Protein evolution along phylogenetic histories under structurally constrained substitution models

Abstract

Motivation: Models of molecular evolution aim at describing the evolutionary processes at the molecular level. However, current models rarely incorporate information from protein structure. Conversely, structure-based models of protein evolution have not been commonly applied to simulate sequence evolution in a phylogenetic framework, and they often ignore relevant evolutionary processes such as recombination. A simulation evolutionary framework that integrates substitution models that account for protein structure stability should be able to generate more realistic in silico evolved proteins for a variety of purposes.

Results: We developed a method to simulate protein evolution that combines models of protein folding stability, such that the fitness depends on the stability of the native state both with respect to unfolding and misfolding, with phylogenetic histories that can be either specified by the user or simulated with the coalescent under complex evolutionary scenarios, including recombination, demographics and migration. We have implemented this framework in a computer program called ProteinEvolver. Remarkably, comparing these models with empirical amino acid replacement models, we found that the former produce amino acid distributions closer to distributions observed in real protein families, and proteins that are predicted to be more stable. Therefore, we conclude that evolutionary models that consider protein stability and realistic evolutionary histories constitute a better approximation of the real evolutionary process.

Figure 1

An example of protein evolution along the ARG. White and grey circles correspond to coalescence and recombination parental nodes, respectively. (1) Starting from the GMRCA, the protein is evolved along branches according to the SCS substitution model and the branch lengths. (3) The process encounters a recombinant node and because its parental node has not been assigned to a protein yet, the evolutionary process continues towards other direction (4). (5) Later, the process encounters the parental recombinant node, and because the other parental has already been assigned to a protein, (6) it combines the two proteins according to the recombination breakpoint.

Figure 2

Improvement of the Kullback-Leibler distance to the real protein alignments of the simulated alignments by the neutral and fitness SCS models with respect to the empirical amino acid substitution model. The “y” axis indicates decline of the distance of the neutral and fitness (best and worst conditions) SCS models respect to the distance of the empirical model. Note that the neutral SCS model was overall more robust than the fitness SCS model under different thermodynamic conditions (see Figures S1A and S1B). On the other hand, the fitness SCS model under the best conditions (see Figures S2A, S2B and S3, left plot) could improve the neutral model in half of protein families, however the worst conditions may lead to results without any improvement respect to the empirical model.

Figure 3

DOPE energy computed in the simulated proteins under the empirical and the neutral SCS substitution models and in the native protein, for the protein family “Phototactive yellow proteins”. Note that the DOPE energy is unnormalized with respect to the protein size and therefore scores from different proteins cannot be compared directly.