A distance-dependent atomic knowledge-based potential for improved protein structure selection.

A heavy atom distance-dependent knowledge-based pairwise potential has been developed. This statistical potential is first evaluated and optimized with the native structure z-scores from gapless threading. The potential is then used to recognize the native and near-native structures from both published decoy test sets, as well as decoys obtained from our group's protein structure prediction program. In the gapless threading test, there is an average z-score improvement of 4 units in the optimized atomic potential over the residue-based quasichemical potential. Examination of the z-scores for individual pairwise distance shells indicates that the specificity for the native protein structure is greatest at pairwise distances of 3.5-6.5 A, i.e., in the first solvation shell. On applying the current atomic potential to test sets obtained from the web, composed of native protein and decoy structures, the current generation of the potential performs better than residue-based potentials as well as the other published atomic potentials in the task of selecting native and near-native structures. This newly developed potential is also applied to structures of varying quality generated by our group's protein structure prediction program. The current atomic potential tends to pick lower RMSD structures than do residue-based contact potentials. In particular, this atomic pairwise interaction potential has better selectivity especially for near-native structures. As such, it can be used to select near-native folds generated by structure prediction algorithms as well as for protein structure refinement.     

Averaging interaction energies over homologs improves protein fold recognition in gapless threading.

Protein structure prediction is limited by the inaccuracy of the simplified energy functions necessary for efficient sorting over many conformations. It was recently suggested (Finkelstein, Phys Rev Lett 1998;80:4823-4825) that these errors can be reduced by energy averaging over a set of homologous sequences. This conclusion is confirmed in this study by testing protein structure recognition in gapless threading. The accuracy of recognition was estimated by the Z-score values obtained in gapless threading tests. For threading, we used 20 target proteins, each having from 20 to 70 homologs taken from the HSSP sequence base. The energy of the native structures was compared with the energy from 34 to 75 thousand of alternative structures generated by threading. The energy calculations were done with our recently developed Calpha atom-based phenomenological potentials. We show that averaging of protein energies over homologs reduces the Z-score from approximately -6.1 (average Z-score for individual chains) to approximately -8.1. This means that a correct fold can be found among 3 x 10(9) random folds in the first case and among 3 x 10(15) in the second. Such increase in selectivity is important for recognition of protein folds.     

Derivation and testing of pair potentials for protein folding. When is the quasichemical approximation correct?

Many existing derivations of knowledge-based statistical pair potentials invoke the quasichemical approximation to estimate the expected side-chain contact frequency if there were no amino acid pair-specific interactions. At first glance, the quasichemical approximation that treats the residues in a protein as being disconnected and expresses the side-chain contact probability as being proportional to the product of the mole fractions of the pair of residues would appear to be rather severe. To investigate the validity of this approximation, we introduce two new reference states in which no specific pair interactions between amino acids are allowed, but in which the connectivity of the protein chain is retained. The first estimates the expected number of side-chain contracts by treating the protein as a Gaussian random coil polymer. The second, more realistic reference state includes the effects of chain connectivity, secondary structure, and chain compactness by estimating the expected side-chain contrast probability by placing the sequence of interest in each member of a library of structures of comparable compactness to the native conformation. The side-chain contact maps are not allowed to readjust to the sequence of interest, i.e., the side chains cannot repack. This situation would hold rigorously if all amino acids were the same size. Both reference states effectively permit the factorization of the side-chain contact probability into sequence-dependent and structure-dependent terms. Then, because the sequence distribution of amino acids in proteins is random, the quasichemical approximation to each of these reference states is shown to be excellent. Thus, the range of validity of the quasichemical approximation is determined by the magnitude of the side-chain repacking term, which is, at present, unknown. Finally, the performance of these two sets of pair interaction potentials as well as side-chain contact fraction-based interaction scales is assessed by inverse folding tests both without and with allowing for gaps.     

A reduced protein model with accurate native-structure identification ability

A protein model that is simple enough to be used in protein-folding simulations but accurate enough to identify a protein native fold is described. Its geometry consists of describing the residues by one, two, or three pseudoatoms, depending on the residue size. Its energy is given by a pairwise, knowledge-based potential obtained for all the pseudoatoms as a function of their relative distance. The pseudoatomic potential is also a function of the primary chain separation and residue order. The model is tested by gapless threading on a large, representative set of known protein and decoy structures obtained from the "Decoys 'R' Us" database. It is also tested by threading on gapped decoys generated for proteins with many homologs. The gapless threading tests show near 98% native-structure recognition as the lowest energy structure and almost 100% as one of the three lowest energy structures for over 2200 test proteins. In decoy threading tests, the model recognized the majority of the native structures. It is also able to recognize native structures among gapped decoys, in spite of close structural similarities. The results indicate that the pseudoatomic model has native recognition ability similar to comparable atomic-based models but much better than equivalent residue-based models.     

Four-body contact potentials derived from two protein datasets to discriminate native structures from decoys

Two-body inter-residue contact potentials for proteins have often been extracted and extensively used for threading. Here, we have developed a new scheme to derive four-body contact potentials as a way to consider protein interactions in a more cooperative model. We use several datasets of protein native structures to demonstrate that around 500 chains are sufficient to provide a good estimate of these four-body contact potentials by obtaining convergent threading results. We also have deliberately chosen two sets of protein native structures differing in resolution, one with all chains' resolution better than 1.5 A and the other with 94.2% of the structures having a resolution worse than 1.5 A to investigate whether potentials from well-refined protein datasets perform better in threading. However, potentials from well-refined proteins did not generate statistically significant better threading results. Our four-body contact potentials can discriminate well between native structures and partially unfolded or deliberately misfolded structures. Compared with another set of four-body contact potentials derived by using a Delaunay tessellation algorithm, our four-body contact potentials appear to offer a better characterization of the interactions between backbones and side chains and provide better threading results, somewhat complementary to those found using other potentials.     

Defrosting the frozen approximation: PROSPECTOR--a new approach to threading

PROSPECTOR (PROtein Structure Predictor Employing Combined Threading to Optimize Results) is a new threading approach that uses sequence profiles to generate an initial probe-template alignment and then uses this "partly thawed" alignment in the evaluation of pair interactions. Two types of sequence profiles are used: the close set, composed of sequences in which sequence identity lies between 35% and 90%; and the distant set, composed of sequences with a FASTA E-score less than 10. Thus, a total of four scoring functions are used in a hierarchical method: the close (distant) sequence profiles screen a structural database to provide an initial alignment of the probe sequence in each of the templates. The same database is then screened with a scoring function composed of sequence plus secondary structure plus pair interaction profiles. This combined hierarchical threading method is called PROSPECTOR1. For the original Fischer database, 59 of 68 pairs are correctly identified in the top position. Next, the set of the top 20 scoring sequences (four scoring functions times the top five structures) is used to construct a protein-specific pair potential based on consensus side-chain contacts occurring in 25% of the structures. In subsequent threading iterations, this protein-specific pair potential, when combined in a composite manner, is found to be more sensitive in identifying the correct pairs than when the original statistical potential is used, and it increases the number of recognized structures for the combined scoring functions, termed PROSPECTOR2, to a total of 61 Fischer pairs identified in the top position. Application to a second, smaller Fischer database of 27 probe-template pairs places 18 (17) structures in the top position for PROSPECTOR1 (PROSPECTOR2). Overall, these studies show that the use of pair interactions as assessed by the improved Z-score enhances the specificity of probe-template matches. Thus, when the hierarchy of scoring functions is combined, the ability to identify correct probe-template pairs is significantly enhanced. Finally, a web server has been established for use by the academic community (http://bioinformatics.danforthcenter.org/services/threading.html).     

Fragment-based local statistical potentials derived by combining an alphabet of protein local structures with secondary structures and solvent accessibilities

General and transferable statistical potentials to quantify the compatibility between local structures and local sequences of peptide fragments in proteins were derived. In the derivation, structure clusters of fragments are obtained by clustering five-residue fragments in native proteins based on their conformations represented by a local structure alphabet (de Brevern et al., Proteins 2000;41:271-287), secondary structure states, and solvent accessibilities. On the basis of the native sequences of the structurally clustered fragments, the probabilities of different amino acid sequences were estimated for each structure cluster. From the sequence probabilities, statistical energies as a function of sequence for a given structure were directly derived. The same sequence probabilities were employed in a database-matching approach to derive statistical energies as a function of local structure for a given sequence. Compared with prior models of local statistical potentials, we provided an integrated approach in which local conformations and local environments are treated jointly, structures are treated in units of fragments instead of individual residues so that coupling between the conformations of adjacent residues is included, and strong interdependences between the conformations of overlapping or neighboring fragment units are also considered. In tests including fragment threading, pseudosequence design, and local structure predictions, the potentials performed at least comparably and, in most cases, better than a number of existing models applicable to the same contexts indicating the advantages of such an integrated approach for deriving local potentials and suggesting applicability of the statistical potentials derived here in sequence designs and structure predictions.     

Extracting stacking interaction parameters for RNA from the data set of native structures

A crucial step in the determination of the three-dimensional native structures of RNA is the prediction of their secondary structures, which are stable independent of the tertiary fold. Accurate prediction of the secondary structure requires context-dependent estimates of the interaction parameters. We have exploited the growing database of natively folded RNA structures in the Protein Data Bank (PDB) to obtain stacking interaction parameters using a knowledge-based approach. Remarkably, the calculated values of the resulting statistical potentials (SPs) are in excellent agreement with the parameters determined using measurements in small oligonucleotides. We validate the SPs by predicting 74% of the base-pairs in a dataset of structures using the ViennaRNA package. Interestingly, this number is similar to that obtained using the measured thermodynamic parameters. We also tested the efficacy of the SP in predicting secondary structure by using gapless threading, which we advocate as an alternative method for rapidly predicting RNA structures. For RNA molecules with less than 700 nucleotides, about 70% of the native base-pairs are correctly predicted. As a further validation of the SPs we calculated Z-scores, which measure the relative stability of the native state with respect to a manifold of higher free energy states. The computed Z-scores agree with estimates made using calorimetric measurements for a few RNA molecules. Structural analysis was used to rationalize the success and failures of SP and experimentally determined parameters. First, from the near perfect linear relationship between the number of native base-pairs and sequence length, we show that nearly 46% of nucleotides are not in stacks. Second, by analyzing the suboptimal structures that are generated in gapless threading we show that the SPs and experimentally determined parameters are most successful in predicting stacks that end in hairpins. These results show that further improvement in secondary structure prediction requires reliable estimates of interaction parameters for loops, bulges, and stacks that do not end in hairpins.     

Threading without optimizing weighting factors for scoring function

Optimizing weighting factors for a linear combination of terms in a scoring function is a crucial step for success in developing a threading algorithm. Usually weighting factors are optimized to yield the highest success rate on a training dataset, and the determined constant values for the weighting factors are used for any target sequence. Here we explore completely different approaches to handle weighting factors for a scoring function of threading. Throughout this study we use a model system of gapless threading using a scoring function with two terms combined by a weighting factor, a main chain angle potential and a residue contact potential. First, we demonstrate that the optimal weighting factor for recognizing the native structure differs from target sequence to target sequence. Then, we present three novel threading methods which circumvent training dataset-based weighting factor optimization. The basic idea of the three methods is to employ different weighting factor values and finally select a template structure for a target sequence by examining characteristics of the distribution of scores computed by using the different weighting factor values. Interestingly, the success rate of our approaches is comparable to the conventional threading method where the weighting factor is optimized based on a training dataset. Moreover, when the size of the training set available for the conventional threading method is small, our approach often performs better. In addition, we predict a target-specific weighting factor optimal for a target sequence by an artificial neural network from features of the target sequence. Finally, we show that our novel methods can be used to assess the confidence of prediction of a conventional threading with an optimized constant weighting factor by considering consensus prediction between them. Implication to the underlined energy landscape of protein folding is discussed.     

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.     

Effects of amino acid composition, finite size of proteins, and sparse statistics on distance-dependent statistical pair potentials

Statistical distance dependent pair potentials are frequently used in a variety of folding, threading, and modeling studies of proteins. The applicability of these types of potentials is tightly connected to the reliability of statistical observations. We explored the possible origin and extent of false positive signals in statistical potentials by analyzing their distance dependence in a variety of randomized protein-like models. While on average potentials derived from such models are expected to equal zero at any distance, we demonstrate that systematic and significant distortions exist. These distortions originate from the limited statistical counts in local environments of proteins and from the limited size of protein structures at large distances. We suggest that these systematic errors in statistical potentials are connected to the dependence of amino acid composition on protein size and to variation in protein sizes. Additionally, atom-based potentials are dominated by a false positive signal that is due to correlation among distances measured from atoms of one residue to atoms of another residue. The significance of residue-based pairwise potentials at various spatial pair separations was assessed in this study and it was found that as few as approximately 50% of potential values were statistically significant at distances below 4 A, and only at most approximately 80% of them were significant at larger pair separations. A new definition for reference state, free of the observed systematic errors, is suggested. It has been demonstrated to generate statistical potentials that compare favorably to other publicly available ones.     

Effective knowledge‐based potentials

Empirical or knowledge‐based potentials have many applications in structural biology such as the prediction of protein structure, protein–protein, and protein–ligand interactions and in the evaluation of stability for mutant proteins, the assessment of errors in experimentally solved structures, and the design of new proteins. Here, we describe a simple procedure to derive and use pairwise distance‐dependent potentials that rely on the definition of effective atomic interactions, which attempt to capture interactions that are more likely to be physically relevant. Based on a difficult benchmark test composed of proteins with different secondary structure composition and representing many different folds, we show that the use of effective atomic interactions significantly improves the performance of potentials at discriminating between native and near‐native conformations. We also found that, in agreement with previous reports, the potentials derived from the observed effective atomic interactions in native protein structures contain a larger amount of mutual information. A detailed analysis of the effective energy functions shows that atom connectivity effects, which mostly arise when deriving the potential by the incorporation of those indirect atomic interactions occurring beyond the first atomic shell, are clearly filtered out. The shape of the energy functions for direct atomic interactions representing hydrogen bonding and disulfide and salt bridges formation is almost unaffected when effective interactions are taken into account. On the contrary, the shape of the energy functions for indirect atom interactions (i.e., those describing the interaction between two atoms bound to a direct interacting pair) is clearly different when effective interactions are considered. Effective energy functions for indirect interacting atom pairs are not influenced by the shape or the energy minimum observed for the corresponding direct interacting atom pair. Our results suggest that the dependency between the signals in different energy functions is a key aspect that need to be addressed when empirical energy functions are derived and used, and also highlight the importance of additivity assumptions in the use of potential energy functions.     

A new approach to prediction of short-range conformational propensities in proteins

MOTIVATION: Knowledge-based potentials are valuable tools for protein structure modeling and evaluation of the quality of the structure prediction obtained by a variety of methods. Potentials of such type could be significantly enhanced by a proper exploitation of the evolutionary information encoded in related protein sequences. The new potentials could be valuable components of threading algorithms, ab-initio protein structure prediction, comparative modeling and structure modeling based on fragmentary experimental data. RESULTS: A new potential for scoring local protein geometry is designed and evaluated. The approach is based on the similarity of short protein fragments measured by an alignment of their sequence profiles. Sequence specificity of the resulting energy function has been compared with the specificity of simpler potentials using gapless threading and the ability to predict specific geometry of protein fragments. Significant improvement in threading sensitivity and in the ability to generate sequence-specific protein-like conformations has been achieved.     

Reduced C(beta) statistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.     

Multibody coarse-grained potentials for native structure recognition and quality assessment of protein models

Multibody potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Our goal was to combine long range multibody potentials and short range potentials to improve recognition of native structure among misfolded decoys. We optimized the weights for four-body nonsequential, four-body sequential, and short range potentials to obtain optimal model ranking results for threading and have compared these data against results obtained with other potentials (26 different coarse-grained potentials from the Potentials 'R'Us web server have been used). Our optimized multibody potentials outperform all other contact potentials in the recognition of the native structure among decoys, both for models from homology template-based modeling and from template-free modeling in CASP8 decoy sets. We have compared the results obtained for this optimized coarse-grained potentials, where each residue is represented by a single point, with results obtained by using the DFIRE potential, which takes into account atomic level information of proteins. We found that for all proteins larger than 80 amino acids our optimized coarse-grained potentials yield results comparable to those obtained with the atomic DFIRE potential.     

Linear programming optimization and a double statistical filter for protein threading protocols

The design of scoring functions (or potentials) for threading, differentiating native-like from non-native structures with a limited computational cost, is an active field of research. We revisit two widely used families of threading potentials: the pairwise and profile models. To design optimal scoring functions we use linear programming (LP). The LP protocol makes it possible to measure the difficulty of a particular training set in conjunction with a specific form of the scoring function. Gapless threading demonstrates that pair potentials have larger prediction capacity compared with profile energies. However, alignments with gaps are easier to compute with profile potentials. We therefore search and propose a new profile model with comparable prediction capacity to contact potentials. A protocol to determine optimal energy parameters for gaps, using LP, is also presented. A statistical test, based on a combination of local and global Z-scores, is employed to filter out false-positives. Extensive tests of the new protocol are presented. The new model provides an efficient alternative for threading with pair energies, maintaining comparable accuracy. The code, databases, and a prediction server are available at http://www.tc.cornell.edu/CBIO/loopp.     

Protein threading using PROSPECT: design and evaluation

The computer system PROSPECT for the protein fold recognition using the threading method is described and evaluated in this article. For a given target protein sequence and a template structure, PROSPECT guarantees to find a globally optimal threading alignment between the two. The scoring function for a threading alignment employed in PROSPECT consists of four additive terms: i) a mutation term, ii) a singleton fitness term, iii) a pairwise-contact potential term, and iv) alignment gap penalties. The current version of PROSPECT considers pair contacts only between core (alpha-helix or beta-strand) residues and alignment gaps only in loop regions. PROSPECT finds a globally optimal threading efficiently when pairwise contacts are considered only between residues that are spatially close (7 A or less between the C(beta) atoms in the current implementation). On a test set consisting of 137 pairs of target-template proteins, each pair being from the same superfamily and having sequence identity 相似文献   

Thermo- and Mesostabilizing Protein Interactions Identified by Temperature-Dependent Statistical Potentials

The goal of controlling protein thermostability is tackled here through establishing, by in silico analyses, the relative weight of residue-residue interactions in proteins as a function of temperature. We have designed for that purpose a (melting-) temperature-dependent, statistical distance potential, where the interresidue distances are computed between the side-chain geometric centers or their functional centers. Their separate derivation from proteins of either high or low thermal resistance reveals the interactions that contribute most to stability in different temperature ranges. Thermostabilizing interactions include salt bridges and cation-π interactions (especially those involving arginine), aromatic interactions, and H-bonds between negatively charged and some aromatic residues. In contrast, H-bonds between two polar noncharged residues or between a polar noncharged residue and a negatively charged residue are relatively less stabilizing at high temperatures. An important observation is that it is necessary to consider both repulsive and attractive interactions in overall thermostabilization, as the degree of repulsion may also vary with temperature. These temperature-dependent potentials are not only useful for the identification of meso- and thermostabilizing pair interactions, but also exhibit predictive power, as illustrated by their ability to predict the melting temperature of a protein based on the melting temperature of homologous proteins.     

Inter-residue and solvent-residue interactions in proteins: a statistical study on experimental structures

A large set of protein structures resolved by X-ray or NMR techniques has been extracted from the Protein Data Bank and analyzed using statistical methods. In particular, we investigate the interactions between side chains and the interactions between solvent and side chains, pointing out on the possibility of including the solvent as part of a knowledge-based potential. The solvent-residue contacts are accounted for on the basis of the Voronoi's polyhedron analysis. Our investigation confirms the importance of hydrophobic residues in determining the protein stability. We observe that in general hydrophobic-hydrophobic interactions and, more specifically, aromatic-aromatic contacts tend to be increasingly distally separated in the primary sequence of proteins, thus connecting distinct secondary structure elements. A simple relation expressing the dependence of the protein free energy by the number of residues is proposed. Such a relation includes both the residue-residue and the solvent-residue contributions. The former is dominant for large size proteins, whereas for small sizes (number of residues less than 100) the two terms are comparable. Gapless threading experiments show that the solvent-residue knowledge-based potential yields a significant contribution with respect to discriminating the native structure of proteins. Such contribution is important especially for proteins of small size and is similar to that given by the most favorable residue-residue knowledge-based potential referring to hydrophobic-hydrophobic interactions such as isoleucine-leucine. In general, the inclusion of the solvent-residue interaction produces a relevant increase of the free energy gap between the native structures and decoys.