While the pairwise alignments produced by sequence similarity searches are a powerful tool for identifying homologous proteins - proteins that share a common ancestor and a similar structure; pairwise sequence alignments often fail to represent accurately the structural alignments inferred from three-dimensional coordinates. Since sequence alignment algorithms produce optimal alignments, the best structural alignments must reflect suboptimal sequence alignment scores. Thus, we have examined a range of suboptimal sequence alignments and a range of scoring parameters to understand better which sequence alignments are likely to be more structurally accurate.-5) and the ensemble of probA alignments. We constructed a logistic regression model incorporating three input variables derived from sets of near-optimal alignments: robustness, edge frequency, and maximum bits-per-position. A ROC analysis shows that this model more accurately classifies amino acid pairs  according to the likelihood of appearance in structural alignments than the robustness score alone. We investigated various trimming protocols for removing incorrect edges from the optimal sequence alignment; the most effective protocol is to remove matches from the semi-global optimal alignment that are outside the boundaries of the local alignment, although trimming according to the model-generated probabilities achieves a similar level of improvement. The model can also be used to generate novel alignments by using the probabilities in lieu of a scoring matrix. These alignments are typically better than the optimal sequence alignment, and include novel correct structural edges. We find that the probA alignments sample a larger variety of alignments than the Zuker set, which more frequently results in alignments that are closer to the structural alignments, but that using the probA alignments as input to the regression model does not increase performance.We compared near-optimal protein sequence alignments produced by the Zuker algorithm and a set of probabilistic alignments produced by the probA program with structural alignments produced by four different structure alignment algorithms. There is significant overlap between the solution spaces of structural alignments and both the near-optimal sequence alignments produced by commonly used scoring parameters for sequences that share significant sequence similarity (E-values < 10The pool of suboptimal pairwise protein sequence alignments substantially overlaps structure-based alignments for pairs with statistically significant similarity, and a regression model based on information contained in this alignment pool improves the accuracy of pairwise alignments with respect to structure-based alignments. Pairwise sequence alignment is the most widely used method for extracting information from protein and DNA sequences; it is routinely used to detect protein homologs that diverged more than 2 billion years ago. Homology -common evolutionary ancestry - can be reliably inferred for proteins that share statistically significant sequence similarity. When statistically significant similarity to a known sequence is found, inferences can be made about the structure, function, and biologically significant residues of the unknown sequence. While the inference of homology is quite robust ,  some of The usual gold standard by which sequence alignments are assessed is the structural alignment between two proteins whose three-dimensional 3D) structures are known. The 3D-structure contains more information than the one-dimensional sequence, and diverges more slowly, so that distant evolutionary relationships can be recognized in structures between sequences that do not share statistically significant similarity. However, even clearly related proteins with strong sequence similarity can produce sequence alignments that differ from the most accurate structural alignments Figure . Since dD structuThe most widely used algorithm for generating pairwise sequence alignments is dynamic programming, originally applied to biological sequences by Needleman and Wunsch. DynamicFurthermore, distantly related proteins often have multiple optimal alignments, as well as a large number of suboptimal alignments with scores very close to that of the optimal score ,6-8. As Although the "gold standard" by which sequence alignments are evaluated is a structure-based alignment, structural alignments can vary, and there is no algorithm that guarantees an optimal structural alignment . The assSince structurally accurate alignments often have sub-optimal sequence alignment scores, investigators have explored these sets of alternative alignments, asking whether they provide information about accurate structural alignments. For example, Jaroszewski et al.  examinedVarious authors have taken a probabilistic approach to generating sets of alternative alignments. Miyazawa  calculatWhile it is of theoretical interest to compare sets of individual sequence and structure alignments, it is only of practical use if one can determine which sequence alignment is the correct one in the absence of structural information. One way to address this question is to estimate the reliability of a particular pair of aligned residues . Cline et al.  looked a-10, with an average of 48% identity. The intermediate and most distantly related sequences have 10-10 < E < 10-5 (26.9% identity) and E < 10-5 (22.6% identity), respectively.Our goal is to find characteristics of sub-optimal sequence alignments that can be used to identify alignments, or sub-alignments, that are found in structural alignments. Just as importantly, we seek measures of alignment quality that help us predict which alignments are more likely to be correct. Since homologous proteins are typically identified through similarity searches, we focus on protein sequences that share statistically significant sequence similarity. We divide our protein pairs by sequence similarity, to explore the relationship between sequence similarity  and structural accuracy. The most similar third of the alignment pairs have sequence similarity expectation values E < 10Suboptimal sequence alignments can only be used to produce accurate structural alignments if the sequence and structure alignments overlap each other. Figure Alignments have a score - either a sequence similarity score or a structural similarity score. While the path graphs indicate that the structural alignments are generally in the space of suboptimal sequence alignments, we need to know how the similarity scores compare. Figure -10) and in more than 50% of pairs for moderately similar sequences (E < 10-5). Indeed, 95% sub-optimal sequence alignments were more accurate than the best structural alignment in 10%-20% of the families in both similarity groups. When a sampling of sequence alignment scores that are within 75% of optimal are examined , while the latter has E-values between 10-5 and 0.02 and a mean percent identity of 22.7% (median 22.1%). There is clearly a significant drop-off in alignment quality going from the medium similarity group to the low similarity one, even though the average percent identity does not change very much. The expectation value is much more informative predictor of sequence alignment accuracy than the percent identity, even for sequences that share significant similarity.Figure A single similarity score is only a rough measure of how similar two alignments are. Cline et al.  developeTo make use of the information contained within the set of near-optimal alignments, one needs a way of ranking or assessing the alignments. In particular, one would like to assess the likelihood that a particular pair of residues has been aligned properly. Mevissen and Vingron described one such method . They caLogistic regression is used to predict a discrete response variable using one or more continuous, discrete, and/or dichotomous predictor variables . Thus weWe compared the ability of the model to predict whether an edge will be found in a structural alignment or not with that of alternative models  by creating training and test sets of edges by randomly segregating the alignments, then selecting edges from the pool of training or testing alignments. Figure Since the probA alignments sampled a wider variety of alignments, which tended to overlap with the structural alignments to a greater extent than the Zuker alignments did, we also created a model using the probA alignment edges as input. This model performed slightly worse than that based on the Zuker alignments did . We did not directly examine the edge probabilities that probA uses to construct its alignments, but since the algorithm produces a "statistically weighted distribution"  of alignHaving established that the model is superior at identifying structural edges, we next wanted to make use of this information to produce more structurally accurate alignments. We did this in two ways: by "trimming" the optimal sequence alignments and by generating new alignments using the model probabilities.Given a sequence alignment, some fraction of the aligned residues will be incorrect, compared to a reference alignment.  Furthermore, some fraction of the correct edges will not appear in the sequence alignment. Perhaps the simplest way to make use of an edge classification scheme is to identify suspect edges, and remove them from the alignment. We thus "trimmed" alignments by removing edges from the alignment with low log-odds probabilities produced by the model, or with low robustness or frequency scores. For example, we replaced any edges in an alignment with low log-odds scores e.g. < 0.5) with a gapped alignment (e.g. A/V becomes A-/-V). We then compared the percentage of sequence alignment edges that are correct (true positives) and the shift scores against Dali alignments of "trimmed" alignments with the untrimmed alignments. These results are summarized in Tables  with a gTrimming the alignments with the logistic regression model probabilities clearly improves the percentage of true positives in all similarity categories, in agreement with the ROC curve. This has minimal effects on the sensitivity (coverage); of the edges in the optimal semi-global alignment removed by the model, less than 10% (49/503) are true positives . No more than four true positives are removed in any given pair. For shift scores, trimmed alignments also show clear, if less dramatic, improvement over the optimal alignment. In this trimming analysis, the full model performs similarly to robustness alone and frequency alone.Another way to look at alignment quality is to identify regions of the alignment that are of higher or lower quality, as opposed to individual edges. Since we are aligning structurally defined domains, the default was to use semi-global alignments; however, we hypothesized that the regions of the alignment that were within the local alignment boundaries might be of higher quality, under the assumption that there would be more alignment "signal" within this region. Tables Trimming alignments can help remove incorrect edges, but it is constrained by the initial alignment. We also produced new alignments that were not so constrained, by using the probabilities calculated by the model (equation 2) in place of standard substitution matrix scores and affine gap penalties (see Methods). Tables Previous authors have shown that there is substantial overlap between the near-optimal alignment space and the structural alignment space ,15, and Previous efforts to extract information from the overlap between the structural and sequence alignment spaces have used profile-based methods ,15 to imThere has also been substantial effort put into developing probabilistic methods for exploring alternative pairwise alignments. We have used the probA program to compare this methodology with the Zuker method of sampling different alignments. It appears that probA samples a more diverse range of alignments, which can result in better agreement with the structural alignments; however, it is not obvious that the "correct" alignments (or edges) are any easier to identify within the set of probA alignments. It is intriguing that in some cases the best probA alignment is also the most similar to the structural alignments  program [http://cl.sdsc.edu/ce.html, also with default parameters. We used the Structal method as implemented in the LSQMAN program [http://xray.bmc.uu.se/usf/. Specifically, we used the Fast Force and Improve commands to get an initial alignment, then the DP command to implement the dynamic-programming method of Levitt and Gerstein [The structural alignment programs used were Dali, LSQMAN, CE, and Matras. We used the standalone version of the Dali program , called  program , obtaina program  from theGerstein . We thenGerstein . For MatGerstein  with defindividual metric, such as the Needleman-Wunsch semi-global alignment score  [pairwise alignment scores, which compare two different alignments. For a structural alignment score we used the Structal score [We evaluated sequence and structure alignments using two different metrics: (1) an nalized)  or the sal score  calculatal score .-10, average percent identity 48.0%), medium similarity , and low similarity .The protein pairs were selected from CATH (version 3.2) domains  of knownglm  function with the logit link function and the lrm (logistic regression model) function from the Design library [The logistic regression was performed using the R statistical computing system . Models  library . The bin library  the freqWe evaluated the three predictor variables first by building single parameter models using each of the possible predictors. Individual predictors were evaluated following the strategy described in Hosmer and Lemeshow 2000).; any variable with a p-value less than 0.25 was considered for inclusion in the model.  Second, we built a model using all possible predictors and then selectively omitted one or more parameters until the most parsimonious model was achieved. Parsimony was measured with the Akaike Information Criterion (AIC) . Of all 000.; anyThe final model is represented by the equation:p is the probability that the edge is contained in a structure-based alignment, q is 1-p, r is the robustness of the edge, m is the maximum bits-per-position for an alignment containing that edge, and f is the frequency that the edge is seen in an alignment. a1, a2, and a3 are coefficients. Given (1), the probability of an edge being found in a structural alignment is:where Sequence pairs were partitioned into test and training sets, so that edges from a given sequence pair were not used to both train and test the model. As recommended by Hosmer, et al.  we used We used a modified version of our suboptimal sequence alignment generation code to produce alignments where a diagonal edge in the dynamic programming matrix was scored using the log-odds probability produced by the logistic regression model (Equation 2) in place of the normal substitution matrix score. Gap open/extension penalties of -10/-2 were used. We also constructed alignments using the same method, using only robustness or only frequency to calculate the log-odds probability Tables  and 6.MLS carried out data collection and analysis, and wrote portions of the manuscript. MES wrote the suboptimal sequence alignment code, carried out data collection and analysis, and wrote portions of the manuscript. EJB participated in the design and coordination of the study and edited the manuscript. WRP conceived of the study, participated in its design and coordination, and edited the manuscript. All authors read and approved the final manuscript.Counts of suboptimal Zuker alignments sampled. Maximum and minimum number of suboptimal alignments produced for each sequence pair, for the neighborhoods with alignment scores within the indicated percent of the optimal score. Each neighborhood had six different combinations of scoring matrix and gap penalties.Click here for fileList of CATH domains used in the study. The table lists the pair numbering used throughout the paper, the CATH version 3.2 domain names, the expectation value calculated by SSEARCH in a search of a database of 10,000 domains, the percent identity, and the CATH family of the domains.Click here for file


Frameshift mutations in protein-coding DNA sequences produce a drastic change in the resulting protein sequence, which prevents classic protein alignment methods from revealing the proteins' common origin. Moreover, when a large number of substitutions are additionally involved in the divergence, the homology detection becomes difficult even at the DNA level.http://bioinfo.lifl.fr/path/.We developed a novel method to infer distant homology relations of two proteins, that accounts for frameshift and point mutations that may have affected the coding sequences. We design a dynamic programming alignment algorithm over memory-efficient graph representations of the complete set of putative DNA sequences of each protein, with the goal of determining the two putative DNA sequences which have the best scoring alignment under a powerful scoring system designed to reflect the most probable evolutionary process. Our implementation is freely available at Our approach allows to uncover evolutionary information that is not captured by traditional alignment methods, which is confirmed by biologically significant examples. In protein-coding DNA sequences, frameshift mutations (insertions or deletions of one or more bases) can alter the translation reading frame, affecting all the amino acids encoded from that point forward. Thus, frameshifts produce a drastic change in the resulting protein sequence, preventing any similarity to be visible at the amino acid level. For that reason, classic protein alignment methods, that rely on amino acid comparisons, fail to reveal the proteins' common origins in the case of divergence by frameshift.Consequently, it is natural to handle frameshift mutations at the DNA level, by DNA sequence comparisons. Several papers, including -4 reportHowever, the divergence may also involve additional base substitutions, that can reduce the similarity of the diverged DNA sequences. It has been shown -9 that, In this paper, we address the problem of finding distant protein homologies, in particular when the primary cause of the divergence is a frameshift. We aim at being able to detect the common origins of sequences even if they were affected by an important number of point mutations in addition to the frameshift. Also, when dealing with sequences that have little similarity, we wish to distinguish between sequences that are indeed (distantly) related, and sequences that resemble by chance. We achieve this by computing the best alignment of DNA sequences that encode the target proteins, with respect to a powerful scoring system that evaluates point mutations in their context, based on codon substitution patterns. Our approach implicitly explores all the pairs of DNA sequences that can be translated into these proteins, which allows a wider vision on the match possibilities at the DNA level.We designed and implemented an efficient method for aligning putative coding DNA sequences, which builds expressive alignments between hypothetical nucleotide sequences obtained by back-translating the proteins, that can provide some information about the common ancestral sequence, if such a sequence exists. We perform the analysis on memory-efficient graph representations of the complete set of putative DNA sequences of each protein. The proposed method consists of a dynamic programming alignment algorithm that computes the two putative DNA sequences that have the best scoring alignment under an appropriate scoring system.Back-translation or reverse translation of a protein usually refers to obtaining one of the DNA sequences that encodes the given protein. Several methods for achieving this exist ,11, aimiMethods section.In this paper, we are not interested in just one of the coding sequences, but aim at exploring them exhaustively and aligning them with potential frameshifts. Thus, in the context of our work, the back-translation will refer to all the putative DNA sequences, as explained further in the The idea of using knowledge about coding DNA when aligning amino acid sequences has been explored in several papers.non-statistical approach for analyzing the homology and the "genetic semi-homology" in protein sequences was presented in handling aligning coding DNA in presence of frameshift errors, some related ideas were presented in  of a dynamic programming matrix M, where i and j are positions of GA and GB respectively, and  enumerates the possible pairs of nodes that can be found in GA at position i, and in GB at position j, respectively. An example of matrix M is given in Figure Given input graphs M  is computed as the maximum of 6 types of values:The dynamic programming algorithm begins with a classic local alignment initialization (0 at the top and left borders), followed by the recursion step described in relation (3). The partial alignment score of each matrix entry (a) 0 .αi, βj), denoted score, added to the score of the best partial alignment ending in M , provided that the partially aligned paths contain αi at position i and βj on position j respectively; this condition is ensured by restricting the entries of M  to those labeled with symbols that precede αi and βj in the graphs, and is expressed in (3) by αi-1 ∈αi), βj-1 ∈ βj).(b) the substitution score of symbols  in the first sequence, added to the score of the best partial alignment that ends in a cell M , provided that βj-1 precedes βj in the second graph (βj-1∈ βj)); this case is considered only if the number of allowed frameshifts on the current path is not exceeded, or a gap of size 1 is extended.(c) the cost (d) the cost of a frameshift in the second sequence, added to a partial alignment score defined as above.tripleGapPenalty of removing an entire codon from the first sequence, added to the score of the best partial alignment ending in a cell M .(e) the cost M (f) the cost of removing an entire codon from the second sequence, added to the score of the best partial alignment ending in a cell i) frameshifts - gaps of size 1 or 2, with high penalty, whose number in a local alignment is limited, and ii) codon skips - gaps of size 3 which correspond to the insertion or deletion of a whole codon.We adopted a non-monotonic gap penalty function, where insertions and deletions of full codons are less penalized than reading frame disruptive gaps. Additionally, since frameshifts are considered to be very rare events, their number in an alignment is restricted. More precisely, as can be seen in equation (3), two particular kinds of gaps are considered: Although the algorithm is defined for back-translated protein alignment, it can also be used for aligning two DNA sequences or a DNA sequence to a protein. The graph corresponding to a DNA sequence has only one node at each position. Thus, the method can be used for aligning proteins to longer DNA sequences containing coding regions. However, when long sequences are aligned by dynamic programming methods, time and space complexity issues need to be addressed.In this section we discuss the time and space complexity of our method and show how we can improve the latter using an approach inspired by .P of size n depends linearly on n. Basically, as mentioned in the section dedicated to data structures, the back-translation graph GP =  consists of 3·n groups of nodes {n amino-acids are encoded by sequences of 3 nucleotides). Every group i contains the nodes corresponding to the nucleotides that can appear at position i in at least one of the putative coding sequences (see (1)). The number of nodes in a group is limited by the number of codons that encode an amino acid, that we denote The space necessary for storing the back-translation graph of a protein sequence P of size n is n). The worst case scenario is a protein sequence composed only of the amino acids L, S, R, which are encoded by 6 codons each, and hence have the most complex back-translation. For each such amino acid, 10 nodes and 20 arcs are necessary, yielding a maximum memory size of 30n for the entire graph. For the ambiguous nucleotide symbol encoding though, 6 nodes and 6 arcs are necessary in the worst case for each amino acid, while most amino acids only require 3 nodes and 3 arcs for their back-translated representation.Arcs exist only between nodes in consecutive groups (equation (2)), therefore each node can have a limited number of neighbors. Consequently, the overall memory consumption for storing the back-translation graph of a protein sequence GA and GB be graphs obtained by back-translating proteins PA and PB, of lengths nA and nB respectively. The dynamic programming matrix M computed by the alignment algorithm will have 3·nA + 1 rows and 3·nB+ 1 columns. Each cell of the matrix M  has several entries corresponding to the possible pairs of nodes from each sequence. The number of entries is bounded by the square of the number of nodes that can appear on each position in the graph (2). Consequently, the total number of entries in the matrix is at most 2·(3·nA + 1)·(3·nB + 1), hence nAnB).Let Each entry holds the score of the partial alignment ending at the corresponding positions, as well as the number of frameshifts that occurred on the path so far  and a reference to the previous matrix entry of the alignment path, to facilitate the traceback. The storage space requirements for this supplementary information are bounded by a constant.2, this operation is considered to be performed in constant time. Consequently, the overall time complexity of the algorithm is nAnB). To recover the best alignment and the two actual sequences that produce it, a classic traceback algorithm is used, with an execution time depending linearly on the alignment length, which cannot be larger than (3·nA + 3·nB + 1).For computing each score in the matrix, the expressions that need to be evaluated are given by equation (3), by querying some of the entries from 5 other cells in the matrix. Since the number of entries in each cell is bounded by To overcome the memory issues caused by aligning very large sequences with our dynamic programming method, which requires quadratic space, we used an approach inspired from the linear space algorithm for the LCS problem . Our aimAs a compromise, we choose to split the alignment according to some pre-established cut-points, in submatrices that are small enough to fit into memory, and that are recomputed only once for retrieving the corresponding alignment fragments. In our implementation, the cut-points delimit submatrices that are, by default, 128 columns wide. In this setup, we use a two-step approach: first, we compute the score of the best local alignment in linear space, using a sliding window, while also identifying the intersections of the corresponding path with the established cut-points; in the second step, we recompute separately the submatrices containing parts of the best alignment (restricted to the rows that intersect it), and then rebuild the alignment by pasting the obtained alignment fragments together.For the first pass, we use a sliding window of 4 columns instead of the original 2, because each partial score depends on the scores that are 3 cells to the left or 3 cells above (see equation (3), items (e) and (f)). Each cell of the sliding window memorizes the matrix entry where the alignment path started , as well as the intersections of this path with the cut-points. This information is propagated from the previous cell contributing to the computation of the score, and completed in each cell from the cut-point columns by storing the line number and the node pair that help identify an actual entry in the matrix which belongs to the alignment path. The best scoring entry encountered so far is memorized and updated at each step of the alignment algorithm. When the first pass is completed, the best scoring cell will provide all the necessary information for reconstructing the alignment: the start of the alignment, the intersection with each cut-point, and its end, which is the cell itself. According to these coordinates, subgraphs of the two back-translation graphs are extracted and aligned globally (ensuring that the start and end node pair of each fragment are preserved). The obtained global alignments, combined, will give the best local alignment of the two large sequences.In this section, we present a new translation-dependent scoring system suitable for our alignment algorithm. Our scoring scheme incorporates information about possible mutational patterns for coding sequences, based on a codon substitution model, with the aim of filtering out alignments between sequences that are unlikely to have common origins.Mutation rates have been shown to vary within genomes, under the influence of different factors, including neighbor bases . Consequα, p, a), were α is a nucleotide, p is its position in the codon, and α is the amino acid encoded by that codon, thus differentiating various contexts of a substitution. There are 99 valid triplets out of the total of 240 hypothetical combinations. Pairwise alignment scores are computed for all possible pairs of valid tripletsWith the aim of retracing the sequence's evolution and revealing which base substitutions are more likely to occur within a given codon, our scoring system targets pairs of triplets  = , ) as a classic log-odds ratio:p(tj) is the background probability. This scoring function is used in the algorithm as shown by equation (3)(b), where we refer to it as score, without explicitly mentioning the context - amino acid and position in the corresponding codon - of the paired nucleotides. These details were omitted in equation (3) for generality  and for notation simplicity.where In order to obtain the foreground probabilities The insignificant amount of available real data that fits our hypothesis does not allow classical, statistical computation of the foreground and background probabilities. Therefore, instead of doing statistics on real data directly, we will rely on codon frequency tables and codon substitution models, either mechanistic or empirically constructed.i to codon j as:We can assume that codon substitutions in our scenarios are modeled by a Markov model presented in  that spei ≠ j. Here, the parameter ω represents the nonsynonymous-synonymous rate ratio, κ the transition-transversion rate ratio, and πj the equilibrium frequency of codon j. As in all Markov models of sequence evolution, absolute rates are found by normalizing the relative rates to a mean rate of 1 at equilibrium, that is, by enforcing Q by defining P (θ) = eθQ  ≡ cj [intervalj] states that codon ci restricted to the positions given by intervali is a sequence identical to cj restricted to intervalj . This is equivalent to having a word w obtained by "merging" the two codons. For instance, if ci = CAT and cj = ATG, with their common substring being placed in intervali = [2..3] and intervalj = [1..2] respectively, w is CATG.The notation p the probability to have ci and cj, in the relation described above, and we compute it as the probability of the word w obtained by "merging" the two codons. This function should be symmetric, it should depend on the codon distribution, and the probabilities of all the words w of a given length should sum to 1. However, since we consider the case where the same DNA sequence is translated on two different reading frames, one of the two translated sequences would have an atypical composition. Consequently, the probability of a word w is computed as if the sequence had the known codon composition when translated on the reading frame imposed by the first codon, or on the one imposed by the second. This hypothesis can be formalized as:We denote by w) and w) are the probabilities of the word w in the reading frame imposed by the position of the first and second codon, respectively. This is computed as the products of the probabilities of the codons and codon pieces that compose the word w in the established reading frame. In the previous example, the probabilities of w = CATG in the first and second reading frame are:where p, ) are computed as:The values of foreground probabilities is straightforward:from which obtaining the background probabilities of , The Earlier we have shown how to compute the translation dependent scores for non-ambiguous nucleotide symbols. However, as mentioned in the section concerning data structures, we work with ambiguous nucleotide symbols, because their usage improves time and memory consumption while providing the same final results. The scores for ambiguous nucleotide symbol pairs are easily obtained as follows:pi of the codons that encode the amino acid ai, and setdenotes the set of non-ambiguous nucleotide symbols represented by where By using ambiguous symbols, less triplets are formed for each amino acid when compared with the non-ambiguous symbol case. 17 amino acids can be anti-translated as tri-mers with just one ambiguous symbol per position, while the others have two alternatives each of the three positions. Therefore, there are 69 different triplets with ambiguity codes to be paired (as opposed to 99), which means more than twice less storage space necessary for the score matrix.For the reconstruction of the non-ambiguous putative DNA sequences at traceback, the actual pair of nucleotides that have the highest substitution score from the sets corresponding to two paired ambiguous symbols is required. These are easily obtained for each pair of ambiguous symbols asIn this section we have presented a general framework that helps to compute a translation dependent scoring function for DNA sequence pairs, parametrized by a codon substitution model and an evolutionary time measured in expected number of mutations per codon. We consider that the sequences evolve independently, and the distance is relative to the original sequence.λ and K are computed with the method described in  and [GenBank:AY057880.1] of two homologous proteins.Following the discovered frameshift of Figure Laticauda colubrina and Laticauda laticaudata). It shows that the unidentified peptide is in fact an alternative splicing (or frameshifted) variant of the neurotoxin. Note that BLASTP identification of the frameshifted peptide on the NCBI nr database gives high E-values  and is thus expected to be missed by automatic prediction tools (since most of the features specific to neurotoxin are not present), whereas the non frameshifted peptide fragment, once identified, gives several E-values <10-10 on NCBI nr.Furthermore, Figure human and rat platelet-derived growth factor proteins. The two proteins share high similarity at the amino acid level on the subsequences 1-84 and 113-195. The amino acids 85-112 can be easily aligned with a frameshift, as can be seen in Figure Platelet-derived growth factor is a potent mitogen for cells of mesenchymal origin. Binding of this growth factor to its affinity receptor elicits a variety of cellular responses. It is released by platelets upon wounding and plays an important role in stimulating adjacent cells to grow and thereby heals the wound. In Figure It is interesting to notice that this double frameshift (if confirmed) may have little influence on the protein (only the beginning of the receptor binding interface is modified). It is also interesting to notice that both the "inducing" and "correcting" frameshifts are located on two different exons.In this paper, we addressed the problem of finding distant protein homologies, in particular affected by frameshift events, from a codon evolution perspective. We search for protein common origins by implicitly aligning all their putative coding DNA sequences, stored in efficient data structures called back-translation graphs. Our approach relies on a dynamic programming alignment algorithm for these graphs, which involves a non-monotonic gap penalty that handles frameshifts and full codon indels differently. We designed a powerful translation-dependent scoring function for nucleotide pairs, based on codon substitution models, whose purpose is to reflect the expected dynamics of coding DNA sequences.We illustrated our approach with several alignment examples of known and hypothetical frameshifted proteins, some of which are not detectable via classic alignment methods because of the low coding sequence similarity. Such examples support our method's applicability in the discovery of distant protein homologies and functional frameshifts, without any explicit information about the coding sequences. Future work includes further improvements of the scoring system, for example in order to focus on the detection of short double correcting frameshifts . Such cases have been shown to occur frequently , but areSome natural extensions of our work include the support for multiple alignments of back-translation graphs. This feature can be useful for confirming frameshifts by similarity of the frameshifted subsequence with the corresponding fragments from several members of a family. Also, for boosting the efficiency, seeding techniques for back-translation graphs could be explored, possibly inspired by the BLASTP score-based seeds.The authors declare that they have no competing interests.GK initiated and guided the project, and proposed the first version of the method. MG refined the method, proposed the initial scoring system, did the implementation and the web interface. LN contributed to defining and improving the scoring system, and did most of the experimentation and the analysis of the results. MG drafted the manuscript, which was completed by LN with the "Experimental results" section, and then finalized and approved by GK.


As the scope of microbial surveys expands with the parallel growth in sequencing capacity, a significant bottleneck in data analysis is the ability to generate a biologically meaningful multiple sequence alignment. The most commonly used aligners have varying alignment quality and speed, tend to depend on a specific reference alignment, or lack a complete description of the underlying algorithm. The purpose of this study was to create and validate an aligner with the goal of quickly generating a high quality alignment and having the flexibility to use any reference alignment. Using the simple nearest alignment space termination algorithm, the resulting aligner operates in linear time, requires a small memory footprint, and generates a high quality alignment. In addition, the alignments generated for variable regions were of as high a quality as the alignment of full-length sequences. As implemented, the method was able to align 18 full-length 16S rRNA gene sequences and 58 V2 region sequences per second to the 50,000-column SILVA reference alignment. Most importantly, the resulting alignments were of a quality equal to SILVA-generated alignments. The aligner described in this study will enable scientists to rapidly generate robust multiple sequences alignments that are implicitly based upon the predicted secondary structure of the 16S rRNA molecule. Furthermore, because the implementation is not connected to a specific database it is easy to generalize the method to reference alignments for any DNA sequence. SILVA serves as a repository for aligned rRNA sequences and the SINA aligner The popular software package, ARB http://greengenes.lbl.gov) is not explicitly dependent on secondary structure models; however, the generation of the reference database alignment does take into account the secondary structure , 202 form weak pairs , and 18 do not pair . Although sequences naturally have non-pairing bases within the paring regions of the secondary structure, an excessive number of these is an indicator of poor sequence alignment  alignment from the SILVA database on October 14, 2008, which contained 271,543 bacterial 16S rRNA gene sequences longer than 1,200 bp. Aligned sequences were downloaded from the greengene and RDP databases on November 16, 2008. The SILVA database was selected because it was the longest and visual inspection of the alignment suggested that it had the highest overall quality . Using AE. coli position 28 and ended after position 1491. Sequences beginning before or ending after these coordinates were trimmed. The resulting collection of 14,227 sequences represented my full-length template database. The other 186,206 sequences represented the candidate sequence collection.Because the SILVA reference alignment (i.e. the SEED) is not publicly available, I attempted to replicate the SEED database. First, I parsed the 200,433 sequences to identify those sequences that had an alignment quality score  of 100. Next, I identified those sequences in this pool that started by E. coli positions 28–1491), V12 (28–337), V14 (28–784), V2 (100–337), V23 (100–514), V3 (357–514), V4 (578–784), V6 (986–1045), V89 (1100–1491), and V9 (1300–1491). There were 186,206 candidate sequences for analyzing the V19, V2, V23, V3, V4, and V6 datasets. Because not all sequences extended through the first and ninth variable regions, I further screened these sequences to generate a collection of 139,987 candidate sequences for analyzing the V12 and V14 datasets and a collection of 77,685 sequences for the V89 and V9 datasets. These regions were selected because they are tractable by Sanger , 454 GS-FLX , 454 Titanium , and Illumina  sequencing technologies. Many of these regions have also been used in published studies: V19 I selected 10 regions within the 16S rRNA gene for my simulations. While maintaining the overall 50,000-character alignment, I excised regions V19  The aligner described here is freely available and provided within the mothur software package as source code or as a Windows executable (Table S1Comparison of search methods when using various regions extracted from candidate sequences and full-length template sequences.(0.07 MB PDF)Click here for additional data file.Table S2Comparison of search methods when using various regions extracted from candidate sequences and region-specific template sequences.(0.06 MB PDF)Click here for additional data file.Table S3Summary of alignment improvement for various regions extracted from candidate sequences using the blastn, Gotoh, or Needleman-Wunsch pairwise alignment algorithms when the best full-length template was selected for each candidate sequence.(0.11 MB PDF)Click here for additional data file.Table S4Summary of alignment improvement for various regions extracted from candidate sequences using the blastn, Gotoh, or Needleman-Wunsch pairwise alignment algorithms when the best region-specific template was selected for each candidate sequence.(0.10 MB PDF)Click here for additional data file.


Protein alignments are an essential tool for many bioinformatics analyses. While sequence alignments are accurate for proteins of high sequence similarity, they become unreliable as they approach the so-called 'twilight zone' where sequence similarity gets indistinguishable from random. For such distant pairs, structure alignment is of much better quality. Nevertheless, sequence alignment is the only choice in the majority of cases where structural data is not available. This situation demands development of methods that extend the applicability of accurate sequence alignment to distantly related proteins.We develop a sequence alignment method that combines the prediction of a structural profile based on the protein's sequence with the alignment of that profile using our recently published alignment tool SABERTOOTH. In particular, we predict the contact vector of protein structures using an artificial neural network based on position-specific scoring matrices generated by PSI-BLAST and align these predicted contact vectors. The resulting sequence alignments are assessed using two different tests: First, we assess the alignment quality by measuring the derived structural similarity for cases in which structures are available. In a second test, we quantify the ability of the significance score of the alignments to recognize structural and evolutionary relationships. As a benchmark we use a representative set of the SCOP  database, with similarities ranging from closely related proteins at SCOP family level, to very distantly related proteins at SCOP fold level. Comparing these results with some prominent sequence alignment tools, we find that SABERTOOTH produces sequence alignments of better quality than those of Clustal W, T-Coffee, MUSCLE, and PSI-BLAST. HHpred, one of the most sophisticated and computationally expensive tools available, outperforms our alignment algorithm at family and superfamily levels, while the use of SABERTOOTH is advantageous for alignments at fold level. Our alignment scheme will profit from future improvements of structural profiles prediction.http://www.fkp.tu-darmstadt.de/sabertooth_project/, free for academic users upon request.We present the automatic sequence alignment tool SABERTOOTH that computes pairwise sequence alignments of very high quality. SABERTOOTH is especially advantageous when applied to alignments of remotely related proteins. The source code is available at  Protein alignment tools are key in many protein science applications. For very closely related proteins the alignment problem can easily be solved as a fuzzy string search in the sequences. However, with growing evolutionary distance more sophisticated techniques have to be applied to detect similarities. At about 25% sequence identity, when the alignment problem enters the so-called 'twilight zone' , relatedi-th component represents the number of sites with which site i is in contact. The CV is strongly correlated with more complex descriptions such as solvent accessibility and effective connectivity of the contact matrix. We showed in previous work [Since protein structure evolves much more slowly than sequence, protein structure alignments are usually much more accurate for distantly related proteins and, hence, preferable if structural data is available. However, for the majority of cases only sequence information is available. A possible strategy for such cases would be to predict the unknown structures from their sequences and to perform a structure alignment using these predictions. Unfortunately, the accurate prediction of 3D coordinates is in general not possible yet and results are limited in quality . Neverthous work , that thWe previously developed the SABERTOOTH algorithm for performing protein structure alignments by aligning profiles that represent the protein structure ,4. In thet al. [et al. [We adopted a structural profile based on the contact vector (CV) described above, which produces structural alignments of high quality and is simple to predict. Contact vector prediction is an active field of research: Bastolla et al.  describe [et al.  who empl [et al.  who run  [et al.  to prediThe alignments produced by our algorithm following the strategy described above and detailed in the Methods section were then compared with some of the most commonly used sequence alignments programs, which we classified in three main classes: (1) Programs that take as only input the two sequences to be aligned; (2) Programs that take an additional input in form of a large database of known protein sequences and extract from it two families of proteins evolutionarily related with the query proteins; (3) Programs that, in addition to taking a sequence database as input, build a probabilistic description of the protein families as a Hidden Markov model (HMM). As reference tools of the first class we chose the programs Clustal W , MUSCLE To compare the quality of sequence alignments, we adopted a new method that scores the structure similarity derived from alignments of proteins with known structure. In fact, measures of sequence similarity are not meaningful for distantly related proteins, and their use in the assessment could lead to circular results, since many sequence alignment algorithms are based on the optimization of sequence similarity. Moreover, for many practical applications, such as homology modelling and function prediction, sequence alignments are used to infer a structure alignment, which is the real aim. These arguments have motivated the practice to assess the quality of sequence alignments by using structure alignments as a 'gold standard', either computed by a structure alignment tool or taken from databases like BAliBase  or HOMSTAs an objective measure of structural similarity we adopt the contact overlap. We find this measure preferable to others because of three reasons: (1) It does not require to compute a structure superimposition, avoiding the influence of the choices necessary for defining an optimal rotation matrix; (2) It effectively weights more the sites that belong to the protein core due to the larger number of contacts found here; (3) In the important cases of conformation changes in which one subdomain of the protein moves with respect to the other one, for which superimposition-based measures underestimate the structural relatedness, the contact overlap only penalizes a small number of inter-subdomains contacts that do not match in the two structures, while superimposition-based scores also penalize intra-subdomain contacts. We also consider as additional similarity measure the TM-score , a well-In Fig. In the bottom plot in Fig. Comparing the results in matters of sequence similarity to those found with SABERTOOTH structure alignment ,4 we canAs a second test, we evaluate the ability of the alignment programs to detect relevant relationships between the aligned proteins based on the significance measures they output. This is an important application, since sequence alignments are often used to predict whether two proteins share a similar function, have a close evolutionary relationship, or a similar structure, so that e.g. one can be used as a template for the other. As a test set of relevant relationships, we again consider the SCOP classification at family, superfamily and fold level. Although the SCOP classification is not fully consistent with quantitative measures of structural similarity, it provides a large number of mostly valid relationships that constitute a suitable benchmark.The results of this analysis mostly agree with the first test, as shown in the ROC plots in Fig. r = 0.72. This comparison is in part affected by the fact that single chains and single domains are considered in the test set, so that the observed number of contacts does not include inter-chain and inter-domain contacts, thus underestimating the observed number of contacts with respect to the case in which the whole multi-chain protein is considered. We also measured the variance of the predicted contact vector for each domain, and compared it with the observed variance. The predicted variance is systematically underestimated and not very well predicted, as indicated by the weak correlation coefficient r = 0.385. This suggests that it is still possible to improve the performance of SABERTOOTH by improving the prediction of the contact vector. The quantity relevant for the alignment algorithm is the penalty that has to be paid for aligning the observed and predicted contact vector, Finally, we assessed the accuracy of the prediction of the structural profile that SABERTOOTH uses for sequence alignment. The predicted profile was compared with the profile measured over a test set of 9420 protein domains, disjoint from the training set used. For each domain, we measured the correlation between the predicted and the measured contact vector, finding a length weighted correlation coefficient of The SABERTOOTH algorithm can align vectorial representations of protein structures. This was first applied to cases in which the protein structures are known, so that the algorithm produces a structure alignment. In the present paper, we apply the same algorithm to aligning vectorial representations predicted based on sequence alone, obtaining high quality sequence alignments. This new approach to sequence alignment is made possible because we adopt a very simple structural representation, the contact vector, which can be predicted relatively easily based on sequence, and it presents three main advantages: First, the predicted contact vectors are expected to capture structural features that are more conserved in evolution than the sequence itself, which leads to an increased sensitivity when comparing remotely related proteins. Second, we perform sequence alignment by aligning the same structural profiles that we adopt for structure alignment, which enables us to treat structure and sequence alignment with the same formalism and the same algorithm. Third, sequence alignment quality is expected to further improve through improvements in the profile prediction scheme and adding other types of structure description such as secondary structure. As a caveat, we warn that the application of SABERTOOTH should be limited to proteins predicted to be globular, since the strategy that we apply is not suitable for the alignment of disordered proteins.Our results show that the approach to combine structural profile prediction from sequence with our generic alignment program SABERTOOTH leads to sequence alignment quality better than those of most widely used algorithms we compare with, with the exception of HHpred, which shows the best performance but is also computationally more expensive than SABERTOOTH. It is interesting to notice that SABERTOOTH shows slightly better quality than HHpred for aligning very distantly related pairs, a difficult and important task for the field of homology modelling. Therefore, the use of SABERTOOTH is anticipated to be advantageous at least for these difficult alignments, whereas for less distant alignments users should balance the better quality of HHpred with its heavier computational burden. These improved performances for distantly related alignments can exploit the fact that protein structure is more conserved in evolution than protein sequence, and that the alignment algorithm and parameters used were designed and trained to align contact vectors derived from coordinates. This reduces the bias to overemphasize sequence similarity, which tends to become insignificant at large evolutionary distance, and which is overestimated by most other sequence alignment algorithms. In fact, comparing the quality of the structural similarity measure and the sequence similarity measure for various sequence aligners, we see that the alignment algorithms that output the highest sequence similarity in the region of distantly related proteins also tend to produce the worst results in terms of structure similarity. This tendency is particularly clear when structural aligners are included in the comparison. Moreover, three reference methods output alignments that are of very similar quality as assessed through their structural similarity score, but their sequence similarity scores yield very different values. This implies that absolute sequence similarity values depend strongly on the algorithm used and are therefore not very informative for quantifying the relatedness of distantly related proteins. Consistently, the performances of these algorithms for recognising distant evolutionary or structural relationships are comparable or even worse than random, as the ROC analysis shows. This suggests that sequence similarity values output by sequence alignment programs are not very meaningful for distantly related proteins, and they are not comparable between different programs.The improved alignment accuracy has a cost in computational complexity. The runtime of our alignment routine cannot compete with highly optimized tools even when we pre-compute the profile predictions. While the runtime of the neural network for the prediction of the profiles can be neglected, the computation of the PSSM by PSI-BLAST is quite lengthy, heavily depending on the number of amino acids in the query sequence, PSI-BLAST parameters, and the sequence database used. The runtime of the alignment routine with pre-computed profiles takes approximately as long as the fastest structure alignment tools existing today. Including the computation of the profiles, SABERTOOTH and PSI-BLAST are comparable in computation time, while HHpred is about three times slower due to the larger number of iterations used to compute the PSI-BLAST PSSMs that also underly HHpred's alignments. Taking accuracy and computation time into account, we envisage the application of SABERTOOTH to studies in which a large number of sequence alignments have to be performed, so that HHpred and similar methods would be too costly, but high accuracy is nevertheless required, and to studies that deal with the comparison of very distantly related proteins. Furthermore, there is still room for improving SABERTOOTH in two directions. First, it is possible to improve the quality of the contact vector predictions. If these were perfect, the quality of the produced alignments would be comparable to those obtained with HHpred. Second, it is possible to consider structural information such as predicted secondary structure. Finally, SABERTOOTH facilitates analyses that make use of different types of alignments, since the same program can be used not only for sequence alignment but also for structure alignment  and sequN is the length of the protein sequence, and the contact matrix Cij is a binary symmetric matrix with components equal to one if the corresponding amino acids are in contact in the 3D structure and zero otherwise. Therefore, the contact vector counts the number of contacts that site i has with all other sites in the protein. For convenience, the structural profile that we align consist of the normalized contact vector ci, defined asIn this work, we use the contact vector vi⟩ = ∑ivi/N, so that its average value is one for all proteins.where ⟨α atoms of residues i and j are closer than dth = 17 Å Pairs of sites ij with |i - j| < 3 correspond to non-informative contacts, and their Cij are explicitly set to zero. These parameters were selected because their performances are close to optimal for structural alignments [ci represents the contact density or connectivity of amino acid i within the structure. For our purpose here, we aim to predict the contact vector using an artificial neural network approach. The prediction scheme is discussed in more detail below.Here we define a contact if the Cignments . The norThe algorithm minimizes a penalty function based on commonly used substitution penalties as well as insertion and extension of gaps. The alignment of two amino acids is penalized by the difference of the sites' structural descriptors, plus a contribution for amino acid substitution. Opening gaps is penalized by a term that depends on the components of the structural vector between which the chain has to be 'broken', while extending a gap is modelled by summing over all components opposite that gap. The algorithm, the penalty function, and parameters to perform sequence alignments are identical to those used already for structure alignments before ,4.Aij, analogous in shape to a dot matrix, that start in the top row (or left column) and end in the right column (or bottom row). In the steps though Aij, moving to the right (down) inserts or extends a gap in sequence 1 (sequence 2) while moving right-down in a diagonal step depicts alignment of the respective amino acids. A penalty is added if amino acids of different connectivities are aligned, i.e. component values of the contact vector, and/or different amino acid residue types, and for the insertion or extension of gaps. The penalty function is divided into four terms that depend on the contact vectors ci and cj, and the protein sequences Ai, with Ai one of the twenty natural amino acids types.All possible alignments output by SABERTOOTH can be created by inserting an arbitrary number of gaps of arbitrary lengths into one or the other sequence in the alignment. In this way the sequences stay intact and repetition, mirroring, or exchange of fragments are not permitted. All alignments complying with this definition can be displayed as paths through an alignment matrix i (j) in the first (second) profile, are penalized by a term Mij that grows with their absolute difference raised to a suitable power Aligned components of the structural profiles, corresponding to position Substitution of amino acids is less likely for pairs with very different physiochemical properties just like used in sequence alignments,lambda by Eddy [with the parameters  by Eddy .s between residues i and i + 1 is penalized byBreaking chain s ∈ {1,2} labelling the chain into which the gap is inserted.with parameters nj into chain s at position j + 1 opposite to a gap in the other chain, consisting of the components An insertion of length s ∈ {1,2} selecting the chain.with parameters F combines all these contributions,The total penalty function s)  . It corresponds to the optimal alignment, given penalty parameters and proper definition of F. The parameters used in F are shown in Table where Different algorithms can be used to find this optimal path very efficiently, our implementation uses Dijkstra's shortest path algorithm. A more detailed description of the full alignment algorithm is given in , the speThe CV is predicted here using an artificial neural network (ANN) scheme based on position-specific scoring matrices (PSSMs) computed by PSI-BLAST. Relying on PSSMs we follow an idea already employed by Jones  to predia at site i of the given protein family, where the index a ∈ {1, 20} labels the twenty natural amino acids. The matrix entries are defined asFormally the PSSM components characterized probabilities propensities to find a specific amino acid of type Qi(a) quantifies the probability to find the amino acid a at site i in a sequence belonging to the same protein family and P(a) characterizes the background distribution, independent of the position in the sequence.where th Feb. 2009) after filtering out biased regions using pfilt by Jones and Swindells [We used the non-redundant sequence database 'NR' from NCBI  and by modelling the length dependent mean value of the variance as a power law (with parameters b and c). Furthermore, a lower bound value vãrmin = 0.05 is used to suppress artificially low variance values.consisting of a term that describes the scattering of the variance  with 9420 protein domains.The quality of the alignments produced by SABERTOOTH and by the reference tools described below was assessed on three sets of alignments from the major levels of SCOP family , superfamily (5180), and fold (5097). Pairs in the sets were chosen randomly from the ASTRAL40 subset of SCOP domains that have less than 40% pairwise sequence identity. The fold level test set consists of alignments from the same fold but different superfamilies, and the superfamily test consists of alignments from the same superfamily but different families. We assessed only the alignments for which all reference tools output results, which reduced the sets by about half a percentage in size. SABERTOOTH outputs alignments for all examples in all sets.q that quantifies the similarity between the contact matrices of two protein structures, normalized with the geometric mean of their number of contacts in such a way that q = 1 for identical contact matricesThe alignment quality was quantified using as structural similarity measure the contact overlap As an additional measure of structural similarity we used the TM-score  that quarotation . This merotation .The sequence similaritywith Z-scores, assuming Gaussian distribution of the underlying scores SABERTOOTH outputs two different significance scores N1 and N2. For simplicity, we consider in the following that this dependence only acts through the smaller of the two lengths, N = min. This length dependence is assumed to be of power-law type, and the parameters are obtained by fitting power-laws on a set of alignments of non-related proteins, consisting of 723,217 alignments of domains from different SCOP classes that were tested to have MAMMOTH [Z-score below 0.75 and TM-align TM-score [The mean and the standard deviation of the scores that are used in the above formula depend on the lengths of the compared proteins  MAMMOTH Z-score bTM-score  below 0.r of the PSSM columns for every pair of aligned sites, normalized by shorter chain length,The first similarity score is derived from the same PSSMs already utilized for predicting the structural profiles. It is computed as a sum over Pearson correlation coefficients with power-law fits resulting toThe second score is much less significant, and it is mainly kept for reasons of comparison. It is derived from simple sequence similarity, Eq. (11), computed using a BLOSUM62 and normalized on the length of the shorter chain. The power-law fits result toZcutoff is shifted from its minimum to its maximum value, counting the number of alignments with Z > Zcutoff at each value of Zcutoff. All alignments above the threshold that are also in the same cluster of SCOP, represent true positives TP, i.e. they agree with the classification. All those below the threshold but nevertheless in the same cluster of SCOP are counted as false positives FP that disagree with the classification. The assessment is split into independent analyses on the three major SCOP levels fold, superfamily, and family.With all tools, with the exception of MUSCLE that does not output any significance score, we computed significance scores for the all-vs-all alignments of 498 structures that were randomly selected from the 97 most populated folds in ASTRAL40 (version 1.73), leading to 123,753 alignments. Using these significance scores, we computed Receiver Operating Characteristic (ROC) curves that graphically quantify the agreement of the significance score with the SCOP classification. To create the ROC plots, a cutoff for the respective score The ROC curves show the ratios of TP/P over FP/N, with the total numbers of positives P and negatives N, respectively. The further the curves reach to the left hand side of the plot, the less positives are assigned low values of significance, while pushing the curve up means that more positives are correctly assigned high significance. Hence, the larger the area under the curve (AUC), the better the performance of the significance score output by the respective program in recognising evolutionary and structural relationships given by SCOP. This can also be understood as measuring sensitivity and coverage. The diagonal marks the result for a random score.We chose standard parameters for all alignment tools. Every modification in the parameters would infer previous knowledge about the set of sequences to be aligned. An expert for a specific program with in-depth information about the alignment set could, hence, achieve better results than found here. In this sense, we only assess the most general alignments but with fair chances for all algorithms. SABERTOOTH does not use any specific parameter set either, its sequence dependent alignment penalties rely on the all purpose substitution matrix BLOSUM62, and the profile prediction routine uses the identical PSI-BLAST PSSMs that were also used for the PSI-BLAST alignments.All three multiple sequence alignment programs Clustal W (v1.83) , T-CoffeClustal W, T-Coffee, and MUSCLE were run with standard parameters. For Clustal W that implies in particular to compute 'SLOW' alignments with full dynamic programming for maximum accuracy. T-Coffee was used with the non-standard parameter '-do_normalize 0' to suppress normalisation of the output score which does not change the resulting alignment but improves the score's performance in the classification test.The alignment program PSI-BLAST (v2.2.18)  follows A with a database containing sequence B using the PSSM computed for A, and vice versa. The alignment with higher PSI-BLAST E-value is selected as the final alignment referred to in both evaluations. We found that this choice leads to improved performance in the detection of evolutionary relationships than selecting the alignment with lower E-value or just a random one, as expected. Note that this procedure gives PSI-BLAST a slight advantage over all other tools evaluated here.Since PSI-BLAST aligns a single sequence to a database its alignments are intrinsically asymmetric, depending on the choice of query sequence. To eliminate this ambiguity in our application we perform two separate alignments. After computing PSSMs for both sequences, we align sequence http://www.ebi.ac.uk/Tools/PSIBLAST/. It turned out that results found with the different BLOSUMs differ only very slightly. The results shown are for BLOSUM62.In order to assess the influence of the substitution matrix employed, we used PSI-BLAST with three different matrices: (1) BLOSUM62 with gapopen = 11 and gapextend = 1, the standard parameter set, (2) BLOSUM45 with gapopen = 14 and gapextend = 2, and (3) BLOSUM80 with gapopen = 10 and gapextend = 1. The gap penalty values relative to the choice of BLOSUM were taken from the PSI-BLAST help on EBI's web page at HHpred (v.1.5.0) constructs Hidden Markov Models (HMM) from alignments of the non-redundant database 'NR' from NCBI against a query sequence. These alignments are obtained by PSI-BLAST. HHpred then computes the final alignment, maximising a score based on the coemission probability of the two HMMs and predicted secondary structure. For the alignment overlap test, we used the global alignment mode of HHpred while we used the local alignment mode for the fold recognition test, thus yielding the best results for the respective analysis. The local alignment mode performs worse in the alignment overlap test because it aligns residues in the conserved core, only. Please note that this proceeding is to the advantage of HHpred in comparison to all other alignment tools used here, since all other tools use identical sets of alignments for both tests.The data set used for alignment quality assessment consists of a random selection of pairs from the ASTRAL40 subset of SCOP domains that have less than 40% pairwise sequence identity. It contains three sets of alignments from the major levels of SCOP family , superfamily (5180), and fold (5097). All alignments from the different similarity levels are from different clusters of the underlying level, i.e. alignments from the same fold are from different superfamilies and so on.Z-score below 0.75 or TM-align TM-score [Statistics over 723,217 alignments, randomly selected from different SCOP classes, were used to fit the length dependent mean and standard deviation values used in the SABERTOOTH significant scores. Alignments with MAMMOTH Z-score bTM-score  below 0.The 123,753 alignments underlying the ROC curve analyses include the all-vs-all alignments of 498 structures that were randomly selected from the 97 most populated folds in ASTRAL40 (version 1.73).pdbtm [ad hoc criterion introduced by Bastolla et al. [For the contact vector prediction we selected at random about 3000 sequences from a PDB clusters set at 50% sequence identity level (rank 1) with chain lengths between 30 and 300 residues. Only X-ray resolved structures not classified as transmembrane according to pdbtm  were acca et al. .For the assessment of the contact vector prediction the whole ASTRAL40 (version 1.73) database with 9420 protein domains was applied. This test set is disjunct from the training set used.Project name: SABERTOOTH Sequence Alignmenthttp://www2.fkp.tu-darmstadt.de/bioinf/sabertooth_project/Project home page: Licence: Source code available on request to academic users, free of charge.ANN: Artificial Neural Network; AUC: Area Under Curve; BLOSUM: BLOcks SUbstitution Matrix; CRN: Critical Random Network; CV: Contact Vector; HMM: Hidden Markov Models; PSI: Percentage of Structural Identity; PSSM: Position-Specific Scoring Matrix; ROC: Receiver Operating Characteristic; SCOP: Structural Classification Of Proteins.MP and UB designed research; FT and MP developed the alignment algorithm; FT coded and tested the alignment algorithm; MP and JM developed the profile prediction scheme; JM coded and tested the profile prediction scheme; FT, JM, UB, and MP analysed results; FT, JM, UB, and MP wrote the paper. All authors read and approved the final manuscript.Alignment Quality Test Set. The zip archive includes the three test sets used for alignment quality assessment in this work: 5238 alignments at SCOP family level, 5180 alignments at SCOP superfamily level and 5097 alignments at SCOP fold level. Each line identifies an alignment through two domain identifiers relative to SCOP version 1.73. PDB-formatted files for these domains can be found in the ASTRAL40 domain database version 1.73 at http://astral.berkeley.edu/. A more detailed description of the composition of the test sets is given in the Methods section.Click here for fileSignificance Score Assessment Set. The file contains the set of 123,753 alignments used for significance score assessment in this work. The alignments comprise the all-vs-all combination of 497 ASTRAL40 domains (version 1.73). Each row describing one alignment, the columns list the following information that allows retracing the SCOP classification: ASTRAL identifiers for first and second domain in the alignment, chain length of the first and the second. After that, in pairs of columns relative to the first and the second domain, the SCOP classification is listed: class (cl), fold (cf), superfamily (sf), family (fa), domain (dm), and species (sp) identifiers. A more detailed description of the composition of the set is given in the Methods section.Click here for file