Measurements of protein sequence-structure correlations

Correlations between protein structures and amino acid sequences are widely used for protein structure prediction. For example, secondary structure predictors generally use correlations between a secondary structure sequence and corresponding primary structure sequence, whereas threading algorithms and similar tertiary structure predictors typically incorporate interresidue contact potentials. To investigate the relative importance of these sequence-structure interactions, we measured the mutual information among the primary structure, secondary structure and side-chain surface exposure, both for adjacent residues along the amino acid sequence and for tertiary structure contacts between residues distantly separated along the backbone. We found that local interactions along the amino acid chain are far more important than non-local contacts and that correlations between proximate amino acids are essentially uninformative. This suggests that knowledge-based contact potentials may be less important for structure predication than is generally believed.     

A fast, stochastic threading algorithm for proteins

MOTIVATION: Sequences for new proteins are being determined at a rapid rate, as a result of the Human Genome Project, and related genome research. The ability to predict the three-dimensional structure of proteins from sequence alone would be useful in discovering and understanding their function. Threading, or fold recognition, aims to predict the tertiary structure of a protein by aligning its amino acid sequence with a large number of structures, and finding the best fit. This approach depends on obtaining good performance from both the scoring function, which simulates the free energy for given trial alignments, and the threading algorithm, which searches for the lowest-score alignment. It appears that current scoring functions and threading algorithms need improvement. RESULTS: This paper presents a new threading algorithm. Numerical tests demonstrate that it is more powerful than two popular approximate algorithms, and much faster than exact methods.     

Statistical significance of hierarchical multi-body potentials based on Delaunay tessellation and their application in sequence-structure alignment.

Statistical potentials based on pairwise interactions between C alpha atoms are commonly used in protein threading/fold-recognition attempts. Inclusion of higher order interaction is a possible means of improving the specificity of these potentials. Delaunay tessellation of the C alpha-atom representation of protein structure has been suggested as a means of defining multi-body interactions. A large number of parameters are required to define all four-body interactions of 20 amino acid types (20(4) = 160,000). Assuming that residue order within a four-body contact is irrelevant reduces this to a manageable 8,855 parameters, using a nonredundant dataset of 608 protein structures. Three lines of evidence support the significance and utility of the four-body potential for sequence-structure matching. First, compared to the four-body model, all lower-order interaction models (three-body, two-body, one-body) are found statistically inadequate to explain the frequency distribution of residue contacts. Second, coherent patterns of interaction are seen in a graphic presentation of the four-body potential. Many patterns have plausible biophysical explanations and are consistent across sets of residues sharing certain properties (e.g., size, hydrophobicity, or charge). Third, the utility of the multi-body potential is tested on a test set of 12 same-length pairs of proteins of known structure for two protocols: Sequence-recognizes-structure, where a query sequence is threaded (without gap) through the native and a non-native structure; and structure-recognizes-sequence, where a query structure is threaded by its native and another non-native sequence. Using cross-validated training, protein sequences correctly recognized their native structure in all 24 cases. Conversely, structures recognized the native sequence in 23 of 24 cases. Further, the score differences between correct and decoy structures increased significantly using the three- or four-body potential compared to potentials of lower order.     

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.     

Homology modelling of protein-protein complexes: a simple method and its possibilities and limitations

Background  

Structure-based computational methods are needed to help identify and characterize protein-protein complexes and their function. For individual proteins, the most successful technique is homology modelling. We investigate a simple extension of this technique to protein-protein complexes. We consider a large set of complexes of known structures, involving pairs of single-domain proteins. The complexes are compared with each other to establish their sequence and structural similarities and the relation between the two. Compared to earlier studies, a simpler dataset, a simpler structural alignment procedure, and an additional energy criterion are used. Next, we compare the Xray structures to models obtained by threading the native sequence onto other, homologous complexes. An elementary requirement for a successful energy function is to rank the native structure above any threaded structure. We use the DFIRE _β energy function, whose quality and complexity are typical of the models used today. Finally, we compare near-native models to distinctly non-native models.     

Protein structure prediction by threading methods: Evaluation of current techniques

This paper evaluates the results of a protein structure prediction contest. The predictions were made using threading procedures, which employ techniques for aligning sequences with 3D structures to select the correct fold of a given sequence from a set of alternatives. Nine different teams submitted 86 predictions, on a total of 21 target proteins with little or no sequence homology to proteins of known structure. The 3D structures of these proteins were newly determined by experimental methods, but not yet published or otherwise available to the predictors. The predictions, made from the amino acid sequence alone, thus represent a genuine test of the current performance of threading methods. Only a subset of all the predictions is evaluated here. It corresponds to the 44 predictions submitted for the 11 target proteins seen to adopt known folds. The predictions for the remaining 10 proteins were not analyzed, although weak similarities with known folds may also exist in these proteins. We find that threading methods are capable of identifying the correct fold in many cases, but not reliably enough as yet. Every team predicts correctly a different set of targets, with virtually all targets predicted correctly by at least one team. Also, common folds such as TIM barrels are recognized more readily than folds with only a few known examples. However, quite surprisingly, the quality of the sequence-structure alignments, corresponding to correctly recognized folds, is generally very poor, as judged by comparison with the corresponding 3D structure alignments. Thus, threading can presently not be relied upon to derive a detailed 3D model from the amino acid sequence. This raises a very intriguing question: how is fold recognition achieved? Our analysis suggests that it may be achieved because threading procedures maximize hydrophobic interactions in the protein core, and are reasonably good at recognizing local secondary structure. © 1995 Wiley-Liss, Inc.     

Identifying sequence-structure pairs undetected by sequence alignments

We examine how effectively simple potential functions previously developed can identify compatibilities between sequences and structures of proteins for database searches. The potential function consists of pairwise contact energies, repulsive packing potentials of residues for overly dense arrangement and short-range potentials for secondary structures, all of which were estimated from statistical preferences observed in known protein structures. Each potential energy term was modified to represent compatibilities between sequences and structures for globular proteins. Pairwise contact interactions in a sequence-structure alignment are evaluated in a mean field approximation on the basis of probabilities of site pairs to be aligned. Gap penalties are assumed to be proportional to the number of contacts at each residue position, and as a result gaps will be more frequently placed on protein surfaces than in cores. In addition to minimum energy alignments, we use probability alignments made by successively aligning site pairs in order by pairwise alignment probabilities. The results show that the present energy function and alignment method can detect well both folds compatible with a given sequence and, inversely, sequences compatible with a given fold, and yield mostly similar alignments for these two types of sequence and structure pairs. Probability alignments consisting of most reliable site pairs only can yield extremely small root mean square deviations, and including less reliable pairs increases the deviations. Also, it is observed that secondary structure potentials are usefully complementary to yield improved alignments with this method. Remarkably, by this method some individual sequence-structure pairs are detected having only 5-20% sequence identity.     

Local structure-based sequence profile database for local and global protein structure predictions

MOTIVATION: A large body of evidence suggests that protein structural information is frequently encoded in local sequences-sequence-structure relationships derived from local structure/sequence analyses could significantly enhance the capacities of protein structure prediction methods. In this paper, the prediction capacity of a database (LSBSP2) that organizes local sequence-structure relationships encoded in local structures with two consecutive secondary structure elements is tested with two computational procedures for protein structure prediction. The goal is twofold: to test the folding hypothesis that local structures are determined by local sequences, and to enhance our capacity in predicting protein structures from their amino acid sequences. RESULTS: The LSBSP2 database contains a large set of sequence profiles derived from exhaustive pair-wise structural alignments for local structures with two consecutive secondary structure elements. One computational procedure makes use of the PSI-BLAST alignment program to predict local structures for testing sequence fragments by matching the testing sequence fragments onto the sequence profiles in the LSBSP2 database. The results show that 54% of the test sequence fragments were predicted with local structures that match closely with their native local structures. The other computational procedure is a filter system that is capable of removing false positives as possible from a set of PSI-BLAST hits. An assessment with a large set of non-redundant protein structures shows that the PSI-BLAST + filter system improves the prediction specificity by up to two-fold over the prediction specificity of the PSI-BLAST program for distantly related protein pairs. Tests with the two computational procedures above demonstrate that local sequence-structure relationships can indeed enhance our capacity in protein structure prediction. The results also indicate that local sequences encoded with strong local structure propensities play an important role in determining the native state folding topology.     

Protein fold recognition without Boltzmann statistics or explicit physical basis.

We present a fast method for finding optimal parameters for a low-resolution (threading) force field intended to distinguish correct from incorrect folds for a given protein sequence. In contrast to other methods, the parameterization uses information from >10(7) misfolded structures as well as a set of native sequence-structure pairs. In addition to testing the resulting force field's performance on the protein sequence threading problem, results are shown that characterize the number of parameters necessary for effective structure recognition.     

HMMSTR: a hidden Markov model for local sequence-structure correlations in proteins

We describe a hidden Markov model, HMMSTR, for general protein sequence based on the I-sites library of sequence-structure motifs. Unlike the linear hidden Markov models used to model individual protein families, HMMSTR has a highly branched topology and captures recurrent local features of protein sequences and structures that transcend protein family boundaries. The model extends the I-sites library by describing the adjacencies of different sequence-structure motifs as observed in the protein database and, by representing overlapping motifs in a much more compact form, achieves a great reduction in parameters. The HMM attributes a considerably higher probability to coding sequence than does an equivalent dipeptide model, predicts secondary structure with an accuracy of 74.3 %, backbone torsion angles better than any previously reported method and the structural context of beta strands and turns with an accuracy that should be useful for tertiary structure prediction.     

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 .     

Prediction of protein tertiary structure using PROFESY, a novel method based on fragment assembly and conformational space annealing

A novel method for ab initio prediction of protein tertiary structures, PROFESY (PROFile Enumerating SYstem), is proposed. This method utilizes the secondary structure prediction information of a query sequence and the fragment assembly procedure based on global optimization. Fifteen-residue-long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full-length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low-lying local minima of the energy. We apply PROFESY for benchmark tests to proteins with known structures to demonstrate its feasibility. In addition, we participated in CASP5 and applied PROFESY to four new-fold targets for blind prediction. The results are quite promising, despite the fact that PROFESY was in its early stages of development. In particular, PROFESY successfully provided us the best model-one structure for the target T0161.     

A Bayes-optimal sequence-structure theory that unifies protein sequence-structure recognition and alignment

A rigorous Bayesian analysis is presented that unifies protein sequence-structure alignment and recognition. Given a sequence, explicit formulae are derived to select (1) its globally most probable core structure from a structure library; (2) its globally most probable alignment to a given core structure; (3) its most probable joint core structure and alignment chosen globally across the entire library; and (4) its most probable individual segments, secondary structure, and super-secondary structures across the entire library. The computations involved are NP-hard in the general case (3D-3D). Fast exact recursions for the restricted sequence singleton-only (1D-3D) case are given. Conclusions include: (a) the most probable joint core structure and alignment is not necessarily the most probable alignment of the most probable core structure, but rather maximizes the product of core and alignment probabilities; (b) use of a sequence-independent linear or affine gap penalty may result in the highest-probability threading not having the lowest score; (c) selecting the most probable core structure from the library (core structure selection or fold recognition only) involves comparing probabilities summed over all possible alignments of the sequence to the core, and not comparing individual optimal (or near-optimal) sequence-structure alignments; and (d) assuming uninformative priors, core structure selection is equivalent to comparing the ratio of two global means.     

MARNA: multiple alignment and consensus structure prediction of RNAs based on sequence structure comparisons

MOTIVATION: Due to the importance of considering secondary structures in aligning functional RNAs, several pairwise sequence-structure alignment methods have been developed. They use extended alignment scores that evaluate secondary structure information in addition to sequence information. However, two problems for the multiple alignment step remain. First, how to combine pairwise sequence-structure alignments into a multiple alignment and second, how to generate secondary structure information for sequences whose explicit structural information is missing. RESULTS: We describe a novel approach for multiple alignment of RNAs (MARNA) taking into consideration both the primary and the secondary structures. It is based on pairwise sequence-structure comparisons of RNAs. From these sequence-structure alignments, libraries of weighted alignment edges are generated. The weights reflect the sequential and structural conservation. For sequences whose secondary structures are missing, the libraries are generated by sampling low energy conformations. The libraries are then processed by the T-Coffee system, which is a consistency based multiple alignment method. Furthermore, we are able to extract a consensus-sequence and -structure from a multiple alignment. We have successfully tested MARNA on several datasets taken from the Rfam database.     

Tertiary structure predictions on a comprehensive benchmark of medium to large size proteins

We evaluate tertiary structure predictions on medium to large size proteins by TASSER, a new algorithm that assembles protein structures through rearranging the rigid fragments from threading templates guided by a reduced Calpha and side-chain based potential consistent with threading based tertiary restraints. Predictions were generated for 745 proteins 201-300 residues in length that cover the Protein Data Bank (PDB) at the level of 35% sequence identity. With homologous proteins excluded, in 365 cases, the templates identified by our threading program, PROSPECTOR_3, have a root-mean-square deviation (RMSD) to native < 6.5 angstroms, with >70% alignment coverage. After TASSER assembly, in 408 cases the best of the top five full-length models has a RMSD < 6.5 angstroms. Among the 745 targets are 18 membrane proteins, with one-third having a predicted RMSD < 5.5 A. For all representative proteins less than or equal to 300 residues that have corresponding multiple NMR structures in the Protein Data Bank, approximately 20% of the models generated by TASSER are closer to the NMR structure centroid than the farthest individual NMR model. These results suggest that reasonable structure predictions for nonhomologous large size proteins can be automatically generated on a proteomic scale, and the application of this approach to structural as well as functional genomics represent promising applications of TASSER.     

Structure of the adenovirus E4 Orf6 protein predicted by fold recognition and comparative protein modeling

To facilitate investigation of the molecular and biochemical functions of the adenovirus E4 Orf6 protein, we sought to derive three-dimensional structural information using computational methods, particularly threading and comparative protein modeling. The amino acid sequence of the protein was used for secondary structure and hidden Markov model (HMM) analyses, and for fold recognition by the ProCeryon program. Six alternative models were generated from the top-scoring folds identified by threading. These models were examined by 3D-1D analysis and evaluated in the light of available experimental evidence. The final model of the E4 protein derived from these and additional threading calculations was a chimera, with the tertiary structure of its C-terminal 226 residues derived from a TIM barrel template and a mainly alpha-nonbundle topology for its poorly conserved N-terminal 68 residues. To assess the accuracy of this model, additional threading calculations were performed with E4 Orf6 sequences altered as in previous experimental studies. The proposed structural model is consistent with the reported secondary structure of a functionally important C-terminal sequence and can account for the properties of proteins carrying alterations in functionally important sequences or of those that disrupt an unusual zinc-coordination motif.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.     

Computer-assisted re-design of spectrin SH3 residue clusters

We have developed a protein design computer program, called Perla, which performs searches in sequence space to uncover optimal amino acid sequences for desired protein three-dimensional structures. Optimal sequences are localised at the minima of a sequence-structure energy landscape defined using a complex scoring function (an all-atom molecular mechanics force field plus statistical terms including entropy and solvation) measured with respect to a reference state simulating a denatured protein. Sequence choices eventually optimise side chain packing, secondary structure propensities, and hydrogen bonding and electrostatics interactions. Perla was used to re-design clusters of residues of the SH3 domain of alpha-spectrin. Several mutant proteins were produced and characterised. Some of our designed proteins have significantly higher stabilities (stability enhancements about 0.25, 0.70 and 1.0 kcal mol(-1)) than the wild-type protein. These successful protein re-designs, and similar examples found in the literature, establish the quality of the structure-based computational approach to protein design.