Denatured-state energy landscapes of a protein structural database reveal the energetic determinants of a framework model for folding

Position-specific denatured-state thermodynamics were determined for a database of human proteins by use of an ensemble-based model of protein structure. The results of modeling denatured protein in this manner reveal important sequence-dependent thermodynamic properties in the denatured ensembles as well as fundamental differences between the denatured and native ensembles in overall thermodynamic character. The generality and robustness of these results were validated by performing fold-recognition experiments, whereby sequences were matched with their respective folds based on amino acid propensities for the different energetic environments in the protein, as determined through cluster analysis. Correlation analysis between structure and energetic information revealed that sequence segments destined for β-sheet in the final native fold are energetically more predisposed to a broader repertoire of states than are sequence segments destined for α-helix. These results suggest that within the subensemble of mostly unstructured states, the energy landscapes are dominated by states in which parts of helices adopt structure, whereas structure formation for sequences destined for β-strand is far less probable. These results support a framework model of folding, which suggests that, in general, the denatured state has evolutionarily evolved to avoid low-energy conformations in sequences that ultimately adopt β-strand. Instead, the denatured state evolved so that sequence segments that ultimately adopt α-helix and coil will have a high intrinsic structure formation capability, thus serving as potential nucleation sites.     

Accuracy of sequence alignment and fold assessment using reduced amino acid alphabets

Reduced or simplified amino acid alphabets group the 20 naturally occurring amino acids into a smaller number of representative protein residues. To date, several reduced amino acid alphabets have been proposed, which have been derived and optimized by a variety of methods. The resulting reduced amino acid alphabets have been applied to pattern recognition, generation of consensus sequences from multiple alignments, protein folding, and protein structure prediction. In this work, amino acid substitution matrices and statistical potentials were derived based on several reduced amino acid alphabets and their performance assessed in a large benchmark for the tasks of sequence alignment and fold assessment of protein structure models, using as a reference frame the standard alphabet of 20 amino acids. The results showed that a large reduction in the total number of residue types does not necessarily translate into a significant loss of discriminative power for sequence alignment and fold assessment. Therefore, some definitions of a few residue types are able to encode most of the relevant sequence/structure information that is present in the 20 standard amino acids. Based on these results, we suggest that the use of reduced amino acid alphabets may allow to increasing the accuracy of current substitution matrices and statistical potentials for the prediction of protein structure of remote homologs.     

Comparative modeling of the conformational stability of chymotrypsin inhibitor 2 protein mutants using amino acid sequence autocorrelation (AASA) and amino acid 3D autocorrelation (AA3DA) vectors and ensembles of Bayesian-regularized genetic neural networks

Predicting protein stability changes upon point mutation is important for understanding protein structure and designing new proteins. Autocorrelation vector formalism was extended to amino acid sequences and 3D conformations for encoding protein structural information with modeling purpose. Protein autocorrelation vectors were weighted by 48 amino acid/residue properties selected from the AAindex database. Ensembles of Bayesian-regularized genetic neural networks (BRGNNs) trained with amino acid sequence autocorrelation (AASA) vectors and amino acid 3D autocorrelation (AA3DA) vectors yielded predictive models of the change of unfolding Gibbs free energy change (ΔΔG) of chymotrypsin Inhibitor 2 protein mutants. The ensemble predictor described about 58 and 72% of the data variances in test sets for AASA and AA3DA models, respectively. Optimum sequence and 3D-based ensembles exhibit high effects on relevant structural (volume, solvent-accessible surface area), physico-chemical (hydrophilicity/hydrophobicity-related) and thermodynamic (hydration parameters) properties.     

Evaluation of local structure alphabets based on residue burial

Residue burial, which describes a protein residue's exposure to solvent and neighboring atoms, is key to protein structure prediction, modeling, and analysis. We assessed 21 alphabets representing residue burial, according to their predictability from amino acid sequence, conservation in structural alignments, and utility in one fold-recognition scenario. This follows upon our previous work in assessing nine representations of backbone geometry.1 The alphabet found to be most effective overall has seven states and is based on a count of C(beta) atoms within a 14 A-radius sphere centered at the C(beta) of a residue of interest. When incorporated into a hidden Markov model (HMM), this alphabet gave us a 38% performance boost in fold recognition and 23% in alignment quality.     

What is the minimum number of letters required to fold a protein?

Experimental studies have shown that the full sequence complexity of naturally occurring proteins is not required to generate rapidly folding and functional proteins, i.e. proteins can be designed with fewer than 20 letters. This raises the question of what is the minimum number of amino acid types required to encode complex protein folds? Here, we investigate this issue from three aspects. First, we study the minimum sequence complexity that can reserve the necessary structural information for detection of distantly related homologues. Second, we compare the ability of designing foldable model sequences over a wide range of reduced amino acid alphabets, which find the minimum number of letters that have the similar design ability as 20. Finally, we survey the lower bound of alphabet size of globular proteins in a non-redundant protein database. These different approaches give a remarkably consistent view, that the minimum number of letters required to fold a protein is around ten.     

Protein homology detection and fold inference through multiple alignment entropy profiles

Homology detection and protein structure prediction are central themes in bioinformatics. Establishment of relationship between protein sequences or prediction of their structure by sequence comparison methods finds limitations when there is low sequence similarity. Recent works demonstrate that the use of profiles improves homology detection and protein structure prediction. Profiles can be inferred from protein multiple alignments using different approaches. The "Conservatism-of-Conservatism" is an effective profile analysis method to identify structural features between proteins having the same fold but no detectable sequence similarity. The information obtained from protein multiple alignments varies according to the amino acid classification employed to calculate the profile. In this work, we calculated entropy profiles from PSI-BLAST-derived multiple alignments and used different amino acid classifications summarizing almost 500 different attributes. These entropy profiles were converted into pseudocodes which were compared using the FASTA program with an ad-hoc matrix. We tested the performance of our method to identify relationships between proteins with similar fold using a nonredundant subset of sequences having less than 40% of identity. We then compared our results using Coverage Versus Error per query curves, to those obtained by methods like PSI-BLAST, COMPASS and HHSEARCH. Our method, named HIP (Homology Identification with Profiles) presented higher accuracy detecting relationships between proteins with the same fold. The use of different amino acid classifications reflecting a large number of amino acid attributes, improved the recognition of distantly related folds. We propose the use of pseudocodes representing profile information as a fast and powerful tool for homology detection, fold assignment and analysis of evolutionary information enclosed in protein profiles.     

Direct prediction of profiles of sequences compatible with a protein structure by neural networks with fragment‐based local and energy‐based nonlocal profiles

Locating sequences compatible with a protein structural fold is the well‐known inverse protein‐folding problem. While significant progress has been made, the success rate of protein design remains low. As a result, a library of designed sequences or profile of sequences is currently employed for guiding experimental screening or directed evolution. Sequence profiles can be computationally predicted by iterative mutations of a random sequence to produce energy‐optimized sequences, or by combining sequences of structurally similar fragments in a template library. The latter approach is computationally more efficient but yields less accurate profiles than the former because of lacking tertiary structural information. Here we present a method called SPIN that predicts Sequence Profiles by Integrated Neural network based on fragment‐derived sequence profiles and structure‐derived energy profiles. SPIN improves over the fragment‐derived profile by 6.7% (from 23.6 to 30.3%) in sequence identity between predicted and wild‐type sequences. The method also reduces the number of residues in low complex regions by 15.7% and has a significantly better balance of hydrophilic and hydrophobic residues at protein surface. The accuracy of sequence profiles obtained is comparable to those generated from the protein design program RosettaDesign 3.5. This highly efficient method for predicting sequence profiles from structures will be useful as a single‐body scoring term for improving scoring functions used in protein design and fold recognition. It also complements protein design programs in guiding experimental design of the sequence library for screening and directed evolution of designed sequences. The SPIN server is available at http://sparks‐lab.org . Proteins 2014; 82:2565–2573. © 2014 Wiley Periodicals, Inc.     

Evolutionary information hidden in a single protein structure

The knowledge of conserved sequences in proteins is valuable in identifying functionally or structurally important residues. Generating the conservation profile of a sequence requires aligning families of homologous sequences and having knowledge of their evolutionary relationships. Here, we report that the conservation profile at the residue level can be quantitatively derived from a single protein structure with only backbone information. We found that the reciprocal packing density profiles of protein structures closely resemble their sequence conservation profiles. For a set of 554 nonhomologous enzymes, 74% (408/554) of the proteins have a correlation coefficient > 0.5 between these two profiles. Our results indicate that the three-dimensional structure, instead of being a mere scaffold for positioning amino acid residues, exerts such strong evolutionary constraints on the residues of the protein that its profile of sequence conservation essentially reflects that of its structural characteristics.     

Fold recognition by combining sequence profiles derived from evolution and from depth-dependent structural alignment of fragments

Recognizing structural similarity without significant sequence identity has proved to be a challenging task. Sequence-based and structure-based methods as well as their combinations have been developed. Here, we propose a fold-recognition method that incorporates structural information without the need of sequence-to-structure threading. This is accomplished by generating sequence profiles from protein structural fragments. The structure-derived sequence profiles allow a simple integration with evolution-derived sequence profiles and secondary-structural information for an optimized alignment by efficient dynamic programming. The resulting method (called SP(3)) is found to make a statistically significant improvement in both sensitivity of fold recognition and accuracy of alignment over the method based on evolution-derived sequence profiles alone (SP) and the method based on evolution-derived sequence profile and secondary structure profile (SP(2)). SP(3) was tested in SALIGN benchmark for alignment accuracy and Lindahl, PROSPECTOR 3.0, and LiveBench 8.0 benchmarks for remote-homology detection and model accuracy. SP(3) is found to be the most sensitive and accurate single-method server in all benchmarks tested where other methods are available for comparison (although its results are statistically indistinguishable from the next best in some cases and the comparison is subjected to the limitation of time-dependent sequence and/or structural library used by different methods.). In LiveBench 8.0, its accuracy rivals some of the consensus methods such as ShotGun-INBGU, Pmodeller3, Pcons4, and ROBETTA. SP(3) fold-recognition server is available on http://theory.med.buffalo.edu.     

Estimation of amino acid residue substitution rates at local spatial regions and application in protein function inference: a Bayesian Monte Carlo approach

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent-exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.     

Use of residue pairs in protein sequence-sequence and sequence-structure alignments

Two new sets of scoring matrices are introduced: H2 for the protein sequence comparison and T2 for the protein sequence-structure correlation. Each element of H2 or T2 measures the frequency with which a pair of amino acid types in one protein, k-residues apart in the sequence, is aligned with another pair of residues, of given amino acid types (for H2) or in given structural states (for T2), in other structurally homologous proteins. There are four types, corresponding to the k-values of 1 to 4, for both H2 and T2. These matrices were set up using a large number of structurally homologous protein pairs, with little sequence homology between the pair, that were recently generated using the structure comparison program SHEBA. The two scoring matrices were incorporated into the main body of the sequence alignment program SSEARCH in the FASTA package and tested in a fold recognition setting in which a set of 107 test sequences were aligned to each of a panel of 3,539 domains that represent all known protein structures. Six procedures were tested; the straight Smith-Waterman (SW) and FASTA procedures, which used the Blosum62 single residue type substitution matrix; BLAST and PSI-BLAST procedures, which also used the Blosum62 matrix; PASH, which used Blosum62 and H2 matrices; and PASSC, which used Blosum62, H2, and T2 matrices. All procedures gave similar results when the probe and target sequences had greater than 30% sequence identity. However, when the sequence identity was below 30%, a similar structure could be found for more sequences using PASSC than using any other procedure. PASH and PSI-BLAST gave the next best results.     

Use of a structural alphabet to find compatible folds for amino acid sequences

The structural annotation of proteins with no detectable homologs of known 3D structure identified using sequence‐search methods is a major challenge today. We propose an original method that computes the conditional probabilities for the amino‐acid sequence of a protein to fit to known protein 3D structures using a structural alphabet, known as “Protein Blocks” (PBs). PBs constitute a library of 16 local structural prototypes that approximate every part of protein backbone structures. It is used to encode 3D protein structures into 1D PB sequences and to capture sequence to structure relationships. Our method relies on amino acid occurrence matrices, one for each PB, to score global and local threading of query amino acid sequences to protein folds encoded into PB sequences. It does not use any information from residue contacts or sequence‐search methods or explicit incorporation of hydrophobic effect. The performance of the method was assessed with independent test datasets derived from SCOP 1.75A. With a Z‐score cutoff that achieved 95% specificity (i.e., less than 5% false positives), global and local threading showed sensitivity of 64.1% and 34.2%, respectively. We further tested its performance on 57 difficult CASP10 targets that had no known homologs in PDB: 38 compatible templates were identified by our approach and 66% of these hits yielded correctly predicted structures. This method scales‐up well and offers promising perspectives for structural annotations at genomic level. It has been implemented in the form of a web‐server that is freely available at http://www.bo‐protscience.fr/forsa .     

Fold recognition by concurrent use of solvent accessibility and residue depth

Recognizing the structural similarity without significant sequence identity (called fold recognition) is the key for bridging the gap between the number of known protein sequences and the number of structures solved. Previously, we developed a fold-recognition method called SP(3) which combines sequence-derived sequence profiles, secondary-structure profiles and residue-depth dependent, structure-derived sequence profiles. The use of residue-depth-dependent profiles makes SP(3) one of the best automatic predictors in CASP 6. Because residue depth (RD) and solvent accessible surface area (solvent accessibility) are complementary in describing the exposure of a residue to solvent, we test whether or not incorporation of solvent-accessibility profiles into SP(3) could further increase the accuracy of fold recognition. The resulting method, called SP(4), was tested in SALIGN benchmark for alignment accuracy and Lindahl, LiveBench 8 and CASP7 blind prediction for fold recognition sensitivity and model-structure accuracy. For remote homologs, SP(4) is found to consistently improve over SP(3) in the accuracy of sequence alignment and predicted structural models as well as in the sensitivity of fold recognition. Our result suggests that RD and solvent accessibility can be used concurrently for improving the accuracy and sensitivity of fold recognition. The SP(4) server and its local usage package are available on http://sparks.informatics.iupui.edu/SP4.     

Funnel-like organization in sequence space determines the distributions of protein stability and folding rate preferred by evolution

To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.     

An empirical energy potential with a reference state for protein fold and sequence recognition.

We consider modifications of an empirical energy potential for fold and sequence recognition to represent approximately the stabilities of proteins in various environments. A potential used here includes a secondary structure potential representing short-range interactions for secondary structures of proteins, and a tertiary structure potential consisting of a long-range, pairwise contact potential and a repulsive packing potential. This potential is devised to evaluate together the total conformational energy of a protein at the coarse grained residue level. It was previously estimated from the observed frequencies of secondary structures, from contact frequencies between residues, and from the distributions of the number of residues in contact in known protein structures by regarding those distributions as the equilibrium distributions with the Boltzmann factor of these interaction energies. The stability of native structures is assumed as a primary requirement for proteins to fold into their native structures. A collapse energy is subtracted from the contact energies to remove the protein size dependence and to represent protein stabilities for monomeric and multimeric states. The free energy of the whole ensemble of protein conformations that is subtracted from the conformational energy to represent protein stability is approximated as the average energy expected for a typical native structure with the same amino acid composition. This term may be constant in fold recognition but essentially varies in sequence recognition. A simple test of threading sequences into structures without gaps is employed to demonstrate the importance of the present modifications that permit the same potential to be utilized for both fold and sequence recognition. Proteins 1999;36:357-369. Published 1999 Wiley-Liss, Inc.