Protein topology and stability define the space of allowed sequences

An integrated view of protein evolution

Why do proteins evolve at different rates? Advances in systems biology and genomics have facilitated a move from studying individual proteins to characterizing global cellular factors. Systematic surveys indicate that protein evolution is not determined exclusively by selection on protein structure and function, but is also affected by the genomic position of the encoding genes, their expression patterns, their position in biological networks and possibly their robustness to mistranslation. Recent work has allowed insights into the relative importance of these factors. We discuss the status of a much-needed coherent view that integrates studies on protein evolution with biochemistry and functional and structural genomics.

Evaluation of models for the evolution of protein sequences and functions under structural constraint

In the field of evolutionary structural genomics, methods are needed to evaluate why genomes evolved to contain the fold distributions that are observed. In order to study the effects of population dynamics in the evolved genomes we need fast and accurate evolutionary models which can analyze the effects of selection, drift and fixation of a protein sequence in a population that are grounded by physical parameters governing the folding and binding properties of the sequence. In this study, various knowledge-based, force field, and statistical methods for protein folding have been evaluated with four different folds: SH2 domains, SH3 domains, Globin-like, and Flavodoxin-like, to evaluate the speed and accuracy of the energy functions. Similarly, knowledge-based and force field methods have been used to predict ligand binding specificity in SH2 domain. To demonstrate the applicability of these methods, the dynamics of evolution of new binding capabilities by an SH2 domain is demonstrated.

Structural determinants of the rate of protein evolution in yeast

We investigate how a protein's structure influences the rate at which its sequence evolves. Our basic hypothesis is that proteins with highly designable structures (structures that are encoded by many sequences) will evolve more rapidly. Recent theoretical advances argue that structures with a higher density of interresidue contacts are more designable, and we show that high contact density is correlated with an increased rate of sequence evolution in yeast. In addition, we investigate the correlations between the rate of sequence evolution and several other structural descriptors, carefully controlling for the strong effect of expression level on evolutionary rate. Overall, we find that the structural descriptors that we consider appear to explain roughly 10% of the variation in rates of protein evolution in yeast. We also show that despite the well-known trend for buried residues to be more conserved, proteins with a higher fraction of buried residues, nonetheless, tend to evolve their sequences more rapidly. We suggest that this effect is due to the increased designability of structures with more buried residues. Our results provide evidence that protein structure plays an important role in shaping the rate of sequence evolution and provide evidence to support recent theoretical advances linking structural designability to contact density.

Sequence optimization and designability of enzyme active sites

We recently found that many residues in enzyme active sites can be computationally predicted by the optimization of scoring functions based on substrate binding affinity, subject to constraints on the geometry of catalytic residues and protein stability. Here, we explore the generality of this surprising observation. First, the impact of hydrogen-bonding networks necessary for catalysis on the accuracy of sequence optimization is assessed; incorporation of these networks, where relevant, into the set of catalytic constraints is found to be essential. Next, the impact of multiple substrate selectivity on sequence optimization is probed by carrying out independent calculations for complexes of deoxyribonucleoside kinases with various cognate ligands, revealing how simultaneous selection pressures determined active-site sequences of these enzymes. Including previous calculations on simpler enzymes, computational sequence optimization correctly predicts 76% of all active-site residues tested (86% correct, with 93% similar, for naturally conserved residues). In these studies, the ligand is fixed in its native conformation. To assess the applicability of these methods to de novo active-site design, the effect of small ligand motions around the native pose is also examined. Robustness of sequence accuracy for topologically similar poses is demonstrated for selected kinases, but not for a model peptidase. Based on these observations, we introduce the notion of the designability of an enzyme active site, a metric that may be used to guide the search for protein scaffolds suitable for the introduction of de novo activity for a desired chemical reaction.

Computational prediction of native protein ligand-binding and enzyme active site sequences

Recent studies reveal that the core sequences of many proteins were nearly optimized for stability by natural evolution. Surface residues, by contrast, are not so optimized, presumably because protein function is mediated through surface interactions with other molecules. Here, we sought to determine the extent to which the sequences of protein ligand-binding and enzyme active sites could be predicted by optimization of scoring functions based on protein ligand-binding affinity rather than structural stability. Optimization of binding affinity under constraints on the folding free energy correctly predicted 83% of amino acid residues (94% similar) in the binding sites of two model receptor-ligand complexes, streptavidin-biotin and glucose-binding protein. To explore the applicability of this methodology to enzymes, we applied an identical algorithm to the active sites of diverse enzymes from the peptidase, beta-gal, and nucleotide synthase families. Although simple optimization of binding affinity reproduced the sequences of some enzyme active sites with high precision, imposition of additional, geometric constraints on side-chain conformations based on the catalytic mechanism was required in other cases. With these modifications, our sequence optimization algorithm correctly predicted 78% of residues from all of the enzymes, with 83% similar to native (90% correct, with 95% similar, excluding residues with high variability in multiple sequence alignments). Furthermore, the conformations of the selected side chains were often correctly predicted within crystallographic error. These findings suggest that simple selection pressures may have played a predominant role in determining the sequences of ligand-binding and active sites in proteins.

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.

Protein sequence entropy is closely related to packing density and hydrophobicity

We investigated the correlation between the Shannon information entropy, 'sequence entropy', with respect to the local flexibility of native globular proteins as described by inverse packing density. These are determined at each residue position for a total set of 130 query proteins, where sequence entropies are calculated from each set of aligned residues. For the accompanying aggregate set of 130 alignments, a strong linear correlation is observed between the calculated sequence entropy and the corresponding inverse packing density determined at an associated residue position. This region of linearity spans the range of C(alpha) packing densities from 12 to 25 amino acids within a sphere of 9 angstrom radius. Three different hydrophobicity scales all mimic the behavior of the sequence entropies. This confirms the idea that the ability to accommodate mutations is strongly dependent on the available space and on the propensity for each amino acid type to be buried. Future applications of these types of methods may prove useful in identifying both core and flexible residues within a protein.

Protein structure and evolutionary history determine sequence space topology

Understanding the observed variability in the number of homologs of a gene is a very important unsolved problem that has broad implications for research into coevolution of structure and function, gene duplication, pseudogene formation, and possibly for emerging diseases. Here, we attempt to define and elucidate some possible causes behind the observed irregularity in sequence space. We present evidence that sequence variability and functional diversity of a gene or fold family is influenced by quantifiable characteristics of the protein structure. These characteristics reflect the structural potential for sequence plasticity, i.e., the ability to accept mutation without losing thermodynamic stability. We identify a structural feature of a protein domain-contact density-that serves as a determinant of entropy in sequence space, i.e., the ability of a protein to accept mutations without destroying the fold (also known as fold designability). We show that (log) of average gene family size exhibits statistical correlation (R(2) > 0.9.) with contact density of its three-dimensional structure. We present evidence that the size of individual gene families are influenced not only by the designability of the structure, but also by evolutionary history, e.g., the amount of time the gene family was in existence. We further show that our observed statistical correlation between gene family size and contact density of the structure is valid on many levels of evolutionary divergence, i.e., not only for closely related sequence, but also for less-related fold and superfamily levels of homology.

Symmetry and frustration in protein energy landscapes: a near degeneracy resolves the Rop dimer-folding mystery

Protein folding has become one of the best understood biochemical reactions from a kinetic viewpoint. The funneled energy landscape, a consequence of the minimal frustration achieved by evolution in sequences, explains how most proteins fold efficiently and robustly to their functional structure and allows robust prediction of folding kinetics. The folding of Rop (repressor of primer) dimer is exceptional because some of its mutants with a redesigned hydrophobic core both fold and unfold much faster than the WT protein, which seems to conflict with a simple funneled energy landscape for which topology mainly determines the kinetics. We propose that the mystery of Rop folding can be unraveled by assuming a double-funneled energy landscape on which there are two basins that correspond to distinct but related topological structures. Because of the near symmetry of the molecule, mutations can cause a conformational switch to a nearly degenerate yet distinct topology or lead to a mixture of both topologies. The topology predicted to have the lower free-energy barrier height for folding was further found by all-atom modeling to give a better structural fit for those mutants with the extreme folding and unfolding rates. Thus, the non-Hammond effects can be understood within energy-landscape theory if there are in fact two different but nearly degenerate structures for Rop. Mutations in symmetric and regular structures may give rise to frustration and thus result in degeneracy.

Comparing folding codes in simple heteropolymer models of protein evolutionary landscape: robustness of the superfunnel paradigm

Understanding the evolution of biopolymers is a key element in rationalizing their structures and functions. Simple exact models (SEMs) are well-positioned to address general principles of evolution as they permit the exhaustive enumeration of both sequence and structure (conformational) spaces. The physics-based models of the complete mapping between genotypes and phenotypes afforded by SEMs have proven valuable for gaining insight into how adaptation and selection operate among large collections of sequences and structures. This study compares the properties of evolutionary landscapes of a variety of SEMs to delineate robust predictions and possible model-specific artifacts. Among the models studied, the ruggedness of evolutionary landscape is significantly model-dependent; those derived from more protein-like models appear to be smoother. We found that a common practice of restricting protein structure space to maximally compact lattice conformations results in (i.e., "designs in") many encodable (designable) structures that are not otherwise encodable in the corresponding unrestrained structure space. This discrepancy is especially severe for model potentials that seek to mimic the major role of hydrophobic interactions in protein folding. In general, restricting conformations to be maximally compact leads to larger changes in the model genotype-phenotype mapping than a moderate shifting of reference state energy of the model potential function to allow for more specific encoding via the "designing out" effects of repulsive interactions. Despite these variations, the superfunnel paradigm applies to all SEMs we have tested: For a majority of neutral nets across different models, there exists a funnel-like organization of native stabilities for the sequences in a neutral net encoding for the same structure, and the thermodynamically most stable sequence is also the most robust against mutation.

Protein family comparison using statistical models and predicted structural information

Background

This paper presents a simple method to increase the sensitivity of protein family comparisons by incorporating secondary structure (SS) information. We build upon the effective information theory approach towards profile-profile comparison described in [Yona & Levitt 2002]. Our method augments profile columns using PSIPRED secondary structure predictions and assesses statistical similarity using information theoretical principles.

Results

Our tests show that this tool detects more similarities between protein families of distant homology than the previous primary sequence-based method. A very significant improvement in performance is observed when the real secondary structure is used.

Conclusions

Integration of primary and secondary structure information can substantially improve detection of relationships between remotely related protein families.

Computational analysis of sequence selection mechanisms

Mechanisms leading to gene variations are responsible for the diversity of species and are important components of the theory of evolution. One constraint on gene evolution is that of protein foldability; the three-dimensional shapes of proteins must be thermodynamically stable. We explore the impact of this constraint and calculate properties of foldable sequences using 3660 structures from the Protein Data Bank. We seek a selection function that receives sequences as input, and outputs survival probability based on sequence fitness to structure. We compute the number of sequences that match a particular protein structure with energy lower than the native sequence, the density of the number of sequences, the entropy, and the "selection" temperature. The mechanism of structure selection for sequences longer than 200 amino acids is approximately universal. For shorter sequences, it is not. We speculate on concrete evolutionary mechanisms that show this behavior.

Prediction of site-specific amino acid distributions and limits of divergent evolutionary changes in protein sequences

We derive an analytic expression for site-specific stationary distributions of amino acids from the structurally constrained neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e., the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, as a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.

Stability and the evolvability of function in a model protein

Functional proteins must fold with some minimal stability to a structure that can perform a biochemical task. Here we use a simple model to investigate the relationship between the stability requirement and the capacity of a protein to evolve the function of binding to a ligand. Although our model contains no built-in tradeoff between stability and function, proteins evolved function more efficiently when the stability requirement was relaxed. Proteins with both high stability and high function evolved more efficiently when the stability requirement was gradually increased than when there was constant selection for high stability. These results show that in our model, the evolution of function is enhanced by allowing proteins to explore sequences corresponding to marginally stable structures, and that it is easier to improve stability while maintaining high function than to improve function while maintaining high stability. Our model also demonstrates that even in the absence of a fundamental biophysical tradeoff between stability and function, the speed with which function can evolve is limited by the stability requirement imposed on the protein.

Using protein design for homology detection and active site searches

We describe a method of designing artificial sequences that resemble naturally occurring sequences in terms of their compatibility with a template structure and its functional constraints. The design procedure is a Monte Carlo simulation of amino acid substitution process. The selective fixation of substitutions is dictated by a simple scoring function derived from the template structure and a multiple alignment of its homologs. Designed sequences represent an enlargement of sequence space around native sequences. We show that the use of designed sequences improves the performance of profile-based homology detection. The difference in position-specific conservation between designed sequences and native sequences is helpful for prediction of functionally important residues. Our sequence selection criteria in evolutionary simulations introduce amino acid substitution rate variation among sites in a natural way, providing a better model to test phylogenetic methods.

Energy landscape and dynamics of the beta-hairpin G peptide and its isomers: Topology and sequences

We have investigated free energy landscape [MM/PBSA + normal modes entropy] of permutations in the G peptide (41-56) from the protein G B1 domain by studying six isomers corresponding to moving the hydrophobic cluster along the beta-strands (toward the turn: T1, AGEWTYDDKTFTVTET; T2, GEDTWDYATFTVTKTE; T3, GEDDWTYATFTVTKTE; toward the end: E1, WTYDDAGETKTFTVT; E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV). The free energy terms include molecular mechanics energy, Poisson-Boltzmann electrostatic solvation energy, surface area solvation energy, and conformational entropy estimated by using normal mode analysis. From the wild type to T1, then T3, and finally T2, we see a progressively changing energy landscape, toward a less stable beta-hairpin structure. Moving the hydrophobic cluster outside toward the end region causes a greater change in the energy landscape. alpha-Helical instead of a beta-hairpin structure was the most stable form for the E2 isomer. However, no matter how much the sequence changes, for all variants studied, ideal "native" beta-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. In general, we find that the energy landscape is dependent on the hydrophobic cluster topology and on the sequence. Our present study indicates that the key is the relative conformational energies of the different conformations. Changes in the sequence strongly modulate the relative stabilities of topologically similar regions in the energy landscape, rather than redefine the topology space. This finding is consistent with a population redistribution in the process of protein folding. The limited variation of topological space, compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance.

Natural selection of more designable folds: a mechanism for thermophilic adaptation

An open question of great interest in biophysics is whether variations in structure cause protein folds to differ in the number of amino acid sequences that can fold to them stably, i.e., in their designability. Recently, we have shown that a novel quantitative measure of a fold's tertiary topology, called its contact trace, strongly correlates with the fold's designability. Here, we investigate the relationship between a fold's contact trace and its relative frequency of usage in mesophilic vs. thermophilic eubacteria. We observe that thermophilic organisms exhibit a bias toward using folds of higher contact trace when compared with mesophiles. We establish this difference both for the distributions of folds at the whole-proteome level and also through more focused structural comparisons of orthologous proteins. Our findings suggest that thermophilic adaptation in bacterial genomes occurs in part through natural selection of more designable folds, pointing to designability as a key component of protein fitness.

Structural determinant of protein designability

Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with the most low-energy sequences are the same as those predicted by the theory. We argue that, given sufficiently strict requirements for foldability, these structures are the most designable, and we propose a simple means to test whether the results in this paper hold true for real proteins.

Evolutionary aspects of protein structure and folding

The traditional reconstruction of molecular events of the past based on sequence conservation becomes very vague beyond one to two billion years ago. There are certain molecular features, however, such as polymer flexibility and loop closure, that are conserved merely because of their physical nature. This allows one to penetrate the earliest stages of protein evolution.

Thoroughly sampling sequence space: large-scale protein design of structural ensembles

Modeling the inherent flexibility of the protein backbone as part of computational protein design is necessary to capture the behavior of real proteins and is a prerequisite for the accurate exploration of protein sequence space. We present the results of a broad exploration of sequence space, with backbone flexibility, through a novel approach: large-scale protein design to structural ensembles. A distributed computing architecture has allowed us to generate hundreds of thousands of diverse sequences for a set of 253 naturally occurring proteins, allowing exciting insights into the nature of protein sequence space. Designing to a structural ensemble produces a much greater diversity of sequences than previous studies have reported, and homology searches using profiles derived from the designed sequences against the Protein Data Bank show that the relevance and quality of the sequences is not diminished. The designed sequences have greater overall diversity than corresponding natural sequence alignments, and no direct correlations are seen between the diversity of natural sequence alignments and the diversity of the corresponding designed sequences. For structures in the same fold, the sequence entropies of the designed sequences cluster together tightly. This tight clustering of sequence entropies within a fold and the separation of sequence entropy distributions for different folds suggest that the diversity of designed sequences is primarily determined by a structure's overall fold, and that the designability principle postulated from studies of simple models holds in real proteins. This has important implications for experimental protein design and engineering, as well as providing insight into protein evolution.

Sequence variations within protein families are linearly related to structural variations

It is commonly believed that similarities between the sequences of two proteins infer similarities between their structures. Sequence alignments reliably recognize pairs of protein of similar structures provided that the percentage sequence identity between their two sequences is sufficiently high. This distinction, however, is statistically less reliable when the percentage sequence identity is lower than 30% and little is known then about the detailed relationship between the two measures of similarity. Here, we investigate the inverse correlation between structural similarity and sequence similarity on 12 protein structure families. We define the structure similarity between two proteins as the cRMS distance between their structures. The sequence similarity for a pair of proteins is measured as the mean distance between the sequences in the subsets of sequence space compatible with their structures. We obtain an approximation of the sequence space compatible with a protein by designing a collection of protein sequences both stable and specific to the structure of that protein. Using these measures of sequence and structure similarities, we find that structural changes within a protein family are linearly related to changes in sequence similarity.

Folding free energy function selects native-like protein sequences in the core but not on the surface

An automatic protein design procedure is used to select amino acid sequences that optimize the folding free energy function for a given protein. The only information used in designing the sequences is a set of known backbone structures for each protein, a rotamer library, and a well established classical empirical force field, which relies on basic physical chemical principles that underlie molecular interactions and protein stability, and has not been adjusted to yield native-like sequences. Applying the procedure to 7 different known protein folds, representing a total of 45 different native protein structures, yields ensembles of designed sequences displaying remarkable similarity to their natural counterparts in the protein core, but which are distinctly non-native on the protein surface. We show that natural and designed sequences for a given fold score significantly higher than random sequences against profiles derived from both, designed and natural sequence ensembles. Furthermore, we find that designed sequence profiles can be used to retrieve the native sequences for many of the analyzed proteins using standard PSI-BLAST searches in sequence databases. These findings may have important implications for our understanding the selection pressures operating on natural protein sequences and hold promise for improving fold recognition.

Knowledge-based potential functions in protein design

Predicting protein sequences that fold into specific native three-dimensional structures is a problem of great potential complexity. Although the complete solution is ultimately rooted in understanding the physical chemistry underlying the complex interactions between amino acid residues that determine protein stability, recent work shows that empirical information about these first principles is embedded in the statistics of protein sequence and structure databases. This review focuses on the use of 'knowledge-based' potentials derived from these databases in designing proteins. In addition, the data suggest how the study of these empirical potentials might impact our fundamental understanding of the energetic principles of protein structure.