Evolution of off-lattice model proteins under ligand binding constraints

Quantifying evolutionary importance of protein sites: A Tale of two measures

A key challenge in evolutionary biology is the accurate quantification of selective pressure on proteins and other biological macromolecules at single-site resolution. The evolutionary importance of a protein site under purifying selection is typically measured by the degree of conservation of the protein site itself. A possible alternative measure is the strength of the site-induced conservation gradient in the rest of the protein structure. However, the quantitative relationship between these two measures remains unknown. Here, we show that despite major differences, there is a strong linear relationship between the two measures such that more conserved protein sites also induce stronger conservation gradient in the rest of the protein. This linear relationship is universal as it holds for different types of proteins and functional sites in proteins. Our results show that the strong selective pressure acting on the functional site in general percolates through the rest of the protein via residue-residue contacts. Surprisingly however, catalytic sites in enzymes are the principal exception to this rule. Catalytic sites induce significantly stronger conservation gradients in the rest of the protein than expected from the degree of conservation of the site alone. The unique requirement for the active site to selectively stabilize the transition state of the catalyzed chemical reaction imposes additional selective constraints on the rest of the enzyme.

Sites within proteins which are important for stability or function are under stronger selective pressure and evolve more slowly than other sites. Catalytic sites in enzymes are such highly conserved sites with relatively low evolutionary rates. Recently, catalytic sites were shown to induce a strong gradient of conservation such that the closer a residue is to the catalytic site, the more conserved it is. Here we show that there is a universal linear relationship between the degree of evolutionary conservation of a protein site and the conservation gradient it induces in the protein tertiary structure, applicable to all types of sites. Our findings suggest that selective pressure acting on a protein site generally percolates through the rest of the protein via residue-residue contacts. Remarkably however, catalytic sites induce significantly stronger conservation gradients than expected from their degree of conservation alone. Our results indicate that the strong conservation gradient induced by catalytic sites is driven by the unique function of enzyme catalysis, which requires the participation of many residues beyond the few key catalytic residues. Our results provide insights into evolutionary conservation patterns of and surrounding proteins functional sites, with implications for functional site prediction and protein design.

Nature of Long-Range Evolutionary Constraint in Enzymes: Insights from Comparison to Pseudoenzymes with Similar Structures

Enzymes are known to fine-tune their sequences to optimize catalytic function, yet quantitative evolutionary design principles of enzymes remain elusive on the proteomic scale. Recently, it was found that the catalytic site in enzymes induces long-range evolutionary constraint, where even sites distant to the catalytic site are more conserved than expected. Given that protein-fold usage is generally different between enzymes and nonenzymes, it remains an open question to what extent this long-range evolutionary constraint in enzymes is dictated, either directly or indirectly, by the special three-dimensional structure of the enzyme. To investigate this question, we have compared evolutionary properties of enzymes with those of counterpart pseudoenzymes that share the same protein fold but are catalytically inactive. We found that the long-range evolutionary constraint observed in enzymes is significantly reduced in pseudoenzyme counterparts, despite very high structural similarity (∼1.5 Å RMSD on average). Furthermore, this significant reduction in long-range evolutionary constraint is observed even in pseudoenzyme counterparts which retain the ligand-binding ability of enzymes. Finally, the distance between the site that induces the highest gradient of sequence conservation and the pseudocatalytic site in pseudoenzymes is significantly larger than the corresponding distance in enzymes. Taken together, our results suggest that the long-range evolutionary constraint in enzymes is induced mainly by the presence of the catalytic site rather than by the special three-dimensional structure of the enzyme, and that such long-range evolutionary constraint in enzymes depends mainly on the catalytic function of the active site rather than on the ligand-binding ability of the enzyme.

Inference of epistatic effects in a key mitochondrial protein

We use Potts model inference to predict pair epistatic effects in a key mitochondrial protein-cytochrome c oxidase subunit 2-for ray-finned fishes. We examine the effect of phylogenetic correlations on our predictions using a simple exact fitness model, and we find that, although epistatic effects are underpredicted, they maintain a roughly linear relationship to their true (model) values. After accounting for this correction, epistatic effects in the protein are still relatively weak, leading to fitness valleys of depth 2Ns≃-5 in compensatory double mutants. Interestingly, positive epistasis is more pronounced than negative epistasis, and the strongest positive effects capture nearly all sites subject to positive selection in fishes, similar to virus proteins evolving under selection pressure in the context of drug therapy.

Biophysical Models of Protein Evolution: Understanding the Patterns of Evolutionary Sequence Divergence

For decades, rates of protein evolution have been interpreted in terms of the vague concept of functional importance. Slowly evolving proteins or sites within proteins were assumed to be more functionally important and thus subject to stronger selection pressure. More recently, biophysical models of protein evolution, which combine evolutionary theory with protein biophysics, have completely revolutionized our view of the forces that shape sequence divergence. Slowly evolving proteins have been found to evolve slowly because of selection against toxic misfolding and misinteractions, linking their rate of evolution primarily to their abundance. Similarly, most slowly evolving sites in proteins are not directly involved in function, but mutating these sites has a large impact on protein structure and stability. In this article, we review the studies in the emerging field of biophysical protein evolution that have shaped our current understanding of sequence divergence patterns. We also propose future research directions to develop this nascent field.

Long-Range Epistasis Mediated by Structural Change in a Model of Ligand Binding Proteins

Recent analyses of amino acid mutations in proteins reveal that mutations at many pairs of sites are epistatic-i.e., their effects on fitness are non-additive-the combined effect of two mutations being significantly larger or smaller than the sum of their effects considered independently. Interestingly, epistatic sites are not necessarily near each other in the folded structure of a protein, and may even be located on opposite sides of a molecule. However, the mechanistic reasons for long-range epistasis remain obscure. Here, we study long-range epistasis in proteins using a previously developed model in which off-lattice polymers are evolved under ligand binding constraints. Epistatic effects in the model are qualitatively similar to those recently reported for small proteins, and many are long-range. We find that a major reason for long-range epistasis is conformational change-a recurrent theme in both positive and negative epistasis being the transfer, or exchange of material between the ordered nucleus, which supports the binding site, and the liquid-like surface of a folded molecule. These local transitions in phase and folded structure are largely responsible for long-range epistasis in our model.