A widely used method to find conserved secondary structure in RNA is to first construct a multiple sequence alignment, and then fold the alignment, optimizing a score based on thermodynamics and covariance. This method works best around 75% sequence similarity. However, in a "twilight zone" below 55% similarity, the sequence alignment tends to obscure the covariance signal used in the second phase. Therefore, while the overall shape of the consensus structure may still be found, the degree of conservation cannot be estimated reliably.planACstar for improving structure conservation in structural alignments in the twilight zone. After constructing a consensus structure by alignment folding, planACstar abandons the original sequence alignment, refolds the sequences individually, but consistent with the consensus, aligns the structures, irrespective of sequence, by a pure structure alignment method, and derives an improved sequence alignment from the alignment of structures, to be re-submitted to alignment folding, etc.. This circle may be iterated as long as structural conservation improves, but normally, one step suffices.Based on a combination of available methods, we present a method named ClustalW, RNAalifold, and RNAforester, we find that for sequences with 30-55% sequence identity, structural conservation can be improved by 10% on average, with a large variation, measured in terms of RNAalifold's own criterion, the structure conservation index.Employing the tools  The biological function of an RNA molecule is often determined by the three dimensional structure of the molecule. The structure is often more conserved than the exact sequence of bases in the course of evolution. Therefore, a strong structural consensus among related, but diverged sequences can be taken as an indicator of a preserved functional role.Following a classification introduced in , the strPlan B is theoretically optimal, as it jointly solves the two optimization problems of alignment and folding under arbitrary scoring functions [O(nm3) time and O(nm2) space, where n is sequence length and m is the number of sequences, are rather high. Implementations are for example Foldalign, Dynalign, PMComp [unctions . Howevertions [Onm time an, PMComp , making Plan C applies to sequences that are too diverged to be meaningfully aligned based on sequence conservation. First, sequences are folded individually. This must be done with care. One cannot simply compute MFE structures and then align them with a structure alignment program. In an evaluation of 69 sequences from 10 RNA families, the MFE predictions had the same abstract shape (i.e. arrangement of helices) as the consensus structure only in 32 cases (see Table two in [RNAforester [MARNA [RNAcast [R-Coffee [e two in ). Such lforester , MARNA [r [MARNA ). RNAcas[RNAcast  was the R-Coffee .Plan A is probably the most widely used approach and is the one we are going to strengthen further here. It applies when sequences can be meaningfully aligned using an off-the-shelf multiple sequence alignment tool . Then, T [PFOLD , RNAalifAalifold ,19, ILM old [ILM , ConStruonStruct ).MURLET or MXSCARNA [WAR web server for aligning structural RNAs [The above listing of Plan A, B, and C methods is far from complete, as the difficulty of the problem is reflected by a large number of approaches. Numerous heuristics have been suggested to retain the power of Plan B approaches, but reduce its high computational cost and overcome its limitation to pairs of sequences, e.g. MXSCARNA ,23. The ral RNAs , where praison d'être when sequence conservation is above 90%. While the sequence alignment is certainly reliable, it carries little extra information compared to folding the sequences individually. The method works best around 75% of sequence similarity. Below 55%, measurements [planACstar, as it constitutes an iterated combination of steps from Plan A and Plan C.Plan A loses its urements  show a durements   [To evaluate the performance of Plan A in detail, consider Figure ex (SCI) . The lowsystematically obscure the covariance signal. As this observation has not been reported in the literature (to the best of our knowledge), let us explicate this phenomenon here.Let us look at the situation in some detail. It is generally known that with increasing divergence, sequence alignment will fail to align bases representing compensatory mutations and carry the covariance signal to be exploited in the subsequent phase. In fact, in the presence of gaps, sequence alignment will We use the familiar dot-bracket notation, where paired bases are indicated by matching parentheses, and unpaired bases by dots. For structures ..((....)).. and ..(....).., the expected structure alignmentAAGGAAAACCAA and AACAAAAGA, aligning two bases GG with a single base C, the algorithm has to insert a gap either to the left of C, or to the right. As the resulting score is not affected by this choice, the gap position may be chosen arbitrarily. Let us assume that the alignment algorithm first produces the mismatch, and then inserts a gap to the right of the mismatched base. So far, so good. Exactly the same situation arises in the alignment of CC and G. Again, the algorithm inserts the gap at the right side of G, and aligns the sequences this way:might show good sequence conservation, two gaps and a compensating base pair change. In any sequence alignment of Now, joint folding of the aligned sequences will produce:which prevents the second base pair in the upper sequence from being formed: Pairing the second G with the second C would create non-nested base pairing, which is not allowed in the folding algorithm.structure alignment program [In the 30-55% sequence identity range, we conjecture that the resulting consensus structure is often correct in its overall shape, while structural detail is lost due to the obscured covariance signal. Therefore, we disassemble the alignment and refold the sequences separately, with respect to the preliminary consensus. This separate folding will produce additional base pairs compatible with the consensus. We then align the resulting structures with a  program . This alThere is a clear limitation in this approach: We may recover base pairs missed in the first alignment folding, but we never undo consensus base pairs which were actually formed in the initial step. These base pairs will always persist in the improved structures, although they may be aligned in a different way. This is why we consider our approach a fine-tuning add-on to Plan A, rather than (yet another) new approach. This is in good analogy to tuning your guitar without reference to a perfect pitch device. You assume that one of the six strings, say A, is on pitch, and tune the other strings to the A string. While your guitar now sounds in harmony, in absolute terms, it may be more out of pitch than before. Our assumption is that, in the twilight zone, the initial alignment will be good enough to point to the string A which is closest to pitch in absolute terms.ClustalW, RNAalifold, and RNAforester. The quality of the consensus is assessed by RNAalifold's SCI score, the structure conservation index, which according to Gruber et al. [RNAalifold results in the consensus minimum free energy (MFE) EA as output. EA includes pseudo-energy contributions from observed covariation. Folding the sequences B1,.. Bn separately, we can compute their average MFE EA/This idea has been implemented using the tools r et al.  is the bRNAalifold's own quality criterion, the achieved SCI.Thus, we measure an improvement in terms of X. It does not preclude the existence of yet another, low energy consensus structure X', which may be structurally quite different and may actually be the relevant one for the RNA's function. Refolding all sequences from their MFE structures into X' instead of X might require only marginally more energy than with consensus X, but again, this does NOT imply that X and X' are structurally similar. X' might be the "true" structure, but Plan A would not notice it at all. Admittedly, the larger the number of sequences considered, and the more diverged they are, the more unlikely is this situation to occur. Plan A approaches could, in principle, be augmented to safeguard against this situation, but only at the high cost of performing suboptimal consensus folding.Note that the SCI is not a performance measure in the sense that an alignment optimizing the SCI score is closest to a "true" alignment. It serves as an indicator of structural conservation in diverged sequences, whether or not the conserved structure is "true". Mechanistically, the SCI accounts for the energy required to refold the sequences from their MFE structures into the predicted consensus Our new approach is based on the premise that it is worthwhile to increase SCI scores. However, we have also evaluated the resulting consensus structures against curated structures, and report on this in the Conclusion and in Additional File planACstar is an iterated combination of elements of Plan A and Plan C. It uses separate structure predictions, as done in Plan C, but includes information from a multiple sequence alignment and alignment folding as in Plan A. We use ClustalW for the initial alignment step, and RNAalifold for folding the sequences into the consensus structure, because they are most widely used tools for these tasks in practice. Let A be the initial sequence alignment, C is the preliminary consensus and X is its SCI-score. Ci is the projection of the basepairs of the preliminary consensus C to a sequence Bi from the input set of size n, where 1 ≤ i ≤ n. Si is the individual folding of a sequence Bi from the input set into the preliminary consensus structure C. Y is the multiple structure alignment of the folded structures. The multiple structure alignment implies a sequence alignment, which is the improved sequence alignment A* with SCI-score X*.In pseudocode, the procedure is as follows:B1,..., Bn,Given a set of RNA sequences A ← ClustalW - initial sequence alignment1. C ← RNAalifold(A); X ← sci-score(C) - preliminary consensus2. Ci ← Projection of basepairs in C to Bi - (see below)3. Si ← RNAfold -C Ci(Bi) for i = 1,.. n - individual folding of each Bi relative to consensus4. Y ← RNAforester - multiple structure alignment5. A* ← sequence alignment implied by Y - extract improved sequence alignment6. C* ← RNAalifold(A*); X* ← sci-score(C*) - fold improved alignment7. X* >X, set A ← A* and iterate from step 3, else exit with result A, C and X8. if Bi, and yields an unsaturated structure Ci for Bi. The call to RNAfold with option -C Ci (Step 4) may produce additional base pairs aside from those of Ci. These will, in general, be different for each Bi.The "projection" (Step 3) takes the base pairs from the consensus, removes the gaps with respect to sequence planACstar was evaluated on data set 1 of the BRAliBaseII benchmarking database [In the evaluation, we used the most recent version of RNAalifold  and Clusdatabase . BRAliBadatabase .Dataset 1 of BRAliBaseII contains various RNA sequences of Group II introns, 5S rRNA, tRNA and U5 spliceosomal RNA. The sequences were obtained from the Rfam database . Each RNRNAforester, therefore our method is restricted to concrete RNA sequences as input sequences. This restriction reduces the size of our test data set to 340 out of 388 subalignments.Currently, the full IUPAC code is not supported by For comparison, we include the score of the reference alignment. It must be kept in mind that it is scored from the full family alignment. Therefore, the reference alignment does not necessarily represent the optimal subalignment.planACstar and the reference alignment were scored and a filtering with a Savitzky-Golay filter was applied afterwards. The filter uses local polynomial regression to compute a smoothened value for each point.In Figure The results suggest a boundary at 55% sequence similarity. Above 55%, the SCI scores are in agreement, below 55%, the two approaches are outperformed by the reference alignment. This confirms the observation by Gardner, Wilm and Washietl:The results suggest that 60% sequence identity is a crude threshold, whereby the structural content of predicted sequence alignments diverges from reference structural alignments[lignments.planACstar shows an improvement in the zone between 30% and 55% similarity, compared to Plan A. While the underlying RNA sequence is not conserved well, the additional information we extract from its structure improves structure conservation in the overall alignment. Compared to Plan A, planACstar reduces the area in the twilight zone to roughly two thirds of its original size. Our working hypothesis was that the overall shape of the prediction might still be correct in this twilight zone. In fact, planACstar and Plan A. Highlighted in color is the interesting sequence identity range, the twilight zone. Note that almost all significant improvements are within this region.Figure Looking at the full data set, 90% of the dots are on or very close to the diagonal. As expected, above the 55% boundary, our fine-tuning is not necessary. In the twilight zone, we notice that almost 50% of the SCI scores improved.We also tested whether the improvement is related to the gap content in the alignment, but no correlation was observed. This test is documented in Figure planACstar is shown. As an example, we picked an alignment located in the sequence identity's twilight zone, alignment 83 of the Group II introns. The alignment has a sequence identity of 31% and planACstar improves its SCI score from 0.8807 to 1.005.Below, a typical path through the pipeline of A, conducted by ClustalW. The result is the following:The first step is the initial sequence alignment RNAalifold, its preliminary consensus C is calculated. Figure RNAalifold with -27.92, and a SCI score of 0.8807. The string representation of C is the following:Using RNAfold -C. A direct comparison of this procedure to the optimal MFE folding without any consensus is shown in Figure RNAforester calculates the multiple structure alignment Y, from which an improved sequence alignment A* can be easily extracted. Both are shown below:The next step in our pipeline is an individual folding of the single sequences relative to the consensus with C* are shown in Figure RNAalifold MFEA improves to -31.88, that is a SCI score of 1.005. A SCI score above 1.0 indicates a very well conserved secondary structure.Note that there is a new gap at the end of our alignment. The effects on the improved consensus structure Structural conservation in RNA alignments in the twilight zone of 30-55% sequence identity can often be improved. We achieved this by combining already available and widely used RNA tools in the pipeline described above. While the average improvement lies at 10%, a percentage range of improvement cannot be stated, as sometimes, the original SCI value is very close to 0. In the leftmost data point in Figure planACstar reduced the discrepancy between predictions and reference to about two thirds of its original area. This goes hand in hand with the direct comparison of the SCI scores of planACstar and Plan A shown in Figure Comparing Figure planACstar is slower than Plan A by a factor of 30 (sequence length 80) to 50 (sequence length 150). To be concrete, the runtime on a single subalignment  was increased from 0.297 seconds to 14.896 seconds on a 2 GHz Intel Core 2 Duo processor. This extra efforts results from the individual calls of RNAfold for n sequences and the multiple alignment of the refolded structures afterwards, where the former effort grows with O(n), and the latter grows with O(n2). Since each of the pipeline's components may be replaced with a functional equivalent, resource requirements in another implementation may be different. In particular, we are working on a faster version of the pure structure alignment algorithm for the special case when the aligned structures are known in beforehand to share a common overall shape.These improvements are costly to compute. With our data set and particular set of tools employed, we found that RNAalifold program [RNAalifold, yielding an average SCI improvement near 20%. With improved gap handling in RNAalifold, our fine-tuning makes a smaller improvement of the SCI score. But note that the new RNAalifold does not change the alignment, it only scores it more cleverly.On the side, our study also confirmed the recent improvements made to the  program . Our datRNAz [planACstar in place of Plan A must be considered too expensive. Moreover, many folded alignments fall outside the twilight zone, and no improvement is to be expected from fine-tuning anyway. However, once certain alignments have been determined as promising and to be are used for model building, we suggest that fine-tuning with planACstar should be applied. Our implementation is available on the Bielefeld Bioinformatics Server at http://bibiserv.techfak.uni-bielefeld.de/planACstar/.Our evaluation shows that, with a fairly simple combination of available tools, structure conservation in RNA alignments in the twilight zone can be improved. The degree of achievable improvement varies significantly. In a context of large screening for conserved secondary structures, such as genome-wide RNA gene prediction with RNAz , Plan A ClustalW, RNAalifold and RNAforester, note that each of these constituents may be replaced by a functional equivalent to create another instance of planACstar. Recovering the covariance signal obscured by sequence alignment remains the underlying general idea.While we have built our evaluation on the three tools planACstar either confirmed the initial prediction (23 cases), or it improved the SCI and also made the alignment more similar to the reference (22 cases). In 28 cases, the SCI was improved but the alignment became less similar to the reference.. In 26 cases, this was due to moderate local rearrangement of base pairs, while the overall structure was retained. In one case, we found that planACstar was fine-tuning to the wrong string, and in the other remaining case, one (correct) helix was strengthened on account of the other (correct) helix, with an overall negative effect. Details of this study are given in Additional File While often interpreted in this way, a high SCI does not necessarily imply that the associated structure is close to the truth. It is not known currently to what an extent this interpretation is valid, in particular within the twilight zone. We have compiled a second test data set from curated structures, taking their consensus as a standard of truth. We created 80 data sets of 5 sequences each, randomly selected from the Szymanski 5S Ribosomal RNA database , taking ediction 3 cases, planACstar pipeline and performed the first evaluation. SS performed the evaluation of the SCI improvement against reference structures. Both AB and SS contributed equally to this work and should be considered as joint first author. All three cooperated closely on the manuscript. All authors read and approved the final manuscript.RG and SS designed the study. AB implemented the adequacy of SCI improvement. This supplement reports on an evaluation which uses curated reference structures to evaluate whether an improvement of the SCI is linked to bringing a predicted consensus structure closer to the reference.Click here for filearchaea subalignments. This file provides the subalignments of archaea sequences created and used in the study described in Additional File Click here for file


Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (“Forward” scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (“Viterbi” scores) are Gumbel-distributed with constant λ = log 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values  for both Viterbi and Forward scores for probabilistic local alignments.Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution ( statistical significance of scores. For many models and scoring schemes, accurate statistical significance calculations have either involved expensive computational simulations, or not been feasible at all. Here, I introduce a probabilistic model of local sequence alignment that has readily predictable score statistics for position-specific profile scoring systems, and not just for traditional optimal alignment scores, but also for more powerful log-likelihood ratio scores derived in a full probabilistic inference framework. These results remove one of the main obstacles that have impeded the use of more powerful and biologically realistic statistical inference methods in sequence homology searches.Sequence database searches are a fundamental tool of molecular biology, enabling researchers to identify related sequences in other organisms, which often provides invaluable clues to the function and evolutionary history of genes. The power of database searches to detect more and more remote evolutionary relationships – essentially, to look back deeper in time – has improved steadily, with the adoption of more complex and realistic models. However, database searches require not just a realistic scoring model, but also the ability to distinguish good scores from bad ones – the ability to calculate the  Sequence similarity searching was advanced by the introduction of probabilistic modeling methods, such as profile hidden Markov models (profile HMMs) and pair-HMMs More sophisticated scoring models are desirable but not sufficient. It is also necessary to be able to determine the statistical significance of a score efficiently and accurately ungapped alignments using simple position-independent scoring systems. In this case, alignment scores follow a Gumbel distribution with slope parameter λ and location parameter Kgapped local alignments, although scores empirically still follow a Gumbel distribution for a useful range of gap costs λ parameter must be estimated by expensive computational simulation for each new scoring system λλ is not a major limitation. BLAST precalculates Karlin/Altschul parameters K and λ for the small number of general scoring systems in common use K and λ. PSI-BLAST avoids using simulations to determine λ by restricting its profiles to fixed position-invariant gap costs, and assuming  that the λ of a PSI-BLAST profile is equal to the λ of the pairwise scoring system with the same gap costs and the most similar relative entropy (average score) per aligned residue pair The first problem is that Karlin/Altschul statistics only rigorously apply to scores of optimal independent of any particular alignment. The alignment is uncertain, a so-called “nuisance variable” in the inference that one wants to marginalize (integrate out). In closely related sequences, when the alignment is well determined, the optimal alignment score will approximate the total log likelihood ratio, but the more uncertain the alignment, the more the optimal alignment score and the total log-likelihood ratio differ, so remote homology detection  is most affected by the approximation. Benchmarks of profile HMM sensitivity and specificity have shown that “Viterbi” scores  are significantly outperformed by “Forward” scores  The second problem is that in terms of probabilistic inference, an optimal alignment score is not the score we should be calculating in a homology search. The quantity we want to calculate is the total log likelihood ratio for the target sequence(s) given an evolutionary model and a null hypothesis, λ  and that the expected distribution of total log likelihood ratio scores (Forward scores) asymptotes to an exponential tail with the same constant λ. I use simulations to show that these conjectures hold for all the models in the current Pfam database (9318 profile HMMs). In achieving these results, I modified the architecture and parameterization of profile HMMs used by HMMER Here I test two conjectures about the expected distributions of scores for full probabilistic models: that optimal gapped alignment scores (Viterbi scores) follow Gumbel distributions with a constant This work was done as part of a reimplementation of the HMMER profile HMM software package query , and we want to ask if a target sequence x is homologous to our query or not. To set up a hypothesis test, we specify “homology to the query” as a hypothesis  to be compared to (at least) one alternative hypothesis, that x is an unrelated sequence . To apply probabilistic inference, both hypotheses are specified as full probabilistic models, which means that they describe probability distributions P(x|H) and P(x|R), such that x = x1…Lx of length L = 1…∞. H and R would typically be generative stochastic models such as hidden Markov models (HMMs) or stochastic context-free grammars (SCFGs) homology search, not merely a similarity search Let us start with a definition of Viterbi and Forward scores in terms of probabilistic inference. We have a H will generate target residues aligned to (homologous to) residues in the query, along with deletions and insertions relative to the query, so its scoring model depends on an alignment of the query to the target. That is, model H directly expresses a joint probability distribution P, where π represents a particular alignment. To obtain the probability P(x|H), we marginalize the unknown nuisance variable π; that is, we sum over all possible alignments, Typically, model global alignment model. Because biological sequences often only share homologous domains, it is more useful for H to permit any subsequence i…j of the query to align to any subsequence k…l of the target, while treating the remainders of the sequences as nonhomologous – this defines a local sequence alignment model.A model might require the complete query and target sequences to be aligned and homologous – a R is a one-state HMM that generates sequences with each residue drawn from a background frequency distribution. This is the usual independent, identically distributed background model used when calculating standard log-odds scoring matrices, plus a geometric length distribution. In this case, there is only one possible alignment to the target sequence, and P(x|R) is obtained directly.The simplest random model H and R can be used to define at least two different log likelihood ratio scores for a target sequence x. The Viterbi scoreV is the score of the optimal alignment π̅:The likelihoods of Forward scoreF is obtained from the total likelihood of model H, a sum over all possible alignments:The z. By convention, HMMER reports scores in units of bits, log base z = 2. Because both scores are log likelihood ratios, I will be careful to refer to Viterbi versus Forward scores, or to optimal alignment scores versus “total log likelihood ratio” scores.The logarithms may be taken to any base V and F to represent optimal alignment scores and total log likelihood ratio scores in general.The names Viterbi and Forward refer to the standard dynamic programming algorithms used to calculate these scores in the specific case of HMMs x is a homologue of the query – that is, the posterior probability of model H given data x, P(H|x) F:ρ is a constant offset, the prior log odds ratio Traditional search algorithms report optimal alignment scores, so the Viterbi score is the probabilistic analog of traditional methods. However, from a probabilistic inference standpoint, the Forward score is what we want, because we are after the probability that sequence P that can be meaningfully summed. Forward scores cannot be calculated directly for arbitrary (nonprobabilistic) scoring systems, except by using approaches based on renormalization and partition functions, where the arbitrary scores are assumed to be unnormalized log probabilities Forward scores are not generally used in traditional sequence comparison, because they only make sense if individual alignments have probabilities V scores) are expected to follow Karlin/Altschul statistics μ and λ are location and scale parameters. Karlin/Altschul statistics give a specific dependence of μ on query and target sequence lengths N and L, K essentially representing the fraction of the NL residue alignment lattice that is available for initiating independent local alignments. I will use the more general Gumbel notation  as opposed to the more usual Karlin/Altschul notation  for reasons that will become clear when I consider how score distributions depend on target sequence length.Local optimal alignment scores of random sequences  then simple algebra shows that λ for ungapped alignment scores is log z. Likewise Bundschuh's central conjecture would be satisfied by λ = log z for full probabilistic models of local alignment, when indels are included as part of the probability model rather than scored with arbitrary penalties.First, for Viterbi scores, Bundschuh's “central conjecture” about the distribution of optimal gapped local alignment scores states that P(F>t) of log likelihood ratios F for full probabilistic models is an exponential et log z−λ≥log z.Second, for Forward scores, Milosavljević proved in his “algorithmic significance” method that an upper bound for the distribution P(F>t) for scores for probabilistic sequence alignment is likely to be approximated by et log z−, i.e. again, an exponential tail with λ = log zλ = log z. They stated their approximation in the context of a full probabilistic model of global alignment, not local, and then used that result to derive a further approximation for the expected distributions of scores for a nonprobabilistic model of local alignment. However, I believe their approximation only relies on the model being fully probabilistic, not whether it is of global or local alignment.Third, for Forward scores, Yu, Bundschuh, and Hwa argued by a different approach that the high-scoring tail λ), because for the highest scoring sequences, the optimal alignment should contain most of the probability mass.Additionally, one expects the high-scoring tail of Forward scores to approximate the high-scoring tail of Viterbi scores , and a range of 0.517 to 1.337. Though the mean is suggestively close to the conjectured log2 = 0.6931, the variation is unacceptably broad, well outside traditional tolerance for useful λ estimates  has the same probability: i…j. This assumption is implicit in the traditional Smith/Waterman alignment scoring system i and exit j, therefore corresponding to an implicit assumption of a uniform query fragment distribution . HMMER's previous entry/exit distribution, in contrast, was ad hoc and non-uniform, causing scores to be biased by the local alignment's position in the query model. I guessed that a uniform entry/exit distribution might result in simpler, more statistically homogeneous expected score distributions that might asymptotically approach conjectured predictions faster than for nonuniform entry/exit distributions.I modified HMMER's profile HMM architecture in several details, with the main goal of achieving a uniform query entry/exit distribution in local alignments. A uniform query entry/exit distribution means that for a query profile of Besides HMMER's previous model, several other probabilistic local alignment models in the literature also imply nonuniform entry/exit distributions. For example, simple pair-HMMs for pairwise local sequence alignment imply a non-uniform (geometric) distribution over local alignment length, because they use a single residue alignment state with a self-loop and an exit probability The generative probabilistic model of local alignment that I intend to use in HMMER3 is illustrated in core model, which is a standard profile HMM essentially following the original formulation of Krogh et al.search profile, which adds extra states and state transitions to the core model to describe various kinds of alignment modes, including local versus glocal and unihit versus multihit. For locality with respect to a query segment, there are transitions from the begin state to any match state, and exits from any match or delete state to the end. For locality with respect to a target sequence segment, the search profile generates flanking unannotated segments of the target using N and C states. For a “multihit” mode, to generate multiple consistent alignments to the same query in one target sequence , the model may cycle from E to the J state, generate an unannotated segment in J, and cycle back to B. The N, C, and J states are all assumed to emit residues with the same background frequencies as in null model R, so their log-odds emission scores are zero. This is essentially the same as the HMMER2 “Plan 7” profile architecture, but as it cannot be parameterized to achieve a uniform entry/exit distribution, the following step was taken.implicit probabilistic model. To achieve a uniform entry/exit distribution, we imagine replicating all N(N+1)/2 possible chunks i…j of the model, and assigning an entry probability of 2/N(N+1) and exit probability of 1.0 to each of these fragments. Except for these entry/exit probabilities, all other emission and transition probabilities are the same as in the search profile. Now we have a probabilistic model with a uniform entry/exit distribution, but the model is enormous. Dynamic programming on the implicit probabilistic model would be costly. A key observation is that dynamic programming on the search profile with entry probabilities set to 2/N(N+1) and exits to 1.0 is provably equivalent to doing dynamic programming on the implicit probabilistic model. Two conditions are sufficient to make this so: first, that there is a one-to-one correspondence between the sets of possible state paths in the two models, and second, that any given state path is assigned identical probability by either model. (The state transition schemes in the search profile and the implicit probabilistic model were carefully designed to fulfill these conditions.) Therefore dynamic programming on one model to find either the optimal state path or the sum over all state paths must give the same answer as the other model would. This holds so long as the probability of entering at i is independent of exit point j, which is true for a uniform entry distribution.N(N+1) and exit probabilities of 1.0 that are properly normalized with respect to the state diagram for the implicit probabilistic model, not the state diagram for the search profile.Therefore, the search profile is not probabilistic per se. It is a dynamic programming construct that calculates correct probabilities for the implicit probabilistic model. It uses entry probabilities of 2/R, comprise the target length model, so-called because this parameterization largely controls the expected length of the target sequence. For simplicity, the target length model is expressed in terms of three parameters p, q, and r. p is the self-loop transition probability for N, C, and J, so it controls the length of unannotated segments; parameterizing these states identically corresponds to an assumption that prefixes, suffixes, and intervening unannotated regions have identical length distributions. q is the E→J transition probability of looping around for another pass through the core model, controlling the expected number of homologous domains per target sequence . r is the self-loop transition for null model R's single HMM state, controlling the length distribution generated by R.The N, C, J state transitions, plus the self-loop transition in the null hypothesis HMM q = 0, and q = 0.5, and L: both H and R are conditional on L. With these choices, models H and R will both generate approximately the same mean target sequence length L. Previously HMMER2 used q = 0 or q = 0.5 choice of unihit versus multihit mode), independent of target sequence length. Recalculating part of the scoring system based on each target sequence's length is an unusual step, but the reason to condition the hypothesis test (both models H and R) on target length L will become apparent.How should the three target length model parameters be set? I will discuss the rationale in more detail in a later section, in the context of illustrative simulation results. For now I will just state that glocal alignment, also known as a semi-global alignment N, and local with respect to a subsequence k…m of the target; glocal alignment is useful, for example, when a profile HMM models a protein structural domain that may occur one or more times somewhere in a longer, multidomain protein sequence.) Additionally, local and glocal algorithms may allow only one aligned region per target sequence , or they may allow a combination of one or more aligned regions . The Smith/Waterman alignment algorithm Traditional sequence similarity search methods distinguish local, global, and glocal alignments, applying different alignment algorithms, while using the same scoring system. (A H. A full (generative) probabilistic model H must always explicitly model the complete target sequence x1…Lx, not just part(s) of it. This is why the HMMER model includes additional states and transitions that account for unannotated residues in the target sequence, and transitions allowing a model to loop back and generate one or more consistent alignments to the core model in the same target. Thus, an alignment π to a probabilistic model is always complete  in that every residue ix in the target is assigned to a state in the model. The HMM algorithms used to score and align target sequences (Viterbi and Forward) are always the same, regardless of the configuration of the model. In HMMER, searches can be configured in any choice of local, glocal, or global combined with a choice of unihit or multihit, a total of six different standard alignment modes, by reparameterizing the entry/exit distribution and the target length distribution. I only explore local alignment modes in this paper, and I generally concentrate on multihit rather than unihit mode because multihit mode is more powerful.In a probabilistic inference framework, these distinctions are not in the algorithm, but in the parameterization and architecture of the model λ = log 2. To test this prediction on many different profile HMMs, I estimated λ) for 9,318 different profile HMMs built from Pfam 22.0 seed alignments, by collecting multihit local Viterbi score distributions for n = 105 i.i.d. random sequences of length 400 generated with the same residue frequencies as the null model R. λ = log 2 = 0.6931.Viterbi bit scores are predicted to be Gumbel distributed with parametric 8 random sequences). As “typical” models, I chose RRM_1 and Caudal_act from Pfam 22.0. The RRM_1 model is the RNA recognition motif, a ∼72 residue domain, chosen because it is one of the Pfam domains I am most familiar with. The Caudal_act domain is the activation domain of the Caudal-like homeobox transcription factors, chosen because it is literally typical for Pfam, being closest to the median of Pfam seed alignments in three different characteristics: number of seed sequences , model length , and average pairwise identity . Both observed distributions show good agreement to the predicted Gumbel of λ = log 2.As examples, the top right of λ = log 2 fails. If the 9318 trials were all truly Gumbel distributed with λ = log 2, 8 random L = 400 sequences). In both cases, a similar I examined outliers in 0.0025 , , so in 9λ = log 2 than to the maximum likelihood fitted The low outlier DUF851  actually fits better visually to the conjectured λ (steeper slope) than the conjectured log 2. A distinctive feature of Sulfakinin compared to other Pfam models is that it is tiny, just N = 9 consensus positions long. All other high outliers examined were short models. Finite-length sequence comparisons are expected to show an “edge effect” that increases the apparent λ relative to an asymptotic theoretical prediction, and finite-length artifacts are maximal for the shortest query models The high outlier Sulfakinin  does show a higher λ = log 2, with the approximation holding above some score threshold τ:The Forward score distribution is predicted to converge to an exponential with n = 500,000 i.i.d. random sequences of length 400, as a function of fitted tail mass, for 9,318 Pfam 22.0 models. We expect a tradeoff between fitted tail mass and λ = log 2 is expected to occur as fitted tail mass decreases (e.g. as threshold τ increases), but as τ increases, the number of fitted samples decreases, so the accuracy of fitting λ = log 2 exponential distribution of the 0.001 tail for deep (n = 108) simulations for the “typical” RRM_1 and Caudal_act Pfam models, showing that these fits are visually satisfactory.The top right of n = 500,000 scores, the 0.001 tail contains only 500 points, so In this case, the survey of 9,318 models has limited power to detect significant outliers. Even with  0.045 , , and the5 scores.The lower right of λ<log 2 should not occur. The most obvious thing that is unusual about the Ribosomal_L12 seed alignment is that it has strongly biased residue composition.Some low outliers exhibit the same high-identity, discretized-scores, stairstepping-distribution artifact observed with the Viterbi low outliers , but this explanation does not seem reasonable for Ribosomal_L12, where the observed score distribution appears smooth. The Ribosomal_L12 discrepancy (5 scores in the deeper tail). As with the Viterbi scores, XYPPX and these other high outliers are unusually small models (XYPPX is N = 5 consensus residues), and likely to be attributable to finite-length edge effect.The high outlier XYPPX (and some other high outliers examined) remains a high L = 400 residues. However, proteins range in length from a few residues to tens of thousands. One must be able to predict how the expected score distribution depends on target sequence length. For expected Gumbel distributions of traditional optimal local alignment scores, Karlin-Altschul statistics predicts that the location parameter μ scales as N and target length L, and that the λ parameter (aside from finite-length edge effects) is independent of target length. That is, for each two-fold increase in target sequence length, the expected score distribution shifts by one bit.So far, all target sequences have been a typical length of For the old target length model parameterization in HMMER2 (P(H|x) should not increase as the length of a random target sequence increases. If anything, it should decrease. The more data are available (the longer the target), inference should become more accurate, and the more certain we should be that a random sequence was generated by hypothesis R, not hypothesis H.However, from a probabilistic inference standpoint, seeing the expected score increase with increasing target sequence length raises a red flag. The posterior probability τ for a range of different target lengths in order to assign accurate E-values to multihit local Forward scores. Although I show later that τ is not hard to estimate, this is not desirable. This concern becomes a practical issue when multihit local Forward score distributions are examined for models using the HMMER2 target length model, as shown in the top right of H and R, given the length model parameters p, q, and r. The probability that model R generates a target sequence of length L is a geometric density:R is:A simple argument about the target length model appears to suffice to explain this behavior. Consider the length distribution generated by models H is dominated by the N, C, J states and the target length model, and that the core model contributes negligible length , then the probability that model H generates a sequence of length L is a sum of Pascal distributions:j counts over the number of times we start a J segment. The expected length generated by model H can be derived from this, using the expectations for Pascal and binomial distributions:If we assume the length distribution of Intuitively, this follows from the fact that the expected number of times that we include a J segment is We can then approximate the component of the log-odds Forward score that is attributable to target length modeling alone:q = 0), this becomes:p = r (HMMER2's old parameterization), for unihit Forward scores, Equation 2 predicts that the target length model's score contribution will increase as log(L+1), essentially the same scaling for unihit local Forward scores that Karlin/Altschul statistics predicts for Viterbi  scores. However, with p = r, for multihit local Forward scores, Equation 1 predicts that the length model's score contribution will scale as log(L+1) at small L, but will increase more rapidly at larger L. Qualitatively, this appears to be the behavior observed in p = r, model H favors longer sequences than model R, because there are at least two states  generating unannotated segments . The longer the target sequence, the more H is favored, simply because it generates longer sequences with higher probability than R.In the case of unihit modes  = 0.04 (the 4% tail); this t is then taken to be τ for the location of the base of the high-scoring 4% Forward score tail. 4% was carefully chosen. Because Forward scores are not Gumbel distributed, and appear fat-tailed with respect to a maximum likelihood fitted Gumbel of unknown λ, the true tail mass P(F>t) is systematically underestimated by a Gumbel fit. On the other hand, because the Forward survival curve approaches its exponential asymptote of λ = log z from above, if we did accurately estimate P(F>τ) at low score thresholds and used that to locate the base of our exponential tail, that exponential tail would overestimate (be above) the tail probability mass at higher scores. The choice of 4% was optimized by trial and error as a point at which these opposing systematic errors are well balanced; the fitted exponential tail deliberately underestimates P(F>t) at lower scores where the Forward distribution still appears fat-tailed, in order to become accurate in the highest-scoring tail (P(F>t)<0.001 or so) where the Forward distribution has converged to an exponential.After unsuccessfully exploring several alternative approaches, I adopted the following n = 200 Forward scores of random sequences of L = 100 suffices to determine τ with a standard deviation of 0.2 bits, and costs 330 msec for the “typical” Caudal_act model.Using λ for finite-length comparisons is known to increase for smaller sequences and weaker (lower relative entropy) scoring systems. Intuitively, finite length edge effect arises because the number of places that an alignment can start while still achieving a given length is less than NL, and achieving the highest scores requires the longest alignments , and weaker average scores per position require longer alignments to reach a given total score; thus higher-scoring alignments “see” a smaller search space than lower-scoring alignments, so the probability of higher-scoring alignments is lower – the tail of the distribution falls off faster – than the asymptotic λ predicts. Edge effect has significant impact on BLAST's statistics and substantial effort has been made to correct for it For Karlin/Altschul statistics, the apparent ad hoc method to reduce the relative entropy per position .In most of the results in N′ = N−ℓ, L′ = L−ℓ, where ℓ is the expected length of an alignment λ, using λ is the true (asymptotic) value, and α is empirically determined but clearly related to the inverse of the relative entropy per position Two different approaches have been developed for correcting for edge effect. One approach is to use corrected query and target sequence lengths L′ = L−ℓ residues for various schemes of determining an appropriate average local alignment length ℓ, but without satisfactory results. The expected alignment length length ℓ has a complicated dependence on the model, the alignment score, and the query and target lengths. In particular, my schemes tended to break down severely in the small target sequence length regime L≃ℓ.I experimented with setting an edge-corrected target length model such that the flanking nonhomology states generate λ proved more successful. I estimate h is the average relative entropy per match state emission distribution, and the 1.44 factor was empirically determined from slopes of lines fitted to λ versus h. Thus for typical Pfam models (N∼140) parameterized with standard profile HMM multinomial/Dirichlet maximum a posteriori estimation (h∼1.8) the correction is small (0.6931+0.0057), but for short and/or entropy-weighted models the edge effect correction has non-negligible effect.Applying a correction to This is only an empirically derived correction. It appears to suffice in practice, but there is clearly more going on here. A more satisfying and theoretically grounded accounting for edge effects in probabilistic local alignment is needed.λ = log2, determine an edge-corrected effective lambda N and relative entropy per match state emission h, and run two small simulations  to determine location parameters μ and τ for the Viterbi score Gumbel distribution and the Forward score exponential tail. Because I added ad hoc steps (the edge effect correction and the methods for determining μ and τ) on top of the conjectures about λ, one now wants to know, when the complete procedure is put together, how accurate are the resulting E-values for profile HMM searches?In summary, the overall procedure for estimating the expected score distributions is to assume 5 random sequences, of lengths L = 100, 400, and 1600, collecting multihit local Viterbi and Forward scores, and plotting predicted E-value for the top 1000 scoring hits versus rank. If E-value estimation were perfect, we expect these points to disperse around a straight line of slope 1 . As expected, the mean predicted E-values are indeed tightly dispersed around a straight line of slope 1. Each mean is derived from 9,318 trials, so we expect the outlying minimum E-value for the top-ranking score to be on the order of 1/9318, or about 1×10−4. The minimum predicted E-values for each of the six searches  range from 2.2×10−4 down to 3.7×10−6, basically within expectation . Some small systematic deviations from expectation can be seen on close examination, the most significant of which is in the Viterbi scores of entropy-weighted models for long (L = 400 and L = 1600) target sequences: this is where the apparent “edge effect” of low information content models is having its greatest impact.λ than overestimate it. If we underestimate λ, we overestimate E-values and miss some true positive homologs without compromising our false positive rate. A design goal of HMMER is to accurately estimate and control false positive rates in large-scale automated analyses.Though statistically significant errors in E-value accuracy remain, for practical purposes they are tolerably small. Moreover, they are almost invariably in the conservative direction. That is, we would rather slightly underestimate The most immediate benefits from this work are that for profile HMM searches, the statistical significance of both Viterbi and Forward scores can be calculated efficiently without expensive simulation. This enables substantial accelerations in the use of Viterbi scores, and more importantly, it opens the way to a broader use of more powerful Forward scores.O(NL) computational complexity, and the Forward algorithm is a minor modification of Viterbi (replacing max operations with sums). Existing profile HMM implementations are two orders of magnitude slower than BLAST, but this is only because they are still using full dynamic programming (so running times are comparable to other unaccelerated Smith/Waterman implementations). There is no reason why the same heuristics that BLAST uses to accelerate Smith/Waterman cannot be applied to accelerate profile HMM searches. Similarly, existing nonprobabilistic sequence alignment methods, including BLAST, can be modified (with the addition of a few transition parameters) to accomodate the probabilistic parameterization described here.Although I have done the simulations in the specific context of HMMER, the local alignment model is not specific to HMMER. It is a generalized probabilistic local alignment model with a uniform entry/exit distribution. Because position-independent substitution matrix scores and gap costs are just a special case of position-specific profile scores, the same model can be used to parameterize standard Smith/Waterman local alignments The same conjectures are also expected to hold for local alignment scores for probability models of more than just linear sequence alignment. For example, our preliminary results indicate that local alignment scores for profile stochastic-context free grammars  obey the same conjectures for both CYK and Inside scores  , which should help in efficiently and accurately calculating E-values for profile SCFG searches for structural RNAs However, at least three important points limit any conclusions I can try to draw about how widely the conjectures might hold.H and R to be configured in any particular way. However, based on previous work on glocal and global alignment scores, it is unlikely that these score distributions are going to exhibit a λ = log z simple exponential tail for biologically relevant model and sequence lengths λ = log z Gumbels for Viterbi scores and et log z− exponential tails for Forward scores only for the smallest HMMs, the largest target sequences, and the most extreme tails E<<1. This may suggest that the conjectures hold only asymptotically, with glocal or global alignment score distributions converging slower than local score distributions.First, the same conjectures ought to hold for glocal and global alignment models. Nothing in the conjectures' rationale required the probabilistic models H should work, why would the prototype HMMER3 profile HMM architecture and parameterization be necessary to obtain these results, compared to HMMER2's local alignment scores? This again indicates that score distributions are more sensitive to details of model parameterization than the conjectures' generality would suggest. I believe the uniform local entry/exit distribution to be the important difference, again possibly because this makes score distributions reach asymptotic behaviors more quickly. However, I have not dissected the two implementations and tested specific differences one at a time, because it is not feasible to emulate HMMER2 in HMMER3's implementation (and vice versa). Moreover, perhaps inconsistent with my thinking, the other popular profile HMM software package, SAM, uses a nonprobabilistic strategy of scoring zero for local entry/exit by analogy to Smith/Waterman, which ought to produce an implicit uniform entry/exit distribution, but the SAM implementors have gone away from assuming a fixed λ  and now use simulation-calibrated E-values instead Second, if any probabilistic local alignment model H that gives expected score distributions deviating strongly from the conjectures: set H = R, and all log odds ratio scores become zero (and thus λ = ∞). The conjectures must break down as the relative entropy between H and R approaches zero.Third, it is trivial to produce an example of a probabilistic model These issues show the main limitation of the simulation-based approach I have taken. Proper understanding of the regimes in which the conjectures break down requires a mathematical analysis, not simulations limited to a particular problem domain. Such analysis would be desirable, and it could lead in fruitful new directions. For example, the fact that HMMER3 glocal score distributions do appear to asymptote towards the conjectures  seems promising. A general approach for estimating statistical significance of global or glocal gapped alignment scores, under traditional (arbitrary) scoring systems, largely remains elusive, despite significant effort and progress N = 5), a maximum score effect appears to be in play, especially for unihit mode models with low information content (entropy-weighted) parameters. Fortunately, any such errors will be in the conservative direction, compromising sensitivity instead of specificity .Another problem that will need more attention is finite length effects. The finite length edge effect described for BLAST scores λ = log zλ = log z (data not shown). The three scoring systems appear to differ in their susceptibility to finite length effects that increase in low information content models. The distribution of Forward scores seems more robust than Viterbi scores (this is seen in λ).This work was partly inspired by the work of Yu and Hwa, who described a “hybrid” (or “semi-probabilistic”) scoring method that gives Gumbel-distributed scores with E∼1 region where accurate significance estimation is important; this means that HMMER2 multihit glocal (default) mode E-values are overestimated for E<<1, underestimated for E>>1, and most accurate in the E∼1 region, which others have observed empirically I have taken care to distinguish Viterbi from Forward scores, and local from glocal or global alignment modes, all of which are just choices in the same full probabilistic modeling framework. Some prior work has conflated probabilistic modeling and Forward scoring, referring to Forward scores as “probabilistic alignment scores” and arguing that probabilistic alignment scores do not follow Gumbel distributions as opposed to traditional alignment scores a priori , not just of homologs (hypothesis H).A limitation of this work is that I have only examined scores of independent, identically distributed (i.i.d.) random sequences with a single typical amino acid composition. Real sequences often have biased residue composition, repetitive regions, and other heterogeneities that can produce spurious high-scoring aligments, requiring additional methods to compensate H were an accurate model of the sequence space of remote homologs we want to detect. However, query sequence(s) are rarely an unbiased sample from the desired space of homologs. Our model H usually represents a narrow clade of known query sequences, not the broader space of homologs we want to detect. Presented with a remote homolog, the model may correctly assign it a low posterior probability (it doesn't look like it belongs to the same sequence space as our query sequences), but nonetheless, it may have a higher score than one expected by chance. A purist would say that this just shows that our model is inaccurately parameterized for our problem. This is certainly true, but better parameterization requires evolutionary models that can extrapolate what remote homologs will look like, and this has proven to be a difficult problem. Most current probabilistic evolutionary models neglect important inhomogeneities in the evolutionary process, like heterotachy (rate variation between branches), and have so far proven in our hands to be insufficient in schemes for increasing profile HMM sensitivity . E-values and classical statistical significance testing are of immediate utility, while development of more useful probabilistic evolutionary models remains a focus for the future.From a purist Bayesian perspective http://selab.janelia.org/publications/#Eddy08 under the terms of the open source GNU General Public License. This source tarball includes a 00README file with detailed command-line scripts for reproducing the results in the figures. The Pfam database is freely available at http://pfam.janelia.org. The simulation results are generated by the hmmsim program, which takes a profile HMM as input, generates and scores n random i.i.d. sequences, and outputs scores, statistics, and input files for the freely available GRACE graph plotting program (http://plasma-gate.weizmann.ac.il/Grace/). Maximum likelihood fitting of Gumbel and exponential distributions is implemented in the gumbel and exponential modules of Easel, respectively, following methods in The HMMER3 prototype source code  is freely available at kM that is never reached, because the k−1→kM transition probabilities are zero, and imagine that this “dead” match state generates a residue that is for some reason never seen in homologs. If the local alignment model imposed a uniform entry/exit distribution, allowing an entry transition straight into the dead kM state, then local alignments can contain the impossible residue. To avoid this, HMMER ad hoc weights the local entry probabilities into states kM by the probability that each kM is used in sequences generated from the model. Because by default HMMER assigns consensus match states to alignment columns that contain ≥50% residues as opposed to gap characters, the usage of each match state is generally similar and high, so the effect of this weighting is normally small (less than two-fold difference between any pair of entry positions k).In HMMER3's implementation, the local entry/exit distribution is in fact not completely uniform, for the following reason. Imagine (as an extreme illustration) a profile HMM with a “consensus” match state L, and roundoff/truncation error becomes an issue. The precision of HMMER2's internal scaled integer log-odds scores (in units of 0.001 bits) proved insufficient.It was necessary to implement HMMER3 dynamic programming routines as floating point calculations. In the target length model, a ratio like All computational times mentioned in the paper are measured for a single execution thread on a 3.2 GHz Intel Xeon (Dempsey) CPU, using prototype HMMER3 code compiled with the GNU C compiler (gcc) version 3.4.5 with a -O2 optimization level, running a Red Hat Enterprise Linux AS release 4 operating system.


Accurate sequence alignment is required in many bioinformatics applications but, when sequence similarity is low, it is difficult to obtain accurate alignments based on sequence similarity alone. The accuracy improves when the structures are available, but current structure-based sequence alignment procedures still mis-align substantial numbers of residues. In order to correct such errors, we previously explored the possibility of replacing the residue-based dynamic programming algorithm in structure alignment procedures with the Seed Extension algorithm, which does not use a gap penalty. Here, we describe a new procedure called RSE (Refinement with Seed Extension) that iteratively refines a structure-based sequence alignment.RSE uses SE (Seed Extension) in its core, which is an algorithm that we reported recently for obtaining a sequence alignment from two superimposed structures. The RSE procedure was evaluated by comparing the correctly aligned fractions of residues before and after the refinement of the structure-based sequence alignments produced by popular programs. CE, DaliLite, FAST, LOCK2, MATRAS, MATT, TM-align, SHEBA and VAST were included in this analysis and the NCBI's CDD root node set was used as the reference alignments. RSE improved the average accuracy of sequence alignments for all programs tested when no shift error was allowed. The amount of improvement varied depending on the program. The average improvements were small for DaliLite and MATRAS but about 5% for CE and VAST. More substantial improvements have been seen in many individual cases. The additional computation times required for the refinements were negligible compared to the times taken by the structure alignment programs.RSE is a computationally inexpensive way of improving the accuracy of a structure-based sequence alignment. It can be used as a standalone procedure following a regular structure-based sequence alignment or to replace the traditional iterative refinement procedures based on residue-level dynamic programming algorithm in many structure alignment programs. In searching for protein functions and in building homology models, it is desirable to have accurate sequence motifs and profiles -3, whichTherefore, structural alignments, when available, have been used to guide sequence alignments. Such structure-based sequence alignments have been used as the gold standard to evaluate pure sequence alignment methods ,5 and toHowever, structure-based sequence alignments produced by different programs can be different even when the structures are similar ,11. TherDaliLite and VAST use a Monte-Carlo procedure after initial structural alignment ,14, FATCWe previously developed the SE (Seed Extension) algorithm which generates a sequence alignment from a superimposed structure pair without changing the superposition . A numbeIn this study, we report on the development of a fast refinement procedure, which can be used to improve an existing structure-based sequence alignment. The procedure, which we call RSE (Refinement with SE), is an iterative procedure that uses SE in its core. Using CDD (Conserved Domain Database)  "root noCAR(δ), or FCAR(δ), which is fCAR(δ) averaged over all structure pairs in a superfamily, as the measure of accuracy of the alignment for each superfamily [CAR(δ)> (angle brackets for averaging), as the measure of the overall accuracy of alignments for the whole dataset for a given method.In order to see if the RSE procedure improves or degrades alignments produced by different structure comparison programs, we ran the program to be tested with default options to obtain the structure-based sequence alignment for each structure pair. Then the sequence alignment and the corresponding structure pair were fed to the RSE program to obtain a new sequence alignment. We used the fraction of correctly aligned residues with shift error δ, ferfamily . Since tCAR(0)>, for all methods > but not <FCAR(8)> > increased almost as much as <FCAR(0)> by the refinement.The nature of the improvement varied among different methods. For CE, MATT and TM-align, RSE improved <F> Figure , which iCAR(0)> values that were now comparable to that of DaliLite, which is a much slower program >s were computed for each class and method > for most classes (the green tips), but there were cases wherein <FCAR(0)> decreased by a small amount . The <FCAR(0)> increases were most prominent for FAST and VAST across all SCOP classes and for CE for the β-sheet containing classes. The alignments also improved for LOCK2, SHEBA-4, MATT and TM-align for all SCOP classes. The <FCAR(0)> in "others" class in DaliLite increased to a comparatively large extent, indicating that certain defects in its alignments were effectively corrected.In order to see if the improvement of the alignment depended on protein structural types, the structure pairs were grouped according to their SCOP class Table  and <FCAd Figure . The RSECAR(0) decreased for 1589 out of 3591 pairs, making the <FCAR(0)> value to decrease by approximately 5% (Table CAR(0)> value. However, the <FCAR(0)> value remained higher than that from any structure comparison programs . Since SE just derives a sequence alignment from a given structural superposition without changing it, it cannot correct a bad superposition. In contrast, RSE iteratively adjusts the structural superposition, which can result in a large improvement.CAR(0) in RSE-refined CDD alignment decreased by more than 20%. As expected, some of these structure pairs were from the cd00531 (7 pairs) and cd01984 (6 pairs) superfamilies, for which our previous study [8 TIM-barrel structure , for which the inner layer of beta-strands were reasonably alignable but the outer helices were not. There were other helix-containing superfamilies , for which at least one pair of alpha-helices was not unambiguously alignable. For some pairs in cd00158, CDD has pairs of residues aligned, which RSE could not align because they were too far apart from each other in an irregularly shaped region of the superposed structures. These were aligned in CDD presumably by sequence similarity.In order to better understand the nature of the changes of the CDD alignments by the RSE procedure, many cases were visually inspected. There were 136 pairs  from 21 different superfamilies for which the fus study  indicateCAR(0)> with the CDD root node set as the reference, ranged from 81% to 89% depending on the program used. When the five outlier superfamilies [Structure-based sequence alignments are not as robust as one would like. In some cases, they can be inherently ambiguous. But more frequently different structure alignment programs generate alignments that contain errors that can be easily recognized by human experts. We showed in a previous study  that, thfamilies  are exclfamilies  and MATTfamilies , are notCAR(0) more than FCAR(8). For FAST and SHEBA-4, RSE seems to lengthen the alignment also since FCAR(8) and FCAR(0) increased to a similar extent. The alignments improved for structure pairs from all SCOP classes for most of the programs tested > and <fCAR(0)> decreased to about 95% and 96%, respectively (Table CAR(0) fell to a value below 80%, the RSE procedure appears to have found an alternate alignment or to have corrected CDD errors in most cases. We expect that similar causes are at work for at least some of the cases seen in Figure An ideal refinement procedure will fix incorrectly aligned regions without degrading the correctly aligned ones Figure . Unfortuly Table . AccordiRSE greatly improves the alignments from SSEARCH and SALIGN, which are non-structure-based, pure sequence-based alignment procedures Table . This isWe devised a refinement procedure for structure-based sequence alignments, called RSE. It uses the SE algorithm, which produces a sequence alignment without using a gap penalty. When applied to the structure-based sequence alignments generated by various structure comparison/alignment programs, the average accuracy increased for all programs tested. This refinement procedure is fast enough to be routinely used as a supplemental procedure following a regular structure-based sequence alignment or to replace the traditional dynamic programming algorithm-based refinement procedure which is a part of many structural alignment programs.m and B of length n, define two m × n matrices M and SP. M is the matrix of average Cα distances defined as dij is the distance between the Cα atoms of residue i of structure A and residue j of structure B. SP is the matrix of scalar products; SPij, is the scalar product between two unit vectors which bisect the angles formed by three consecutive Cα atoms,  for structure A and  for structure B. A pair of residues  is a seed if its corresponding matrix element Mij is the minimum in both the ith row and the jth column of the matrix and SPij is greater than 0. A set of consecutive (non-gapped) seeds defines a seed segment. The SE algorithm consists of the following steps:We first briefly describe the SE algorithm . Given aseeds and seed segments.1. Find aligned segments by extending seed segments.2. Find aligned segments with the best score.3. Find the consistent set of 4. Discard all other aligned segments.i and j as tied if there is another residue pair involving i or j such that Mi' j - Mij < 0.5 Å or Mij' - Mij < 0.5 Å with a positive SPi' j or SPij', respectively. Then we define a seed segment as a set of 2 (instead of 3 in the previous version) or more consecutive non-tied seeds. The tied seeds are ignored also during the extension of seed segments to obtain the aligned segments. We made this amendment because we observed instances wherein two, not three, consecutive residues are unambiguously aligned, isolated from other aligned regions. The following steps were newly appended.We modified the original SE algorithm slightly as follows. In the original SE, a seed segment was defined as a set of 3 or more consecutive seeds along a diagonal. In the new algorithm, we first label a seed at residue pair aligned segments after discarding the inconsistent aligned segments.5. Extend the surviving tied seeds to extended pairs if they do not overlap with already aligned residue pairs.6. Change 7. Repeat steps 3 to 5.The reason for introducing step 5 is that there may be room for extension after removal of inconsistent segments. The additional steps 6 and 7 were used only in the last refinement cycle (see below) to pick up isolated pairs of alignable residue pairs.dij between Cα atoms of the aligned residues: d0 and n are adjustable parameters with default values of 3.0 Å and 2, respectively. Several combinations of d0 (= 2.5 to 4.0 Å in 0.5 Å steps) and n (= 1 to 4) were tested, but the RSE procedure was rather insensitive to these parameters. During the iteration, the transformation matrix of the superposition that generated the best alignment, in terms of the number of aligned residues, was selected. The final sequence alignment was produced by an additional round of SE that included steps 6 and 7 after two structures were superimposed according to the chosen transformation matrix.For RSE, the sequence alignment by SE without steps 6 and 7 was followed by a rigid body superposition routine KABSCH ,28. Thisesidues: , where d-norefine command line option, in which case the input superposition is used directly to generate the sequence alignment output. The program is downloadable from the following web site: .The RSE procedure accepts as input two superimposed structures or two independent structures with a sequence alignment, in which case a superposition is obtained through KABSCH procedure with unit residue weights. In this work, the RSE was run in the latter mode, since some structure alignment programs did not generate superimposed structures. Different programs produced sequence alignments in different formats, which had to be converted into a standard format (the FASTA format). The iterative refinement steps can be skipped by giving We used the CDD (v.2.07) "root node set" introduced in our previous work  as the rWe included CE  , DaliLitIn order to measure the execution times for the methods including the RSE procedure, time-stamps were recorded before and after system calls for the executables. For the CPU times per refinement cycle with CDD alignments, the elapsed time from after the initial structure superposition to the end of refinement cycles, which did not include the file I/O time, was divided by the number of refinement cycles. The CPU times for each alignment were averaged over three independent runs.BL generated the original idea, CK executed the research, CHT participated in the modification of SE and in the development of the RSE software, and CK and BL wrote the paper. All authors read and approved the final manuscript.


This feature can be used manually to include biological expertise, or automatically, usually by pairwise similarity searches. Multiple local similarities are be expected to be more adequate, as more biologically relevant. However, even good multiple local similarities can prove incompatible with the ordering of an alignment.Determining beforehand specific positions to align  positions in the partial columns that are inconsistent with a multiple alignment. Partial columns can be used, for the time being, as guide only by a few MSA programs: ClustalW 2.0, DIALIGN 2 and T-Coffee. We perform tests on the effect of introducing these columns on the popular benchmark BAliBASE 3.We show that the inclusion of our partial alignment columns, as anchor points, improve on the whole the accuracy of the aligner ClustalW on the benchmark BAliBASE 3. Say σ ≃ Nσ' whenever there is an identical length N word w at the same position relatively to both σ and σ'. A single length N word induces N instances of the relation ≃N, one for each position in the word. The N-local decoding of N of N. Therefore, two sites σ and σ' are clustered together if there is a chain of occurrences of identical length N words that connects them , defined byLetting ambiguous if the leaves of the partition tree that are children of this node form an ambiguous subset of sites.The leaves of the partition tree are the sites in the sequences. Let us say that a node is MS4 partial columns  spanning at least k sequences, as the set of subsets of sites v of the partition tree such that their direct ancestor in the tree is ambiguous  if and only if there exists a sequence i and sites  ∈ C and  ∈ C' that satisfy p <p'. An edge from C to C' means that there exists at least one sequence where C occurs to the left of C'. The C,C') weight  is then defined as the number of sequences i with this property. For convenience purposes, we also add an initial vertex vstart and a terminal one vend. The following result is quite easy to establish.The Lemma 1. The set .Finding a consistent set of partial columns amounts therefore to finding a set of partial columns whose succession graph is a DAG. To turn our possibly inconsistent set of subsets of sites G = SG feedback arc set problem. As a heuristic substitute, we successively remove the lowest weighted edges from the graph until all cycles have disappeared. Namely, let for k ∈ ℕ the edge subsetAn optimal solution to the first problem would suppress a subset of edges of total k* = min{k > 0| is a DAG}.and i Cin the set C' is consistent. The algorithm tries to make the partial ordering on the partial columns induced by the DAG compatible with the linear partial ordering on the sites in the sequences, by removing a minimal set of positions from the partial columns. The subtle point is that deleting the edge  cannot be always interpreted directly as the removal of some positions that belong to partial columns u or v. The procedure is illustrated in Figure We describe now a method that will remove sites from the subsets vstart, u) or , and denote with G* the corresponding graph. Let ≤* be the partial order defined on C by the DAG G*. For each sequence s, let C of s, C j) in s. There are two order relations on Vs = vstart,vend}, namelyThe acyclic graph s induced by the natural order ≼ of • the total order ≼G*• the partial order s and chains, of the relation R are those subsets of occurrences of partial columns that are consistent. To minimise the number of lost sites, we choose a maximal chain.The relation G+ =  be the transitive closure TC(G*) of G*. The graph G+ is also a DAG and defines the same partial order on the set of partial columns. The graph s G=  of the relation R is defined on the vertex set s VbyMore explicitly, let R correspond to paths in sG. Let gs =  be a path from vstart to vend in Gs of maximal length. For all partial columns s, remove the site  from C. Let s ∈ S. The order in which they have been selected does not matter. If we wish to stress the difference between consistent and non-consistent partial columns, we will sometimes refer to the latter as raw partial columns.Chains of Lemma 2. The succession graph SG,..., and ,...,  such that every pair of sites  and ,1 ≤ l ≤ k, belongs to some partial alignment column All current implementations of anchoring options take as input a list of pairs of matching positions. To obtain a set of anchor points from a set In order to evaluate the effect of introducing the MS4 partial columns in multiple alignments, we have used the reference protein multiple alignment benchmark database BAliBASE (release 3) . As is uFor each of the reference sets in BAliBASE 3, we have examined and analyzed the performances of the aligners that accept anchors before and after the inclusion of two types of position subsets: (1) raw MS4 partial columns, computed according to section MS4 method (2) consistent MS4 partial columns, as obtained after applying the algorithm described in section Consistent Partial Columns.l we set the weight to 10|l| for ClustalW and Dialign, and a uniform value of 100M for T-Coffee, where M is the number of sequences in the dataset. For each of the obtained alignments, we have computed the sum-of-pairs (SP) and total-column (TC) scores, and compared it to the scores obtained by the aligner alone. On DIALIGN, the results proved disappointing. With T-Coffee, no improvement nor degradation whatsoever was observed in the overwhelming majority of cases: there is a variation on less than 25 datasets over the whole BAliBASE3 (which consisting of 218), and a substantial one on about 5 only. These results are after all not so surprising, since both DIALIGN and T-Coffee already rely on local strategies. We will henceforth focus our discussion on the results obtained with ClustalW 2.0 alone. We omit "MS4" in what follows.The partial columns must be split into segments of pairwise matching positions, and attributed a weight. For a pair of segments of length smin = 2, 6 and 12, which are somehow representative of the general trend, that we sum up as graphs in Figure smin = 6 and 12. Although the score improvements of our anchors on ClustalW are substantial, they remain inferior to those obtained by modern aligners.Tables aln_compare[aln_compare ref_al test_al computes among all pairs of aligned residues of the reference alignment ref_al, the proportion of residues which are present in the tested alignment test_al. If the arguments are swapped, the result returned counts the proportion of correct pairs among the core pairs aligned in the test alignment. A similar analysis is valid for the Total-Column score. These measures can be considered as specificity scores. We have reported in Table smin = 6, which appears from Tables Detecting a larger amount of correct similarities does not necessarily mean that the obtained alignment is better. Indeed, this effect could be obtained at the cost of including also a lot of wrongly aligned positions. To study this issue, we used the multiple alignment comparison tool n_compare by swappsmin < 5, and a global improvement above this threshold (except for RV30). The score degradation for smin < 5 shows that the raw partial columns include inconsistent similarities for these values, which are eliminated by requiring that a column span a minimum number of sequences in order to be considered.We can observe from Figure smin (except for RV12) is to be seen. This indicates that the consistency algorithm manages to suppress inconsistent similarities even when they only concern as few as 2 sequences. More generally, the improvement due to the inclusion of the consistent partial columns is clearer for RV40 and RV50.Figure This result fits with the expectations, since these two datasets contain respectively large (C- or N-) extensions and large internal deletions. It is well known that supplying local information help global aligners to deal with large indels.smin < 5 with raw partial columns disappears as soon as the columns have been filtered by the consistency algorithm, and gives on the contrary a perceptible improvement (with the notable exception of RV40). This means that, although the actual number of correctly aligned pairs does not greatly increase . A closer examination of the alignments shows that, for BB40040, MS4 detects (rightly) a similar region that extends over 18 sequences, but it turns out that for 1 sequence it should not be aligned with the 17 others. The resulting offset of the positions in this last sequence runs whole columns along the core region . The inclusion of user-defined anchor points being also possible, we have in this way been able to assess the improvement of performance that results from the inclusion of these local primary sequence-based similarities, constructed without score matrices or sliding window of predefined length. With the local aligners for which the inclusion of anchor points is possible, the results are not conclusive, especially with DIALIGN, although they happen to have quite a neutral effect on T-Coffee. It is unfortunate that the anchoring option is not featured in any other aligner, especially any other global aligner, to be able to give more insight on the usefulness of the construction presented here.The improvement obtained for ClustalW is most perceptible for datasets containing sequences of unequal lengths, and the computation of MS4 partial columns seems then justified in view of the gain in accuracy they provide. In other respects, the computation of consistent partial columns can help the eye-expertise of multiple alignments, for the number of obtained position subsets is quite reasonable, and, as the TC score performance seems to indicate, their visualization allows to correct whole columns in the alignment, since they appear to correspond to conserved zones in the considered sequences (like in Figure EC and FP have developed the methods and conducted the tests, FP and CD have performed the expertise, and all three authors have drafted, read and approved the manuscript.


Although multiple templates are frequently used in comparative modeling, the effect of inclusion of additional template(s) on model accuracy (when compared to that of corresponding single-template based models) is not clear. To address this, we systematically analyze two-template models, the simplest case of multiple-template modeling. For an existing target-template pair (single-template modeling), a two-template based model of the target sequence is constructed by including an additional template without changing the original alignment to measure the effect of the second template on model accuracy.Even though in a large number of cases a two-template model showed higher accuracy than the corresponding one-template model, over the entire dataset only a marginal improvement was observed on average, as there were many cases where no change or the reverse change was observed. The increase in accuracy due to the structural complementarity of the templates increases at higher alignment accuracies. The combination of templates showing the highest potential for improvement is that where both templates share similar and low (less than 30%) sequence identity with the target, as well as low sequence identity with each other. The structural similarity between the templates also helps in identifying template combinations having a higher chance of resulting in an improved model.a priori, that tend to show improvement in model quality over the single template model. The benefit derived from the structural complementarity is dependent on the accuracy of the modeling alignment. The study helps to explain the observation that a careful selection of templates together with an accurate target:template alignment are necessary to the benefit from using multiple templates in comparative modeling and provides guidelines to maximize the benefit from using multiple templates. This enables formulation of simple template selection rules to rank targets of a protein family in the context of structural genomics.Inclusion of additional template(s) does not necessarily improve model quality, but there are distinct combinations of the two templates, which can be selected  With the progress of structural genomics initiatives, comparative (or homology) modeling has become an increasingly important method for building protein structure models -3. Not oe models . Due to e models , models e models -9. Howeve models .Three elements that influence the accuracy of comparative models  are: (i)Eqn. 1). Most recently, the use of profile-to-profile alignments [Eqn.1) to improve model accuracy translates into the problem of selecting the template that is structurally closest to the target. In real modeling cases, the structure of the target is unknown and the structural difference between target and template must be estimated by other means. Usually, the template with the highest  sequence similarity is chosen. In spite of some evidences to the contrary [structural complementarity of the templates. Anecdotal evidence indicates that structural complementarity may result in improved model accuracy [Eqn1 . The alignment of Target:Template1 may be different from that of Target:Template1:Template2 and the observed change in the model quality could be due to the difference in the modeling alignment in the two situations. It could also be the case that the Template1:Template2 combination results in a template chimera that is structurally closer to the Target than each of the individual templates  they are a useful benchmark representing error free alignments. At the other end of the spectrum we find pairwise sequence alignments, which rely only on the knowledge of the sequence of the target and the template. Any difference in the quality of models based on these alignment types is solely due to differences in quality of the modeling alignment and has been the subject of our earlier study of single-template models . STR andALN.X.Y nomenclature used here) and the two-template models are named SEQ.2.2 and STR.2.2. ALN stands for alignment type SEQ or STR; and X refers to number of template sequences used to generate the modeling alignment and Y refers to number of template structures used in the actual modeling step after generating the modeling alignment. As discussed above (see Background), the difference between SEQ.1.1 and SEQ.2.2 can be a result of changes in the modeling alignment as well as structural complementarity of the first template by the second template  indirectly by comparing structural complementarity in SEQ and STR models, and ii) directly by evaluating the alignment accuracy of SEQ alignments. Though the latter is the more rigorous comparison, we have deliberately carried out the analysis in both ways as the alignment accuracy is not a directly observable quantity in real modeling casesThroughout the study model accuracy is measured by root mean squared deviation (RMSD) of the equivalent Cα atoms between the modeled and experimental structure of the target sequence. Since the data set has been designed such that coverage of all targets by the models is always 100%, there is no need to include coverage into the accuracy assessment (see methods for details).To identify accuracy improvements due to structural complementarity the SEQ.2.1 models were analyzed  to measure structural complementarity in the absence of alignment errors. Second, a direct comparison of alignment accuracy and structural complementarity in SEQ model was carried out. The comparison of STR models shows that two-template models are more accurate than one-template models Figure . The comALN (RMSDALN.2.1-RMSDALN.2.2) as a function of alignment accuracy , and the observed structural complementarity in SEQ models, ΔRMSDSEQ = (RMSDSEQ.2.1-RMSDSEQ.2.2), clearly correlates with alignment accuracy . A plot of ΔRMSDy Figure  confirmsy Figure .These results, together with those in the previous section, indicate that the positive effect of structural complementarity on the average accuracy of multiple template models can only be obtained when the modeling alignment is highly accurate. The fact that an accurate alignment is necessary to obtain structural complementarity is not surprising. The regions of the templates that are more likely to complement each other are the less conserved regions, which will also contain the most alignment errors. If the complementary regions are not correctly aligned the benefits of the structural information are lost. This same interplay between alignment errors and structural information also affects loop modeling , where aWith the aim of determining if the two-template modeling cases that show the largest accuracy improvement with respect to their one-template counterparts share any common attributes, the model accuracy improvement (ΔRMSD) was measured as a function of the sequence similarity between target and templates (S1 and S2) and the sequence similarity between the two templates (S3)  is in a way a measure of the potential for complementarity between them. For example, if the two templates share very high similarity, there is little chance that they can complement each other, effectively functioning as a single template. On the other hand, if the two templates are very different from each other it may be difficult to find common alignable elements to transit from the use of one template to the other. Figure th member will enhance the modeling accuracy of most of the remaining 96 members by using multiple template models.The results shown above suggest a strategy for choosing templates for two-template modeling. Template pairs should be selected such that S1 – S2) < 5%, S3 < 30%, and the RMSD between the templates is in the range of 3.5–5.5 Å. If these selection criteria are applied to our complete set of STR models we observe that 78.1% of the selected two-template models show no significant change with respect to the one-template model, 2.1% show deterioration, and 19.8% show improvement Figure  and 7B.  – S2 < 5STR = (RMSDSTR.2.1-RMSDSTR.2.2), and the observed structural complementarity in SEQ models, ΔRMSDSEQ = (RMSDSEQ.2.1-RMSDSEQ.2.2), is not only maintained in the optimal subset  show a high probability of resulting in improved model accuracy. In the case of sequence-based alignments this benefit is less pronounced because of the low alignment accuracy. However, in structure-based alignments the effect of selecting optimal template combinations is significant and suggests that if accurate alignments can be achieved the model accuracy gains from template complementarity can be substantial. This is further supported by revisiting the relationship between structural complementarity and alignment accuracy for this subset of optimal template combinations Figure . The abst Figure  but showThe results of this large-scale  comprehensive analysis of multiple-template models explain the previous contradictory examples of improvement and deterioration of model quality on inclusion of additional templates -19. BothSingle-domain chains (size: 100–200 residues) of high resolution (2.5 Å or better) X-ray structures were selected from the Protein Data Bank (PDB)  using doTarget:Template1:Template2 triplet was that of the Target:Template pair with the higher sequence identity. Template1 always refers to the template with the higher sequence identity.Since each chain of a triplet can be the target with the other two as templates, the total number of models for the dataset is 31,923 . The sequence identity assigned to a particular Percent of sequence identity was used as the measure of sequence similarity because it is the most common variable used to describe comparative models making it convenient for comparing our results with previous work addressing the accuracy of comparative models -6. SequeS1 = Target:Template1 sequence identity(i) S2 = Target:Template2 sequence identity(ii) S3 = Template1:Template2 sequence identity(iii) 2. Thus, the corresponding single-template model of the target is based on Template1 and is referred to as Target:Template1. In the results, sequence identity S1 is used as the reference sequence identity for both the two-template model as well as the corresponding single-template model.By definition S1 ≥ SX.Y) notation is used to describe the models. ALN (SEQ or STR) refers to the method used to build the Target:Template alignment: pairwise SEQuence-alignment or STRucture-alignment. X refers to the number of templates used to obtain the alignment and Y refers to the number of the templates used in model building process  was first generated using the ALIGN3D command of MODELLER. The target sequence was aligned to this structural alignment of the templates, using the ALIGN command of MODELLER, without modifying the structural alignment  was generated using the ALIGN3D command of MODELLER.STR.2.1: The sequence of Template2 is eliminated from STR.2.2.Models were calculated using the alignments described below and the template structures as input to the default 'model' routine of program MODELLER version 6v2 . SEQ.2.2Alignment accuracy was measured as defined by Sauder et al. , namely,Idealized template chimeras for particular Target:Template1:Template2 combinations were constructed by selecting the structurally closest equivalent segment (for each non overlapping target segments) from either of the two templates. The combination of these "best" segments from each of the templates results in an ideal template chimera that can be used to evaluate the efficiency with which the modeling program (i.e. MODELLER) combines the information from both templates. Closeness among the equivalent residues is determined by measuring the distance between the target residue backbone atoms and that of the equivalent template residue after optimal pairwise structural superposition of the target with each of the templates.Overall accuracy was measured by computing the root mean square deviation (RMSD) between the equivalent Cα atoms in the optimal superposition of target and model structures as it is the most common evaluation performed systematically for comparative models ,31,32. SSC built the dataset, created the analysis procedure, collected and analyzed the data, and contributed to the design of the study. SG contributed to the creation of specialized alignments. BZ and SB build the first version of the dataset and carried out initial experiments with multiple template modeling that helped shape the project. RS conceived the study, guided the project, and contributed to the design. SC and RS wrote the manuscript.