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.

Non-catalytic Binding Sites Induce Weaker Long-Range Evolutionary Rate Gradients than Catalytic Sites in Enzymes.

Enzymes exhibit a strong long-range evolutionary constraint that extends from their catalytic site and affects even distant sites, where site-specific evolutionary rate increases monotonically with distance. While protein-protein sites in enzymes were previously shown to induce only a weak conservation gradient, a comprehensive relationship between different types of functional sites in proteins and the magnitude of evolutionary rate gradients they induce has yet to be established. Here, we systematically calculate the evolutionary rate (dN/dS) of sites as a function of distance from different types of binding sites in enzymes and other proteins: catalytic sites, non-catalytic ligand binding sites, allosteric binding sites, and protein-protein interaction sites. We show that catalytic sites indeed induce significantly stronger evolutionary rate gradient than all other types of non-catalytic binding sites. In addition, catalytic sites in enzymes with no known allosteric function still induce strong long-range conservation gradients. Notably, the weak long-range conservation gradients induced by non-catalytic binding sites in enzymes is nearly identical in magnitude to those induced by ligand binding sites in non-enzymes. Finally, we show that structural determinants such as local solvent exposure of sites cannot explain the observed difference between catalytic and non-catalytic functional sites. Our results suggest that enzymes and non-enzymes share similar evolutionary constraints only when examined from the perspective of non-catalytic functional sites. Hence, the unique evolutionary rate gradient from catalytic sites in enzymes is likely driven by the optimization of catalysis rather than ligand binding and allosteric functions.

Using Pseudoenzymes to Probe Evolutionary Design Principles of Enzymes.

Enzymes are governed by unique evolutionary design principles as their catalytic sites were shown to induce long-range evolutionary conservation gradients. We have recently used a comparative bioinformatics approach to disentangle structural determinants from other possible determinants of the evolutionary conservation gradients. The approach is based on comparing the evolutionary patterns of enzymes to those of pseudoenzymes with the same tertiary structure where the catalytic functionality is turned off. This approach provides a way to evaluate several hypotheses regarding the origin of the observed evolutionary conservation gradient in enzymes. The conclusions from such comparative analyses are important for a better understanding of the unique evolutionary design principles of enzymes, which can in turn potentially guide the design of new and improved enzymes.

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 ŠRMSD 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.

The Impact of Native State Switching on Protein Sequence Evolution.

For proteins with a single well-defined native state, protein 3Dstructure is a major determinant of sequence evolution. On the other hand, many proteins adopt multiple, distinct native structures under different conditions ("conformational switches"), yet the impact of such native state switching on protein evolution is not fully understood. Here, we performed a proteome-wide analysis of how protein structure impacts sequence evolution for protein conformational switches in Saccharomyces cerevisiae using pooled analysis of sites with similar packing or burial. We observed a strong linear relationship between residue evolutionary rate and residue burial for conformational switches. In addition, we found that conformational switches evolve significantly and consistently more slowly than proteins with a single native state, even after controlling for degree of residue burial or packing. Next, we focused on proteins that switch conformations upon molecular binding. We found that interfacial residues in these conformational switches evolve more slowly than interfacial residues in proteins with a single native state, and that the bound conformation is a better predictor for residue evolutionary rate than the unbound conformation. Our findings suggest that for conformational switches, the necessity to encode multiple distinct native structures under different conditions imposes strong evolutionary constraints on the entire protein, rather than just a few key residues. Our results provide new insights into the structure-evolution relationship of protein conformational switches.

Challenges within the linear response approximation when studying enzyme catalysis and effects of mutations.

Various aspects of the linear response approximation (LRA) approach were examined when calculating reaction barriers within an enzyme and its different mutants. Scaling the electrostatic interactions is shown to slightly affect the absolute values of the barriers but not the overall trend when comparing wild-type and mutants. Convergence of the overall energetics was shown to depend on the sampling. Finally, the contribution of particular residues was shown to be significant, despite its small value.

Valence bond and enzyme catalysis: a time to break down and a time to build up.

Understanding enzyme catalysis and developing ability to control of it are two great challenges in biochemistry. A few successful examples of computational-based enzyme design have proved the fantastic potential of computational approaches in this field, however, relatively modest rate enhancements have been reported and the further development of complementary methods is still required. Herein we propose a conceptually simple scheme to identify the specific role that each residue plays in catalysis. The scheme is based on a breakdown of the total catalytic effect into contributions of individual protein residues, which are further decomposed into chemically interpretable components by using valence bond theory. The scheme is shown to shed light on the origin of catalysis in wild-type haloalkane dehalogenase (wt-DhlA) and its mutants. Furthermore, the understanding gained through our scheme is shown to have great potential in facilitating the selection of non-optimal sites for catalysis and suggesting effective mutations to enhance the enzymatic rate.

VB/MM protein landscapes: a study of the S(N)2 reaction in haloalkane dehalogenase.

QM/MM methods are widely used for studies of reaction mechanisms in water and protein environments. Recently, we have developed the VB/MM method in which the QM part is implemented by the ab initio valence bond (VB) method. Here, we report on further improvement of the VB/MM method which makes it possible to use the method for reactivity studies in systems where the QM and MM parts are connected by covalent bonds followed by first ab initio VB study of reactivity in proteins. We implemented a simple link atom scheme to treat the boundary interactions. We tested the performance of the link atom treatment in combination with the VB/MM method on an S(N)2 reaction and found it to be sufficiently accurate. We then used the VB/MM method to study the S(N)2 reaction in haloalkane dehalogenase (DhlA). We show that the predicted reaction barrier heights are in good agreement with estimated experimental values, thereby validating the method. Finally, we analyze the reaction energetics in terms of contributions of the VB configurations and conclude that such analysis is instrumental in pinpointing the essential features of the catalytic mechanism.

VB/MM--the validity of the underlying approximations.

Two recently developed methods, VB/MM and density embedded VB/MM (DE-VB/MM), are compared, and their respective approximations are examined. The two methods combine valence-bond (VB) calculations with molecular mechanics (MM) and aim to allow VB analysis of reactions in large biological environments. Furthermore, the two methods utilize two major approximations regarding both the overlap and the reduced resonance integral between the various VB configurations. The difference between the two methods, however, is that VB/MM employs these approximations for the overall interaction of the reacting fragments with their surrounding, whereas DE-VB/MM employs the approximations only with regards to the van der Waals (VdW) interactions whereas the electrostatic interactions are calculated rigorously at the quantum level. The approximations that lay the grounds for the two methods involve the assumption that the overlap between the VB configurations and the respective reduced resonance integral are both invariant to the environment. Similar approximations are utilized in several other VB-based QM/MM methods. However, although extensively used, these approximations were never rigorously proved. Here, we exploit the development of the DE-VB/MM method to numerically examine the approximations by calculating the accurate as well as the approximated values of overlap and reduced resonance integral for systems where the environment involves only electrostatic interactions. The quality of the approximations is examined together with their effect on the absolute energies, the wave function, and the overall energetics. Three test cases are chosen, the dissociation of CH 3F and LiF and the identity S N2 reaction. It is shown that the approximations are usually good with the exception of cases where extreme changes are expected in the wave function. Furthermore, the impact of the approximations on the overall wave function and the overall energetics is found to be quite small. It is concluded that VB/MM, where the approximations are used more extensively, can serve as the first method of choice.

A VB/MM view of the identity S(N)2 valence-bond state correlation diagram in aqueous solution.

The valence-bond state correlation diagram (VBSCD), which was developed by Shaik and co-workers is an excellent tool to understand reactivity patterns in chemical reactions. The strength of the model is in its ability to describe the whole spectrum of reaction types and unify them under a single general paradigm. Moreover, it allows one to understand, conceptualize, and predict chemical reactivity in a general as well as specific manner. As such, VBSCD is a valuable model. The model has been largely tested on various systems in the gas phase both qualitatively and quantitatively. However, its application to reactions in solution was given less attention because of the difficulties to represent solvent reorganization and estimate non-equilibrium solvation effects, which, on the basis of the model, are expected to be fundamental. The recently developed valence-bond molecular mechanics (VB/MM) method overcomes these difficulties because it involves explicit solvent molecules and thus allows quantitative examination of these solvent effects. This work presents a study of the identity S(N)2 reaction X(-) + H(3)CX --> XCH(3) + X(-); (X = F, Cl, Br, I) in aqueous solution. The various parameters that form the VBSCD model are calculated and compared with the corresponding model's estimated values. A relatively good agreement between the calculated and estimated values is found. It is shown that when facing quantitative considerations, the picture may not be as simplistic as in the qualitative study; yet, the fundamental nature of the description is unaffected. This indicates that combined together, the VB/MM approach and the VBSCD model offer a very powerful tool to study reactions in complex systems and understand their reactivity patterns.

Density embedded VB/MM: a hybrid ab initio VB/MM with electrostatic embedding.

A hybrid QM/MM method that combines ab initio valence-bond (VB) with molecular mechanics (MM) is presented. The method utilizes the ab initio VB approach to describe the reactive fragments and MM to describe the environment thus allows VB calculations of reactions in large biological systems. The method, termed density embedded VB/MM (DE-VB/MM), is an extension of the recently developed VB/MM method. It involves calculation of the electrostatic interaction between the reactive fragments and their environment using the electrostatic embedding scheme. Namely, the electrostatic interactions are represented as one-electron integrals in the ab initio VB Hamiltonian, hence taking into account the wave function polarization of the reactive fragments due to the environment. Moreover, the assumptions that were utilized in an earlier version of the method, VB/MM, to formulate the electrostatic interactions effect on the off-diagonal matrix elements are no longer required in the DE-VB/MM methodology. Using DE-VB/MM, one can calculate, in addition to the adiabatic ground state reaction profile, the energy of the diabatic VB configurations as well as the VB state correlation diagram for the reaction. The abilities of the method are exemplified on the identity SN2 reaction of a chloride anion with methyl chloride in aqueous solution. Both the VB configurations diagram and the state correlation diagram are presented. The results are shown to be in very good agreement with both experimental and other computational data, suggesting that DE-VB/MM is a proper method for application to different reactivity problems in biological systems.