Information and discrimination in pairwise contact potentials

We examine the information-theoretic characteristics of statistical potentials that describe pairwise long-range contacts between amino acid residues in proteins. In our work, we seek to map out an efficient information-based strategy to detect and optimally utilize the structural information latent in empirical data, to make contact potentials, and other statistically derived folding potentials, more effective tools in protein structure prediction. Foremost, we establish fundamental connections between basic information-theoretic quantities (including the ubiquitous Z-score) and contact "energies" or scores used routinely in protein structure prediction, and demonstrate that the informatic quantity that mediates fold discrimination is the total divergence. We find that pairwise contacts between residues bear a moderate amount of fold information, and if optimized, can assist in the discrimination of native conformations from large ensembles of native-like decoys. Using an extensive battery of threading tests, we demonstrate that parameters that affect the information content of contact potentials (e.g., choice of atoms to define residue location and the cut-off distance between pairs) have a significant influence in their performance in fold recognition. We conclude that potentials that have been optimized for mutual information and that have high number of score events per sequence-structure alignment are superior in identifying the correct fold. We derive the quantity "information product" that embodies these two critical factors. We demonstrate that the information product, which does not require explicit threading to compute, is as effective as the Z-score, which requires expensive decoy threading to evaluate. This new objective function may be able to speed up the multidimensional parameter search for better statistical potentials. Lastly, by demonstrating the functional equivalence of quasi-chemically approximated "energies" to fundamental informatic quantities, we make statistical potentials less dependent on theoretically tenuous biophysical formalisms and more amenable to direct bioinformatic optimization.     

Protein sequence threading: Averaging over structures

Multiple sequence alignments are a routine tool in protein fold recognition, but multiple structure alignments are computationally less cooperative. This work describes a method for protein sequence threading and sequence-to-structure alignments that uses multiple aligned structures, the aim being to improve models from protein threading calculations. Sequences are aligned into a field due to corresponding sites in homologous proteins. On the basis of a test set of more than 570 protein pairs, the procedure does improve alignment quality, although no more than averaging over sequences. For the force field tested, the benefit of structure averaging is smaller than that of adding sequence similarity terms or a contribution from secondary structure predictions. Although there is a significant improvement in the quality of sequence-to-structure alignments, this does not directly translate to an immediate improvement in fold recognition capability.     

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.     

A study on protein sequence alignment quality

One of the most central methods in bioinformatics is the alignment of two protein or DNA sequences. However, so far large-scale benchmarks examining the quality of these alignments are scarce. On the other hand, recently several large-scale studies of the capacity of different methods to identify related sequences has led to new insights about the performance of fold recognition methods. To increase our understanding about fold recognition methods, we present a large-scale benchmark of alignment quality. We compare alignments from several different alignment methods, including sequence alignments, hidden Markov models, PSI-BLAST, CLUSTALW, and threading methods. For most methods, the alignment quality increases significantly at about 20% sequence identity. The difference in alignment quality between different methods is quite small, and the main difference can be seen at the exact positioning of the sharp rise in alignment quality, that is, around 15-20% sequence identity. The alignments are improved by using structural information. In general, the best alignments are obtained by methods that use predicted secondary structure information and sequence profiles obtained from PSI-BLAST. One interesting observation is that for different pairs many different methods create the best alignments. This finding implies that if a method that could select the best alignment method for each pair existed, a significant improvement of the alignment quality could be gained.     

PROSPECT II: protein structure prediction program for genome-scale applications

A new method for fold recognition is developed and added to the general protein structure prediction package PROSPECT (http://compbio.ornl.gov/PROSPECT/). The new method (PROSPECT II) has four key features. (i) We have developed an efficient way to utilize the evolutionary information for evaluating the threading potentials including singleton and pairwise energies. (ii) We have developed a two-stage threading strategy: (a) threading using dynamic programming without considering the pairwise energy and (b) fold recognition considering all the energy terms, including the pairwise energy calculated from the dynamic programming threading alignments. (iii) We have developed a combined z-score scheme for fold recognition, which takes into consideration the z-scores of each energy term. (iv) Based on the z-scores, we have developed a confidence index, which measures the reliability of a prediction and a possible structure-function relationship based on a statistical analysis of a large data set consisting of threadings of 600 query proteins against the entire FSSP templates. Tests on several benchmark sets indicate that the evolutionary information and other new features of PROSPECT II greatly improve the alignment accuracy. We also demonstrate that the performance of PROSPECT II on fold recognition is significantly better than any other method available at all levels of similarity. Improvement in the sensitivity of the fold recognition, especially at the superfamily and fold levels, makes PROSPECT II a reliable and fully automated protein structure and function prediction program for genome-scale applications.     

Multiple Model Approach: Exploring the Limits of Comparative Modeling

One of the biggest problems in modeling distantly related proteins is the quality of the target-template alignment. This problem often results in low quality models that do not utilize all the information available in the template structure. The divergence of alignments at a low sequence identity level, which is a hindrance in most modeling attempts, is used here as a basis for a new technique of Multiple Model Approach (MMA). Alternative alignments prepared here using different mutation matrices and gap penalties, combined with automated model building, are used to create a set of models that explore a range of possible conformations for the target protein. Models are evaluated using different techniques to identify the best model. In the set of examples studied here, the correct target structure is known, which allows the evaluation of various alignment and evaluation strategies. For a randomly selected group of distantly homologous protein pairs representing all structural classes and various fold types, it is shown that a threading score based on simplified statistical potentials of mean force can identify the best models and, consequently, the most reliable alignment. In cases where the difference between target and template structures is significant, the threading score shows clearly that all models are wrong, therefore disqualifying the template.     

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   

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.     

Successful protein fold recognition by optimal sequence threading validated by rigorous blind testing

Analysis of the results of the recent protein structure prediction experiment for our method shows that we achieved a high level of success, Of the 18 available prediction targets of known structure, the assessors have identified 11 chains which either entirely match a previously known fold, or which partially match a substantial region of a known fold. Of these 11 chains, we made predictions for 9, and correctly assigned the folds in 5 cases. We have also identified a further 2 chains which also partially match known folds, and both of these were correctly predicted. The success rate for our method under blind testing is therefore 7 out of 11 chains. A further 2 folds could have easily been recognized but failed due to either overzealous filtering of potential matches, or to simple human error on our part. One of the two targets for which we did not submit a prediction, prosubtilisin, would not have been recognized by our usual criteria, but even in this case, it is possible that a correct prediction could have been made by considerin a combination of pairwise energy and solvation energy Z-scores. Inspection of the threading alignments for the (αβ)₈ barrels provides clues as to how fold recognition by threading works, in that these folds are recognized by parts rather than as a whole. The prospects for developing sequence threading technology further is discussed. © 1995 Wiley-Liss, Inc.     

A method for the improvement of threading-based protein models

A new method for the homology-based modeling of protein three-dimensional structures is proposed and evaluated. The alignment of a query sequence to a structural template produced by threading algorithms usually produces low-resolution molecular models. The proposed method attempts to improve these models. In the first stage, a high-coordination lattice approximation of the query protein fold is built by suitable tracking of the incomplete alignment of the structural template and connection of the alignment gaps. These initial lattice folds are very similar to the structures resulting from standard molecular modeling protocols. Then, a Monte Carlo simulated annealing procedure is used to refine the initial structure. The process is controlled by the model's internal force field and a set of loosely defined restraints that keep the lattice chain in the vicinity of the template conformation. The internal force field consists of several knowledge-based statistical potentials that are enhanced by a proper analysis of multiple sequence alignments. The template restraints are implemented such that the model chain can slide along the template structure or even ignore a substantial fraction of the initial alignment. The resulting lattice models are, in most cases, closer (sometimes much closer) to the target structure than the initial threading-based models. All atom models could easily be built from the lattice chains. The method is illustrated on 12 examples of target/template pairs whose initial threading alignments are of varying quality. Possible applications of the proposed method for use in protein function annotation are briefly discussed.     

Protein fold recognition score functions: unusual construction strategies.

We describe two ways of optimizing score functions for protein sequence to structure threading. The first method adjusts parameters to improve sequence to structure alignment. The second adjusts parameters so as to improve a score function's ability to rank alignments calculated in the first score function. Unlike those functions known as knowledge-based force fields, the resulting parameter sets do not rely on Boltzmann statistics, have no claim to representing free energies and are purely constructions for recognizing protein folds. The methods give a small improvement, but suggest that functions can be profitably optimized for very specific aspects of protein fold recognition. Proteins 1999;36:454-461.     

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.     

Learning scoring schemes for sequence alignment from partial examples

When aligning biological sequences, the choice of parameter values for the alignment scoring function is critical. Small changes in gap penalties, for example, can yield radically different alignments. A rigorous way to compute parameter values that are appropriate for aligning biological sequences is through inverse parametric sequence alignment. Given a collection of examples of biologically correct alignments, this is the problem of finding parameter values that make the scores of the example alignments close to those of optimal alignments for their sequences. We extend prior work on inverse parametric alignment to partial examples, which contain regions where the alignment is left unspecified, and to an improved formulation based on minimizing the average error between the score of an example and the score of an optimal alignment. Experiments on benchmark biological alignments show we can find parameters that generalize across protein families and that boost the accuracy of multiple sequence alignment by as much as 25%.     

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.     

Confidence measures for protein fold recognition

MOTIVATION: We present an extensive evaluation of different methods and criteria to detect remote homologs of a given protein sequence. We investigate two associated problems: first, to develop a sensitive searching method to identify possible candidates and, second, to assign a confidence to the putative candidates in order to select the best one. For searching methods where the score distributions are known, p-values are used as confidence measure with great success. For the cases where such theoretical backing is absent, we propose empirical approximations to p-values for searching procedures. RESULTS: As a baseline, we review the performances of different methods for detecting remote protein folds (sequence alignment and threading, with and without sequence profiles, global and local). The analysis is performed on a large representative set of protein structures. For fold recognition, we find that methods using sequence profiles generally perform better than methods using plain sequences, and that threading methods perform better than sequence alignment methods. In order to assess the quality of the predictions made, we establish and compare several confidence measures, including raw scores, z-scores, raw score gaps, z-score gaps, and different methods of p-value estimation. We work our way from the theoretically well backed local scores towards more explorative global and threading scores. The methods for assessing the statistical significance of predictions are compared using specificity--sensitivity plots. For local alignment techniques we find that p-value methods work best, albeit computationally cheaper methods such as those based on score gaps achieve similar performance. For global methods where no theory is available methods based on score gaps work best. By using the score gap functions as the measure of confidence we improve the more powerful fold recognition methods for which p-values are unavailable. AVAILABILITY: The benchmark set is available upon request.     

Protein fold recognition by total alignment probability

We present a protein fold-recognition method that uses a comprehensive statistical interpretation of structural Hidden Markov Models (HMMs). The structure/fold recognition is done by summing the probabilities of all sequence-to-structure alignments. The optimal alignment can be defined as the most probable, but suboptimal alignments may have comparable probabilities. These suboptimal alignments can be interpreted as optimal alignments to the "other" structures from the ensemble or optimal alignments under minor fluctuations in the scoring function. Summing probabilities for all alignments gives a complete estimate of sequence-model compatibility. In the case of HMMs that produce a sequence, this reflects the fact that due to our indifference to exactly how the HMM produced the sequence, we should sum over all possibilities. We have built a set of structural HMMs for 188 protein structures and have compared two methods for identifying the structure compatible with a sequence: by the optimal alignment probability and by the total probability. Fold recognition by total probability was 40% more accurate than fold recognition by the optimal alignment probability. Proteins 2000;40:451-462.     

In search for more accurate alignments in the twilight zone

A major bottleneck in comparative modeling is the alignment quality; this is especially true for proteins whose distant relationships could be reliably recognized only by recent advances in fold recognition. The best algorithms excel in recognizing distant homologs but often produce incorrect alignments for over 50% of protein pairs in large fold-prediction benchmarks. The alignments obtained by sequence-sequence or sequence-structure matching algorithms differ significantly from the structural alignments. To study this problem, we developed a simplified method to explicitly enumerate all possible alignments for a pair of proteins. This allowed us to estimate the number of significantly different alignments for a given scoring method that score better than the structural alignment. Using several examples of distantly related proteins, we show that for standard sequence-sequence alignment methods, the number of significantly different alignments is usually large, often about 10(10) alternatives. This distance decreases when the alignment method is improved, but the number is still too large for the brute force enumeration approach. More effective strategies were needed, so we evaluated and compared two well-known approaches for searching the space of suboptimal alignments. We combined their best features and produced a hybrid method, which yielded alignments that surpassed the original alignments for about 50% of protein pairs with minimal computational effort.     

SATe-II: very fast and accurate simultaneous estimation of multiple sequence alignments and phylogenetic trees

Highly accurate estimation of phylogenetic trees for large data sets is difficult, in part because multiple sequence alignments must be accurate for phylogeny estimation methods to be accurate. Coestimation of alignments and trees has been attempted but currently only SATé estimates reasonably accurate trees and alignments for large data sets in practical time frames (Liu K., Raghavan S., Nelesen S., Linder C.R., Warnow T. 2009b. Rapid and accurate large-scale coestimation of sequence alignments and phylogenetic trees. Science. 324:1561-1564). Here, we present a modification to the original SATé algorithm that improves upon SATé (which we now call SATé-I) in terms of speed and of phylogenetic and alignment accuracy. SATé-II uses a different divide-and-conquer strategy than SATé-I and so produces smaller more closely related subsets than SATé-I; as a result, SATé-II produces more accurate alignments and trees, can analyze larger data sets, and runs more efficiently than SATé-I. Generally, SATé is a metamethod that takes an existing multiple sequence alignment method as an input parameter and boosts the quality of that alignment method. SATé-II-boosted alignment methods are significantly more accurate than their unboosted versions, and trees based upon these improved alignments are more accurate than trees based upon the original alignments. Because SATé-I used maximum likelihood (ML) methods that treat gaps as missing data to estimate trees and because we found a correlation between the quality of tree/alignment pairs and ML scores, we explored the degree to which SATé's performance depends on using ML with gaps treated as missing data to determine the best tree/alignment pair. We present two lines of evidence that using ML with gaps treated as missing data to optimize the alignment and tree produces very poor results. First, we show that the optimization problem where a set of unaligned DNA sequences is given and the output is the tree and alignment of those sequences that maximize likelihood under the Jukes-Cantor model is uninformative in the worst possible sense. For all inputs, all trees optimize the likelihood score. Second, we show that a greedy heuristic that uses GTR+Gamma ML to optimize the alignment and the tree can produce very poor alignments and trees. Therefore, the excellent performance of SATé-II and SATé-I is not because ML is used as an optimization criterion for choosing the best tree/alignment pair but rather due to the particular divide-and-conquer realignment techniques employed.     

Improving fold recognition of protein threading by experimental distance constraints

We present a comprehensive analysis of methods for improving the fold recognition rate of the threading approach to protein structure prediction by the utilization of few additional distance constraints. The distance constraints between protein residues may be obtained by experiments such as mass spectrometry or NMR spectroscopy. We applied a post-filtering step with new scoring functions incorporating measures of constraint satisfaction to ranking lists of 123D threading alignments. The detailed analysis of the results on a small representative benchmark set show that the fold recognition rate can be improved significantly by up to 30% from about 54%-65% to 77%-84%, approaching the maximal attainable performance of 90% estimated by structural superposition alignments. This gain in performance adds about 10% to the recognition rate already achieved in our previous study with cross-link constraints only. Additional recent results on a larger benchmark set involving a confidence function for threading predictions also indicate notable improvements by our combined approach, which should be particularly valuable for rapid structure determination and validation of protein models.