A study of combined structure/sequence profiles

ENSEMBLE VOTING SYSTEM FOR MULTICLASS PROTEIN FOLD RECOGNITION

Protein structure classification is an important issue in understanding the associations between sequence and structure as well as possible functional and evolutionary relationships. Recently structural genomes initiatives and other high-throughput experiments have populated the biological databases at a rapid pace. In this paper, three types of classifiers, k nearest neighbors, class center and nearest neighbor and probabilistic neural networks and their homogenous ensemble for multiclass protein fold recognition problem are evaluated firstly, and then a heterogenous ensemble Voting System is designed for the same problem. The different features and/or their combinations extracted from the protein fold dataset are used in these classification models. The heterogenous classification results are then put into a voting system to get the final result. The experimental results show that the proposed method can improve prediction accuracy by 4%–10% on a benchmark dataset containing 27 SCOP folds.

Trends in template/fragment-free protein structure prediction

Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.

Detection of discriminative sequence patterns in the neighborhood of proline cis peptide bonds and their functional annotation

Background

Polypeptides are composed of amino acids covalently bonded via a peptide bond. The majority of peptide bonds in proteins is found to occur in the trans conformation. In spite of their infrequent occurrence, cis peptide bonds play a key role in the protein structure and function, as well as in many significant biological processes.

Results

We perform a systematic analysis of regions in protein sequences that contain a proline cis peptide bond in order to discover non-random associations between the primary sequence and the nature of proline cis/trans isomerization. For this purpose an efficient pattern discovery algorithm is employed which discovers regular expression-type patterns that are overrepresented (i.e. appear frequently repeated) in a set of sequences. Four types of pattern discovery are performed: i) exact pattern discovery, ii) pattern discovery using a chemical equivalency set, iii) pattern discovery using a structural equivalency set and iv) pattern discovery using certain amino acids' physicochemical properties. The extracted patterns are carefully validated using a specially implemented scoring function and a significance measure (i.e. log-probability estimate) indicative of their specificity. The score threshold for the first three types of pattern discovery is 0.90 while for the last type of pattern discovery 0.80. Regarding the significance measure, all patterns yielded values in the range [-9, -31] which ensure that the derived patterns are highly unlikely to have emerged by chance. Among the highest scoring patterns, most of them are consistent with previous investigations concerning the neighborhood of cis proline peptide bonds, and many new ones are identified. Finally, the extracted patterns are systematically compared against the PROSITE database, in order to gain insight into the functional implications of cis prolyl bonds.

Conclusion

Cis patterns with matches in the PROSITE database fell mostly into two main functional clusters: family signatures and protein signatures. However considerable propensity was also observed for targeting signals, active and phosphorylation sites as well as domain signatures.

Phylogenetic profiles reveal evolutionary relationships within the "twilight zone" of sequence similarity

Inferring evolutionary relationships among highly divergent protein sequences is a daunting task. In particular, when pairwise sequence alignments between protein sequences fall <25% identity, the phylogenetic relationships among sequences cannot be estimated with statistical certainty. Here, we show that phylogenetic profiles generated with the Gestalt Domain Detection Algorithm-Basic Local Alignment Tool (GDDA-BLAST) are capable of deriving, ab initio, phylogenetic relationships for highly divergent proteins in a quantifiable and robust manner. Notably, the results from our computational case study of the highly divergent family of retroelements accord with previous estimates of their evolutionary relationships. Taken together, these data demonstrate that GDDA-BLAST provides an independent and powerful measure of evolutionary relationships that does not rely on potentially subjective sequence alignment. We demonstrate that evolutionary relationships can be measured with phylogenetic profiles, and therefore propose that these measurements can provide key insights into relationships among distantly related and/or rapidly evolving proteins.

MUSTER: Improving protein sequence profile-profile alignments by using multiple sources of structure information

We develop a new threading algorithm MUSTER by extending the previous sequence profile-profile alignment method, PPA. It combines various sequence and structure information into single-body terms which can be conveniently used in dynamic programming search: (1) sequence profiles; (2) secondary structures; (3) structure fragment profiles; (4) solvent accessibility; (5) dihedral torsion angles; (6) hydrophobic scoring matrix. The balance of the weighting parameters is optimized by a grading search based on the average TM-score of 111 training proteins which shows a better performance than using the conventional optimization methods based on the PROSUP database. The algorithm is tested on 500 nonhomologous proteins independent of the training sets. After removing the homologous templates with a sequence identity to the target >30%, in 224 cases, the first template alignment has the correct topology with a TM-score >0.5. Even with a more stringent cutoff by removing the templates with a sequence identity >20% or detectable by PSI-BLAST with an E-value <0.05, MUSTER is able to identify correct folds in 137 cases with the first model of TM-score >0.5. Dependent on the homology cutoffs, the average TM-score of the first threading alignments by MUSTER is 5.1-6.3% higher than that by PPA. This improvement is statistically significant by the Wilcoxon signed rank test with a P-value < 1.0 x 10(-13), which demonstrates the effect of additional structural information on the protein fold recognition. The MUSTER server is freely available to the academic community at http://zhang.bioinformatics.ku.edu/MUSTER.

Folding of small helical proteins assisted by small-angle X-ray scattering profiles

This paper reports a computational method for folding small helical proteins. The goal was to determine the overall topology of proteins given secondary structure assignment on sequence. In doing so, a Monte Carlo protocol, which combines coarse-grained normal modes and a Hamiltonian at a different scale, was developed to enhance sampling. In addition to the knowledge-based potential functions, a small-angle X-ray scattering (SAXS) profile was also used as a weak constraint for guiding the folding. The algorithm can deliver structural models with overall correct topology, which makes them similar to those of 5 approximately 6 A cryo-EM density maps. The success could contribute to make the SAXS technique a fast and inexpensive solution-phase experimental method for determining the overall topology of small, soluble, but noncrystallizable, helical proteins.

Mining sequential patterns for protein fold recognition

Protein data contain discriminative patterns that can be used in many beneficial applications if they are defined correctly. In this work sequential pattern mining (SPM) is utilized for sequence-based fold recognition. Protein classification in terms of fold recognition plays an important role in computational protein analysis, since it can contribute to the determination of the function of a protein whose structure is unknown. Specifically, one of the most efficient SPM algorithms, cSPADE, is employed for the analysis of protein sequence. A classifier uses the extracted sequential patterns to classify proteins in the appropriate fold category. For training and evaluating the proposed method we used the protein sequences from the Protein Data Bank and the annotation of the SCOP database. The method exhibited an overall accuracy of 25% in a classification problem with 36 candidate categories. The classification performance reaches up to 56% when the five most probable protein folds are considered.

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.

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.

SPARKS 2 and SP3 servers in CASP6

Two single-method servers, SPARKS 2 and SP3, participated in automatic-server predictions in CASP6. The overall results for all as well as detailed performance in comparative modeling targets are presented. It is shown that both SPARKS 2 and SP3 are able to recognize their corresponding best templates for all easy comparative modeling targets. The alignment accuracy, however, is not always the best among all the servers. Possible factors are discussed. SPARKS 2 and SP3 fold recognition servers, as well as their executables, are freely available for all academic users on http://theory.med.buffalo.edu.

A machine learning information retrieval approach to protein fold recognition

MOTIVATION

Recognizing proteins that have similar tertiary structure is the key step of template-based protein structure prediction methods. Traditionally, a variety of alignment methods are used to identify similar folds, based on sequence similarity and sequence-structure compatibility. Although these methods are complementary, their integration has not been thoroughly exploited. Statistical machine learning methods provide tools for integrating multiple features, but so far these methods have been used primarily for protein and fold classification, rather than addressing the retrieval problem of fold recognition-finding a proper template for a given query protein.

RESULTS

Here we present a two-stage machine learning, information retrieval, approach to fold recognition. First, we use alignment methods to derive pairwise similarity features for query-template protein pairs. We also use global profile-profile alignments in combination with predicted secondary structure, relative solvent accessibility, contact map and beta-strand pairing to extract pairwise structural compatibility features. Second, we apply support vector machines to these features to predict the structural relevance (i.e. in the same fold or not) of the query-template pairs. For each query, the continuous relevance scores are used to rank the templates. The FOLDpro approach is modular, scalable and effective. Compared with 11 other fold recognition methods, FOLDpro yields the best results in almost all standard categories on a comprehensive benchmark dataset. Using predictions of the top-ranked template, the sensitivity is approximately 85, 56, and 27% at the family, superfamily and fold levels respectively. Using the 5 top-ranked templates, the sensitivity increases to 90, 70, and 48%.

Protein classification using sequential pattern mining

Protein classification in terms of fold recognition can be employed to determine the structural and functional properties of a newly discovered protein. In this work sequential pattern mining (SPM) is utilized for sequence-based fold recognition. One of the most efficient SPM algorithms, cSPADE, is employed for protein primary structure analysis. Then a classifier uses the extracted sequential patterns for classifying proteins of unknown structure in the appropriate fold category. The proposed methodology exhibited an overall accuracy of 36% in a multi-class problem of 17 candidate categories. The classification performance reaches up to 65% when the three most probable protein folds are considered.

Determining Protein Topology from Skeletons of Secondary Structures

We report a novel computational procedure for determining protein native topology, or fold, by defining loop connectivity based on skeletons of secondary structures that can usually be obtained from low to intermediate-resolution density maps. The procedure primarily involves a knowledge-based geometry filter followed by an energetics-based evaluation. It was tested on a large set of skeletons covering a wide range of protein architecture, including one modeled from an experimentally determined 7.6A cryo-electron microscopy (cryo-EM) density map. The results showed that the new procedure could effectively deduce protein folds without high-resolution structural data, a feature that could also be used to recognize native fold in structure prediction and to interpret data in fields like structure genomics. Most importantly, in the energetics-based evaluation, it was revealed that, despite the inevitable errors in the artificially constructed structures and limited accuracy of knowledge-based potential functions, the average energy of an ensemble of structures with slightly different configurations around the native skeleton is a much more robust parameter for marking native topology than the energy of individual structures in the ensemble. This result implies that, among all the possible topology candidates for a given skeleton, evolution has selected the native topology as the one that can accommodate the largest structural variations, not the one rigidly trapped in a deep, but narrow, conformational energy well.

Single-body residue-level knowledge-based energy score combined with sequence-profile and secondary structure information for fold recognition

An elaborate knowledge-based energy function is designed for fold recognition. It is a residue-level single-body potential so that highly efficient dynamic programming method can be used for alignment optimization. It contains a backbone torsion term, a buried surface term, and a contact-energy term. The energy score combined with sequence profile and secondary structure information leads to an algorithm called SPARKS (Sequence, secondary structure Profiles and Residue-level Knowledge-based energy Score) for fold recognition. Compared with the popular PSI-BLAST, SPARKS is 21% more accurate in sequence-sequence alignment in ProSup benchmark and 10%, 25%, and 20% more sensitive in detecting the family, superfamily, fold similarities in the Lindahl benchmark, respectively. Moreover, it is one of the best methods for sensitivity (the number of correctly recognized proteins), alignment accuracy (based on the MaxSub score), and specificity (the average number of correctly recognized proteins whose scores are higher than the first false positives) in LiveBench 7 among more than twenty servers of non-consensus methods. The simple algorithm used in SPARKS has the potential for further improvement. This highly efficient method can be used for fold recognition on genomic scales. A web server is established for academic users on http://theory.med.buffalo.edu.

A Structural-informatics approach for tracing beta-sheets: building pseudo-C(alpha) traces for beta-strands in intermediate-resolution density maps

We report the development of two computational methods to assist density map interpretation at intermediate resolutions: sheettracer for building pseudo-C(alpha) models of beta-sheets, and a deconvolution method for enhancing features attributed to major secondary structural elements. Sheettracer is tightly coupled with sheetminer, which was developed to locate sheet densities in intermediate-resolution density maps. The results from sheetminer are used as inputs to sheettracer, which employs a multi-step ad hoc morphological analysis of sheet densities to trace individual strands of beta-sheets. The methods were tested on simulated density maps from 12 protein crystal structures that represent a reasonably complete sampling of sheet morphology. The sheet-tracing results were quantitatively assessed in terms of sensitivity, specificity and rms deviations. Furthermore, sheettracer and the deconvolution method were rigorously tested on experimental maps of the lambda2 protein of reovirus at resolutions of 7.6A and 11.8A. Our results clearly demonstrate the capability of sheettracer in building pseudo-C(alpha) models of beta-sheets in intermediate-resolution density maps and the power of the deconvolution method in enhancing the performance of sheettracer. These computational methods, along with other related ones, should facilitate recognition and analysis of folding motifs from experimental data at intermediate resolutions.

A structural-informatics approach for mining beta-sheets: locating sheets in intermediate-resolution density maps

Here, we report a new computational method, called sheetminer, for mining beta-sheets in the density maps at intermediate resolutions of 6 to 10A. The method employs a multi-step ad hoc morphological analysis of density maps to identify the unique characteristics of beta-sheets. It was tested on density maps from 12 protein crystal structures that were artificially blurred to intermediate resolutions. There are a total of 35 independent beta-sheets with a wide distribution of morphology. The method successfully located 34 of them and missed only one. The method was also applied to an experimental 9A electron cryomicroscopic structure and an 8A X-ray density map. In both cases, the sheet-searching results were found to agree very well with known high-resolution crystal structures. Collectively, these results demonstrate clearly the robustness of sheetminer in locating the regions belonging to beta-sheets in the intermediate-resolution density maps. Furthermore, sheetminer is completely complementary to all other existing computational methods, including helixhunter and threading algorithms. Their combined usage has the potential to significantly enhance the computational modeling capacity for a much more complete interpretation of structural data at intermediate resolutions, from which extraction of functional information would be more effective. This is particularly important in the field of structural genomics, in which the fast screening approach may not always yield crystals that diffract to atomic resolution. An exciting future application of sheetminer is as a valuable tool for revealing the structures of amyloid fibrils that are rich in beta-motifs.

Structural genomics: computational methods for structure analysis

The success of structural genomics initiatives requires the development and application of tools for structure analysis, prediction, and annotation. In this paper we review recent developments in these areas; specifically structure alignment, the detection of remote homologs and analogs, homology modeling and the use of structures to predict function. We also discuss various rationales for structural genomics initiatives. These include the structure-based clustering of sequence space and genome-wide function assignment. It is also argued that structural genomics can be integrated into more traditional biological research if specific biological questions are included in target selection strategies.

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.

3D-1D threading methods for protein fold recognition

The threading approach to protein fold recognition attempts to evaluate how well a query sequence fits into an already-solved fold. 3D-1D threaders rely on matching 1-dimensional strings of 3-dimensional information predicted from the query sequence with corresponding features of the target structure. In many cases this is combined with a sequence comparison. The combination of sequence and structure information has been shown to improve the accuracy of fold recognition, relative to the exclusive use of sequence or structure. In this paper, we review progress made since the introduction of threading methods a decade ago, highlighting recent advances. We focus on two emerging methods that are unconventional 3D-1D threaders: proximity correlation matrices and parallel cascade identification.

Enhanced genome annotation using structural profiles in the program 3D-PSSM

A method (three-dimensional position-specific scoring matrix, 3D-PSSM) to recognise remote protein sequence homologues is described. The method combines the power of multiple sequence profiles with knowledge of protein structure to provide enhanced recognition and thus functional assignment of newly sequenced genomes. The method uses structural alignments of homologous proteins of similar three-dimensional structure in the structural classification of proteins (SCOP) database to obtain a structural equivalence of residues. These equivalences are used to extend multiply aligned sequences obtained by standard sequence searches. The resulting large superfamily-based multiple alignment is converted into a PSSM. Combined with secondary structure matching and solvation potentials, 3D-PSSM can recognise structural and functional relationships beyond state-of-the-art sequence methods. In a cross-validated benchmark on 136 homologous relationships unambiguously undetectable by position-specific iterated basic local alignment search tool (PSI-Blast), 3D-PSSM can confidently assign 18 %. The method was applied to the remaining unassigned regions of the Mycoplasma genitalium genome and an additional 13 regions were assigned with 95 % confidence. 3D-PSSM is available to the community as a web server: http://www.bmm.icnet.uk/servers/3dpssm

Combination of threading potentials and sequence profiles improves fold recognition

Using a benchmark set of structurally similar proteins, we conduct a series of threading experiments intended to identify a scoring function with an optimal combination of contact-potential and sequence-profile terms. The benchmark set is selected to include many medium-difficulty fold recognition targets, where sequence similarity is undetectable by BLAST but structural similarity is extensive. The contact potential is based on the log-odds of non-local contacts involving different amino acid pairs, in native as opposed to randomly compacted structures. The sequence profile term is that used in PSI-BLAST. We find that combination of these terms significantly improves the success rate of fold recognition over use of either term alone, with respect to both recognition sensitivity and the accuracy of threading models. Improvement is greatest for targets between 10 % and 20 % sequence identity and 60 % to 80 % superimposable residues, where the number of models crossing critical accuracy and significance thresholds more than doubles. We suggest that these improvements account for the successful performance of the combined scoring function at CASP3. We discuss possible explanations as to why sequence-profile and contact-potential terms appear complementary.

Identification of related proteins on family, superfamily and fold level

Proteins might have considerable structural similarities even when no evolutionary relationship of their sequences can be detected. This property is often referred to as the proteins sharing only a "fold". Of course, there are also sequences of common origin in each fold, called a "superfamily", and in them groups of sequences with clear similarities, designated "family". Developing algorithms to reliably identify proteins related at any level is one of the most important challenges in the fast growing field of bioinformatics today. However, it is not at all certain that a method proficient at finding sequence similarities performs well at the other levels, or vice versa.Here, we have compared the performance of various search methods on these different levels of similarity. As expected, we show that it becomes much harder to detect proteins as their sequences diverge. For family related sequences the best method gets 75% of the top hits correct. When the sequences differ but the proteins belong to the same superfamily this drops to 29%, and in the case of proteins with only fold similarity it is as low as 15%. We have made a more complete analysis of the performance of different algorithms than earlier studies, also including threading methods in the comparison. Using this method a more detailed picture emerges, showing multiple sequence information to improve detection on the two closer levels of relationship. We have also compared the different methods of including this information in prediction algorithms. For lower specificities, the best scheme to use is a linking method connecting proteins through an intermediate hit. For higher specificities, better performance is obtained by PSI-BLAST and some procedures using hidden Markov models. We also show that a threading method, THREADER, performs significantly better than any other method at fold recognition.

Protein threading by recursive dynamic programming

We present the recursive dynamic programming (RDP) method for the threading approach to three-dimensional protein structure prediction. RDP is based on the divide-and-conquer paradigm and maps the protein sequence whose backbone structure is to be found (the protein target) onto the known backbone structure of a model protein (the protein template) in a stepwise fashion, a technique that is similar to computing local alignments but utilising different cost functions. We begin by mapping parts of the target onto the template that show statistically significant similarity with the template sequence. After mapping, the template structure is modified in order to account for the mapped target residues. Then significant similarities between the yet unmapped parts of the target and the modified template are searched, and the resulting segments of the target are mapped onto the template. This recursive process of identifying segments in the target to be mapped onto the template and modifying the template is continued until no significant similarities between the remaining parts of target and template are found. Those parts which are left unmapped by the procedure are interpreted as gaps. The RDP method is robust in the sense that different local alignment methods can be used, several alternatives of mapping parts of the target onto the template can be handled and compared in the process, and the cost functions can be dynamically adapted to biological needs. Our computer experiments show that the RDP procedure is efficient and effective. We can thread a typical protein sequence against a database of 887 template domains in about 12 hours even on a low-cost workstation (SUN Ultra 5). In statistical evaluations on databases of known protein structures, RDP significantly outperforms competing methods. RDP has been especially valuable in providing accurate alignments for modeling active sites of proteins.RDP is part of the ToPLign system (GMD Toolbox for protein alignment) and can be accessed via the WWW independently or in concert with other ToPLign tools at http://cartan.gmd.de/ToPLign.html.

Protein structure prediction by threading. Why it works and why it does not

We developed a novel Monte Carlo threading algorithm which allows gaps and insertions both in the template structure and threaded sequence. The algorithm is able to find the optimal sequence-structure alignment and sample suboptimal alignments. Using our algorithm we performed sequence-structure alignments for a number of examples for three protein folds (ubiquitin, immunoglobulin and globin) using both "ideal" set of potentials (optimized to provide the best Z-score for a given protein) and more realistic knowledge-based potentials. Two physically different scenarios emerged. If a template structure is similar to the native one (within 2 A RMS), then (i) the optimal threading alignment is correct and robust with respect to deviations of the potential from the "ideal" one; (ii) suboptimal alignments are very similar to the optimal one; (iii) as Monte Carlo temperature decreases a sharp cooperative transition to the optimal alignment is observed. In contrast, if the template structure is only moderately close to the native structure (RMS greater than 3.5 A), then (i) the optimal alignment changes dramatically when an "ideal" potential is substituted by the real one; (ii) the structures of suboptimal alignments are very different from the optimal one, reducing the reliability of the alignment; (iii) the transition to the apparently optimal alignment is non-cooperative. In the intermediate cases when the RMS between the template and the native conformations is in the range between 2 A and 3.5 A, the success of threading alignment may depend on the quality of potentials used. These results are rationalized in terms of a threading free energy landscape. Possible ways to overcome the fundamental limitations of threading are discussed briefly.

The Levinthal paradox: yesterday and today

A change in the perception of the protein folding problem has taken place recently. The nature of the change is outlined and the reasons for it are presented. An essential element is the recognition that a bias toward the native state over much of the effective energy surface may govern the folding process. This has replaced the random search paradigm of Levinthal and suggests that there are many ways of reaching the native state in a reasonable time so that a specific pathway does not have to be postulated. The change in perception is due primarily to the application of statistical mechanical models and lattice simulations to protein folding. Examples of lattice model results on protein folding are presented. It is pointed out that the new optimism about the protein folding problem must be complemented by more detailed studies to determine the structural and energetic factors that introduce the biases which make possible the folding of real proteins.

Protein fold recognition using sequence-derived predictions

In protein fold recognition, one assigns a probe amino acid sequence of unknown structure to one of a library of target 3D structures. Correct assignment depends on effective scoring of the probe sequence for its compatibility with each of the target structures. Here we show that, in addition to the amino acid sequence of the probe, sequence-derived properties of the probe sequence (such as the predicted secondary structure) are useful in fold assignment. The additional measure of compatibility between probe and target is the level of agreement between the predicted secondary structure of the probe and the known secondary structure of the target fold. That is, we recommend a sequence-structure compatibility function that combines previously developed compatibility functions (such as the 3D-1D scores of Bowie et al. [1991] or sequence-sequence replacement tables) with the predicted secondary structure of the probe sequence. The effect on fold assignment of adding predicted secondary structure is evaluated here by using a benchmark set of proteins (Fischer et al., 1996a). The 3D structures of the probe sequences of the benchmark are actually known, but are ignored by our method. The results show that the inclusion of the predicted secondary structure improves fold assignment by about 25%. The results also show that, if the true secondary structure of the probe were known, correct fold assignment would increase by an additional 8-32%. We conclude that incorporating sequence-derived predictions significantly improves assignment of sequences to known 3D folds. Finally, we apply the new method to assign folds to sequences in the SWISSPROT database; six fold assignments are given that are not detectable by standard sequence-sequence comparison methods; for two of these, the fold is known from X-ray crystallography and the fold assignment is correct.