A new formulation of protein evolutionary models that account for structural constraints

Selection among site-dependent structurally constrained substitution models of protein evolution by approximate Bayesian computation

MOTIVATION

The selection among substitution models of molecular evolution is fundamental for obtaining accurate phylogenetic inferences. At the protein level, evolutionary analyses are traditionally based on empirical substitution models but these models make unrealistic assumptions and are being surpassed by structurally constrained substitution (SCS) models. The SCS models often consider site-dependent evolution, a process that provides realism but complicates their implementation into likelihood functions that are commonly used for substitution model selection.

RESULTS

We present a method to perform selection among site-dependent SCS models, also among empirical and site-dependent SCS models, based on the approximate Bayesian computation (ABC) approach and its implementation into the computational framework ProteinModelerABC. The framework implements ABC with and without regression adjustments and includes diverse empirical and site-dependent SCS models of protein evolution. Using extensive simulated data, we found that it provides selection among SCS and empirical models with acceptable accuracy. As illustrative examples, we applied the framework to analyze a variety of protein families observing that SCS models fit them better than the corresponding best-fitting empirical substitution models.

AVAILABILITY AND IMPLEMENTATION

ProteinModelerABC is freely available from https://github.com/DavidFerreiro/ProteinModelerABC, can run in parallel and includes a graphical user interface. The framework is distributed with detailed documentation and ready-to-use examples.

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.

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.

Consequences of Genetic Recombination on Protein Folding Stability

Genetic recombination is a common evolutionary mechanism that produces molecular diversity. However, its consequences on protein folding stability have not attracted the same attention as in the case of point mutations. Here, we studied the effects of homologous recombination on the computationally predicted protein folding stability for several protein families, finding less detrimental effects than we previously expected. Although recombination can affect multiple protein sites, we found that the fraction of recombined proteins that are eliminated by negative selection because of insufficient stability is not significantly larger than the corresponding fraction of proteins produced by mutation events. Indeed, although recombination disrupts epistatic interactions, the mean stability of recombinant proteins is not lower than that of their parents. On the other hand, the difference of stability between recombined proteins is amplified with respect to the parents, promoting phenotypic diversity. As a result, at least one third of recombined proteins present stability between those of their parents, and a substantial fraction have higher or lower stability than those of both parents. As expected, we found that parents with similar sequences tend to produce recombined proteins with stability close to that of the parents. Finally, the simulation of protein evolution along the ancestral recombination graph with empirical substitution models commonly used in phylogenetics, which ignore constraints on protein folding stability, showed that recombination favors the decrease of folding stability, supporting the convenience of adopting structurally constrained models when possible for inferences of protein evolutionary histories with recombination.

The evolution of the HIV-1 protease folding stability

The evolution of structural proteins is generally constrained by the folding stability. However, little is known about the particular capacity of viral proteins to accommodate mutations that can potentially affect the protein stability and, in general, the evolution of the protein stability over time. As an illustrative model case, here, we investigated the evolution of the stability of the human immunodeficiency virus (HIV-1) protease (PR), which is a common HIV-1 drug target, under diverse evolutionary scenarios that include (1) intra-host virus evolution in a cohort of seventy-five patients sampled over time, (2) intra-host virus evolution sampled before and after specific PR-based treatments, and (3) inter-host evolution considering extant and ancestral (reconstructed) PR sequences from diverse HIV-1 subtypes. We also investigated the specific influence of currently known HIV-1 PR resistance mutations on the PR folding stability. We found that the HIV-1 PR stability fluctuated over time within a constant and wide range in any studied evolutionary scenario, accommodating multiple mutations that partially affected the stability while maintaining activity. We did not identify relationships between change of PR stability and diverse clinical parameters such as viral load, CD4⁺ T-cell counts, and a surrogate of time from infection. Counterintuitively, we predicted that nearly half of the studied HIV-1 PR resistance mutations do not significantly decrease stability, which, together with compensatory mutations, would allow the protein to adapt without requiring dramatic stability changes. We conclude that the HIV-1 PR presents a wide structural plasticity to acquire molecular adaptations without affecting the overall evolution of stability.

Methodologies for Microbial Ancestral Sequence Reconstruction

The reconstruction of genetic material of ancestral organisms constitutes a powerful application of evolutionary biology. A fundamental step in this inference is the ancestral sequence reconstruction (ASR), which can be performed with diverse methodologies implemented in computer frameworks. However, most of these methodologies ignore evolutionary properties frequently observed in microbes, such as genetic recombination and complex selection processes, that can bias the traditional ASR. From a practical perspective, here I review methodologies for the reconstruction of ancestral DNA and protein sequences, with particular focus on microbes, and including biases, recommendations, and software implementations. I conclude that microbial ASR is a complex analysis that should be carefully performed and that there is a need for methods to infer more realistic ancestral microbial sequences.

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

Diverse phylogenetic methods require a substitution model of evolution that should mimic, as accurately as possible, the real substitution process. At the protein level, empirical substitution models have traditionally been based on a large number of different proteins from particular taxonomic levels. However, these models assume that all of the proteins of a taxonomic level evolve under the same substitution patterns. We believe that this assumption is highly unrealistic and should be relaxed by considering protein-specific substitution models that account for protein-specific selection processes. In order to test this hypothesis, we inferred and evaluated four new empirical substitution models for the protease and integrase of HIV and other viruses. We found that these models more accurately fit, compared with any of the currently available empirical substitution models, the evolutionary process of these proteins. We conclude that evolutionary inferences from protein sequences are more accurate if they are based on protein-specific substitution models rather than taxonomic-specific (generalist) substitution models. We also present four new empirical substitution models of protein evolution that could be useful for phylogenetic inferences of viral protease and integrase.

Shifts in amino acid preferences as proteins evolve: A synthesis of experimental and theoretical work

Amino acid preferences vary across sites and time. While variation across sites is widely accepted, the extent and frequency of temporal shifts are contentious. Our understanding of the drivers of amino acid preference change is incomplete: To what extent are temporal shifts driven by adaptive versus nonadaptive evolutionary processes? We review phenomena that cause preferences to vary (e.g., evolutionary Stokes shift, contingency, and entrenchment) and clarify how they differ. To determine the extent and prevalence of shifted preferences, we review experimental and theoretical studies. Analyses of natural sequence alignments often detect decreases in homoplasy (convergence and reversions) rates, and variation in replacement rates with time-signals that are consistent with temporally changing preferences. While approaches inferring shifts in preferences from patterns in natural alignments are valuable, they are indirect since multiple mechanisms (both adaptive and nonadaptive) could lead to the observed signal. Alternatively, site-directed mutagenesis experiments allow for a more direct assessment of shifted preferences. They corroborate evidence from multiple sequence alignments, revealing that the preference for an amino acid at a site varies depending on the background sequence. However, shifts in preferences are usually minor in magnitude and sites with significantly shifted preferences are low in frequency. The small yet consistent perturbations in preferences could, nevertheless, jeopardize the accuracy of inference procedures, which assume constant preferences. We conclude by discussing if and how such shifts in preferences might influence widely used time-homogenous inference procedures and potential ways to mitigate such effects.

ProteinEvolverABC: coestimation of recombination and substitution rates in protein sequences by approximate Bayesian computation

MOTIVATION

The evolutionary processes of mutation and recombination, upon which selection operates, are fundamental to understand the observed molecular diversity. Unlike nucleotide sequences, the estimation of the recombination rate in protein sequences has been little explored, neither implemented in evolutionary frameworks, despite protein sequencing methods are largely used.

RESULTS

In order to accommodate this need, here I present a computational framework, called ProteinEvolverABC, to jointly estimate recombination and substitution rates from alignments of protein sequences. The framework implements the approximate Bayesian computation approach, with and without regression adjustments and includes a variety of substitution models of protein evolution, demographics and longitudinal sampling. It also implements several nuisance parameters such as heterogeneous amino acid frequencies and rate of change among sites and, proportion of invariable sites. The framework produces accurate coestimation of recombination and substitution rates under diverse evolutionary scenarios. As illustrative examples of usage, I applied it to several viral protein families, including coronaviruses, showing heterogeneous substitution and recombination rates.

AVAILABILITY AND IMPLEMENTATION

ProteinEvolverABC is freely available from https://github.com/miguelarenas/proteinevolverabc, includes a graphical user interface for helping the specification of the input settings, extensive documentation and ready-to-use examples. Conveniently, the simulations can run in parallel on multicore machines.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Relative Efficiencies of Simple and Complex Substitution Models in Estimating Divergence Times in Phylogenomics

The conventional wisdom in molecular evolution is to apply parameter-rich models of nucleotide and amino acid substitutions for estimating divergence times. However, the actual extent of the difference between time estimates produced by highly complex models compared with those from simple models is yet to be quantified for contemporary data sets that frequently contain sequences from many species and genes. In a reanalysis of many large multispecies alignments from diverse groups of taxa, we found that the use of the simplest models can produce divergence time estimates and credibility intervals similar to those obtained from the complex models applied in the original studies. This result is surprising because the use of simple models underestimates sequence divergence for all the data sets analyzed. We found three fundamental reasons for the observed robustness of time estimates to model complexity in many practical data sets. First, the estimates of branch lengths and node-to-tip distances under the simplest model show an approximately linear relationship with those produced by using the most complex models applied on data sets with many sequences. Second, relaxed clock methods automatically adjust rates on branches that experience considerable underestimation of sequence divergences, resulting in time estimates that are similar to those from complex models. And, third, the inclusion of even a few good calibrations in an analysis can reduce the difference in time estimates from simple and complex models. The robustness of time estimates to model complexity in these empirical data analyses is encouraging, because all phylogenomics studies use statistical models that are oversimplified descriptions of actual evolutionary substitution processes.

Protein Evolution in the Flaviviruses

Proteins are commonly used as molecular targets against pathogens such as viruses and bacteria. However, pathogens can evolve rapidly permitting their populations to increase in protein diversity over time and thus escape to the activity of a molecular therapy. Subsequently, in order to design more durable and robust therapies as well as to understand viral evolution in a host and subsequent transmission, it is central to understand the evolution of pathogen proteins. This understanding can enable the detection of protein regions that can be potential targets for therapies and predict the emergence of molecular resistance against therapies. In this direction, two articles published recently in the Journal of Molecular Evolution investigated the evolution of proteomes of diverse flaviviruses, including Zika virus, Dengue virus and West Nile virus. Here I discuss the importance of considering the evolution of viral proteins, with the use of as realistic as possible models and methods that mimic protein evolution, to improve the design of antiviral therapies.

The Influence of Protein Stability on Sequence Evolution: Applications to Phylogenetic Inference

Phylogenetic inference from protein data is traditionally based on empirical substitution models of evolution that assume that protein sites evolve independently of each other and under the same substitution process. However, it is well known that the structural properties of a protein site in the native state affect its evolution, in particular the sequence entropy and the substitution rate. Starting from the seminal proposal by Halpern and Bruno, where structural properties are incorporated in the evolutionary model through site-specific amino acid frequencies, several models have been developed to tackle the influence of protein structure on sequence evolution. Here we describe stability-constrained substitution (SCS) models that explicitly consider the stability of the native state against both unfolded and misfolded states. One of them, the mean-field model, provides an independent sites approximation that can be readily incorporated in maximum likelihood methods of phylogenetic inference, including ancestral sequence reconstruction. Next, we describe its validation with simulated and real proteins and its limitations and advantages with respect to empirical models that lack site specificity. We finally provide guidelines and recommendations to analyze protein data accounting for stability constraints, including computer simulations and inferences of protein evolution based on maximum likelihood. Some practical examples are included to illustrate these procedures.

Modeling site-specific amino-acid preferences deepens phylogenetic estimates of viral sequence divergence

Molecular phylogenetics is often used to estimate the time since the divergence of modern gene sequences. For highly diverged sequences, such phylogenetic techniques sometimes estimate surprisingly recent divergence times. In the case of viruses, independent evidence indicates that the estimates of deep divergence times from molecular phylogenetics are sometimes too recent. This discrepancy is caused in part by inadequate models of purifying selection leading to branch-length underestimation. Here we examine the effect on branch-length estimation of using models that incorporate experimental measurements of purifying selection. We find that models informed by experimentally measured site-specific amino-acid preferences estimate longer deep branches on phylogenies of influenza virus hemagglutinin. This lengthening of branches is due to more realistic stationary states of the models, and is mostly independent of the branch-length extension from modeling site-to-site variation in amino-acid substitution rate. The branch-length extension from experimentally informed site-specific models is similar to that achieved by other approaches that allow the stationary state to vary across sites. However, the improvements from all of these site-specific but time homogeneous and site independent models are limited by the fact that a protein’s amino-acid preferences gradually shift as it evolves. Overall, our work underscores the importance of modeling site-specific amino-acid preferences when estimating deep divergence times—but also shows the inherent limitations of approaches that fail to account for how these preferences shift over time.

Trends in substitution models of molecular evolution

Substitution models of evolution describe the process of genetic variation through fixed mutations and constitute the basis of the evolutionary analysis at the molecular level. Almost 40 years after the development of first substitution models, highly sophisticated, and data-specific substitution models continue emerging with the aim of better mimicking real evolutionary processes. Here I describe current trends in substitution models of DNA, codon and amino acid sequence evolution, including advantages and pitfalls of the most popular models. The perspective concludes that despite the large number of currently available substitution models, further research is required for more realistic modeling, especially for DNA coding and amino acid data. Additionally, the development of more accurate complex models should be coupled with new implementations and improvements of methods and frameworks for substitution model selection and downstream evolutionary analysis.

Site-Specific Amino Acid Preferences Are Mostly Conserved in Two Closely Related Protein Homologs

Evolution drives changes in a protein’s sequence over time. The extent to which these changes in sequence lead to shifts in the underlying preference for each amino acid at each site is an important question with implications for comparative sequence-analysis methods, such as molecular phylogenetics. To quantify the extent that site-specific amino acid preferences shift during evolution, we performed deep mutational scanning on two homologs of human influenza nucleoprotein with 94% amino acid identity. We found that only a modest fraction of sites exhibited shifts in amino acid preferences that exceeded the noise in our experiments. Furthermore, even among sites that did exhibit detectable shifts, the magnitude tended to be small relative to differences between nonhomologous proteins. Given the limited change in amino acid preferences between these close homologs, we tested whether our measurements could inform site-specific substitution models that describe the evolution of nucleoproteins from more diverse influenza viruses. We found that site-specific evolutionary models informed by our experiments greatly outperformed nonsite-specific alternatives in fitting phylogenies of nucleoproteins from human, swine, equine, and avian influenza. Combining the experimental data from both homologs improved phylogenetic fit, partly because measurements in multiple genetic contexts better captured the evolutionary average of the amino acid preferences for sites with shifting preferences. Our results show that site-specific amino acid preferences are sufficiently conserved that measuring mutational effects in one protein provides information that can improve quantitative evolutionary modeling of nearby homologs.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Maximum-Likelihood Phylogenetic Inference with Selection on Protein Folding Stability

Despite intense work, incorporating constraints on protein native structures into the mathematical models of molecular evolution remains difficult, because most models and programs assume that protein sites evolve independently, whereas protein stability is maintained by interactions between sites. Here, we address this problem by developing a new mean-field substitution model that generates independent site-specific amino acid distributions with constraints on the stability of the native state against both unfolding and misfolding. The model depends on a background distribution of amino acids and one selection parameter that we fix maximizing the likelihood of the observed protein sequence. The analytic solution of the model shows that the main determinant of the site-specific distributions is the number of native contacts of the site and that the most variable sites are those with an intermediate number of native contacts. The mean-field models obtained, taking into account misfolded conformations, yield larger likelihood than models that only consider the native state, because their average hydrophobicity is more realistic, and they produce on the average stable sequences for most proteins. We evaluated the mean-field model with respect to empirical substitution models on 12 test data sets of different protein families. In all cases, the observed site-specific sequence profiles presented smaller Kullback-Leibler divergence from the mean-field distributions than from the empirical substitution model. Next, we obtained substitution rates combining the mean-field frequencies with an empirical substitution model. The resulting mean-field substitution model assigns larger likelihood than the empirical model to all studied families when we consider sequences with identity larger than 0.35, plausibly a condition that enforces conservation of the native structure across the family. We found that the mean-field model performs better than other structurally constrained models with similar or higher complexity. With respect to the much more complex model recently developed by Bordner and Mittelmann, which takes into account pairwise terms in the amino acid distributions and also optimizes the exchangeability matrix, our model performed worse for data with small sequence divergence but better for data with larger sequence divergence. The mean-field model has been implemented into the computer program Prot_Evol that is freely available at http://ub.cbm.uam.es/software/Prot_Evol.php.

Predicting evolutionary site variability from structure in viral proteins: buriedness, packing, flexibility, and design

Several recent works have shown that protein structure can predict site-specific evolutionary sequence variation. In particular, sites that are buried and/or have many contacts with other sites in a structure have been shown to evolve more slowly, on average, than surface sites with few contacts. Here, we present a comprehensive study of the extent to which numerous structural properties can predict sequence variation. The quantities we considered include buriedness (as measured by relative solvent accessibility), packing density (as measured by contact number), structural flexibility (as measured by B factors, root-mean-square fluctuations, and variation in dihedral angles), and variability in designed structures. We obtained structural flexibility measures both from molecular dynamics simulations performed on nine non-homologous viral protein structures and from variation in homologous variants of those proteins, where they were available. We obtained measures of variability in designed structures from flexible-backbone design in the Rosetta software. We found that most of the structural properties correlate with site variation in the majority of structures, though the correlations are generally weak (correlation coefficients of 0.1-0.4). Moreover, we found that buriedness and packing density were better predictors of evolutionary variation than structural flexibility. Finally, variability in designed structures was a weaker predictor of evolutionary variability than buriedness or packing density, but it was comparable in its predictive power to the best structural flexibility measures. We conclude that simple measures of buriedness and packing density are better predictors of evolutionary variation than the more complicated predictors obtained from dynamic simulations, ensembles of homologous structures, or computational protein design.