood of each 1-PAM matrix of empirical amino acid (JTT, WAG, and LG) and codon (KHG) substitution matrices. Then, selective constraints specific to given proteins are approximated as a linear function of those estimated from the empirical substitution matrices.

Results: Akaike information criterion (AIC) values indicate that a model allowing multiple nucleotide changes fits the empirical substitution matrices significantly better. Also, the ML estimates of transition-transversion bias obtained from these empirical matrices are not so large as previously estimated. The selective constraints are characteristic of proteins rather than species. However, their relative strengths among amino acid pairs can be approximated not to depend very much on protein families but amino acid pairs, because the present model, in which selective constraints are approximated to be a linear function of those estimated from the JTT/WAG/LG/KHG matrices, can provide a good fit to other empirical substitution matrices including cpREV for chloroplast proteins and mtREV for vertebrate mitochondrial proteins.

Conclusions/significance: The present codon-based model with the ML estimates of selective constraints and with adjustable mutation rates of nucleotide would be useful as a simple substitution model in ML and Bayesian inferences of molecular phylogenetic trees, and enables us to obtain biologically meaningful information at both nucleotide and amino acid levels from codon and protein sequences.

Figure 1. The ML-87 and the ML-91 models fitted to JTT.

Each element log- of the log-odds matrices of (A) the ML-87 and (B) the ML-91 models fitted to the 1-PAM JTT matrix is plotted against the log-odds log- calculated from JTT. Plus, circle, and cross marks show the log-odds values for the types of substitutions requiring single, double and triple nucleotide changes, respectively. The dotted line in each figure shows the line of equal values between the ordinate and the abscissa.

Figure 2. The ML-200 model fitted to KHG.

Each element log- of the log-odds matrix corresponding to (A) single, (B) double, and (C) triple nucleotide changes in the ML-200 model fitted to the 1-PAM KHG codon substitution matrix is plotted against the log-odds log- calculated from KHG. In (D), codon log-exchangeabilities of the 1-PAM KHG codon substitution matrix corresponding to triple nucleotide changes are plotted against the log-odds log- calculated from KHG. The log-exchangeability of the 1-PAM KHG is defined as . Upper triangle, plus, circle, and cross marks show the log-odds values for synonymous pairs and one-, two-, and three-step amino acid pairs, respectively. Log-exchangeabilities for the codon pairs whose instantaneous rates are estimated to be in KHG are shown to be about in this figure. The dotted line in each figure shows the line of equal values between the ordinate and the abscissa.

Figure 3. Selective constraint for each amino acid pair estimated from JTT and from KHG.

The ML estimate, (A) in the ML-91+ model fitted to the 1-PAM JTT amino acid substitution matrix and (B) in the ML-200 model fitted to the 1-PAM KHG codon substitution matrix, for each amino acid pair is plotted against the mean energy increment due to an amino acid substitution, () defined by Eqs. S1-4, S1-5, and S1-6 in Text S1. In (A), the estimates for the least exchangeable class of multi-step amino acid pairs are not shown. Plus, circle, and cross marks show the values for one-, two-, and three-step amino acid pairs, respectively.

Figure 4. The KHG-ML200-11 model fitted to each of JTT, WAG, LG, and mtREV.

Each element log- of the log-odds matrices of the KHG-ML200-11 model fitted to the 1-PAM matrices of (A) JTT, (B) WAG, (C) LG, and (D) mtREV is plotted against the log-odds log- calculated from the corresponding empirical substitution matrices. Plus, circle, and cross marks show the log-odds values for one-, two-, and three-step amino acid pairs, respectively. The dotted line in each figure shows the line of equal values between the ordinate and the abscissa. The log-odds elements of mtREV whose values are smaller than about are all assumed to be ; see the original paper .