HIV Protease and Integrase Empirical Substitution Models of Evolution: Protein-Specific Models Outperform Generalist Models

Substitution Models of Protein Evolution with Selection on Enzymatic Activity

Substitution models of evolution are necessary for diverse evolutionary analyses including phylogenetic tree and ancestral sequence reconstructions. At the protein level, empirical substitution models are traditionally used due to their simplicity, but they ignore the variability of substitution patterns among protein sites. Next, in order to improve the realism of the modeling of protein evolution, a series of structurally constrained substitution models were presented, but still they usually ignore constraints on the protein activity. Here, we present a substitution model of protein evolution with selection on both protein structure and enzymatic activity, and that can be applied to phylogenetics. In particular, the model considers the binding affinity of the enzyme-substrate complex as well as structural constraints that include the flexibility of structural flaps, hydrogen bonds, amino acids backbone radius of gyration, and solvent-accessible surface area that are quantified through molecular dynamics simulations. We applied the model to the HIV-1 protease and evaluated it by phylogenetic likelihood in comparison with the best-fitting empirical substitution model and a structurally constrained substitution model that ignores the enzymatic activity. We found that accounting for selection on the protein activity improves the fitting of the modeled functional regions with the real observations, especially in data with high molecular identity, which recommends considering constraints on the protein activity in the development of substitution models of evolution.

Data-specific substitution models improve protein-based phylogenetics

Calculating amino-acid substitution models that are specific for individual protein data sets is often difficult due to the computational burden of estimating large numbers of rate parameters. In this study, we tested the computational efficiency and accuracy of five methods used to estimate substitution models, namely Codeml, FastMG, IQ-TREE, P4 (maximum likelihood), and P4 (Bayesian inference). Data-specific substitution models were estimated from simulated alignments (with different lengths) that were generated from a known simulation model and simulation tree. Each of the resulting data-specific substitution models was used to calculate the maximum likelihood score of the simulation tree and simulated data that was used to calculate the model, and compared with the maximum likelihood scores of the known simulation model and simulation tree on the same simulated data. Additionally, the commonly-used empirical models, cpREV and WAG, were assessed similarly. Data-specific models performed better than the empirical models, which under-fitted the simulated alignments, had the highest difference to the simulation model maximum-likelihood score, clustered further from the simulation model in principal component analysis ordination, and inferred less accurate trees. Data-specific models and the simulation model shared statistically indistinguishable maximum-likelihood scores, indicating that the five methods were reasonably accurate at estimating substitution models by this measure. Nevertheless, tree statistics showed differences between optimal maximum likelihood trees. Unlike other model estimating methods, trees inferred using data-specific models generated with IQ-TREE and P4 (maximum likelihood) were not significantly different from the trees derived from the simulation model in each analysis, indicating that these two methods alone were the most accurate at estimating data-specific models. To show the benefits of using data-specific protein models several published data sets were reanalysed using IQ-TREE-estimated models. These newly estimated models were a better fit to the data than the empirical models that were used by the original authors, often inferred longer trees, and resulted in different tree topologies in more than half of the re-analysed data sets. The results of this study show that software availability and high computation burden are not limitations to generating better-fitting data-specific amino-acid substitution models for phylogenetic analyses.

Influence of substitution model selection on protein phylogenetic tree reconstruction

Probabilistic phylogenetic tree reconstruction is traditionally performed under a best-fitting substitution model of molecular evolution previously selected according to diverse statistical criteria. Interestingly, some recent studies proposed that this procedure is unnecessary for phylogenetic tree reconstruction leading to a debate in the field. In contrast to DNA sequences, phylogenetic tree reconstruction from protein sequences is traditionally based on empirical exchangeability matrices that can differ among taxonomic groups and protein families. Considering this aspect, here we investigated the influence of selecting a substitution model of protein evolution on phylogenetic tree reconstruction by the analyses of real and simulated data. We found that phylogenetic tree reconstructions based on a selected best-fitting substitution model of protein evolution are the most accurate, in terms of topology and branch lengths, compared with those derived from substitution models with amino acid replacement matrices far from the selected best-fitting model, especially when the data has large genetic diversity. Indeed, we found that substitution models with similar amino acid replacement matrices produce similar reconstructed phylogenetic trees, suggesting the use of substitution models as similar as possible to a selected best-fitting model when the latter cannot be used. Therefore, we recommend the use of the traditional protocol of selection among substitution models of evolution for protein phylogenetic tree reconstruction.

The Structure of Evolutionary Model Space for Proteins across the Tree of Life

The factors that determine the relative rates of amino acid substitution during protein evolution are complex and known to vary among taxa. We estimated relative exchangeabilities for pairs of amino acids from clades spread across the tree of life and assessed the historical signal in the distances among these clade-specific models. We separately trained these models on collections of arbitrarily selected protein alignments and on ribosomal protein alignments. In both cases, we found a clear separation between the models trained using multiple sequence alignments from bacterial clades and the models trained on archaeal and eukaryotic data. We assessed the predictive power of our novel clade-specific models of sequence evolution by asking whether fit to the models could be used to identify the source of multiple sequence alignments. Model fit was generally able to correctly classify protein alignments at the level of domain (bacterial versus archaeal), but the accuracy of classification at finer scales was much lower. The only exceptions to this were the relatively high classification accuracy for two archaeal lineages: Halobacteriaceae and Thermoprotei. Genomic GC content had a modest impact on relative exchangeabilities despite having a large impact on amino acid frequencies. Relative exchangeabilities involving aromatic residues exhibited the largest differences among models. There were a small number of exchangeabilities that exhibited large differences in comparisons among major clades and between generalized models and ribosomal protein models. Taken as a whole, these results reveal that a small number of relative exchangeabilities are responsible for much of the structure of the "model space" for protein sequence evolution. The clade-specific models we generated may be useful tools for protein phylogenetics, and the structure of evolutionary model space that they revealed has implications for phylogenomic inference across the tree of life.

Consequences of Substitution Model Selection on Protein Ancestral Sequence Reconstruction

The selection of the best-fitting substitution model of molecular evolution is a traditional step for phylogenetic inferences, including ancestral sequence reconstruction (ASR). However, a few recent studies suggested that applying this procedure does not affect the accuracy of phylogenetic tree reconstruction. Here, we revisited this debate topic by analyzing the influence of selection among substitution models of protein evolution, with focus on exchangeability matrices, on the accuracy of ASR using simulated and real data. We found that the selected best-fitting substitution model produces the most accurate ancestral sequences, especially if the data present large genetic diversity. Indeed, ancestral sequences reconstructed under substitution models with similar exchangeability matrices were similar, suggesting that if the selected best-fitting model cannot be used for the reconstruction, applying a model similar to the selected one is preferred. We conclude that selecting among substitution models of protein evolution is recommended for reconstructing accurate ancestral sequences.