Detecting conserved noncoding sequences (CNSs) across species highlights the functional elements. Alignment procedures combined with computational prediction of transcription factor binding sites (TFBSs) can narrow down key regulatory elements. Repeat masking processes are often performed before alignment to mask insertion sequences such as transposable elements (TEs). However, recently such TEs have been reported to influence the gene regulatory network evolution. Therefore, an alignment approach that is robust to TE insertions is meaningful for finding novel conserved TFBSs in TEs.We constructed a web server 'ReAlignerV' for complex alignment of genomic sequences. ReAlignerV returns ladder-like schematic alignments that integrate predicted TFBSs and the location of TEs. It also provides pair-wise alignments in which the predicted TFBS sites and their names are shown alongside each sequence. Furthermore, we evaluated false positive aligned sites by focusing on the species-specific TEs (SSTEs), and found that ReAlignerV has a higher specificity and robustness to insertions for sequences having more than 20% TE content, compared to LAGAN, AVID, MAVID and BLASTZ..ReAlignerV can be applied successfully to TE-insertion-rich sequences without prior repeat masking, and this increases the chances of finding regulatory sequences hidden in TEs, which are important sources of the regulatory network evolution. ReAlignerV can be accessed through and downloaded from  Cross-species comparisons of genome sequences have provided an efficient means of identifying conserved functional elements. Alignment procedures of related species are the mainstay for comparative genomics . IdentifThe aligners described above adopt heuristic index-based approaches to decrease processing time and memory usage. In order to obtain sufficiently long alignments, they utilize a chaining strategy based on the highly similar aligned sequences which are called anchors or seeds. In addition, repeat masking processes are, in many cases, a prerequisite in advance of alignment. These approaches indeed fulfill a demand to deal quickly with genome-wide long sequences and to obtain sufficiently long aligned blocks. However, this genome-wide resolution may not always be an optimal answer; for instance, to the researchers specifically focusing on noncoding regions stretching no more than several tens of kbs or those using alignment tools to construct the best short list in advance of laborious experimental validations.cis-elements are overlapped with TEs and those cis-elements correspond to ~4.5% genes examined [One reason is that the demand to obtain as-long-as-possible alignments tends to result in over-extended aligned stretches, which reduces the sharpness of the boundary of short conserved sequences. Another is the possibility that repeat masking processes, that are in many cases performed as a preprocess, can hide the important functional elements that are embedded in the TE insertion sequences. In fact, TE insertions are now recognized as an important source of evolutionary processes of regulatory elements. The majority of duplicated repressor element 1 (RE1) sequences have been reported to exist within TEs . Experimexamined .Consequently, in this report, we describe the features of ReAlignerV with emphasis on robustness to TE insertions in aligning genomic sequences. To estimate the robustness to TE insertions we focused on SSTEs, i.e. TEs specific to human or rodent. Since the SSTEs have been inserted into the genomes after the divergence of human and rodents (mouse and rat) from their common ancestor, if the SSTE regions are aligned to the orthologous counterpart sequence between human and rodents, the counterpart nucleotide sites corresponding to the SSTEs are expected to be gaps in the alignment. Therefore, we have deemed SSTEs to be negative control probes and evaluated the specificity of the aligners using 1,490 trios  of orthologous 8-kb noncoding sequences immediately upstream of the protein-coding sequences. We applied this evaluation procedure to ReAlignerV, BLASTZ, LAGAN, MAVID and AVID .A pair of FASTA format nucleotide sequences are minimally required as input for the pair-wise alignment Figure . The webTo align two sequences, users can select the '2-species ReAlignerV' from the ReAlingerV homepage, and either paste the FASTA format sequences or upload the sequence files. After submission, the results page is automatically refreshed every few seconds until the resulting alignment is presented. Before submission, users can adjust the alignment parameters as necessary. Input 'sequence 1' is always presented as the lower black line of the schematic alignment presentation. Below the alignment, the GC and ATGC contents for sequence 1 are shown by the specified scanning window length Figure , if the i.e. sequence 1 vs. sequence 2 and sequence 1 vs. sequence 3, rather than multiple alignment. The resultant two pair-wise alignments are integrated into one schematic presentation together with the annotations to the three input sequences. The graphs of the GC and ATGC contents of the three sequences are also provided. Sequence 1 is always presented as two lines in the middle of the two alignments  and annotation files ,24 of huWe executed RepeatMasker to identify the SSTE insertions. For all the 8 kb stretches of 1,490 human sequences, the "primspec" option was used to detect only the primate-specific TEs, and "rodspec" option was used for all the mouse and rat 8-kb upstream sequences. Other RepeatMasker options used were "gccalc", to follow the actual GC contents of the input sequences, and "norna", not to mask putative small RNA genes that may be encoded in the upstream region.We conducted alignment procedures for the 1,490 trios of orthologous sequences using the aligner of ReAlingerV in a local machine setting. The conditions used were the same as the default settings of the ReAlignerV web service.We downloaded BLASTZ packaged in the PiPMaker distribution (beta-version) pipmaker-2005-10-26-01 , and useWe downloaded the lagan12 source code . After iWe downloaded MAVID (mavid-package-2.0.4)  after reAfter having obtained authorization, we downloaded and installed AVID (version 2.1 build 0)  accordinf), alignment cover rate (ACR) and significance index (z), to assess the robustness of the alignment procedures to TE insertions. To investigate the relationship of these statistics to the content of the SSTEs, we applied ranges based on the number of SSTE sites for the human. For the human statistics, we summed the number of sites in both the human-mouse and human-rat alignments. The following notations are used for each range in the human sequences.We use three statistics, namely specificity  against the SSTE is computed as,Taking To estimate how extensively an aligner makes alignments, we define the ACR as,p of an aligned site being located within the SSTE sites by chance is given as,The probability m  follows the binominal distribution with a probability p and the number of trials a. Thus, the standard deviation is computed as,Then, for each range, we assume that e) as,and its expectation (We define the significance index (z) as,i.e. ACR) for each aligner to assess how extensively it makes alignments. The results show that LAGAN performed best by making extensive alignments, followed by AVID and MAVID, while ReAlignerV yielded modest lengths of aligned stretches  to measure specifically how an aligner avoids SSTE sites and extends the alignments. The significance index of each aligner tends to decline according to the increase in proportion of SSTEs  several kb lengths of orthologous upstream sequences ii) of human and rodent, iii) without repeat masking, and iv) focusing on the search for conserved TFBSs around promoter regions. The condition of no repeat masking can particularly affect the performance of BLASTZ which is presupposed to deal with SSTE-masked sequences in its original setup. Therefore, the drop in significance index in the ranges of high SSTE contents is attributable to the unintended use, and the highest significance index in the ranges of low SSTE contents is more indicative of the original worth of BLASTZ. On the other hand, this result indicates that the evaluation scheme is reliable. Since AVID and MAVID also utilize the repeat sequence information for the anchor selection step, the condition of not having repeat sequence information available could negatively affect the performances. LAGAN, AVID and MAVID adopt complex approaches in which the Needleman-Wunsch algorithm is compositely used, for example, in the case where an inter-anchor region to be aligned is sufficiently short, and furthermore the three aligners and BLASTZ adopt a recursive call to the alignment procedure, which leads to high ACRs. Compared to these, ReAlignerV uses a straightforward strategy to set the single anchor at the last nucleotide of each query sequence and performs no recursive alignment process after the seed extension. Despite such a simple approach, ReAlignerV shows a good agreement between specificity and ACR, indicated by the high significance index for the dataset used. The expected advantage of the eager alignment approaches may not always give the best significance particularly under the conditions described above that are suitable to search for conserved TFBS including TE-related ones around promoter regions.et al. unpublished data). This result indicates that ReAlignerV is useful in efficiently narrowing down the TFBS candidates in advance of experimental studies. In our analysis, we did not find any conserved TFBS candidates that overlapped with TEs by RepeatMasker . Besides the conserved sites, however, we found that 11 predicted CRE sites for human were located in primate-specific Alu sequences and 2 sites for mouse in a rodent-specific B2 (SINE) sequence. These CRE sites could be SSTE-mediated TFBS candidates worth further investigation as to whether they could affect the linage-specific transcriptional control.To identify the cAMP response element (CRE) candidates located in the upstream regions of mouse chemokine (C-C motif) ligand 3 (CCL3) or the MIP1a gene, we used the locally installed ReAlignerV together with the results of TRANSFAC Match and RepeatMasker searches. The integrated presentation of the human-mouse sequence comparison of the CCL3 8-kb genomic sequences upstream of the translation start site indicated several conserved CRE candidates Figure  and 4B. We have shown that ReAlignerV has a high degree of specificity and robustness regarding TE insertions in aligning TE-rich noncoding sequences. Thus, ReAlignerV is applicable to aligning insertion-rich sequences without prior repeat masking. This feature could present the possibility of detecting novel functional elements hidden in TE insertions. ReAlignerV provides intuitively understandable presentations and a web-based interactive alignment annotation method, which helps identify a best short list of functional elements in advance of experimental validations. Future extensions to this work include i) smoother interconnections with TRANSFAC database searches and RepeatMasker, ii) wider acceptability of the other TFBS prediction methods, iii) focusing on 3' noncoding regions, and vi) speed- and scale-up of the aligner by reprogramming using a faster language.Project name: Research Program on Gene Regulatory NetworkProject home page: Programming language: PerlLicense: GNU General Public LicenseAny restrictions to use by non-academics: The restrictions specified by the organizations that maintain bl2seq, Match™, TRANSFAC(R) and RepeatMasker, apply to the use of the programs and databases.HI initiated this web server project, wrote the original source code, performed the comparison of the aligners on specificity and robustness, and wrote the manuscript for ReAlignerV. YH arranged the source code, constructed the web interface, and implemented it on the server. K Matsumoto, K Murao and TI performed all the experimental studies on the CCL3 regulatory elements. A limited part of their results was used as the example for actual usage of ReAlignerV, and they cooperatively designed the web service particularly from the viewpoint of an experimental research field.


The task of computing highly accurate structural alignments of proteins in very short computation time is still challenging. This is partly due to the complexity of protein structures. Therefore, instead of manipulating coordinates directly, matrices of inter-atomic distances, sets of vectors between protein backbone atoms, and other reduced representations are used. These decrease the effort of comparing large sets of coordinates, but protein structural alignment still remains computationally expensive.We represent the topology of a protein structure through a structural profile that expresses the global effective connectivity of each residue. We have shown recently that this representation allows explicitly expressing the relationship between protein structure and protein sequence. Based on this very condensed vectorial representation, we develop a structural alignment framework that recognizes structural similarities with accuracy comparable to established alignment tools. Furthermore, our algorithm has favourable scaling of computation time with chain length. Since the algorithm is independent of the details of the structural representation, our framework can be applied to sequence-to-sequence and sequence-to-structure comparison within the same setup, and it is therefore more general than other existing tools..We show that protein comparison based on a vectorial representation of protein structure performs comparably to established algorithms based on coordinates. The conceptually new approach presented in this publication might assist to unify the view on protein comparison by unifying structure and sequence descriptions in this context. The framework discussed here is implemented in the 'SABERTOOTH' alignment server, freely accessible at  Structure comparison allows discovering evolutionary and functional relationships that are beyond the reach of methods based only on sequences. There are two major demands for an alignment algorithm: First, it has to recognize small but significant structural similarities very efficiently and it has to produce accurate alignments even for far relatives, in order to get maximum profit from available data. Second, it must perform its computation in very short time. In fact, when all-vs-all comparison of all structures in a database is needed, a very large amount of pairwise alignments is required. For the Protein Data Bank (PDB ) all-vs-If comparisons are not carried out accurately enough, evolutionary and functional information gets shrouded in background noise. If comparisons are too slow, some large scale analyses could become unfeasible. The above stipulates requirements for an alignment framework that go beyond currently available tools.Here we propose a novel alignment framework that allows dealing with structure-to-structure, structure-to-sequence and sequence-to-sequence alignments in the same scheme, exploiting a vectorial representation of both sequences and structures . On the To represent protein structural information in form of three-dimensional coordinates is highly redundant. Due to the stiffness of the polypeptide backbone, volume exclusion, and restrictions imposed by physical interactions between atoms, only a small subset of the combinatorially possible set of conformations is feasible for physical protein structures. This implies that a reduction of the mathematical description should be possible with minor loss of information.ij, which is a binary matrix representing all amino acid pairs i and j whose distances lie below a cutoff distance dth. In the present work, contacts are defined based on minimum distances between heavy atoms  of amino acid pairs with a cutoff of dth = 4.5 Å. A contact matrix defined by the protein backbone, for instance by Cα atom distances, would have the advantage that it is less dependent on the details of the side-chains and more conserved in evolution. Nevertheless, we prefer to adopt here a contact definition based on heavy atoms since this has a closer relationship to protein energetics and it yielded better results in our tests.A reduced representation of protein structure that is often used consists of the so-called contact matrix CIt was numerically shown in  that thei with a single real number vi can be derived from the contact matrix in a natural way. In [Several structural profiles associating each protein site  way. In  it was sAn 'ad hoc' generalization of the PE, described in , is alsoci self-consistently represent the effective contact density at site i in the native protein structure. The effective connectivity ci depends not only on the local contacts at site i, but it is a global property of protein structure. The principal eigenvector of the contact matrix is a specific member of this GEC family of profiles.Another more systematic way to extend the properties of the PE to modular protein structures consists of defining the 'generalized effective connectivity' profiles (GEC)   to each amino acid Ai. In the framework of folding models based on contact interactions, it is possible to show that the hydrophobicity profile (HP) associated with the optimally stable protein sequence belongs to the GEC family of the corresponding native structure [The relevance of the GEC structural profiles for the description of proteins derives from the fact that it is possible to naturally define a vectorial representation for protein sequences by associating the corresponding hydrophobicity value tructure . This imIn UB, A.R.Ortíz, MP, FT: Effective Connectivity: A structural profile for multi-domain proteins, submitted, we proposed how to select a particular profile belonging to the GEC family in such a way that it depends only on protein structure and that it is strongly correlated with the average HP over a broad range of mean hydrophobicity values. In the following this profile will simply be called 'effective connectivity' (EC). For small single-domain protein structures without internal modularity, the EC essentially coincides with the PE.  In the same paper, it was also shown that the revised PE is related to a vector of the GEC family through a non-linear transformation, and that the revised PE and the EC are very strongly correlated, with correlation coefficient typically as large as 0.95.Both the EC and the revised PE have been employed in the alignment framework discussed in this paper. We observed slightly better performance for the EC, which was therefore used as the standard for the alignment routine, whereas the revised PE is mentioned for some special cases where significantly different alignments are found using this profile. Nevertheless, the revised PE may be the better choice if fast computation of the profiles outbalances slightly higher accuracy.The vectorial structure profiles revised PE and EC, together with contact maps and sequences can be freely downloaded from our web server at . For morIn the framework discussed here, the task of finding a proper alignment of two protein structures is translated into the recognition of similar connectivity patterns in their corresponding structural profiles. This analogy is grounded on the assumption that the structural profile is conserved in protein evolution, like the overall topology of the protein structure that it describes.In this way, we can use fast and simple comparison algorithms, while relevant non-local properties of protein structure are retained. Moreover, the resulting alignment is little dependent on spurious local similarities that could obliterate the recognition of far homologs. However, these local structural details have to be reintroduced in a second step, in order to obtain a more precise structural match.Following this idea, we developed a structural alignment routine that consists of two steps. First, the alignment of the structural profiles is used to recognize global similarities. Second, a refinement step employs the atomic coordinates in order to improve the local structural superimposition.Aij, as the one shown in Fig. The profile alignment was designed similarly to 'traditional' sequence alignment routines like e.g. dot-matrix alignments. We represent every possible alignment of two proteins by a path through an alignment matrix Ai-1, j-1 → Aij along the alignment matrix in Fig. Building up this path, a diagonal step The optimum alignment path minimizes the cost function described below, which depends on a set of parameters that are analogous to traditional 'substitution probabilities' for alignments and 'open/extend' penalties for gaps. However, in contrast to those, the penalties used here are directly dependent on the structures through their explicit dependence on profile components.Evidently, the cost function must be such that the alignment of amino acids The entangled use of these 'break' and 'insert' contributions to the gap penalty models the inherent ignorance of whether a gap in the alignment was caused by the deletion of a fragment from one chain during evolution, or by the insertion of a fragment in the other chain.A detailed description of the path cost function and the parameters used can be found in the Methods section below.Being equipped with a cost function, the cheapest path can be selected through very efficient standard algorithms. Here we used Dijkstra's shortest path algorithm , but dynThe resulting optimal alignment can be represented in the form of superposed profiles, as in Fig. Up to this point our alignment algorithm does not use any other information besides of that encoded into the structural representation and the scoring function. The results presented below show that the algorithm is able to identify significant similarities in around 95% of the alignments of distant relatives from the test set discussed below.We are aware that introducing other sources of information, such as secondary structure, prior domain decomposition, or biological knowledge of protein function, to name but a few, could further improve the alignments. However, this was deliberately omitted to keep the algorithm general, moving these issues to the structural representations and their possible future improvements.In order to assess the alignment, we apply the standard MaxSub routine to the set of aligned residue pairs and compute the optimal rigid body rotation and translation that maximize the spatial superimposition of the two proteins, as described in  for MaxSAs described above, through the MaxSub routine and the set of aligned residues we can derive the optimally superimposed set of coordinates, and from that we can compute the pairwise distances of all combinations of amino acids connecting the two protein chains. This detailed local information can then be exploited in a second alignment step in order to refine the alignment itself, similar in principle to other structural alignment algorithms.α atoms that are closer in space than a threshold l ≥ lminare relevant. The values of these parameters must be chosen carefully since the result of the whole procedure is strongly influenced by their selection. By increasing the distance threshold and decreasing the minimum length parameter, more and more incidental pairs are selected. On the one hand, this results in a larger percentage of structural identity (PSI) for the refined alignment but, on the other hand, it lessens the significance of the alignment by interspersing it with spurious pairs that should actually not be included. Taking these factors into account we choose a minimum group length of four amino acids, lmin= 4, and a distance threshold of For this goal, we firstly identify pairs of CThe set of amino acids effectively close in space is then used to restrict the possible paths through the alignment matrix, so that the second run of Dijkstra's optimization routine looks for the optimal path only around these identified groups of close pairs.This second run of Dijkstra's algorithm incorporates close pair groups into the alignment where unambiguously assigned, it picks out the best choice in cases where more than one alternative is present, and it simply minimizes the path cost as before in areas that are not constrained.Obviously, this kind of refinement is only able to improve the input alignment if the initial spatial superposition was already close to optimal. From comparison of the plots in Fig. Z-score measuring the statistical significance is computed from the PSI, as discussed below. Scores specific for profile alignments state the total optimized path cost, the summed cost of aligned regions, and the gap penalties.After the refinement step, a second run of the MaxSub algorithm is used to obtain the optimal spatial superimposition through which we assess quality and significance of the final alignment. To this aim, we calculate the number of aligned residues and gaps, the number of residues close in space and the percentage, which is named percentage of structural identity (PSI), the coordinate RMSD (cRMSD), the sequence similarity of aligned residues, and the contact overlap. Furthermore, a α or all-atoms shape, as well as plots of aligned profiles are included. Figure In addition, different visualizations of the alignment result are computed: PDB-style coordinate files and a RASMOL  script fThe program can be used freely at our web server Z-score of the PSI, which measures the difference between observed and average PSI for optimal superimposition of unrelated pairs of structures, in units of standard deviation.In order to distinguish biologically relevant relationships from superimpositions arising by chance, we assess the statistical significance of the alignments through the Z-score computation is described in detail in the Methods section, the fits are shown in Fig. Since the PSI of a pair of unrelated structures strongly depends on their lengths, we computed its mean and standard deviation as a function of the length of the shorter chain in each alignment using a set of 31284 alignments of pairs of non-related structures. The resulting PSI is represented in Fig. Z-scores produced by our algorithm give an intrinsic and meaningful measure of the significance of the structural alignments, we tested whether they agree with those that result from other well-known algorithms (see Methods).To verify that the Z-scores obtained through different algorithms for pairs of related proteins, finding correlation coefficients up to cc1 = 0.90 for SABERTOOTH vs. DaliLite and cc2 = 0.84 for SABERTOOTH vs. MAMMOTH. These high correlations show that the different algorithms are sensitive to the same 'signals' even though their individual accuracy is different. We show this pairwise correlation in Table We performed this test by computing correlations between the Z-scores are obtained directly from the output of each program, in contrast to all other scores that are computed through our own assessment algorithm using the alignment merely as an input. This is necessary since the Z-score depends on the statistical properties of the optimal superimposition of unrelated pairs as computed through the very algorithm. Moreover, different programs can take care of the dependence on chain length in different ways. SHEBA does not output a  Z-score but from its high PSI correlation we expect comparable recognition behaviour in the sense of the above.For this analysis the __ ' and 'd2gdm__' after optimal rotation according to the SABERTOOTH alignment. A RASMOL script file for this example can be found in Additional File Since our algorithm compares protein structures using a representation that embodies the overall topology of a protein chain, it is expected to be largely tolerant in cases where local distortions tend to hide structural similarities. In fact, SABERTOOTH assigns PSI > 40% in nearly 95% of the alignments from the test set which consists of distant relatives that are related on superfamily level having less than 40% sequence identity. This proves a high recognition rate of the common core of distantly related proteins. The alignment is very accurate in the details as well. Figure Aligned amino acid pairs that are closer in space than 4Å are coloured in green, marking the common core, whose size corresponds to the PSI, sections coloured in yellow are aligned but they are further in space than the PSI threshold. Light blue and light red chain sections are opposite to gaps. It can be seen that yellow parts point to local distortions that are correctly aligned, while gaps are introduced before the N- and after the C-terminus of the first chain and in loops of different lengths in the two chains.Z-score, SABERTOOTH assigns high PSI values to a number of alignments, even though the set consists of pairs from different folds that were checked to have MAMMOTH and DaliLite Z-score < 3.With respect to the set of unrelated pairs used to fit the Visual inspection of these alignments confirms that these high PSI values do not arise by chance but due to truly recognized similarities. In fact, the pairs with highest scores share a common module consisting of large portions of correctly aligned secondary structure elements, whereas tilted helices, twisted beta-sheets, and large insertions (or deletions) demand to assign them to different folds.RASMOL script files for some examples from the test set can be found as supplementary material in Additional File Some specific problems of the algorithm are revealed by looking at alignments of related pairs from the test set that yield very small PSI values. The eight worst such cases consist of alignments between members of the SCOP superfamily 'Riboflavin synthase domain-like' (sf = 63380). These have barrel structure and are built up by anti-parallel beta sheets known also as the 'Greek key' motif. A rather complicated case from this superfamily is the chain with ASTRAL-ID 'd1ddga1'. Despite being considered as single-domain in the SCOP classification, it actually consists of two structural domains, the Greek key domain and an additional all-alpha domain, the latter built up from a number of loosely connected short helices. In some alignments with this structure, our algorithm fails to align the domains correctly, which seems to result partly from the structural representation used.When comparing the results to those computed using the revised PE instead of the EC profile, some of the formerly problematic structures show very good results, i.e. the worst combination using the EC ('d1fdr_1' vs. 'd1ddga1') improves to PSI= 76% when using the revised PE as structural representation. But still, the abundance of anti-parallel beta structures in the problematic cases is obvious. Anti-parallel beta sheets are highly connected through hydrogen bonds of relatively short range along the sequence, a fact that is not explicitly considered in the profiles. This suggests that the structural representation used in the alignment routine might be improved through adequate incorporation of the hydrogen bonding network or secondary structure information.Another negative influence on alignment performance could result from the symmetry in the structures of the above-mentioned superfamily that contain two opposing Greek key motifs. Alignment of structures with high symmetry leads to scoring functions with multiple solutions having very similar score.To evaluate the quality of SABERTOOTH's alignments it is necessary to compare it to competing algorithms. The best way to compare structural alignments is by visual inspection, but to make the comparison objective one has to use a quantitative score. In our opinion, the most expressive such score for a structural alignment is the PSI. As we mentioned above, when using the PSI one should take care that only truly significant superimpositions are counted in. Hence, PSI values have to be cleared from contributions from short spatial superimpositions, which may very likely arise by chance. Even if these matches are relevant, their expressiveness in this context is arguable and different tools deal very differently with this issue. Some algorithms apparently enhance the PSI to some extent by scattering tiny fragments of one to three amino acids along the alignments. This is quantified in Fig. The DaliLite algorithm shows a kink at length four in this distribution, with shorter fragments strongly penalized and also MAMMOTH attenuates short fragments. In contrast, the TMalign and the SHEBA algorithm over-represent these fragments.To take this into account, we use a modification of the PSI throughout this paper that does not count in superimposed residues in fragments shorter than four continuous residues. We call this value the relevant PSI (rPSI). A hint that this treatment is reasonable follows from the comparison of sequence similarities with and without short fragments. Removing short fragments, sequence similarities increase for all algorithms which indicates that the mean sequence similarity of the removed fragments is smaller than for longer aligned fragments, suggesting that several of these short fragments are indeed spurious matches. A number of assessment scores, including sequence similarity based on the BloSum62 matrix, cRMSD, the number of aligned amino acids, and the number of aligned amino acids that are effectively close in space are listed in Table In Fig. To assess the computation speed of the different algorithms examined here, we measured the total time needed to compute all alignments in the test set. The fastest algorithm is the pairwise MAMMOTH. The slowest but most accurate competitor is DaliLite, which needs about 26.70 times as much CPU time as MAMMOTH. SABERTOOTH is only 4.23 times slower than MAMMOTH in the current implementation but it is nearly as accurate as DaliLite. In this sense, SABERTOOTH represents a good compromise between runtime and accuracy. A more detailed comparison is shown in Table The MAMMOTH program  is the fMAMMOTH was initially developed for comparison of large numbers of theoretical models, making computational time the prime duty. In this sense it may be viewed as a maximum speed benchmark. Due to its high speed, MAMMOTH is applicable to very large sets of alignments as those needed for database clustering. In contrast, its recognition rate is low. It is similar to that of SABERTOOTH's profile alignment routine without refinement (data not shown), which indicates that the quality of MAMMOTH alignments can be improved through a similar post-processing when higher accuracy is needed.This has indeed been done for the multiple alignment program MAMMOTH-mult . It carrα trace, which results in a high ability to recognize structural similarities and in a high precision in the details. Unfortunately, the algorithm is slow so that its applicability is very restricted.The DaliLite algorithm  uses a sSince DaliLite does not output any alignment when it does not find significant similarity, the pairs for which this happened were removed from the test set, although this may favour DaliLite in comparison to the other programs. Surprisingly, in 31 out of 36 of the cases in question (data not shown) SABERTOOTH finds PSI > 40% and in 14 cases even PSI > 75%. This behaviour could be due to a systematic weakness of the DaliLite algorithm, which is a bit too strict when trying to sort out alignments of unrelated structures to improve its speed on large data sets.Besides of this, DaliLite assigns significant PSI values in nearly all alignments of the test set which makes it  first choice for an accuracy benchmark.The TM-align algorithm , at firsZ-score) values obtained with the CE algorithm are significantly less correlated with those of the other algorithms than those are between each other, as shown in Table The CE algorithm  seems toThe SHEBA algorithm , like TMWe present a new approach to protein structural alignments. We could show that structure representations in form of vectorial profiles based on the global topology of protein structure allow structural alignments of a quality comparable to other state-of-the-art methods. The SABERTOOTH structural alignment server implements this alignment framework. It performs comparably to algorithms based on coordinate derived descriptions and represents a good compromise between alignment accuracy and computational speed. We could show this by statistical analyses and comparison to established competitors which we use as objective references.One of the strengths of our alignment scheme is its generality, since it can be applied to different vectorial structure representations and, hence, allows for incorporation of more elaborated structural profiles developed in the future. Even more interesting is the possibility to utilize structural profiles predicted from sequences in future uses of the framework. Doing so, all flavours of protein alignments, i.e. structure-to-structure, sequence-to-sequence, and sequence-to-structure, can be carried out within the same scheme. Furthermore, extension to multiple alignments using mixed sets of sequence and structure profiles is possible.We are positive that when doing so our approach can help to better exploit available protein structure and sequence data by allowing for analyses of correlations between different vectorial structure representations derived from structure on the one hand and from sequences on the other hand. This might assist in gaining deeper insight into protein folding.Cij of a protein structure is a binary symmetric matrix with elements Cij = 1 if amino acids at positions i and j are in contact and Cij = 0, otherwise [The contact matrix therwise . Two resα distances, are possible [Cij = 0 if |i - j| < 3, to ignore trivial short range contacts.Other contact definitions, e.g. based on Cpossible . AdditioCij is a symmetric matrix, all its eigenvalues are real and it has a complete orthonormal set of real eigenvectors. The principal eigenvector ci (PE), i.e. the eigenvector associated with the largest eigenvalue, is a structural profile that embodies the most relevant properties of protein structure. Its components are all of the same sign, which we chose to be positive. The PE maximizes the quadratic form ∑ij Cij cicj under the normalization constraint ci can be interpreted as the effective connectivity of the amino acid at position i embedded in the structure, since positions with large ci are in contact with as many as possible positions j with large cj.Since As shown in  the PE cε(N) = min{εmax, ε0/(log N - ε1)} with εmax = 0.01, ε0 = 0.02, and ε1 = 2, instead of zero. The principal eigenvector of this revised contact matrix An 'ad hoc' generalization of the principal eigenvector, introduced in , extendsThis revised definition permits consistent description of single- and multi-domain protein structures, keeping crucial properties of the original definition.Another approach to define a vectorial representation for single- and multi-domain protein structures is described in   their mean value is fixed to ⟨c⟩ = 1 to choose a normalization of the GEC components, (c) their mean square component is fixed to ⟨c2⟩ = B > 1.All members of the GEC family share the properties that (a) they maximize the quadratic form Q = ∑i = ∑j Cij, the contact vector, we obtain the effective connectivity profile EC that is used in this paper. This profile can be expressed as a weighted sum of the vectors of the eigensystem of the contact matrix Cij, with weights gradually introducing contributions from more eigenvectors from Cij's eigensystem when structures described get more modular.For the special choice of It was also shown that the EC is nearly identical to the PE for small single-domain structures with low internal modularity, and that for all structures it is highly correlated with the revised PE. The significant correlation between the hydrophobicity profile of the protein sequence HP and the PE, valid for small single-domain proteins, is translated to multi-domain structures when using EC or revised PE profiles.Z-score, we used a set of structures derived from the '29SCOPsf' set described in more detail in [For training and testing the algorithm and for fitting the etail in  superfamThe penalties that build up the path cost function are divided into three terms.i in the first profile and position j in the second profile, are penalized by a term that grows with their absolute difference,1. Aligned components of the structural profiles, corresponding to position palign,exp as a tuneable parameter that will be referred to as scaling exponent.with s between residue i and i + 1 is penalized by2. Breaking chain pbreak,fac and pbreak,exp. This is based on the expectation that it is less likely to break a chain at a strongly constrained position with large components ci and ci+1.with parameters nj in chain s at position j + 1 opposite to a gap in the other chain, consisting of the components 3. An insertion of length pinsert,fac and pinsert,exp and with s = {1, 2} selecting the chain. This is based on the expectation that strongly connected residues are less likely to form part of an insertion, or to be deleted from the other chain.with parameters As a result, the complete path cost function is given byi after which chain s is broken, and n after position j in chain s.where For our implementation we found that the set of parameters displayed in Table As any automatic alignment procedure, the algorithm described depends on adequate selection of its six parameters for opening and extending gaps. To obtain an optimal set of parameters, a Monte Carlo scheme was conducted starting from a manually adjusted parameter set. The decision whether to accept a preliminary parameter change or not was based on the value of the sum of residues close in space after optimal rotation, not using the refinement routine.Z-scores smaller than four were removed from the training set, to ensure that it only contains pairs for which a well defined result exists. The training set consists of 235 alignments.The training set used is a randomly selected subset of the pairs of chains from the 29SCOPsf set that are assigned to the same superfamily. Alignments with a DaliLite  or MAMMOAn automatic routine was set up to assess the quality of the alignments produced by our algorithm, as well as of alternative ones produced by well established programs. Alignments were computed for the 3566 pairs of structures from the same SCOP superfamily in our dataset not used in the training set, so that test and training sets are disjoint.For all examples, the results of the different algorithms were inserted into our own procedure for computing the optimal rotation using MaxSub and the scores for quality assessment that are listed in Table To allow for objective quality assessment and comparison of the algorithms used here, the following scores were computed.α atoms that are closer in space then 4 Å after optimal rotation normalized by the length of the shorter chain in the alignment. rPSI discards fragments shorter than four aligned amino acids from this value.The percentage of structural similarity (PSI) counts the number of aligned amino acid pairs whose CThe root-mean-square deviation of the coordinates (cRMSD) is computed over all aligned pairs or, in the 'core only' case, over those pairs only that contribute to the PSI.The contact overlap is deifned asCij and dth = 4.5 Å.Where The sequence similarity is computed using the BloSum62 similarity matrix and is normalized to a percentage. rSeqSim again discards aligned residues in short fragments.The alignment test set is available as Additional File Z-score is generally defined asThe σPSI needed to compute the Z-score we aligned 31284 pairs of unrelated structures. We used the same set of structures introduced above, but this time we aligned structures from different SCOP superfamilies where pairs with DaliLite or Mammoth Z-score larger than 3 were sorted out to make sure that the structures in the sample alignments are reasonably unrelated. The values for ⟨PSI⟩ and σPSI were obtained by fitting functions to the data shown in Fig. To determine the quantities ⟨PSI⟩ and While the mean follows a power-law decaythe standard deviation is better matched by an exponential functionThe fits resulted toandas shown in Fig. The computational complexity of the procedure is composed of that of Dijkstra's shortest path algorithm  and the E| + |V| log |V|), where |V| is the number of vertices and |E| is the number of edges, i.e. the elements and arrows in the alignment matrix. For the initial profile alignment |V| = (N1 + 1)·(N2 + 1) + 1 with N1 and N2 as the number of amino acids in the protein chains, taking also into account the additional first row and column that permit leading gaps.We implemented the Dijkstra algorithm using a Fibonacci heap to find the cheapest vertex in each step. In this case, the algorithm has complexity From this we findfor edges leaving the 'start' element,  leaving first row and column elements,  from inner matrix elements,  connected to 'end', and  additional double steps needed to implement the break/insert behaviour.NMaxSub ≤ min  is the number of aligned amino acid pairs.The complexity of the MaxSub algorithm is For the second run of Dijkstra's algorithm the refinement routine the restrictions imposed on the possible paths largely reduce the number of edges in the alignment matrix. This reduces the combined run time of Dijkstra's algorithm together with MaxSub in the second run to approximately 20% of that of the first run, over the test set discussed above.The overall complexity isNDijkstra = N1·N2. Both algorithms can be implemented very efficiently and allow for very short computation times, as discussed below.with The current program was implemented in C++ making extensive use of object-oriented design principles. Data representations and algorithms from the Standard Template Library and the Boost C++ libraries  were utiSix different alignment algorithms that are freely available on the Internet have been used as references for comparison.MAMMOTH algorithm [The lgorithm  was seleMAMMOTH-mult algorithm [The lgorithm  uses theDaliLite algorithm [α contact matrices in a heuristic scheme of combining overlapping submatrices to get the final result. This makes the algorithm the slowest of our references but the precise coordinate representation results in the highest accuracy found here. We consequently use DaliLite as the accuracy benchmark.The lgorithm  aligns CTM-align algorithm [The lgorithm  achievesCE algorithm [The lgorithm  performsSHEBA algorithm [α-traces.The lgorithm  utilizesProject name: SABERTOOTH Alignment ServerProject home page: Licence: The web services provided may be freely used without any charge.MP and UB designed research; FT and MP developed the alignment algorithm; FT coded and tested the alignment algorithm; FT, UB, and MP analyzed results; FT, UB, and MP wrote the paper. All authors read and approved the final manuscript.RASMOL Script File for Alignment Example Fig. Click here for fileRASMOL Script Files. The file contains RASMOL script files '1-d1bhe__d1daba__maxSub.tcl', '2-d1cd9b2 d1bpv maxSub.tcl', and '3-d1gca__d1dbqa__maxSub.tcl' for alignments of structures from the test set in quality assessment colour coding. The files '4-d1k0ma2 d1de4c3 maxSub.tcl', '5-d1gnwa2_d1dp4a__maxSub.tcl', and '6-d1iyha2_d1cg2a1_maxSub.tcl' contain RASMOL script files in all atoms depiction with alignments of structures from different SCOP folds but from the same secondary structure classes.Click here for fileAlignment Test Set. The file 'alignment_testset.dat' contains the test set used for quality assessment. Two columns listing ASTRAL-IDs of the 3566 alignments as described above.Click here for file


The prediction is based on a multiple alignment that contains both reference sequences with known structures and the sequence whose unknown structure is predicted. Intensive research has been made to improve the quality of multiple alignments, since misaligned parts of the multiple alignment yield misleading predictions. However, sometimes all methods fail to predict the correct alignment, because the evolutionary signal is too weak to find the homologous parts due to the large number of mutations that separate the sequences.Comparative methods have been the standard techniques for Cα amino acids in superimposed tertiary structures.Stochastic sequence alignment methods define a posterior distribution of possible multiple alignments. They can highlight the most likely alignment, and above that, they can give posterior probabilities for each alignment column. We made a comprehensive study on the HOMSTRAD database of structural alignments, predicting secondary structures in four different ways. We showed that alignment posterior probabilities correlate with the reliability of secondary structure predictions, though the strength of the correlation is different for different protocols. The correspondence between the reliability of secondary structure predictions and alignment posterior probabilities is the closest to the identity function when the secondary structure posterior probabilities are calculated from the posterior distribution of multiple alignments. The largest deviation from the identity function has been obtained in the case of predicting secondary structures from a single optimal pairwise alignment. We also showed that alignment posterior probabilities correlate with the 3D distances between priori detect errors in comparative models on the sequence alignment level.Alignment posterior probabilities can be used to a  As a result, demand for reliable computational methods today is higher than ever, while The central assumption of comparative bioinformatics methods for proteins is that the structures of proteins are more conserved than their amino-acid sequences. This allows homology modelling, namely, mapping the structure of a sequence onto homologous sequences. As insertions and deletions separating two homologous sequences accumulate, homologous characters in the two sequences will occupy different positions, which causes a non-trivial problem of identifying homologous positions. This problem can be solved by sequence alignment algorithms -4, whichThe relationship between gap-penalties and similarity scores can be set such that they maximise the number of correctly aligned positions in a benchmark set of alignments ,6. By coThe uncertainty in the sequence alignment can be slightly reduced when more than two sequences are simultaneously aligned together, and hence, much effort has been put in developing accurate multiple sequence alignment methods. Although efficient algorithms exist for any type of pairwise alignment problem, the multiple sequence alignment problem is hard. It has been proved that the optimal multiple sequence alignment problem under the sum-of-pairs scoring scheme is NP-hard , and it Iterative approaches have been introduced for score-based methods in the eighties ,18 and hThe Markov chain Monte Carlo (MCMC) method represents a third way to attack the multiple stochastic alignment problem. It was first introduced for assessing the Bayesian distribution of evolutionary parameters of the TKF91 model aligning two sequences , and hasSince the above mentioned methods for multiple stochastic sequence alignment problems have been introduced only recently, no large-scale, comprehensive analysis on the performance of methods for protein structure prediction has been published yet. In this paper, we present a survey on how stochastic alignment methods can be used for protein secondary structure predictions. The prediction can be based on pairwise or multiple alignments and in both cases, either only a single, optimal alignment or the whole posterior distribution of alignments is used for prediction. We are interested in the question how much one can gain by involving more sequences and the posterior distribution of the alignments into the secondary structure prediction.We implemented a stochastic pairwise and a stochastic multiple sequence alignment method in Java programming language . In this case, the most likely – a.k.a. Viterbi – alignment was obtained for all pairs of sequences and was used to map the secondary structure of one of the sequences onto the other sequence.• Based on the posterior distribution of pairwise alignments using the Forward-Backward algorithm ("Forward"). In this case, the posterior probabilities that two amino acids are aligned together were obtained for all pairs of sequences and all pairs of amino acids. The secondary structure of one of the sequences was mapped onto the other sequence in a fuzzy way using the posterior probabilities.• Based on the Maximum Posterior Decoding estimation from samples of a Markov chain Monte Carlo (MCMC) stochastic multiple alignment ("MPD"). In this case, the Maximum Posterior Decoding (MPD) alignments were predicted from MCMC samples and were used to map the secondary structure of one of the sequences onto the other sequences. The MPD alignment maximizes the product of the posterior probabilities of its alignment columns. See the Methods section for an explanation why the MPD alignment can be more accurately estimated from MCMC samples than the Viterbi alignment.• Based on the posterior distribution of multiple alignments obtained by MCMC stochastic multiple alignment ("Bayesian"). In this case, the posterior probabilities that two amino acids are aligned together were estimated from the MCMC samples for all pair of sequences choosable from a multiple alignment and all pair of amino acids. The secondary structure of one of the sequences was mapped onto the other sequence in a fuzzy way using the posterior probabilities.10 helices), the percentage of the correctly estimated secondary structure types was calculated and plotted on Fig. Amino acid sequences were divided into 100 categories based on their alignment posterior probabilities in the case of pairwise sequence alignments – or on their posterior structure prediction probabilities  in the case of Viterbi and Forward estimations, respectively. The 100 categories were evenly distributed on the  interval. For each category and the three general types of secondary structures  in the case of MPD and Bayesian estimation, respectively. The 10 categories were evenly distributed on the  interval. For each category and the three general types of secondary structures, the percentage of the correctly estimated secondary structure types was calculated and plotted on Fig. For a fair comparison, we repeated the pairwise sequence comparison protocols on the selected 12 families, the generated statistics are shown on Fig. Our results indicate that methods predicting secondary structures based on a single alignment are over-pessimistic about their performance on alpha helices and beta sheets, namely, the posterior probabilities associated to the prediction are lower than the actual probability that the prediction is correct. Methods that predict structures based on the whole distribution of sequence alignments are less pessimistic – the alignment posterior probabilities better approximate the observed probabilities that the prediction is correct. All pairwise alignment methods proved to be over-optimistic estimating the reliability of their predictions for alpha helices and beta sheets with posterior probability above 0.8.10 helix predictions turned out to be the toughest of all secondary structure types. Each method except the Bayesian estimation on multiple sequence alignments is much over-optimistic on their power of predicting 310 helices. MPD is less optimistic than pairwise methods.Predicting the correctness of 310 helices, which makes MCMC-based multiple alignment methods successful candidates for promotion to a fundamental tool in protein structure prediction.Among all methods studied, Bayesian estimation based on multiple alignments was the only one that was able to correctly predict its prediction power of all secondary structure types, including 3Cα atoms for each aligned pair of amino acids. The alignment posterior probabilities were evenly divided into 10 categories, and the average 3D distances as well as the low and high quartiles have been plotted for each category.To show that the alignment posterior probabilities correlate not only with the goodness of secondary structure predictions but they also correlate with the similarities in the 3D structures, we calculated from the HOMSTRAD superimposed 3D structures the 3D distances between the 10 helices.Fig. The differences between the predictions of different secondary structure elements can be explained by their general attributes. Alpha helices are typically formed by 10 amino acids or more. Substitutions are frequent in alpha helices and they are surrounded by loop sequences where insertions and deletions often occur, therefore stochastic alignment methods realise some uncertainty, which yields relatively low posterior probabilities when aligning these regions. However, since alpha helices are relatively long, and the substitutions that occur in them rarely change the chemical behaviour of the affected amino acids, the long runs of chemically similar amino acids in the two sequences to be aligned give a strong statistical signal that helps align alpha helices.Beta sheet elements are typically shorter than alpha helices, and are also surrounded by non-structured fragments accumulating insertions and deletions, which also yields relatively low alignment posterior probabilities. However, beta sheet elements are more likely to be misaligned, since their short length keeps them from carrying a statistical signal that alpha helices do.10 helices are the least conserved secondary structure elements. Even if the actual amino acid sequence does not change, mutations at other parts of the sequence might indicate a conformation change that can shift the 310 helix or transform it into a different structure type, see for example, Fig. 10 structure is mapped onto other sequences that do not contain this secondary structure motif. The fact that different secondary structure motifs can build up the same region of a functional protein implies that the given region might not be crucial to maintaining the structure and function of the protein and thus mutations can accumulate in the vicinity of the given region. Stochastic multiple sequence alignment can reveal the uncertainty in aligning that region, which explains why multiple alignment methods improve in predicting their predicting power on 310 helices.The 3There is a similar explanation for the overoptimism in the region of 0.8 and higher posterior probabilities in the case of alpha helices and beta sheets: slight structural changes might shift the position where an alpha helix or a beta sheet starts or ends, even if the amino acids in the positions of question do not change. Fig. Predictions based on a single, optimal pairwise or multiple alignment are over-pessimistic: alignment columns from both the Viterbi alignments and the MPD multiple alignments are labelled with posterior probabilities that are typically lower than the actual probability that the secondary structure predictions are correct for these columns. When the whole posterior ensemble of alignments is the basis of the secondary structure prediction, the posterior probabilities are closer to the actual probabilities that the prediction is correct. One main difference between the two strategies – prediction based on a single optimal alignment and prediction based on the posterior distribution of alignments – is that in the latter case posterior probabilities of all secondary structure types are given for each amino acid, while in the former case, the Viterbi or MPD alignment assigns at most one secondary structure element to each amino acid. This suggests the hypothesis that prediction methods based on the posterior distribution of alignments are less over-pessimistic due to possessing such false positive predictions with small posterior probabilities that are not part of a Viterbi or MPD alignment-based estimation.To test this hypothesis, we predicted alpha helices and beta sheets from the posterior distribution of pairwise alignments in an alternative way. In this alternative prediction, each amino acid has been assigned to at most one secondary structure element that had maximal posterior probability .The correlation between alignment posterior probabilities and probabilities of correctly predicting a secondary structure type is obviously the same under the two different protocols if the posterior probability is greater than 0.5, since an event having probability greater than 0.5 must be the most likely event. The two types of curves split very soon below 0.5 (data not shown), and the second type of prediction protocol (considering at most one secondary structure type prediction for an amino acid) gets less over-pessimistic than the other protocol. This means that there are more true positive predictions than false positive predictions with non-maximal posterior probabilities.This result is just the opposite of what our hypothesis suggested, therefore we also plotted the number of false positive and true positive predictions for each secondary structure type and prediction methods, see Fig. High alignment posterior probabilities indicate that the aligned residues are close to each other in the superimposed 3D structures. The average 3D distance between the aligned residues increases as the alignment posterior probability decreases. However, the distribution of residue distances become flatter for small alignment posterior probabilities, namely, a small alignment posterior probability does not necessarily mean that the aligned residues are far from each other. For example, 0.5 alignment posterior probability in a pairwise alignment means that there is still about 25% probability that the aligned residues are closer to each other than the average distance between amino acids that are aligned together with more than 0.9 posterior probability. The distance distribution is even flatter in case of multiple alignments. One possible explanation is that the alignment posterior probabilities are calculated for multiple alignment columns while distances are calculated for all possible pairs of amino acids in alignment columns. A small alignment posterior probability indicates possible differences in the 3D structures, however, some of the 3D structures might be still similar. Averaging the 3D distances in alignment columns naturally makes the distribution more centred (data not shown).10 helices, i.e., posterior probabilities for these alignment columns are greater than the probabilities that the secondary structure prediction for these amino acids is correct. Multiple alignment methods provide slightly more reliable predictions about their reliability of secondary structure predictions – they are less overoptimistic on 310 helix predictions.In this paper, we studied how posterior probabilities of aligning characters in pairwise or multiple alignments might indicate whether secondary structure predictions based on the alignments in question are correct. We found that pairwise alignment methods are over-pessimistic on predicting alpha helices and beta sheets, namely, posterior probabilities of alignment columns are lower than the actual probability that the structure prediction based on the alignment column is correct, while they are overoptimistic on predicting 3Secondary structure predictions can be given based on single, optimal pairwise or multiple alignments and also based on the posterior ensemble of alignments. In the latter case, posterior probabilities are closer to the probabilities that the secondary structure prediction is correct, especially when the structure prediction is based on the posterior distribution of multiple sequence alignments.ab initio threading methods [The multiple sequence alignment is the Holy Grail of bioinformatics  since wh methods -36.a priori knowledge on the substitution, insertion and deletion processes of secondary structures, and we expect that such combined approaches will have a better performance in structure prediction. Nevertheless, secondary structures can be predicted not only in a comparative way, but also using a single sequence, based on the statistical properties of the amino acids in different secondary structure types [It is worth mentioning that the alignment methods we applied in this work do not consider any information about how secondary structures evolve. It is well-known that different secondary structure elements follow different substitution processes, and this difference in the substitution pattern can be used for secondary structure prediction . It is fre types ,39. PoteThe running time of the methods obviously increases with the complexity of the background models, and analyses utilising such combined methods currently take too long to be applicable for everyday use on personal computers. However, the speed of processors keeps increasing exponentially following Moore's law, and will soon reach a level when it won't pose barrier to such combined approaches. Nevertheless, there are also promising channels to improve the running time of the methods. The standard approach for statistical multiple alignment is going to be MCMC, and current implementations make use of very basic tricks only, like the alignment window cut algorithm described in the Methods section. Several groups are working on making MCMC alignment methods more efficient and quickly mixing, and significant improvements are expected in the coming years.10 helix or none). We predicted the secondary structures of the sequences as described below.The HOMSTRAD database  has beenWe used a simplified version of the TKF92 model . The simFor each family in the HOMSTRAD database, each pair of sequences has been aligned using the above described pair-HMM. Since the jumping probabilities in the pair-HMM are interdependent via common parameters, the usual EM algorithm  cannot bPs(ai) that a particular amino acid ai from sequence A has a secondary structure s given that it is related to sequence B is calculated asWe also predicted secondary structures based on the distribution of alignments in the stochastic model. Posterior probabilities for each pair of characters from the two sequences have been obtained with the Forward and Backward algorithms using the Maximum Likelihood parameters. The posterior probability m is the length of sequence B, P  is the posterior probability that characters ai and bj are aligned, and bj is s, 0 otherwise.where a priori. These priors together with the likelihood of a tree and multiple alignment on the tree define the joint posterior distribution of multiple sequence alignments, evolutionary trees and model parameters.The transducer theory  has beenextended alignment.Since the joint distribution of alignments, trees and parameters is a high dimensional distribution that is too complicated for direct, analytical inferring, Markov chain Monte Carlo ,30 has bThe Markov chain performs a random walk on the space comprising the following components:• Edge lengths of the tree• Model parameters• Extended alignment, described above• Tree topologyWe applied Metropolis-Hastings moves to change one of the components randomly, each component selected with a fixed, prescribed probability that was chosen to maximise the mixing of the Markov chain. Standard techniques were used for modifying edge lengths and parameters in the model, for a reference, see .are not within the window, then regardless of insertions or deletions at the beginning or end of the new alignment, the same window will be available for selection and this way the original alignment for (back)proposal. However, if the borders of the window were indicated by the first and last Felsenstein wildcards within the window, the proposal might not always be reversible – for an example, see Fig. Changing the alignment is the most time-consuming event, since the running time of proposing a new alignment is proportional to the product of the lengths of the aligned sequences. A possible solution is modifying only a part of the alignment , which decreases the running time of this type of proposal. Although it also decreases the mixing of the Markov chain, the overall performance of the Markov chain in terms of total computational time improves ,25. The Sequences are iteratively realigned on the selected subtree within the selected window. In each iteration, the new alignment is drawn by the Forward-Backward sampling algorithm  with a pWe used nearest neighbour interchanges (NNI) for altering the topology as described in , which tBecause the MCMC analysis is time-consuming, we selected 12 families from the HOMSTRAD database, see Table a posteriori (MAP) estimation from an MCMC sample is unstable, since there are many suboptimal alignments, and typically almost all sampled alignments from a Markov chain will be different. The same alignment showing up occasionally in multiple samples is merely due to the non-optimal mixing of the Markov chain, and such an alignment cannot be regarded as the most probable in the posterior distribution in any sense. Instead, we estimated the Maximum Posterior Decoding (MPD) alignment [In an earlier work , we showlignment ,47 that ai from sequence A having a secondary structure s given that it is related to sequence B isWe also predicted secondary structures based on all the alignments sampled from the Markov chain. The estimation for the posterior probability for a particular amino acid N is the number of alignments in the Markov chain, fk(ai) is the amino acid in sequence B with which ai is aligned in the kth alignment, and δs,x is 1 if the known secondary structure of character x is s, otherwise 0.where IM proposed the research, contributed to the MCMC code and wrote some parts of the software for posterior analysis. AN wrote the majority of the MCMC code and the majority of the software for posterior processing. BD wrote the software for pairwise analysis. JH encouraged the research and wrote the manuscript.Structure Projector package. Java source code and public licence in a   tar.gz archiveClick here for file


Sequence alignments form part of many investigations in molecular biology, including the determination of phylogenetic relationships, the prediction of protein structure and function, and the measurement of evolutionary rates. However, to obtain meaningful results, a significant degree of sequence similarity is required to ensure that the alignments are accurate and the inferences correct. Limitations arise when sequence similarity is low, which is particularly problematic when working with fast-evolving genes, evolutionary distant taxa, genomes with nucleotide biases, and cases of convergent evolution.Functional Inference using the Rates of Evolution), which aligns sequences using the evolutionary rate at codon sites, as measured by the dN/dS ratio, rather than nucleotide or amino acid residues. FIRE was used to test the hypotheses that evolutionary rates can be used to align sequences and that the alignments may be used to infer protein domain function. Using a range of test data, we found that aligning domains based on evolutionary rates was possible even when sequence similarity was very low . Furthermore, the alignment has the potential to infer protein domain function, indicating that domains with similar functions are subject to similar evolutionary constraints. These data suggest that an evolutionary rate-based approach to sequence analysis  may be used to study cases of convergent evolution or when sequences have very low similarity. However, when aligning homologous gene sets with sequence similarity, FIRE did not perform as well as the best traditional alignment algorithms indicating that the conventional approach of aligning residues as opposed to evolutionary rates remains the method of choice in these cases.A novel approach was conceptualized to address the "low sequence similarity" alignment problem. We developed an alignment algorithm termed FIRE (FIRE provides proof of concept that it is possible to align sequences and infer domain function by using evolutionary rates rather than residue similarity. This represents a new approach to sequence analysis with a wide range of potential applications in molecular biology. Investigations in molecular biology frequently require the analysis of sequence alignments and several methods are available for this purpose. Once a correct alignment is obtained, inferences may be made concerning phylogenetic relationships and putative functions . A fundaFunctional Inference using Rates of Evolution) algorithm developed. This method uses the evolutionary rate at codon sites, rather than individual residues, to align sequences. Evolutionary pressures are inferred from the parameter ω (ratio of non-synonymous (dN) to synonymous (dS) substitutions, corrected for opportunity) . The maximum difference between two ω values is capped to ωmax and is parameterized - we chose 1.5 as a default, since it is biologically more meaningful to identify sites under positive selection than to emphasize the absolute values of sites with ω>1. Thus, cs = 0, if |ω1-ω2|>ωmax and cs = 1-(|ω1-ω2|)/ωmax otherwise. The FIRE score is the sum of the cs scores over all aligned codon pairs, normalized for sequence length by dividing the FIRE score by the number of codons in the longer sequence. The opening and extension gap penalties are parameterized and the defaults of 0.5 and 0.05, respectively, were used for the analyses in this study. The FIRE algorithm produces a normalized score, percentage similarity plot, histogram listing the number of codons in the alignment with similar scores per decile, and an alignment of the amino acid sequences. The FIRE software and a User Information file providing further details are freely available at http://dept.ee.wits.ac.za/~scott/fire and are attached as additional files The FIRE algorithm was developed in order to perform a pairwise alignment using lgorithm  and find range 0,. The max, csω1, ω = 0, if ω MLEs at codon sites were obtained for 15 data sets using the PAML  v4.0 software [ω MLE range (0-9), dN range (0.2-55.0), and paralogous sequences (metazoan MYB1 and MYB2). The number of sequences per data set ranged from 4-12. The data sets with low sequence number were used to examine the effect of this on FIRE outputs, and as expected, sets with fewer sequences produced less accurate ω MLEs and decreased FIRE reliability. Sequence divergence  varied from 2.1 to 48.1, which is within PAML suggested limits of <50 [dS = 216.1); however, it is unlikely this led to erroneous results since high dS values falsely elevate ω values and in this set all the ω MLEs were <0.3.The Bayes Empirical Bayes (model M2) or Naïve Empirical Bayes (model M3) posterior mean software  and a FIsoftware ; (ii) MYsoftware ; (iv) a software ; and (v)software . Variatis of <50 . An exceω MLEs obtained from PAML analyses under model M3 (NSsites = 3). In general, FIRE results for ω MLEs with model M3 were the same or better than M2, the likely reason being that ω MLEs under M3 are less constrained.The results of salient examples are discussed. FIRE scores and similarity plots are provided in Table ω MLEs, significantly different sequence lengths (>100 codons) and non-contiguous evolutionary conserved codons [Following normalization for sequence length, homologous domains with similar functions produced FIRE scores >0.60 and FIRE plots with the majority of codon similarities >60%. For example, alignments for two orthologous sets (metazoan MYB1/protozoan MYB1) and two paralogous sets (metazoan MYB1/MYB2) produced scores of 0.93 and 0.94, respectively, and similarity plots nearing 100% over most of the sequence. The metazoan GK/protozoan GK alignment provided a comparison of two orthologous sets with a greater range in d codons . The difω MLEs <0.3 across the entire sequence) of similar lengths were aligned (data not shown). Including other computational methods such as structure determination would be valuable to identify these cases.Conserved domains with dissimilar functions produced poor alignments, for example the metazoan MYB1/GK alignment (FIRE score = 0.09). The MYB1/p53 DBD alignment provided an interesting test case. Both are transcription factors, however, the domains are implicated in very different biological functions and, according to our hypothesis, this difference should result in a poor FIRE alignment. This was indeed the case (FIRE score = 0.45). We did, however, note that FIRE produced false positives when two unrelated highly conserved domains , plots and alignments between the two κ sets, and the κ and λ sets suggested that these domains are under similar evolutionary pressures, which correlates with their similar functions. Alignments of the κ and λ antibody sets with any of the domains that are functionally unrelated, for example MYB1, GK or p53, produced poor FIRE results.Flexible structure Alignmen T by Chaining Aligned fragment pairs allowing Twists) [Distance matrix Alignment program) [To compare the performance of FIRE against the more conventional ClustalW , MAFFT  and stru Twists)  and DALIprogram)  algorithprogram) . As a meω MLEs, such as occurs in highly conserved domains like the MYB transcription factor in data set 2, there is a risk that a gap (possibly due to an insertion/deletion elsewhere in one of the sequences) is introduced causing a misalignment over the conserved region.The T-Coffee and MAFFT algorithms performed the same or better than FIRE or ClustalW for all data sets. The T-Coffee performance is unsurprising since (i) the same structure files used by FATCAT and DALI were included in the T-Coffee algorithm, and (ii) it is well known that structure-based alignments or a combination of structural information with other approaches  produce the most accurate alignments when sequence similarity is low . AlthougThe main findings from these results indicate that it is conceptually and methodologically possible to align functionally similar domains accurately using the evolutionary rate at codon sites. In addition, good alignment scores were only obtained for sequences coding for similar functions, indicating that domains with similar functions are subject to similar evolutionary constraints. This suggests that the FIRE approach may be valuable for inferring domain function in situations such as convergent evolution or when sequences are highly divergent. However, it was noted that for homologous genes where there is some sequence similarity, FIRE was not as accurate as MAFFT or T-Coffee. In these cases, the conventional algorithms remain the method of choice.The value of the FIRE approach currently lies in its ability to align sequences independent of residue similarity. This is helpful for analyzing sequences with poor similarity, which typically occurs with evolutionary distant genes, convergent evolution and sequences with extreme nucleotide biases . It is kFIRE provides proof of concept that it is possible to align sequences and infer domain function by using evolutionary rates. It complements the arsenal of available computational methods and represents a new approach to sequence analyses with a wide range of potential applications in molecular biology.http://www.ncbi.nlm.nih.gov and PlasmoDB v5.5 http://www.plasmodb.org databases. MSAs were performed with MAFFT [ω MLEs at codon sites. Each data set (comprising a list of ω MLEs) was aligned with every other data set with the program FIRE, which was specifically developed for this purpose . A list of accession numbers, sequence details, and PAML sequence and tree files are available from the corresponding author.Coding sequences were extracted from NCBI th MAFFT  and phylth MAFFT  and PAUPth MAFFT . MSAs anth MAFFT  to obtaiω MLEs and perform an alignment. Two examples of the PAML rst and mlc raw output files of the protozoan GK and λ light chain variable regions data set are provided in additional file ω MLEs and mlc files provide statistical details regarding the analysis, for example dN, dS and kappa (transition/transversion ratio) values. The FIRE results for all data sets aligned with each other are available from the corresponding author.FIRE uses the rst output files from a PAML analysis (using either NSsites 2 or 3) to extract the http://tcoffee.vital-it.ch/cgi-bin/Tcoffee/tcoffee_cgi/index.cgi, the European Bioinformatics Institute http://www.ebi.ac.uk/Tools/ and the MAFFT homepage http://align.bmr.kyushu-u.ac.jp/mafft/software, respectively. The T-Coffee advanced algorithm combined a ClustalW alignment with the available PDB structure files, which were selected based on the corresponding data set sequence files and downloaded from the World Wide Protein Databank http://www.wwpdb.org. The E. coli crystal structure PDB file (ID: 1BO5) was used for a T-Coffee analysis of the glycerol kinase set due to a lack of metazoan and protozoan structural data. Default settings were used for ClustalW2 alignments. For the MAFFT analysis, the E-INS-i algorithm was used.T-Coffee, ClustalW and MAFFT analyses were performed using online servers at the Swiss Institute of Bioinformatics http://fatcat.burnham.org and DALI http://ekhidna.biocenter.helsinki.fi/dali_server online servers. The two PDB structures used for each alignment are representative sequences taken from the two clades being aligned with FIRE. The same structures were included in T-Coffee alignments. Due to a lack of structural data for the GK sequence set (data set 4), the FUGUE threading algorithm [E. histolytica GK (XM_650121.1) with the E. coli crystal structure (PBD ID: 1BO5) as a template. FATCAT, DALI and FUGUE structure alignments were used as reference alignments to which FIRE, T-Coffee, ClustalW and MAFFT alignments were compared.Sequence-structure alignments were performed with FATCAT lgorithm  was usedet al. , which demonstrated that probability distributions of evolutionary rates in coding sequences may be used as identifiers of genes. Furthermore, using rapidly evolving RNA viruses as test data, they found that genes within the same functional group have similar evolutionary fingerprints. The findings presented by Kosakovsky Pond et al. and the data in this manuscript suggest that the molecular signatures left behind by evolution represent a tier of information that is untapped by current sequence analysis methods.Our results complement a recent publication by S.L. Kosakovsky Pond PMD conceptualized the study. PMD and SH performed the experiments. SH scripted the FIRE algorithm. PMD, SH and TLC analyzed the results and wrote the manuscript. All authors read and approved the final manuscript.FIRE script. Python code for the FIRE algorithm.Click here for fileFIRE User Information File. Information for users of FIRE algorithm.Click here for fileFIRE alignments. Alignments correspond to the plots in Figure Click here for filePAML rst and mlc output examples. Two examples of the raw data PAML 4.0 mlc and rst output files for the protozoan GK and lambda light chain antibody data sets.Click here for file