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

Keywords: threading, protein structure prediction, TM-score, solvent accessibility, dihedral angle prediction, hydrophobic scoring matrix

Scoring functions

The scoring function of MUSTER for aligning the ith residue on the query and the jth residue on the template is Score(i,j)

where “q” stands for the query and “t” for the template proteins. We explain the specific terms as follows.

Sequence profiles

The first term in Eq. (1) is the sequence-derived profiles. Pc_q(i,k) is the frequency of the kth amino acid at the ith position of the multiple sequence alignments (MSA) obtained by a PSI-BLAST search⁴⁰ of the query sequence against a nonredundant sequence database (ftp://ftp.ncbi.nih.gov/blast/db) with an E-value cutoff of 0.001. This is the frequency profile from “close” homologies. A more “distant” frequency matrix Pd_q(i,k) is generated using a higher E-value cutoff of 1.0. The combination of both close and distant sequence profiles follows Skolnick’s idea^25,26,43 which helps increase the MUSTER alignment sensitivity in different homology area. We tried to use different weights to the close and distance profiles and found that the equal weights give the best performance. In calculating the frequency profiles of Pc_q(i,k) and Pd_q(i,k), the Henikoff and Henikoff⁴⁴ weights are used to reduce the redundancy of aligned multiple sequences. Moreover, to emphasize the sequence of more significant PSI-BLAST hits, we give stronger weights to the sequences of lower E-value than those of higher E-value. That is, the sequences with E-value of <10⁻¹⁰ are given a weight of 1.0. The weight is linearly decreased with the logarithm of the E-values until a weight of 0.5 is used for sequences with E-value of 1.0. L_t(j,k) is the log-odds profile (Position-Specific Substitution Matrix in PSI-BLAST) of the template sequence for the kth amino acid at the jth position. The template log-odds profile is obtained by the PSI-BLAST search with an E-value of 0.001. We attempted to combine L_t(j,k) with the “distant” log-odds profiles with an E-value of 1.0 for the template sequence too. But it turned out not to increase the prediction accuracy.

Secondary structure match

The second term compares the predicted secondary structure s_q(i) at the ith position of the query and the real secondary structures s_t(j) at the jth position of the template. δ(s_q(i), s_t(j)) equals to 1 if s_q(i) = s_t(j) and −1 otherwise. The secondary structure for the query is predicted by PSI-PRED⁴¹ and that for the template is assigned by the STRIDE program,⁴⁵ both having three states of helix, strand, and coil.

Structure profiles

The third term is a depth-dependent structure-derived profile which is similar as that used by Zhou et al.¹⁴ Each template structure is split into small fragments with nine residues, which, as seed fragments, are compared by gapless threading with nine-residue fragments from a set of non-homologous PDB proteins selected by PISCES.⁴⁶ The fragments similar as the seed fragment are collected from the database and used to calculate the frequency profile at each position of the template, where the similarity is defined by RMSD and the fragment depth similarity⁴⁷ between the seed fragment and the fragments in the database. Following Zhou and Zhou,¹⁴ we collect top 25 database fragments for each seed fragment. Thus, we have 225 fragment sequences aligned at each position on the template, where Ps_t(j,k) is the frequency of the kth amino acid appearing in the 225 sequences corresponding to the jth position on the template. L_q(i,k) is the log-odds profile for the kth amino acid at the ith position of the query sequence from the PSI-BLAST search with a E-value cutoff of 0.001.

Solvent accessibility

The fourth term in Eq. (1) computes the match between the predicted solvent accessibility SA_q(i) for the ith residue of the query and the real SA value SA_t(j) of the jth residue of the template as assigned by STRIDE.⁴⁵ To predict SA_q(i), we first trained a two-state (exposure/burial) neural network machine⁴² on 3365 nonredundant high-resolution protein structures on the basis of their sequence profile from PSI-BLAST.⁴⁰ The maximum SA value in an extended tripeptide (Ala-X-Ala) is taken from Ahmad et al.⁴⁸ Seventeen different SA cutoffs (0.05, 0.1, . . ., 0.85) are used to define the residue exposure status in the NN training. The residue exposure index isSAq(i)=∑m=117aim/17 where a_im is the two-state neural network prediction of exposure (a_im = 1) or burial (a_im = 0) with the mth SA cutoff for ith residue of the query, which has a strong correlation with the real value of SA. For an independent set of 2234 nonhomologous proteins used by Zhang and Skolnick,^49,50 the overall correlation coefficient between the predicted SA_q(i) and the real exposed area assigned by STRIDE⁴⁵ is 0.71, while the same correlation for the widely-used Hopp-Woods⁵¹ and Kyte-Doolittle⁵² hydrophobicity indices are 0.42 and 0.39, respectively.

Backbone dihedral torsion angles

The fifth (and sixth) term computes the match between the predicted Psi (and Phi) angle φ_q(i) (and φ_q(i)) for the ith residue of the query and the real Psi (and Phi) angle φ_t(j) (and φ_t(i)) of the jth residue of templates. Here both φ_q(i) (and φ_q(i)) and φ_t(j) (and φ_t(i)) are normalized by 360° so that the angle values stay in [−0.5, 0.5]. The predicted dihedral angles for queries are obtained from our SVR-ANGLE program (Wu and Zhang, submitted), which exploits the support vector regression (SVR) technique⁵³ (with LIB-SVM⁵⁴ as an implementation) to train the dihedral angles on an input vector of three feature sets: sequence profile, secondary structure, and solvent accessibility. The output of SVR-ANGLE is the real value of predicted torsion angles for each residue. Based on a test of 500 nonredundant testing proteins, the correlation coefficient between the predicted Psi (Phi) angles and the experimental Psi (Phi) angles assigned by DSSP⁵⁵ is 0.71 (0.63). The average absolute error for the Psi (Phi) predictions is 0.140 (0.091).

Hydrophobic scoring matrix

The seventh term is a 20 × 20 hydrophobic scoring matrix taken from Silva,³⁶ which is designed to match the hydrophobic patterns of query and template. The idea was inspired by the observation of Gaboriaud et al.,³⁷ where sequences with similar distribution patterns of the hydrophobic residues (V, I, L, F, Y, W, M) are often structural homologues. The hydrophobic scoring matrix is assigned as: M(AA_q(i), AA_t(j)) equals 1 when both AA_q(i) and AA_t(j) are from the set of hydrophobic residues. The matches between all identical residue pairs (except for Pro and Gly that are scored as 1) are scored as 0.7. All other matches are assigned a null score.

Dynamic programming

The Needleman-Wunsch³⁸ dynamic programming algorithm is used to identify the best match between the query and the template sequences. A position-dependent gap penalty in the dynamic programming is employed, that is no gap is allowed inside the secondary structure regions (helices and strands); gap opening (g_o); and gap extension (g_e) penalties apply to other regions; ending gap-penalty is neglected. The shift constant c₇ is introduced to avoid the alignment of unrelated residues in the local regions.

Template ranking scheme

In the original PPA program,³⁰ the templates are ranked based on a raw alignment score (R_score) divided by the full alignment length (L_full) (including query and template ending gaps) as shown in Figure 1. In MUSTER, we use R_score/L_partial as another possible ranking scheme, where L_partial is the partial alignment length excluding query ending gap as shown in Figure 1. A combined ranking is taken as following: if the sequence identity of the first template selected by R_score/L_partial to the query is higher than that selected by R_score/L_full, we use the template ranking by R_score/L_partial. Otherwise, we use the template ranking by R_score/L_full.

Parameter training

There are overall nine parameters in the MUSTER algorithm (i.e. c₁ to c₇, g_o and g_e), which need to be appropriately tuned. One of the often-used tuning methods is based on the PROSUP database,⁵⁶ which includes 127 nonhomologous proteins pairs with the best possible alignment obtained by the structural alignment program PROSUP. To train the threading algorithms, one can tune the parameters by maximizing the number of threading-aligned residue-pairs which are identical to that in the structural alignments.^14,30,57,58

There are a few protein pairs in the PROSUP databases which do not have similar topology. The residue-pairs by the PROSUP structural alignments in this portion of protein pairs do not correspond to meaningful topology coincidence and may mislead the trained threading algorithms. Therefore, we remove all PROSUP protein pairs with a TM-score <0.5 in our training. Here, TM-score has been defined by Zhang and Skolnick²⁹ to assess the topological similarity of protein structure pairs with a score in [0,1] Statistically, a TM-score <0.17 means a randomly selected protein pair with gapless alignment taken from PDB; TM-score >0.5 corresponds to the protein pairs of similar fold. The statistical meaning of TM-score is independent of protein sizes.²⁹

Because the number of protein pairs in PROSUP is relatively small (110 with TM-score >0.5) compared with the number of free parameters in MUSTER, we add a new set of 190 nonredundant protein structure pairs to our training set. These 190 pairs are selected with a TM-score >0.5 from 558 randomly chosen SCOP families,⁵⁹ where 120 pairs share the same “class” and “fold” but different “super-family” and 70 pairs share the same “class,” “fold,” and “super-family” but different “family.” The protein length of the 190 protein pairs ranges from 43 to 812 with sequence identity between any pair is less than 30%. The sequence identity between any of the 190 proteins pairs and any of the 110 PROSUP protein pairs is also below 30%. A complete list of the composite 300 protein pairs are listed at our website: http://zhang.bioinformatic-s.ku.edu/MUSTER/data1.html with the structural alignments of the 190 protein pairs generated by TM-align⁶⁰ and that of the other 110 pairs taken from PROSUP.⁵⁶

The second way of training the MUSTER parameters is to directly run the threading program on a small set of training proteins and optimize the parameters based on the overall TM-score of the final threading results. An advantage of this real-case training is that the target needs to scan all template proteins in the template library and the ranking system is naturally trained. For this purpose, we construct another set of 111 nonhomologous proteins, which include 39 “Easy” targets and 61 “Hard” targets taken from the PDB library (according to the PPA categorization) plus 11 new fold (NF) targets from the CASP6 experiment. This training set and the experimental structures are listed at: http://zhang.bioinformatics.ku.edu/MUSTER/data2.html.

We use a grid-search technique for both sets of training data, which split the 9-dimensional parameter space into lattices and try all the lattice points. In the training set 1, because the alignment searching on 300 protein pairs is quick, we use a finer parameter grid system and select the lattice with the highest average alignment accuracy. The program with this set of parameters is called MUSTER1. The final parameters used in MUSTER1 are c₁ = 0.65, c₂ = 1.10, c₃ = 4.49, c₄ = 2.01, c₅ = 0.59, c₆ = 0.20, c₇ = 1.00, g_o = 6.99, g_e = 0.54. In the training set 2, because MUSTER needs to scan all templates in the MUSTER library, the threading time is slower than that in the training set 1. We therefore use a more coarse-grained lattice system. After the initial selection, a finer tuning near the first selected lattice is performed. To avoid the homologous contamination, we exclude all templates with a sequence identity higher than 30% to the target proteins. The lattice with the highest average TM-score is selected. The program with this set of parameters is called MUSTER2. The final parameters used in MUSTER2 are c₁ = 0.66, c₂ = 0.39, c₃ = 1.60, c₄ = 0.19, c₅ = 0.19, c₆ = 0.31, c₇ = 0.99, g_o = 7.01, g_e = 0.55.

Z-score and target categorization

For the purpose of predicting the quality of threading alignments, we define a Z-score as

where Rscore′ is the normalized score R_score/L_full or R_score/L_partial as described above; 〈⋯ 〉 indicates the average over all templates. In Figure 2, we present the data of TM-score versus Z-score for all 5550 threading alignments by MUSTER2 (top 50 templates from each of the 111 train proteins). There is obviously a correlation between TM-score and Z-score, which allows us to use Z-score as an indication of the quality of the threading models. If we use Z-score = 7.5 as a cutoff of the successful alignment, the false positive and false negative rates for TM-score >0.5 are 1.2 and 5.3%, respectively. In the following, we will define the target as “Easy” (“Hard”) target if the Z-score of the first alignment is higher (lower) than 7.5.

Template library

The protein structure templates are taken from the PDB library with a sequence identity cutoff = 70%. The theoretical models and the obsolete structures are discarded. If a template has multiple domains (e.g. Domains A and B), both the whole chain and the individual domains (e.g. Chain AB, Domain A, and Domain B) are included in the library. We found that the inclusion of individual domains increases the sensitivity of the MUSTER algorithm. As of August 1, 2007, the MUSTER template library includes 20,878 protein structures.

Results on training proteins

In Table I, we present the results of three programs (PPA, MUSTER1, and MUSTER2) on the two training protein sets. Column 3 is the average alignment accuracy (Acc) that is defined as fraction of the “correctly” aligned residue pairs which are the same as the golden-standard structure alignments. Column 4 is the average alignment accuracy (Acc₄) that is similar as Acc but allows a four-residue shift when compared with the structure alignments. Column 5 is the TM-score of the rank-1 models together with the RMSD and alignment coverage. Column 6 is that for the best in top-five models. As expected, the performance of the algorithms depends on whether the trained parameters are used. In the training set 1, MUSTER1 generates more accurate alignments than both PPA and MUSTER2; in the training set 2, the TM-score of the alignments by MUSTER2 is higher than that by both PPA and MUSTER1. A fair comparison has to be made based on an independent test set of proteins.

Results on testing proteins

Using PDBSELECT (2006 March),⁶¹ we select a set of 500 nonhomologous proteins of sequence identity <25% and with length from 50 to 633, which includes 120(/53/327) α(/β/αβ) proteins. These proteins are also nonhomologous to the two sets of training proteins. A list of the 500 testing proteins and their PDB structures are available at http://zhang.bioinformatics.ku.edu/MUSTER/data3.html. For a fair comparison, the template library (including 20,878 templates) used for PPA is the same as those for MUSTER, where all the templates with sequence identity >30% to the query are excluded.

Overall performance

The performance and comparison of PPA and MUSTER on the 500 testing proteins are summarized in Table II. For the first (and the best in top-five) models, MUSTER1 identifies template alignments with an average TM-score of 0.4410 (and 0.4787), which is 2.9% (and 2.3%) higher than 0.4285 (and 0.4680) by PPA. If we use the parameters trained by threading the 111 proteins, MUSTER2 identifies even better template alignments with an average TM-score of 0.4503 (and 0.4830), which is 5.1% (and 3.2%) higher than that by PPA for the first (and the best in top-five) models. Based on the TM-score, MUSTER2 certainly outperforms MUSTER1. Especially, the average alignment coverage of MUSTER2 is lower than MUSTER1 although the alignments of higher coverage tend to have higher TM-score.²⁹ This means that the higher TM-score in MUSTER2 is because of more accurate residue alignments. One reason for the better training in MUSTER2 than MUSTER1 is that the number of protein pairs in the second training set (111 × 20,878) is much larger than that of the first training set (300). Although the first training set allows a quick and much finer grids training, it could be over-trained by the small set of protein pairs especially when a number of parameters are trained. The second reason may be that the training process of the first training method does not consider the ranking scheme because there is only one template for each protein pair, while the ranking is naturally trained in the second training method. In the following, our analysis will only focus on the result of MUSTER2 (or MUSTER) unless explicitly mentioned.

The higher TM-score of MUSTER over PPA is because of both longer alignment coverage and the more accurate alignment as indicated by the smaller average RMSD. The difference between MUSTER and PPA is examined by the Wilcoxon signed rank test with a P-value < 1.0 × 10⁻¹⁶ for the first model and a P-value < 1.0 × 10⁻⁶ for the best in the top-five models. On 92 out of 500 proteins, MUSTER generates the first threading alignment with a TM-score 0.05 higher than PPA. Only on 24 targets, PPA does better than MUSTER with a TM-score difference >0.05. A head-to-head comparison of the first template alignments by PPA and MUSTER is presented in Figure 3(a) where there are obviously more points above the diagonal line which indicates that in more cases MUSTER identifies a better template alignment than PPA.

In Figure 4, we show a typical example from the target “1eq1A” where MUSTER does better than PPA. In this example, the first model identified by MUSTER has a TM-score = 0.71 with the template structure from “1aep_”; the first model by PPA has a TM-score = 0.19 with an incorrect template structure from “1av1A.” Although the correct template “1aep_” is ranked as the 3rd model in PPA, the alignment is still not correct with a TM-score = 0.25 [Fig. 4 (b)]. Here, both the target “1eq1A” and the template “1aep_” are α-helix proteins and the secondary structure match is not the main driven force for the correct alignment. Actually, in PPA alignment, most aligned residue pairs are helix–helix matches but there is about an 11-residue shift from the correct alignment (see the lower panel of Fig. 4). From the 3D superposition of the threading model and native structure shown in Figure 4(b), the orientation of C-terminal tail is mismatched and there are big gaps between residues 27–45 and 90–107. Second, the sequence identity between “1eq1A” and “1aep_” is low (19%) and the contribution from the sequence profile alignment is small as well. When we specifically check the terms of the alignment path, the values of the seven terms for MUSTER are: 29.4 (sequence profiles), 72.6 (secondary structure match), −27.1 (structured profiles), 169.1 (solvent accessibility), 24.2 (Psi angle), 24.9 (Phi angle), and 8.9 (hydrophobic scoring matrix). The values of the two terms for PPA are 143.05 (sequence profiles) and 45.5 (secondary structure match) respectively. Obviously the main contribution to the correct alignments is from the new structure terms (solvent accessibility and dihedral angles in this example—the sum of new structural terms is much larger than the profile and secondary structure matches), which explains the reason of improvement of MUSTER over PPA by introducing additional features.

“Easy” versus “Hard” targets

In the lower part of Table II, we split the targets into “Easy” and “Hard” targets. Here we define an “Easy” target when both MUSTER and PPA categorize it as “Easy,” that is Z-score (MUSTER) >7.5 and Z-score (PPA) >7.0; a “Hard” target is defined when both MUSTER and PPA categorize them as “Hard,” that is Z-score (MUSTER) <7.5 and Z-score (PPA) <7.0. There are thus overall 203/255 “Easy”/ “Hard” targets. The other 42 targets with nonidentical categorizations by PPA and MUSTER are not considered here.

For the “Easy” targets, the average TM-score of MUSTER is 0.6571 (0.6795) for the first (the best in top-five) models, which is 2.2% (0.9%) higher than 0.6430 (0.6734) by PPA. The percentage of the improvements is smaller than the overall testing set (5.1 and 3.2%, respectively) mainly because both the PPA and MUSTER alignments are closer to the perfect alignments and therefore there is less room for improvements. The average TM-score of the structural alignment identified by TM-align⁶⁰ for the first pair of target/template is 0.6930, which sets an upper bar where the best threading alignment can go. However, the improvement is still statistically significant as examined by the Wilcoxon signed rank test with a P-value < 1.0 × 10⁻⁷ for the first model and a P-value < 1.0 × 10⁻⁶ for the best in the top-five models.

For the “Hard” targets, the average TM-score of MUSTER is 0.2842 (0.3242) for the first (the best in top-five models), which is 10.8% (6.6%) higher than 0.2564 (0.3040) by PPA. This improvement is higher than the overall testing set mainly because the performance of PPA in this set is much worse than the best structural alignment and there is a larger room for improvement. The TM-score by TM-align for the first target-template pairs is 0.3742. Obviously, even after the improvement, the average quality of MUSTER performance is considerably lower than the best structure alignment. This will be the major category of proteins which MUSTER has to deal with in future developments. Statistically, the improvement of MUSTER over PPA in the “Hard” targets is by Wilcoxon signed rank test with a P-value < 1.0 × 10⁻⁹ for the first model and a P-value < 1.0 × 10⁻⁹ for the best in top-five models.

Effect of using stringent cutoffs

Although we excluded the homologous templates using a sequence identity cutoff >30% to the target in the above testing as many previous studies did,^26,49,50,63 there are still some relatively “trivial” targets where homologous templates can be detected by PSI-BLAST.⁴⁰ Here, we use a second and more stringent homology cutoff where all threading templates with a sequence identity >20% to targets or can be detected by PSI-BLAST with an E-value < 0.05 are removed, which is called Cutoff-2 where the former one is referred to Cutoff-1.

The overall performance of PPA and MUSTER under Cutoff-2 is listed in Lines 6–8 of Table II. As expected, the average TM-scores of both PPA and MUSTER models are decreased compared with Cutoff-1. However, the average TM-score 0.3638 (0.4022) by MUSTER2 for the first (the best in top-five) model is still 6.3% (or 5.2%) higher than that of 0.3423 (0.3824) by PPA. The data is consistent with the result of Cutoff-1 in that MUSTER2 outperforms MUSTER1. The slightly larger increasing of MUSTER over PPA in Cutoff-2 is partly due to the fact that the effect of profile–profile match is somewhat reduced by the removing of the PSI-BLAST detectable templates which is the major driving force in the PPA alignment. The overall improvement from PPA to MUSTER in Cutoff-2 is examined by the Wilcoxon signed rank test with a P-value < 1.0 × 10⁻¹³ for the first model and a P-value < 1.0 × 10⁻¹⁸ for the best in top-five models.

In Figure 3(b), we present a head-to-head comparison of MUSTER and PPA under Cutoff-2. Again, there are more targets with a higher TM-score by MUSTER than that by PPA: In 105 out of 500 proteins, the TM-score difference is larger than 0.05 for MUSER over PPA; only in 34 cases, PPA does better than MUSTER with a TM-score difference larger than 0.05.

Under the Cutoff-2, there are respectively 93 “Easy” targets and 365 “Hard” targets. The comparison of PPA and MUSTER in both two categories is listed in Lines 11–12, and 15–16 of Table II. Both the first model and the best in top-five models of MUSTER have a higher average TM-score than that of PPA in the two sets, which demonstrates the robustness of the improvement of the MUSTER algorithm.

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