Thermodynamic stability is a crucial fitness constraint in protein evolution and is a central factor in shaping the sequence landscapes of proteins. The correlation between stability and molecular fitness depends on the mechanism that relates the biophysical property with biological function. In the simplest case, stability and fitness are related by the amount of folded protein. However, when proteins are toxic in the unfolded state, the fitness function shifts, resulting in higher stability under mutation-selection balance. Likewise, a higher population size results in a similar change in protein stability, as it magnifies the effect of the selection pressure in evolutionary dynamics. This study investigates how such factors affect the evolution of protein stability, site-specific mutation rates, and residue-residue covariation. To simulate evolutionary trajectories with realistic modeling of protein energetics, we develop an all-atom simulator of protein evolution, RosettaEvolve. By evolving proteins under different fitness functions, we can study how the fitness function affects the distribution of proposed and accepted mutations, site-specific rates, and the prevalence of correlated amino acid substitutions. We demonstrate that fitness pressure affects the proposal distribution of mutational effects, that changes in stability can largely explain variations in site-specific substitution rates in evolutionary trajectories, and that increased fitness pressure results in a stronger covariation signal. Our results give mechanistic insight into the evolutionary consequences of variation in protein stability and provide a basis to rationalize the strong covariation signal observed in natural sequence alignments.

MOTIVATION: Most protein-structure superimposition tools consider only Cartesian coordinates. Yet, much of biology happens on the surface of proteins, which is why proteins with shared ancestry and similar function often have comparable surface shapes. Superposition of proteins based on surface shape can enable comparison of highly divergent proteins, identify convergent evolution and enable detailed comparison of surface features and binding sites. RESULTS: We present ZEAL, an interactive tool to superpose global and local protein structures based on their shape resemblance using 3D (Zernike-Canterakis) functions to represent the molecular surface. In a benchmark study of structures with the same fold, we show that ZEAL outperforms two other methods for shape-based superposition. In addition, alignments from ZEAL were of comparable quality to the coordinate-based superpositions provided by TM-align. For comparisons of proteins with limited sequence and backbone-fold similarity, where coordinate-based methods typically fail, ZEAL can often find alignments with substantial surface-shape correspondence. In combination with shape-based matching, ZEAL can be used as a general tool to study relationships between shape and protein function. We identify several categories of protein functions where global shape similarity is significantly more likely than expected by random chance, when comparing proteins with little similarity on the fold level. In particular, we find that global surface shape similarity is particular common among DNA binding proteins. AVAILABILITY AND IMPLEMENTATION: ZEAL can be used online at https://andrelab.org/zeal or as a standalone program with command line or graphical user interface. Source files and installers are available at https://github.com/Andre-lab/ZEAL. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Many proteins consist of folded domains connected by regions with higher flexibility. The details of the resulting conformational ensemble play a central role in controlling interactions between domains and with binding partners. Small-Angle Scattering (SAS) is well-suited to study the conformational states adopted by proteins in solution. However, analysis is complicated by the limited information content in SAS data and care must be taken to avoid constructing overly complex ensemble models and fitting to noise in the experimental data. To address these challenges, we developed a method based on Bayesian statistics that infers conformational ensembles from a structural library generated by all-atom Monte Carlo simulations. The first stage of the method involves a fast model selection based on variational Bayesian inference that maximizes the model evidence of the selected ensemble. This is followed by a complete Bayesian inference of population weights in the selected ensemble. Experiments with simulated ensembles demonstrate that model evidence is capable of identifying the correct ensemble and that correct number of ensemble members can be recovered up to high level of noise. Using experimental data, we demonstrate how the method can be extended to include data from Nuclear Magnetic Resonance (NMR) and structural energies of conformers extracted from the all-atom energy functions. We show that the data from SAXS, NMR chemical shifts and energies calculated from conformers can work synergistically to improve the definition of the conformational ensemble.