Threading with Explicit Models for Evolutionary Conservation of Structure and Sequence

Anna Panchenko, Aron Marchler-Bauer, Stephen H. Bryant*

PROTEINS: Structure, Function, and Genetics Supplement 3:133-140, 1999

We have attempted to predict the three-dimensional structures of 19 proteins for the CASP3 experiment, each showing less than 25% sequence identity with known structures. Predictions were based on a threading method that aligns the target sequence with the conserved cores of structural templates, as identified from structure-structure alignments of the template with homologous neighbors. Alternative alignments were scored using contact potentials and a position-specific score matrix derived from sequence neighbors of the template. We find that this method identified the correct structural family for 11 of the 19 targets and predicted the remaining 8 targets to be similar to "NONE" of the templates, avoiding false positives. Threading alignments were relatively accurate for 10 of the 11 targets, including alignments for 6 of 7 identified at CASP3 as fold-recognition targets. These predictions were ranked "first place" by the CASP3 assessor when compared to fold-recognition predictions made by other methods. It appears that threading with family-specific models for structure and sequence conservation has improved threading prediction accuracy.

Introduction

Threading algorithms use the database of known three-dimensional structures to classify new protein sequences and to predict their structures. Their premise is that detection of structural similarity by sequence-structure threading will recognize remote evolutionary relationships that are not detectable by sequence comparison alone. This assumption is logical, since protein evolution is known to strongly conserve the core structures of protein families, but at the same time it is not clear how much improvement one should expect. The structures of remote homologs differ greatly in detail, with backbone root mean square residuals (RMS) only in the range of 2-3 Angstroms, and the conformational energy calculations used by threading algorithms may easily reject model structures with this level of error(1-3). Sequence-based classification is also becoming ever more powerful, with the growth of the sequence databases and development of sophisticated methods for construction of position specific score matrices (PSSM)(4-6). Thus, while there are certainly some successes from threading methods (7-9), one may question whether they in practice greatly improve computational biologist's ability to recognize remote relationships and/or produce more accurate molecular models.

To address this question we have undertaken a number of blind threading predictions for the CASP3 experiment10. We have chosen CASP3 targets where the appropriate structural template and/or alignment was not apparent from sequence comparison and where we might hope to measure the improvement in recognition and modeling performance attributable to use of three-dimensional structure information. We applied to these targets a threading method that considers sequence similarity, as the score of the target sequence vs. a PSSM for the template. We add to this a threading score based on explicit definition of the conserved core of the template structure, as obtained from analysis of homologous structural neighbors, and on the conformational energy of the predicted three-dimensional structure, as estimated by empirical contact potentials. Our goal in this combined threading method is to identify molecular models that are physically plausible and at the same time consistent with the evolutionary history of candidate templates.

Here we assess the accuracy of these predictions in the light of the true structures of the target proteins. We find that models crossed specific accuracy thresholds for nearly all targets where a template with sufficient structural similarity was available and that our method was successful in avoiding false positive predictions for the remaining targets. We also find that model accuracy was almost always improved by combining information derived from the three-dimensional structures of template proteins with descriptions of sequence conservation. Our conclusions are largely consistent with those of the independent assessor for CASP3 fold-recognition predictions, who ranked our method ahead of those based on sequence comparison alone and ahead of threading methods lacking explicit definition of the evolutionary cores of template structures11. It seems that fold recognition may be improved by combining contact potentials with explicit models for evolutionary conservation of structure and sequence.

Methods

Physically Plausible Models

Models for CASP3 were derived from a database of structural templates containing 2233 experimentally determined chain and/or domain structures. Structures were taken from the Protein Data Bank (PDB)(12) as of August 5, 1998 or earlier, with definitions of structurally compact domains taken from Entrez (13). The template set is chosen by single-linkage clustering, with no two chains having BLAST6 p-values less than 10-7, and with representatives of sequence-similar groups selected according to the completeness and resolution of structural data (14).

Target sequences are aligned with template structures using the core element threading algorithm(3). Core elements from the template are aligned with chain-continuous segments from the sequence with gaps allowed only in intervening loop regions. Alternative alignments and core element endpoints are sampled one at a time with new values accepted according to probabilities given by a Boltzmann factor. The lengths of intervening loop segments are required to be long enough to physically span the distance between core element endpoints.

Conformational energy is calculated as a sum of contact potentials. Potential terms are derived from the log-odds ratios of contacts between different amino-acid pair types in native structures from the PDB, as compared to a shuffled-sequence reference state (15). Contacts are defined as virtual Ca or peptide group coordinates greater than 5 residues apart in the chain, falling in distance shells up to 10 Angstroms. To correct for composition bias, threading scores are calculated as the sum of contact potentials less the sum expected for random shuffles of the aligned residues(15-16).

Conserved Core Structures

Conserved regions of the template are identified as a subset of backbone coordinates conserved in structure-structure alignments with homologous structural neighbors(17). Chain-continuous segments from this Homologous Core Structure (HCS) are extended to give minimum-length core elements used in threading. Extension adds residues within the same secondary structure element (SSE) to either end of HCS segments, up to the point that 65% of inter-SSE contacts are included(18). SSE segments present in 50% or more of structural neighbors also define conserved regions, provided that inter-SSE contacts per residue are at least 45% of the mean for all SSEs. These segments are similarly extended to define minimum-length core elements. The maximum lengths of loops in threading models are set in proportion to the maximum number of unaligned residues observed in the corresponding loop region in structure-structure alignments with homologous neighbors.

Structure-structure alignments defining the HCS are taken from Entrez(13). Each neighbor is weighted based on mutual sequence similarity19 and we identify a template residue as part of the HCS when the sum of weights for neighbors aligning that residue is 80% or more of the total. This threshold is lowered if necessary to bring HCS size over 25% of domain size. Homologous neighbors are initially identified as those in the same SCOP superfamily(20) or with greater than 12% sequence identity in structural alignment if no SCOP classification is available. The HCS calculated from these neighbors is used to calculate HCS-overlap scores for other structural neighbors and those crossing an empirical threshold of .9 are identified as homologous(17). This calculation is repeated until no further homologous neighbors are identified. The HCS is used for threading core definition only when the sum of weights corresponds to 2.5 or more independent neighbors, derived from 5 or more structures. Otherwise the threading core is based on SSE segments contributing 65% of inter-SSE contacts with loop length constraints obtained from a database survey(18).

Conserved Sequence Motifs

Conserved motifs within template sequences are identified by comparison to other sequences in the NCBI non-redundant database using PSI-BLAST(6). Sequences with E-values less than .01 are collected automatically and used to compute a PSSM for each template. The similarity of target sequences to the template PSSM is expressed as a score relative to the mean value expected for random shuffles of the aligned target residues. We note that while template PSSM's are developed using the BLAST alignment algorithm, target sequences are aligned with templates using the core element threading algorithm.

Threading and sequence-similarity scores for candidate alignments are combined using a weighting factor w that is allowed to assume values between 0 and 1:

DG =  w DG^S +  (1-w) DG^T

Here DG is the combined score, DG^S the sequence similarity score and DG^T the threading score. We did not attempt to estimate the optimal value of w but instead conducted threading searches with a range of values. When scores were comparable we submitted alternative alignments based on different w values, to the extent allowed by the CASP3 restriction of no more than 5 models per target. For models based on the same template those with greater w were arbitrarily ranked first and assigned a lower model number.

Surprising Similarities Only

The statistical significance of threading scores is judged by comparison to the score distribution obtained for shuffled target sequences optimally realigned to the structural template. This distribution is assumed to be approximately normal over the range of scores encountered in practice and p-values are calculated accordingly(16). For targets where no template achieved a significant score we predicted the target to be similar to "NONE", to indicate that our method could not identify a suitable template. For some targets with borderline scores we included the corresponding models as alternative predictions, in addition to "NONE", but in no case did these alternative models prove to be accurate as judged by criteria employed below.

Since it is impractical to compute threading p-values for each target-template combination by shuffling and realigning the target sequence many times we employ an empirical method to estimate the mean and standard deviation of this background distribution. The method relies on the observation that these parameters vary in a regular fashion with the number of alternative alignments allowed by the length of the target sequence and the core definition (not shown). We have calibrated this procedure for threading scores with w=0, and statistical significance of threading scores is thus judged by p-values that omit sequence-similarity terms. For top hits we confirm p-values for other w values by direct estimation from shuffled sequences.

Results

An Example Prediction

To illustrate the performance of threading with family-specific core definitions we consider a single example in detail, a prediction for CASP3 target 81, methylglyoxal synthase from E. Coli(10). Threading search of the template database with the sequence of target 81 revealed a single hit, 1JDB-K-8, the eighth domain of E. Coli carbamoyl phosphate synthase chain K(21). The threading p-value was highly significant, .00005, and we submitted as our prediction automatically generated alignments based on relative weights of sequence-similarity vs. contact potential terms of w=1, w=.5, and w=0 . 1JDB-K-8 was not identified with low p-value using a core definition based on central fragments of helices and b-strands, as employed at CASP1(18) and CASP2(8). This indicates that the core definition based on structure neighbors is more specific, reducing the number of possible threading alignments and the chance that a shuffled sequence would score equally well.

The conservation profile derived from the structure neighbors of template 1JDB-K-8 is shown in Figure 1a. One may see that the conserved core elements identified from this profile overlap secondary structure elements but are not coincident with them. One helix at the C-terminus is not conserved across the protein family, for example, and is omitted from the threading core definition. The sequence conservation profile of 1JDB-K8 is shown in Figure 1b. Sequence conservation across this family is not strong, and the information content of this profile was insufficient to identify the target 81 sequence in a PSI-BLAST search. Nonetheless, one may see some weakly conserved features, including a phosphate binding site near residue 970 and a proline at the C-terminus of the ninth core element. As it turns out the threading core of 1JDB-K-8 and these sequence motifs are conserved in target 81, and this has allowed us to easily recognize target 81 as a member of this protein family(22).

Figure 1. Structure (a) and sequence (b) conservation profiles for domain 8 of carbamoyl phosphate synthase, 1JDB-K-8. The horizontal axis indicates residue number in chain K of 1JDB. For structure conservation (a) the vertical axis indicates the fraction of the structure-structure neighbors of 1JDB-K-8 in which a structurally equivalent residue is present at each position. Open segments at the top indicate the location of secondary structure elements within 1JDB-K-8, and closed segments just below the extent of the minimum-length threading core elements. For sequence conservation (b) the vertical axis indicates information in the PSSM based on sequence neighbors of 1JDB-K, measured in bits. The most frequent residues at sites of relatively high information content are indicated by the single-letter amino-acid codes plotted on the figure. Phosphate binding residues of 1JDB-K-8 are indicated by arrows.

In Figure 2 we compare the predicted model for target 81 to its experimental structure. The threading alignment of the target sequence with the template was almost entirely correct, resulting in a model with a Ca RMS of 3.0 Angstroms and a Contact Specificity(23) of 69% for an alignment spanning 84% of the template residues. These values are for the model with id=1, derived with w=1, 100% of the score derived from the sequence-similarity score. The model with id=2, is perhaps more accurate, with RMS of 3.2 Angstroms and Contact Specificity of 72% for an alignment spanning 92% of template residues. This model was derived with w=.5, equal weight on the contact potential and sequence similarity scores. The model with id=3, w=0, is somewhat worse with RMS 3.6 Angstroms and Contact Specificity 65%. It would appear that the greatest threading alignment accuracy was obtained when contact potential and sequence similarity scores were combined with equal weight.

Figure 2. Predicted and experimental structures of methylglyoxal synthase, CASP3 target 81. The model structure based on 1JDB-K-8 is shown on the left and the observed structure on the right. Red coloring indicates regions where the threading and structure-structure alignments of target 81 and 1JDB-K-8 agree exactly. Orange coloring indicates regions assigned coordinates in either the threading or structure-structure alignment but not both, i.e. where the predicted coordinates differ from the observed structure. Yellow coloring indicates regions where coordinates were omitted from both the threading and structure-structure alignments, i.e. where structural differences were detected and the corresponding region omitted by threading. The location of the phosphate binding site in 1JDB-K-8 is indicated by green coloring. The figure was prepared using InsightII from MSI.

The prediction for target 81 hardly approaches the accuracy of an experimental structure. 1JDB-K-8 was the most similar template available in the database, according to the VAST algorithm22, but the RMS of the structure-structure alignment is only 2.2 Angstroms, and one could not hope to have done better in a threading prediction. Nonetheless, it would appear that the threading model is sufficiently accurate to make useful predictions of functional properties. One may see in Figure 2 that residues forming a phosphate binding site in 1JDB-K-8 are conserved in target 81 and correctly aligned with the coordinates forming this site. From the threading model one might thus infer the likely location of a binding site for anionic substrates. This is perhaps the most specific functional prediction one could expect for proteins as remotely related as carbamoyl phosphate synthase and glyoxal synthase.

Sustained Model Accuracy

We submitted blind predictions for a total of 19 targets whose structures were determined in time for the CASP3 workshop. For 8 of these targets our prediction was "NONE", to indicate that our method could not find a statistically significant threading match with any structural template in the library. For the remaining 11 targets predictions were based on a single structural template or, in the case of targets 46, 54, 63, 71 and 74, on two structurally similar templates. For these 11 targets we may directly measure the accuracy of the models generated by the core element threading algorithm, as shown in Table I.

Legend to Table I: Model ID gives the sequential identifier (between 1 and 5) assigned to this model. CASP3 Type gives the difficulty category assigned at the CASP3 workshop, CM for comparative modeling and FR for fold recognition. PSSM Weight gives the relative weight that was put on sequence similarity scores in threading alignment. Template PDB-Id lists the PDB accession code and chain identifier of the template used in the model. Core indicates the core definition method used with this template. E stands for "evolutionary core", based on structural neighbors and C for "contact core" based on secondary structure elements. M stands for "manual", indicating manual adjustment of core elements and/or alignment constraints based on examination of sequence and structure neighbors of the template. Model Length is the number of Ca coordinates in the predicted model. Model RMSD gives the Ca RMS of the model superimposed on the true structure of the target. Shift Error is the average difference in template residue number for target residues in the threading and structure-structure alignments(23). CSpc is Contact Specificity, the fraction of residue pairs with Ca distance under 8 Angstroms that are present in both the predicted and true structure of the target(23). Asp4 is Alignment Specificity (+/-4), the fraction of aligned residue pairs which agree to within a difference of 4 in template residue number(23). The VAST alignment for the beta-spiral structures of target 68 and 1RMG is that most consistent with the sequence similarity of these proteins(22). Submitted models for target 70 were affected by an error in data transcription to CASP3 format; the intended alignments were more accurate than shown. The two submitted models for target 79 spanned two disjoint regions of the target and were intended as independent domain predictions; the more accurate prediction for the C-terminal domain is shown.

We employ measures of accuracy from the CASP2 experiment(23). These include two measures of global accuracy, conventional Ca RMS and average Alignment Shift Error, which compares threading alignments to the structure-structure alignments generated by VAST(24), as distributed to predictors prior to the workshop(22). The table also lists Contact Specificity, the fraction of predicted Ca contacts present in the experimental structure, and Alignment Specificity, the fraction of aligned residue pairs in the threading alignment also present in the VAST alignment. These latter measures detect partially correct models by indicating the extent of any correctly modeled substructure. We list accuracy measures for the "best" model predicted for each of these 11 templates, that with the greatest Contact Specificity. Values for alternative models submitted as CASP3 predictions are available electronically(22).

It is arbitrary to choose a particular accuracy measure and threshold and to classify as "correct" all models that exceed this threshold. And it is clear that none of the models in Table I approaches the accuracy of an experimental structure. But we note that by the "critical" accuracy threshold suggested two years ago for CASP2, threading predictions for all but one of the models in Table I are "correct". For all but one of the models Alignment Specificity is either greater than 50% or Contact Specificity is greater than 25%(1-2). This includes the 4 models identified at CASP3 as comparative modeling targets and 6 of the 7 models identified as fold-recognition targets(10-11). While we made no attempt to rank alternative models we note that the model with id=1 was "correct" for 5 of the 7 fold-recognition targets (targets 46, 53, 54, 79, 81), and that all alternative models were "correct" for 4 of them (targets 53, 54, 79, 81) (22). By these measures the core element threading algorithm appears to have attained some level of sustained prediction accuracy.

Evaluation of these predictions by the CASP3 assessor employed different accuracy measures, but his conclusions seem largely consistent. Predicted models for all 7 fold-recognition targets were assigned a letter between "B" and "D"11, indicating that they were in the assessor's opinion based on a correct template and that the model with id=1 has ranked between "second place" and "fourth place" with respect to the "sf0+sf4" accuracy measure(25). The quantity "sf0+sf4" corresponds to the number of correctly aligned residues when comparing threading and structure-structure alignments and is highly correlated with Alignment Specificity multiplied by the length of the model (not shown). Ranking with respect to "sh0+sf4" does not correspond to a specific accuracy threshold, but it indicates that all 7 models were "competitive" with respect to threading alignment accuracy. We note that assessment using the CASP2 criteria appears to be more critical, considering the model for target 63 to be "incorrect", with Alignment Specificity zero, while "sf0+sf4" identifies 14 correctly aligned residues(25). This is presumably because the PROSUP(26) algorithm used to compute "sf0+sf4" has searched among alternative structure-structure alignments and chosen the one most favorable to the prediction(10).

Sustained Fold-Recognition Specificity

For 8 of 19 CASP3 targets we predicted the target to be similar to "NONE" of the available templates. To determine whether these predictions are in any sense "correct" we compare the true structures of the CASP3 targets to the structures in the template database, to see whether there is indeed less similarity to available templates. This analysis is shown in Figure 3, where we plot two measures of structural similarity for all 19 targets, the fraction of the target structure that may be superimposed on the template and percentage of identical residues in that structure-structure alignment. A plot of this type was previously suggested as a "phase diagram" of target difficulty(2).

Figure 3. Structural similarity of CASP3 targets to template structures in the database. The horizontal axis indicates the percentage of identical residues in structure-structure alignments computed by the VAST algorithm(22). The vertical axis indicates the fraction of the target structure that is superimposable on the template structure. Values plotted are an average taken over structural neighbors with the most extensive structural similarity, where structure-structure alignment length is 85% or more of the longest alignment. Large symbols indicate either a "correct" model as described in the text (square) or a prediction where "NONE" was included in the predicted models (triangle). The line on the plot indicates an apparent difficulty boundary, such that targets to the top and right were modeled correctly. Small symbols indicate other aspects of sequence and structure similarity: (+) targets where similarity to the template could be recognized by PSI-BLAST; (x) targets with characteristic sequence motifs; (o) targets recognized by VAST; (filled circle) targets not recognized by VAST or superimposed with less than 50% of their residues and fewer than 25% of target structure contacts conserved. For all but one case where "NONE" was predicted (target 77) the model with id=1 was identified as "NONE".

The 10 targets where predicted models were "correct" fall to the upper right in Figure 3, with a greater fraction of their structure superimposable on a database template and/or a greater fraction of identical residues. The 8 targets where we predicted "NONE" fall to the lower left, with less extensive similarity to database templates and/or a lower fraction of identical residues. One may in fact draw a line on the plot to separate these two groups. It appears that the core element threading algorithm can reliably produce accurate models when structural similarity exceeds a certain threshold and reliably avoid a "false positive" prediction when structural similarity falls below that threshold. Critical values are about 60% of target residues superimposable on a database template, when sequence similarity is at the chance/background level of about 10%, or about 40% of target residues superimposable when sequence similarity reaches 20%, a level indicative of conserved side-chain interactions(27).

One exception to this pattern is apparent in Figure 3, the prediction for target 63, where we find an "incorrect" model even though there is extensive similarity to templates in the database. Target 63 was classified as a two-domain structure by both the CASP3 assessor(11) and the automated domain identification algorithm used by VAST(22). Our prediction treated the target 63 sequence as a single domain, however, and the threading alignment in effect "exchanged" strands of b-sheet from one domain to another. The test statistic we employ indicated a borderline p-value for this alignment and in retrospect it is clear that this indicated an inaccurate model. We thus emphasize that the summary of sustained fold-recognition performance presented in Figure 3 applies to targets with a single domain, or where domain boundaries could be identified in advance.

The CASP3 assessor considered only 1 of the 8 targets where we predicted "NONE" to be "new folds"(11). By this classification our CASP3 predictions achieved an overall sensitivity of 53% for fold recognition targets, 8 folds recognized (7 known and 1 new) out of 15 attempts. One can see from Figure 3 that 4 of these targets have less than 50% of residues superimposable on template structures and less than 25% of contacts conserved, a level of similarity that may prove insufficient for reliable recognition by threading methods. If these 4 targets are considered "new folds" overall sensitivity is 73%, 11 folds recognized (7 known and 4 new) out of 15 attempts. While it is difficult to define a "new fold" objectively, one can expect that the threshold for reliable prediction will move to lower levels of structural similarity as threading methods improve.

Combined Threading and Motif Analysis

For CASP3 predictions we introduced a combined threading score based on the sum of conformational energy and sequence similarity terms, and for some targets we submitted alternative alignments computed with different relative weights on these terms. It is now interesting to compare model accuracy for these alternative alignments to see what combination was most successful.

In Table II we show Contact Specificity for threading alignments computed with the contact potential term only and with a sum of contact potential and PSSM terms. One may see that model accuracy is in most cases improved by combining terms, even though the PSSM was insufficient for recognition of these targets by PSI-BLAST. In some cases, as for target 81, it is clear that the PSSM detects sequence motifs that are weakly preserved between the target and template. In other cases the PSSM seems to encode little more than a preference for hydrophobic vs. hydrophilic residues, information that is also encoded in the contact potential terms. Even in these cases it would appear that the two kinds of information are complementary, however.

An exception is also apparent in Table II. The best model for the N-terminal domain of rat alpha adaptin10, target 71, was obtained with contact potentials only(22). The template used for this model was 3DPA, the PapD chaperone protein from E. Coli(28). Target 71 and 3DPA are structurally similar, but there is no detectable sequence similarity and the CASP3 assessor has classified target 71 as belonging to a different SCOP superfamily, suggesting that these proteins are not evolutionarily related(11,20). It would seem that the PSSM for 3DPA is irrelevant to target 71 and has simply added "noise" to the "signal" from contact potentials. It would appear that the sequence similarity term improves model accuracy only when the target and template indeed share a common evolutionary ancestor.

Discussion

Of 35 targets solved in time for the workshop 13 were classified by the CASP3 assessors as homology modeling targets, indicating that similarity of these targets to known structures could be recognized by sequence comparison alone(11,29). Among the remaining 22 fold-recognition targets the core element threading method identified the correct structural family for 7 and produced relatively accurate models for 6. While the CASP3 targets are not a representative sample of newly determined sequences, it seems clear that use of structure information has improved the success rate in sequence classification. The overall success rate increased from 37% (13 of 35 recognized by sequence comparison) to 57% (20 out of 35 recognized by either sequence comparison or threading).

It was also possible to identify the correct evolutionary family for some CASP3 fold-recognition targets by consideration of their functions and the presence of sequence motifs. In our hands this was the case for targets 54 and 79, for example. The improvement in classification success rate due to use of three-dimensional structure information might thus be stated more conservatively as from 43% (15 of 35) to 57% (20 of 35). It seems clear that sequence-structure alignment accuracy for these targets improved with use of structural information, however, and this seems to have been the case for some comparative-modeling targets as well(28). We thus emphasize that threading alignment algorithms may improve the quality of predicted models, even in cases where they are not essential for correct classification per se.

While we conclude that the core element threading algorithm has improved fold recognition beyond what was possible by sequence comparison, we also note that the limitations of current threading methods are easy to see. It was apparent from the CASP2 experiment that fold-recognition success was determined primarily by the difficulty of the target, which could be measured as the extent of structural similarity to known templates (1,2). This same pattern is clearly evident for CASP3 predictions, as shown in the "phase diagram" of target difficulty in Figure 3. To succeed, threading methods require a template matching roughly 60% of the target structure to a resolution of roughly 2.5 Angstroms. "New folds" are often defined by a unique topological arrangement of helices and beta strands. Even an "old fold" may be unrecognized by threading, however, if it does not contain a highly similar core structure with conserved side-chain interactions.

Acknowledgements

We thank the CASP3 organizers and assessors and the experimental groups who have provided target sequences and structures. We thank Tom Madej and Ken Addess for calculating VAST structure comparison results and the NIH Intramural Research Program for support.

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