Existing approaches typically consider membrane-related information either by using membrane-specific substitution matrices or by assigning distinct penalties for gap creation in transmembrane and non-transmembrane regions. Here, we ask whether favoring matching of predicted transmembrane segments within a standard dynamic programming algorithm can improve the accuracy of pairwise membrane protein sequence alignments. We tested various strategies using a specifically designed program called AlignMe. An updated set of homologous membrane protein structures, called HOMEP2, was used as a reference for optimizing the gap penalties. The best of the membrane-protein optimized approaches were then tested on an independent reference set of membrane protein sequence alignments from the BAliBASE collection. When secondary structure (S) matching was combined with evolutionary information (using a position-specific substitution matrix (P)), in an approach we called AlignMePS, the resultant pairwise alignments were typically among the most accurate over a broad range of sequence similarities when compared to available methods. Matching transmembrane predictions (T), in addition to evolutionary information, and secondary-structure predictions, in an approach called AlignMePST, generally reduces the accuracy of the alignments of closely-related proteins in the BAliBASE set relative to AlignMePS, but may be useful in cases of extremely distantly related proteins for which sequence information is less informative. The open source AlignMe code is available at  This situation has motivated many researchers to turn to remote-template homology modeling, in which the unknown structure of a target sequence is modeled on a known (template) structure of a distantly-related protein, in order to gain insights into membrane protein function. Such studies rely on methods for detecting relationships between two proteins, and subsequently, for accurately aligning their sequences; both of these procedures become increasingly difficult as the similarity between the proteins decreases, particularly below ∼20% identity. The membrane-protein-specific multiple-sequence alignment method PRALINE™ Integral membrane proteins constitute 25–30% of the genes in a given genome Membrane proteins have distinct properties from their water-soluble counterparts, because of their more complex environment. For example, there are only two major classes of structure: α-helical or β-barrel. Also, the membrane-spanning regions of proteins in the α-helical class have a distinctive hydrophobic character. The latter property inspired the early use of hydropathy profiles for locating transmembrane regions in a sequence Aside from the hydropathy-based approach, not many sequence alignment methodologies have been specifically developed for, and trained and tested on, membrane proteins. This reflects in part the limited data available for testing. Only recently have a sufficient number of structures become available that a dataset of known membrane protein structural homologues could be constructed to provide knowledge-based reference alignments, as, for example, in the HOMEP dataset Two multiple sequence alignment (MSA) methods, T-Coffee Other methodologies developed specifically for membrane proteins include the MSA methods STAM Here, we use our membrane protein sequence alignment program, AlignMe, to ask whether favoring matching of transmembrane regions – predicted either using hydrophobicity profiles or more sophisticated transmembrane predictions – increases the accuracy of pairwise alignments relative to the matching of secondary-structure elements alone, in the context of a profile-profile type alignment. We also test different methods for treating substitution rates, using either general or position-specific substitution matrices (PSSMs). We update the dataset of homologous helical membrane proteins for optimization and evaluation of the different strategies. We then compare the best of the different AlignMe strategies to other available methods using the BAliBASE membrane protein reference set 7 Alignment of Membrane proteins) is a protein sequence alignment tool developed in C++, which was designed to allow multiple different (membrane) protein descriptors to be considered simultaneously when defining the similarity between two aligned positions. Thus, structural properties such as transmembrane location or secondary structure represented in the form of profiles, can be combined with sequence and evolutionary information represented in the form of substitution rates (see below for more details). The description of the transmembrane location can be a window-averaged hydropathy plot  at a given alignment position is calculated as a linear combination of values from M input substitution matrices (S), and differences between residue property values (V) from N input profiles:w) for each input is intended to minimize bias towards a specific input. For example, a hydrophobicity scale containing values from –3.0 to 1.0  would be assigned w = 5 when used in combination with a substitution matrix whose values range from –5 to 15 .The similarity Within AlignMe, gap-opening and gap-extension penalties can be assigned different values according to whether the gap is at a terminus  at which an amino acid (A) from one sequence (i) is replaced by the amino acid (B) of the other sequence (j), and of the rate of the reverse substitution:To account for the variability in evolutionary pressure for different positions along the sequence we consider the position-specific substitution rates of the residue types in the two input sequences taken from position-specific substitution matrices (PSSMs). Thus, the similarity is an average of the substitution rate  for MEMSAT-SVM and a version of Uniref90 filtered for transmembrane proteins (from 4th August 2010) for OCTOPUS Three different predictors for α-helical transmembrane segments were tested: TMHMM st August 2010) and Uniref90 (from 28th April 2009), respectively. Each method produces a three-state prediction of the probability of a position being in a coil, α-helix or β-sheet; all three were used as input profiles for AlignMe, with each state contributing one third of the whole. A position was assigned to an α-helix if the predicted probability thereof was >0.5.Two secondary structure predictors were tested: Jufo th March 2010) The original HOMEP dataset contained 36 structures This non-redundant set was then clustered to identify families of related structures. The clustering method  is based on the protein structure distance (PSD) value that is calculated during SKA structural alignments The accuracy of a sequence alignment is often evaluated using a score that counts the fraction of correctly aligned positions with respect to the reference alignment The Alignment Difference (AD) score used here is similar to the mean shift error (MSE) score 6 = 1012 alignments.A Monte Carlo scheme was used to optimize the gap penalty values for each combination of inputs tested. Note that a systematic optimization In each step of the optimization process, AlignMe alignments were created using the current set of gap penalties and evaluated using the AD score. To minimize bias towards large families, all proteins in each HOMEP2 family were aligned with all others in that family and their AD scores were averaged; the overall alignment accuracy score for a given set of gap penalty parameters was the sum over the scores for each family.Starting with a randomly selected set of values (between 0 and 30) for each gap penalty parameter, the search procedure then involved random modifications of one or more gap penalty values from those values, or from the optimal values identified so far. The range of allowed modifications was initially set to be very small  to encourage a detailed examination of the score landscape around the current optimal gap penalty combination. A given combination of gap penalties was accepted if the overall alignment accuracy score was better than the best score found so far, in which case the maximal step size was reset to its initial value. Otherwise, that combination of gap penalties was rejected and the search space was expanded by increasing the maximum step size by 0.06. However, the gap penalty values were limited to the range 0 to 30, with a maximum step size of 30. If no improvements were found after reaching the maximum step size, the search was repeated, starting with the initial maximal step size of 0.06.For each set of input descriptors, this optimization was repeated 20 times with different initial gap penalty values, which was found to be sufficient for reasonable convergence (data not shown). The parameters for which the alignments had the best score were then used for that set of input descriptors. The optimal gap penalties obtained using the JTT membrane substitution matrix were ues e.g. , providiN+M and the parameters did not converge reliably.Optimization of the weights assigned to each input parameter was found to be computationally impractical because the search space increases by the power of Reference 7 set of BAliBASE The so-called ‘core’ regions provided by BAliBASE were not analyzed, as they have been shown to correspond only weakly to conserved secondary structure elements in this set The accuracy of the alignments in the HOMEP2 set was also assessed by building homology models based on each of the alignments, and comparing them to the native structure. For every pair of protein sequences, each protein was modeled using the structure of the other protein as a template. In each case, five models were created using Modeller v9.9 and the one with the best (lowest) DOPE score was evaluated using GDT_TS  and AL4  scores th August 2010, with five iterations, an E-value cut-off of 10−4 and a maximum of 2500 sequences. Sequences in the PSI-BLAST results that were more than twice the length of the query were filtered out. The remaining sequences were clustered using UCLUST Alignments were also calculated with HMAP There are two different possible approaches for generating a MSA from two query sequences and their respective homologues. In the standard approach, all results of both PSI-BLAST searches (including the two query sequences) are combined and aligned as a single large MSA, before extracting out the two query sequences for scoring. The second approach, which we call the “profile-profile” strategy, is to create MSAs for each query and its homologues. The resulting two MSAs or “profiles” are then aligned to one another to create a single MSA, from which the query sequences are then extracted for scoring.HHalign uses a similar strategy to the MSA “profile-to-profile” approach, but each query is described by a hidden Markov model (HMM) based on the results from a PSI-BLAST search , as well as by secondary structure predictions from PSIPRED, generated as described above. Those HMMs were then globally aligned to each other by using the “-mact 0.0″ maximum accuracy flag and by assigning all other parameters their default values.HMAP was also used to calculate profile-to-profile alignments. In this case, one of the sequences was assigned to be the query, and its profile included evolutionary information  combined with predicted secondary-structure from PSIPRED v3.2; the other sequence was assigned to be the template, and its profile was similar except that the secondary structure was assigned from the structure, where available. The two profiles were then globally aligned using HMAP.We also tested TM-Coffee We first describe the selection of input descriptors for AlignMe. To make the comparison between descriptors as fair as possible, gap penalties were optimized for each input tested. To this end, we first constructed an updated set of homologous membrane protein structures , and structure-based sequence alignments of these proteins were used as a reference. Input descriptors were considered to be effective if the AlignMe alignments had both more correctly aligned positions and smaller shift errors, measured as less negative AD scores (see Section 1.4). By also considering the shift error, we expect to help identify methods that are effective for very distantly related proteins. The findings are described for single inputs (Section 2.1) and then for combinations of inputs (Section 2.2). Finally, we compare three of the optimized AlignMe strategies with available alignment programs for the HOMEP2 set (Section 2.3) and the BAliBASE reference set 7 (Section 2.4).Various substitution matrices, hydrophobicity scales, secondary-structure and transmembrane predictions were tested as individual inputs (see Section 1.2).p<10−9). Of the general substitution matrices, the closest agreement with the reference alignments was obtained with the membrane-specific JTT matrix, followed by the general-purpose VTML matrix, although the differences between JTT and the others were not very significant  than those from other approaches (p<0.05). Window-averaging the hydrophobicity values as in a hydropathy plot  did not significantly improve the alignments compared to using PSSMs  is equivalent to using a substitution matrix, except with a focus on one specific physicochemical property. Alignments constructed using hydrophobicity scales were not significantly different from the best of the general substitution matrices  if all nSSMs cf..−4) more accurate than those generated using the best of the hydrophobicity scales . We note that the other differences are not significant (p>0.05) because of a disproportionate contribution of good PSIPRED2.6 alignments in the (large) aquaporin family; this contribution is not reflected in the AD scores in p<0.05) for the HOMEP2 protein set, using DSSP assignments as a reference When representing the sequences as profiles of predicted secondary structure type, the alignments in closest agreement with the reference alignments were obtained using PSIPRED3.2 predictions . Howeverp = 2×10−5), and transmembrane predictions  , followed by secondary structure predictions  . This fiUsing the results for single inputs, we next tested alignments for which the best two or three input descriptors were used in combination, since inclusion of complementary information is expected to progressively improve alignment accuracy . The explanation could be that OCTOPUS predictions of two related proteins match one another better than those of MEMSAT-SVM, or that the OCTOPUS predictions have a simpler form, perhaps providing more orthogonal (complementary) information to the PSSMs than the more detailed profiles obtained from MEMSAT-SVM . Alternatively, the fact that the MEMSAT-SVM values are more evenly distributed over a wider range of values than the OCTOPUS scores  and are thus given a smaller weighting (see Section 1.1) could mean that the MEMSAT-SVM scores can have less influence on the alignments.A potentially useful combination for membrane proteins is evolutionary information plus transmembrane propensity. The latter can be in the form of either a smoothed hydrophobicity value or a transmembrane prediction propensity. Interestingly, in AlignMe, nearly all such combinations resulted in significantly more accurate alignments than those based on the corresponding individual input parameters, but only when gap penalties were allowed to differ between membrane and non-membrane regions  more accurate alignments than when using the transmembrane positions for assigning the thresholds , the latter may be defined using either secondary structure or membrane propensity. We found that using α-helix positions for this distinction  were next tested in combination, which resulted in significantly more accurate alignments than any approach tested so far , with gap penalties of We compared the three AlignMe versions, i.e., with and without secondary structure or membrane matching, to several available multiple-sequence alignment programs, as well as the profile-to-profile alignment program HMAP, and the HMM alignment program HHalign (see Section 1.8). Here, we assess alignments of the training HOMEP2 dataset, first using the structure-based alignments as a reference, and then using the accuracy of homology models built from those alignments as a reference-independent measure.For close homologues  in the HOMEP2 set, the AlignMe alignments are not significantly more accurate than other methods: AlignMeP, AlignMePS, AlignMePST and HHalign alignments all have a high fraction of correctly aligned residues, for example .cf. AlignMePS) does come at the cost of some correctly-aligned positions, especially for sequences with moderate similarity. As mentioned above, for homology modeling of distantly-related pairs of proteins it can be useful to reduce the magnitude of large shift errors since manual adjustment of an alignment can be aided relatively easily by conservation mapping once the helices are approximately aligned. For similar reasons, it is also interesting to know whether the transmembrane helices have been matched to some extent, as many  functional residues lie in these regions. The matching of transmembrane helices in the HOMEP2 set by AlignMe appears to be particularly effective: using AlignMePS and AlignMePST, ≥97% of the known transmembrane helices overlap by at least half of their residues, and ≥62% of the helices (at least 10% more than the next best method) overlap by at least 90% of their residues  is overtraining of the gap penalties and other parameters due to the limited number of membrane protein structures available. We first tested this by using cross-validation: the optimization of AlignMePST was repeated using 20 of the 22 families and the resultant gap penalties used to evaluate the alignment accuracy of the remaining two families. As shown in As a measure of alignment accuracy that is independent of the reference alignments, we also constructed structural (homology) models from the test alignments. The models were compared to the native structures by calculating GDT_TS and AL4 values (see Section 1.7), and also compared to “gold standard” models built using sequence alignments extracted from the SKA structural alignments.cf.Measured by the GDT_TS structural similarity score, several methods have similar accuracy on average . This reThe alignment accuracy of the various methods was also evaluated on an independent data set of membrane protein sequences . This dataset contains manually-curated multiple-sequence alignments, based on PFAM alignments and optimized to improve amino acid and secondary structure matching; no structural information was available at the time to help guide the dataset construction AlignMePS alignments have the most correctly aligned residues in BAliBASE set 7 on average, as well as for 7 of the 8 families , includiTo assess whether the inclusion of transmembrane information is useful for distantly-related proteins, we separated the BAliBASE set into sequences assigned to the same subgroup  or to diWithin the predicted transmembrane regions of the BAliBASE sequences , AlignMeFinally, we also calculated the shift error in the BAliBASE alignments, which is smallest on average for the AlignMePST and AlignMePS alignments, followed by MSAProbs and HHalign, while HMAP has the smallest shift error for the acr and Nat families . MatchinIn this work, we developed a sequence alignment method called AlignMe, which we trained on a dataset of membrane protein structural homologues (HOMEP2). Three different strategies  were assessed using the BAliBASE membrane protein dataset set 7), and compared with other available methods. Overall, the BAliBASE analysis suggests that versions of AlignMe that match secondary structure prediction profiles may be generally useful for aligning membrane proteins  may be discrepancies between the secondary-structure and transmembrane predictions. Quantifying the matching of secondary-structure prediction profiles as described above indicates that the secondary structure profiles match less well in alignments generated with transmembrane predictions (profile difference score for AlignMePST is 0.060) than those without (profile difference score for AlignMePS is 0.055). In other words, transmembrane matching occurs at the expense of secondary-structure matching.A third possible cause of the reduced accuracy for closely-related sequences using AlignMePST is that including a third parameter (the transmembrane prediction) in the score for each position diminishes the contribution of the PSSM in a deleterious way.The above discussion notwithstanding, the BAliBASE results indicate that incorporating transmembrane matching is useful for very distantly-related proteins, particularly for reducing the overall shift error ,9,10. ThOf the other available methods tested, HMAP alignments were most frequently ranked towards the top ,7,8,9,10The profile-to-profile alignments strategy used with MUSCLE and T-Coffee typically resulted in fewer correctly-aligned positions and larger shifts than the other methods tested ,7,8,9,10This study focuses on α-helical membrane protein sequences, so that we obtain gap penalties that are optimal for long helices and are not biased by the inclusion of short β-stranded regions A concern about the current study is the fact that no structural informational was available to aid with the alignments when the BAliBASE reference set 7 was constructed, and therefore it is possible that these alignments contain errors whose effect we cannot yet know As the size of the database of membrane protein structures grows, further assessment of the various methods will be useful. Nevertheless, the results presented here suggest that there is potential for using the specific properties of membrane proteins for training and design in a way that aids the alignment of their sequences.File S1Figure S1 Clustering principle used for generation of the HOMEP2 data set. Figure S2 Correlations between alignment accuracy measures. Figure S3 Comparison of alignment accuracy when using hydrophobicity scales as input descriptors in AlignMe. Figure S4 Profiles of the predicted membrane propensity from the three different transmembrane helix prediction methods tested for AlignMe. Figure S5 Accuracy of HOMEP2 alignments generated by different methods. Figure S6 Accuracy of homology models built from HOMEP2 alignments generated by different methods. Table S1 Proteins in the HOMEP2 data set, listed by family Table S2 Sequence identities between pairs of proteins in the same HOMEP2 family, based on their SKA structural alignments.Contains Figures S1 through S6 and Tables S1 and S2. (DOCX)Click here for additional data file.File S2Dataset of HOMEP2 homologous membrane proteins.(GZ)Click here for additional data file.File S3Manual for AlignMe.(PDF)Click here for additional data file.File S4Source code for AlignMe.(GZ)Click here for additional data file.


Classification methods of DNA most commonly use comparison of the differences in DNA symbolic records, which requires the global multiple sequence alignment. This solution is often inappropriate, causing a number of imprecisions and requires additional user intervention for exact alignment of the similar segments. The similar segments in DNA represented as a signal are characterized by a similar shape of the curve. The DNA alignment in genomic signals may adjust whole sections not only individual symbols. The dynamic time warping (DTW) is suitable for this purpose and can replace the multiple alignment of symbolic sequences in applications, such as phylogenetic analysis.The proposed method is composed of three main parts. The first part represent conversion of symbolic representation of DNA sequences in the form of a string of A,C,G,T symbols to signal representation in the form of cumulated phase of complex components defined for each symbol. Next part represents signals size adjustment realized by standard signal preprocessing methods: median filtration, detrendization and resampling. The final part necessary for genomic signals comparison is position and length alignment of genomic signals by dynamic time warping (DTW).The application of the DTW on set of genomic signals was evaluated in dendrogram construction using cluster analysis. The resulting tree was compared with a classical phylogenetic tree reconstructed using multiple alignment. The classification of genomic signals using the DTW is evolutionary closer to phylogeny of organisms. This method is more resistant to errors in the sequences and less dependent on the number of input sequences.Classification of genomic signals using dynamic time warping is an adequate variant to phylogenetic analysis using the symbolic DNA sequences alignment; in addition, it is robust, quick and more precise technique. The classification of biological sequences  based on their similarity is a well-known procedure. The similarity between two DNA sequences determined by their evolutionary distance can be used to evaluate the evolutionary relationships of organisms. The evolutionary tree of all living organisms was constructed this way. However, all common methods use a symbolic notation of biological sequences . These methods are usually slow due to high computational complexity. They have low level resistance to errors in the sequences and the application of mathematical evaluation is difficult. The transformation of the biological sequence to a digital genomic signal is a known approach; however there exist only a few methods for subsequent signal analysis ,2.One of the possible DNA representations as a genomic signal is a phase determination of complex numbers assigned to the four symbols of DNA record ,4. The pPhylogenetic analysis represents the typical application of multiple alignments. However, each incorrect assessment causes many imprecisions resulting to incorrect taxonomical classifications ,10. ThisActin is a globular structural protein occurring in almost all eukaryotic cells. The highly conserved primary structure between all eukaryotes is one of the most unique properties of actin. The difference in the primary structure of the human and the yeast actin consists in about 5 percent of amino acids. The actin coding genes in different organisms are also very similar. We chose these genes to demonstrate the proposed classification method, because every individual change of a position in a symbolic representation influences a result of mutual similarity. Therefore, the comparison of sequences is complicated.http://www.ncbi.nlm.nih.gov/). The sequences represent complete ACTA1 genes from whole genome shotgun sequences with segments corresponding to mRNA splicing (introns) and they do not reflect only final protein product, but complete genetic information of ACTA1. The length of used sequences is about 2900 ± 200 bp. The corresponding protein products have the same length of 377 aminoacids, without substitutions.The actin occurs in six different isoforms differing in a function and a sequence structure. We chose one of them, the alpha actin 1 (ACTA1), which is expressed in a skeletal muscle cells . Ten difThe first step of the DNA classification method is the transformation of DNA symbolic record to numerical form. This procedure is very important, because all biological properties described in the original symbolical form must be maintained in the final genomic signal. We chose the method of conversion representing DNA sequence by the cumulated phase .The transformation technique replaces each of four symbols by its complex value: A ; C ; G ; T . The final cumulated phase corresponds to the value of gradually accumulated sum of angles in complex representation of a DNA sequence and can be calculated for every single position in the DNA sequence by: (1)A, nC, nG, and nT are numbers of adenine, cytosine, guanine, and thymine nucleotides in the sequence, from the first to the current location.where nThe representation of the DNA sequence by cumulated phase maintains the chemical and structural information about original sequence ,4. The pThis fact points to the suitability of the alignment techniques to assess the similarity of sequences. The classical symbolical methods for reconstruction of the similarity diagram from the set of sequences employ the global multiple sequence alignment. These techniques find local similarity in equal positions in sequences and thus are errors inclinable. An approach based on evaluation of similarity between complete signals is expected to be more robust. The resulting distance between genes depends on a trend of each curve.The dynamic time warping seems suitable for adjustment of derived genomic signals. DTW originally serves for processing of digital signals sampled at defined time instances. In genomic signals, time instances are represented by indexes of nucleotides. The signals based on cumulated phase carry not only useful information, but also noise. Genomic signals preprocessing is necessary to accentuate the position information.The preprocessing of genomic signals consists of four steps. The aim is to obtain size adjusted signals suitable for time alignment or, in our case the signals with adjusted size of phase suitable for sequence position alignment. In the first step, the genomic signals were filtered by a simple median filter with a window size of four samples. This signal modification ensures that the values of individual samples do not affect the similarity comparison, but only the significant trend in the signal.s) of the signal was set with respect to preserve 99.5 % of signal spectral energy.One of the main disadvantages of the symbolic sequence alignment is the requirement to compare all positions. Alignment of the signal representation of genes compares the common segments. Thus, we need to keep only the important components of the signal and we do not need all samples. The second step of preprocessing consists in resampling of signals. The resampling (downsampling) depending on spectral distribution of signal components represents the second stage of preprocessing. The ratio of resampling was estimated based on the power spectrum of genomic signals. The downsampling factor was set to the value of 10. The new sampling frequency  step of genomic signals preprocessing. The estimation of polynomial trend and resulting signal after its removal is shown in Figure Three signals from Figure The dynamic time warping is mostly used for the speech analysis . The samWe know that ACTA1 protein sequences have 100 % consensus in amino acids. The differences between organisms are only in sequence segments of gene, which are not translated to protein i.e. introns. These segments have dynamic position in sequences; therefore it is necessary to use the methods of dynamic programming, such as DTW. The principle of biological signal alignment using DTW is shown in . This tewhere D symbolizes accumulated distance and d is a value of pairwise distance. The value of accumulated distance D  is determined by pairwise distance d  and minimum from the previous values of accumulated distances. This set of accumulated distances for each pair of samples forms a table. The results sequence warping is derived on the basis of minimization of the backward way from the right upper corner to the left lower corner.The application of the DTW on genomic signals is shown in Figure The proposed method is based on alignment of each pair of genomic signals. The described genomic signals preprocessing in combination with a pairwise alignment by the DTW allows mutual adaptation of signals pairs. The resulting genomic signals have generally different lengths than the both original signals.The similarity of two adapted signals is determined by their Euclidean distance normalized to the length of aligned signals. The distance matrix for cluster analysis is constructed from the mutual similarity values calculated for each pair of signals adapted by the DTW. The distances were normalized to the range <0,1>, because the level of signals pairwise similarity does not have any physical meaning for evolutionary relationships in final dendrogram. These normalized values reflect only the mutual similarity of the set of genomic signals without information about length and amplitude of genomic signals, which is desirable.The result of our new approach for sequence similarity analysis is represented by the dendrogram reconstructed from 10 genomic signals of ACTA1. The same dendrogram or phylogenetic tree was reconstructed from the same 10 ACTA1 in classical symbolic form. The method UPGMA (Unweighted Pair Group Method with Arithmetic Mean) was used for phylogenetic tree reconstruction . It alloeuarchontoglires (supraprimates) and laurasiatheria is correct. The mammals' clustering in phylogenetic tree reconstructed by a classical phylogenetic method from symbolic records of sequences is not identical with this.The result trees are shown in Figure The robustness of trees is represented by operational taxonomic unit (OTU) Jackknife analysis . The staThe result values of OTU Jackknifing are evaluated in both trees. The topology of the tree reconstructed by our method Figure  will notThe utilisation of the proposed method for very different sequences (different genes with different lengths) could cause inappropriate setting of preprocessing parameters and thus errors in similarity evaluation. This problem is similar to setting of parameters of global multiple sequence alignment as scoring matrix or gaps penalties. Low computational load is the greatest advantage of the similarity analysis of DNA represented by genomic signals. Moreover, the signal processing time decreases exponentially with increasing downsampling factor; this fact is presented in Figure The results show that the genomic signal processing should have an important place in DNA analysis. Our application of digital signal processing for the similarity analysis is only one of the possible solutions. The main principle of DNA sequences alignment using the genomic signals is an adequate variant to the symbolic DNA sequences alignment; in addition, it is robust, quick and more precise technique. The advantage of alignment of the whole joint sections in signals, not only one position, suggests the use for finding the common motifs or the coding segments. Moreover, the signal character is so specific that the decoding of his features can bring a new perspective on the issues of content and coding of DNA sequences.The authors declare that they have no competing interests.HS, MV and IP conceived the project and wrote the manuscript. HS implemented the algorithm and evaluated the results. MV designed the blocks of signal preprocessing. IP supervised the work. PB and RK ensured the biological aspects of the project. All authors read and approved the final manuscript.


Protein structures can be reliably predicted by template-based modeling (TBM) when experimental structures of homologous proteins are available. However, it is challenging to obtain structures more accurate than the single best templates by either combining information from multiple templates or by modeling regions that vary among templates or are not covered by any templates.ab initio method. This TBM method is based on “Seok-server,” which was tested in CASP9 and assessed to be amongst the top TBM servers. The accuracy of the initial core modeling is enhanced by focusing on more conserved regions in the multiple-template selection and multiple sequence alignment stages. Additional improvement is achieved by ab initio modeling of up to 3 unreliable local regions in the fixed framework of the core structure. Overall, GalaxyTBM reproduced the performance of Seok-server, with GalaxyTBM and Seok-server resulting in average GDT-TS of 68.1 and 68.4, respectively, when tested on 68 single-domain CASP9 TBM targets. For application to multi-domain proteins, GalaxyTBM must be combined with domain-splitting methods.We introduce GalaxyTBM, a new TBM method in which the more reliable core region is modeled first from multiple templates and less reliable, variable local regions, such as loops or termini, are then detected and re-modeled by an ab initio modeling of variable regions can further enhance the model quality.Application of GalaxyTBM to CASP9 targets demonstrates that accurate protein structure prediction is possible by use of a multiple-template-based approach, and  Three-dimensional protein structures provide invaluable insights into the molecular basis of protein functions, and such insights are essential for rational design of molecules regulating these functions. Nowadays, in an increasing number of cases, it has become possible to model protein structures with acceptable accuracy by employing much less effort than that required in experimental methods. Progress in computational protein structure prediction has been boosted by methodological improvements in the technique called template-based modeling (TBM), which uses experimental structures of homologous proteins as templates. As biological sequence and structure databases expand continuously, TBM is expected to become an even more promising tool for practical molecular biology, pharmaceutical chemistry, and protein engineering problems .Template-based modeling, also called homology modeling or comparative modeling, generally consists of the following steps ,2: (1) iDespite recent progresses, there still remain challenges for each stage mentioned above. One of the important challenges is how to optimally combine information from multiple templates to build a single model when experimental structures of multiple homologues are available. Using multiple templates rather than a single template offers several obvious benefits: the possibility of including a better template increases, and the fraction of the target sequence covered by templates is extended -5. In adAnother challenge is to model structurally variable regions among templates or those regions not covered by any templates, which we call ULRs . Unless the target sequence is quite similar to those of the templates , the expected quality of template-based models could be limited by such regions. Moreover, such ill-conserved regions where sequence insertion/deletion occurs may not be the subject of typical TBM. Despite previous efforts, progress in modeling such regions seems to be rather limited . Since hab initio ULR modeling. Therefore, ULRs can be modeled in a more accurate framework structure, and the conformational search space for ULR modeling is also effectively reduced to the local regions. Related approaches that construct a reliable core and refine unreliable regions have been proposed previously [We recognize that the above 2 challenges are not independent of each other. For example, the performance of ULR modeling can be limited by the quality of the framework structure constructed from multiple templates ,11. We teviously ,13. The We call this new method GalaxyTBM, as it is based on the GALAXY molecular modeling package ,14-16. GAll components of the prediction pipeline were tested in the 9th critical assessment of techniques for protein structure prediction (CASP9) as a predictor named “Seok-server.” According to the official results of CASP9, Seok-server is recognized as one of the top 6 servers . Since tWe used a simple but effective rescoring strategy to select multiple templates from the homologues detected by HHsearch , as descOverall, top rankers obtained by the rescoring scheme were closer to the native structures of the target proteins than the HHsearch top rankers, when tested on the 68 single-domain CASP9 TBM targets. Different proteins ranked as top by rescoring in 19 out of the 68 cases, with an average improvement of 0.046 in TM-score. TM-score increased for 15 out of the 19 targets and decreased for the remaining 4 targets, with average increases of 0.072 and −0.033, respectively. A paired t-test for the TM-score changes for the 19 targets showed that the improvement is statistically significant, with a P-value of 0.0072.As can be seen from Figure -10 . To assess the improvement achieved by using multiple templates, model structures built from the multiple templates were compared with those built from the single top template (after rescoring) Figure A and tho0 Figure B. The avBy using the current multiple template approach, GDT-TS improved when compared to the values obtained using the single-template approach (the sum over 68 domains increased by 3.4% from 4429.3 to 4580.9 with an average improvement of 2.23 per domain) and the naïve multiple-template method (the sum increased by 3.8% from 4412.7 to 4580.9 with an average improvement of 2.47 per domain). The GDT-TS improvement is statistically significant, with P-values of 0.006 and 0.02, respectively. Improvement over the naïve method was prominent when high-ranking proteins by HHsearch have diverse structures, implying that the current multiple-template selection scheme that excludes dissimilar structures is fairly successful. For example, for T0539, mean GDT-TS of generated models is 75.59 and 59.14 by the current approach and by the naïve approach, respectively. Similar type of large GDT-TS improvement of > 5 was also found in T0532, T0552, T0559, T0614, and T0643.To determine whether the model improvement by the multiple-template approach is a consequence of covering more residues by additional templates, we checked whether a similar improvement was found for core regions Figure . The corIn conclusion, the current multiple template selection method contributes to improving the core structure by utilizing useful information from additional templates selected by the current pipeline.In GalaxyTBM, model building is performed by the MODELLER-CSA  module iAs in the previous subsection, 100 model structures were generated for each target. Overall, model building by MODELLER-CSA improved the sum of GDT-TS by 0.6% (from 4580.9 to 4622.2) compared to MODELLER, with a P-value of 0.002. Average GDT-TS improvement was 0.13 for the 25 targets for which single templates were used and 0.87 for the 43 targets for which multiple templates were used. The better GDT-TS improvement in the multiple-template cases can be explained by the fact that the more complex target restraint functions for the multiple-template problems can be better optimized with the more rigorous optimization method .et al.[In addition to the backbone structure quality, the side-chain structure quality was also improved by the better optimization during model building. The χ1 accuracy  was improved in 65 out of 68 targets, with an average improvement of 5.9%. The χ1 + χ2 accuracy  was also improved . This improvement is consistent with the findings of the previous report by Joo et al..To illustrate the effects of the overall multiple-template strategy in more detail, the relationship between the model quality improvement and the template quality improvement achieved by the use of multiple templates is demonstrated in Figure The above analysis indicates that the positive effects of using multiple templates can be maximized by the current template selection strategy that considers core structure consensus and the more rigorous optimization during model-building, and the common adverse effects caused by including inconsistent templates in typical multiple-template methods can be minimized by use of such a combination.Here we present the results of the final stage of the pipeline, i.e., refinement of ULRs. A total of 204 ULRs (56 termini and 148 loops) were detected in the initial stage, and 132 ULRs were finally subject to reconstruction following the selection rule described in METHODS. These reconstructed ULRs consisted not only of the regions that were not aligned to any template residues but also of the regions that were structurally inconsistent among templates.Of the 132 reconstructed ULRs, 45 ULRs corresponded to the regions in which more than half of the residues are disordered in experimental structures and thus were neglected in the following analysis. In Figure Template selection and multiple sequence alignment take a few minutes on a single core. The median time required for model building with MODELLER-CSA and refinement was 6.2 and 1.1 hours, respectively, when 32 cores were used in parallel.ab initio loop or terminus modeling in the fixed framework of the core structure. The current multiple-template strategy maximizes the positive effects of using multiple templates by selecting complementary multiple templates that do not contaminate the information from the best template significantly and by thorough optimization of possibly conflicting template restraints during model building. When model refinement by detection and re-building of unreliable loop or terminus regions is applied, additional improvement in model quality is observed. Several sound elements of the current strategy, such as template rescoring, multiple-template selection based on core-structure alignment, and multiple sequence alignment of core sequences could be easily incorporated into other TBM methods to enhance their performance.In this article, we report a new TBM method—GalaxyTBM—that builds reliable core structure from multiple templates and reconstructs unreliable regions by The overall modeling procedure by the GalaxyTBM pipeline is shown in Figure S expressed as a weighted sum of the Z-score of the sequence similarity score, Zseq, and that of the secondary structure similarity score, ZssMultiple templates were selected by rescoring the results of HHsearch (version 1.5.0) , one of w depends on the target difficulty estimated by the HHsearch probability for the top ranker, p, aswhere the raw sequence and secondary structure similarity scores were taken from HHsearch results. The weight factor The probability bins and the corresponding weight factors for rescoring were determined by maximizing the qualities of the top templates for the CASP8 TBM targets using a grid search in pre-set ranges of the parameters.S within 95% of the top ranker’s score) and low-rankers (the remaining ones). Second, those proteins that had dissimilar structures from a “background pool” of structures were removed. The background pool consisted of either the high-rankers or top 3 rankers, whichever was the greatest. The similarity of a protein structure to the background pool was measured by the mean TM-score from the pool structures, and the proteins that had lower similarity than the cut-off value, mpool and α was set to 1 for the high-rankers and to the ratio of the protein’s S score to that of the top ranker for the low-rankers. When calculating TM-score between 2 protein structures, only the residues aligned to the target sequence by HHalign were considered, and the target sequence length was used as the reference length. Finally, proteins dissimilar from the top ranker, with TM-score < 0.5, were removed [Multiple templates were then selected from the 20 top-ranked proteins as follows. First, the top 20 proteins were divided into high-rankers (those with the score  removed , where tab initio refinement stage. By neglecting those regions, the alignment effort was focused on the more reliable core region, increasing the possibility of generating a more reliable model structure for the core.Alignment between the target sequence and the template sequences was generated using PROMALS3D , one of Using the template structures and the MSA as input, a template-based model was constructed with the MODELLER-CSA  module, In the final stage, the single best template-based model structure was extensively refined by GalaxyREFINE , a high-de novo by FALC [In the current application of GalaxyREFINE to the model refinement in GalaxyTBM, a few modifications were made to enhance the computational efficiency over that of the original version used in CASP9. First, ULRs detected by the model consensus method  were sub by FALC  in CASP9P-values were obtained from paired two-tailed Student’s t-test.The authors declare that they have no competing interests.All authors conceived of the study together. JK developed the template-based modelling method, wrote the scripts for the prediction pipeline, and drafted the manuscript. HB developed the refinement method and helped to draft the manuscript. CS participated in the design and coordination of the study and helped to draft the manuscript. All authors read and approved the final manuscript.


Clustering of unannotated transcripts is an important task to identify novel families of noncoding RNAs (ncRNAs). Several hierarchical clustering methods have been developed using similarity measures based on the scores of structural alignment. However, the high computational cost of exact structural alignment requires these methods to employ approximate algorithms. Such heuristics degrade the quality of clustering results, especially when the similarity among family members is not detectable at the primary sequence level.all possible sequence alignments and all possible secondary structures, whereas the existing methods only use one optimal sequence alignment and one optimal secondary structure. We demonstrate that this strategy can achieve the best balance between the computational cost and the quality of the clustering. In particular, our method can keep its high performance even when the sequence identity of family members is less than 60%.We describe a new similarity measure for the hierarchical clustering of ncRNAs. The idea is that the reliability of approximate algorithms can be improved by utilizing the information of suboptimal solutions in their dynamic programming frameworks. We approximate structural alignment in a more simplified manner than the existing methods. Instead, our method utilizes http://bpla-kernel.dna.bio.keio.ac.jp/clustering/.Our method enables fast and accurate clustering of ncRNAs. The software is available for download at  A groupfamilies ,6.i.e., structural alignment); thus, the obtained alignment score can be a suitable choice for a similarity measure. However, the original Sankoff algorithm is too time-consuming to deal with an all-against-all comparison of many sequences required in clustering procedures. To address this problem, similarity measures based on the approximation of the Sankoff algorithm have been proposed, and shown to be applicable to hierarchical clustering [et al. [et al. [et al. [Accurate clustering of ncRNAs needs a reliable similarity measure that takes into account primary sequences and secondary structures. Given a pair of sequences without known structures, the Sankoff algorithm  simultanustering -10. Each [et al.  have dev [et al.  have dev [et al.  that dynAlthough the approximate Sankoff-style algorithms have enabled similarity measures based on structural alignment, the quality of clustering results has not been so high. In the previous studies ,8,12, reone optimal structural alignment. This means that these methods ignore the scores of suboptimal structural alignments, and only use one optimal sequence alignment and one optimal secondary structure. In contrast, Stem kernel sums up the scores of structural alignments allowed in the approximate Sankoff-style algorithm, incorporating a subset of sequence alignments and a subset of secondary structures. Thanks to this strategy, Stem kernel gives comparable clustering results to LocARNA, while employing the more reduced dynamic programming matrix. These observations suggest the possibility that we can design a more reliable similarity measure by utilizing all possible sequence alignments and all possible secondary structures. This is not trivial because if we naively try to incorporate all possible structural alignments, it will require the full-size dynamic programming matrix used in the original Sankoff algorithm with the prohibitive computational cost.To improve the reliability of the approximate Sankoff-style algorithms, we focus attention on the information of suboptimal structural alignments. Among the existing methods, LocARNA and FOLDALIGN calculate the similarity based on the score of In this paper, we describe a new similarity measure for the hierarchical clustering of ncRNAs. We approximate the problem of structural alignment by the two separate problems: the prediction of sequence alignment, and the prediction of secondary structure for each sequence. For this purpose, the Sankoff algorithm for structural alignment is approximated by the combination of the Smith-Waterman (SW) algorithm  for sequWe demonstrate that our method can achieve the best balance between the computational cost and the quality of the clustering among the existing methods. In particular, our method can keep its high performance even when the sequence identity of family members is less than 60%.In this section, we propose a new method for measuring the similarity between two RNA sequences without known structures. The proposed method is applied to the hierarchical clustering of ncRNAs with the weighted pair group method with averaging (WPGMA) algorithm. Given a set of sequences, we calculate an all-against-all similarity matrix using our method. Then, we derive the distance matrix by one minus the similarity, and obtain the cluster tree by the WPGMA algorithm.all possible sequence alignments and all possible secondary structures separately from each of the two algorithms. First, we describe a similarity measure using the scores of all possible sequence alignments between two RNAs. Next, we design a scoring function for these alignments using all possible secondary structures of each of the two RNAs.The idea of our similarity measure is to approximate the Sankoff algorithm for structural alignment by the combination of the SW algorithm for sequence alignment, and the McCaskill algorithm for secondary structures. This approximation allows to utilize the ensembles of all possible sequence alignments rather than one optimal sequence alignment.To measure the similarity between two RNAs, one common approach is to perform pairwise alignment, and to calculate its alignment score. The Sankoff algorithm simultaneously models sequence alignments and secondary structures, and is extremely time-consuming. Therefore, we first approximate the Sankoff algorithm by the SW algorithm that only models sequence alignments apart from secondary structures. Although this is a strong approximation, we attempt to improve the reliability by utilizing x, we denote its length by |x|. For each position 1 ≤ i ≤ |x| in x, we denote the nucleotide by ix∈ {A, C, G, U}.For an RNA sequence x and y, let Πxy be the set of all possible sequence alignments in the SW algorithm. Let πxy denote one particular sequence alignment in Πxy.For two sequences, x and y by accumulating the alignment score of πxy over Πxy. For this purpose, we employ local alignment (LA) kernel [We calculate the similarity between ) kernel  defined β ≥ 0 is a parameter, and Score(πxy) is the alignment score of πxy under a given scoring scheme . In practice, we take the logarithm of LA kernel, and similarity values are normalized to range from 0 to 1:where LA kernel (1) can be computed by the variant of the SW algorithm as follows:Initialization:for i ∈ {0,…, |x|} and j ∈ {0, …, |y|} doM = XI = YI = XT = YT = 0M = XI = YI = XT = YT = 0end forIteration:for i ∈ {1,…,|x|} and j ∈ {1,…,|y|} doM = eβSxy + YI + M)XI = βgMe + βdIXeYI = βge + XI) + βdIYeXT = M + XTYT = M + XT + YTend forTermination:K = 1 + XT + YT + Mg and d are the penalties for gap opening and gap extension, respectively, and Sxy is a scoring function for matching the i-th position in x and the j-th position in y. The design of Sxy impacts the performance of the resulting similarity measure, and will be described later.where the parameters O(|x||y|) time. If we use the exact Sankoff algorithm instead, it takes prohibitive O(|x|3|y|3) time, which is not practical. In the case of the approximate Sankoff-style algorithms employed in the existing methods, all possible sequence alignments cannot be incorporated to the reduced dynamic programming matrix. Therefore, LA kernel based on the SW algorithm is an efficient way to deal with the ensemble of all possible sequence alignments.At this point, we note that our method can take into account all possible sequence alignments in Sxy for LA kernel, we need secondary structures of x and y. As mentioned above, the Sankoff algorithm models secondary structures simultaneously with sequence alignments which we have already modeled by the SW algorithm. Therefore, we next employ the McCaskill algorithm that only models secondary structures apart from sequence alignments. Although this is an additional approximation, we attempt to improve the reliability by utilizing all possible secondary structures rather than one optimal secondary structure.To design a scoring function x, let Θx be the set of all possible secondary structures. Let θx denote one particular secondary structure in Θx. We represent a secondary structure as a set of binary variables θx = {θx}1≤i<j≤|x|, where θx = 1 means that the i-th position and the j-th position in x form a base pair. For each position 1 ≤ i ≤ |x| in x, we represent the state of base-pairing using three kinds of binary variable: Lx(i) = ∑ j:j>i θx = 1 means that a base pair is formed with one of the downstream positions; Rx(i) = ∑ j:j<i θx = 1 means that a base pair is formed with one of the upstream positions; and Ux(i) = 1 – Lx(i) – Rx(i) = 1 means that the position is unpaired. Given a fixed pair of secondary structures, θx and θy, we can measure the similarity between the i-th position in x and the j-th position in y using their state of base pairing:For an RNA sequence Wxy = α (Lx(i)Ly(j) + Rx(i)Ry(j)) + s Ux(i)Uy(j), (3)α ≥ 0 is a weight parameter for structural similarity, and s is a substitution matrix for RNA sequences like the RIBOSUM 85-60 matrix [α when both of the two positions form a base pair with one of their downstream positions, respectively; it takes α when both of the two positions form a base pair with one of their upstream positions, respectively; and it takes s when both of the two positions are unpaired.where 0 matrix . This scP(θx|x) over Θx. The binary variables θx and {Lx(i), Rx(i), Ux(i)} are converted to the probabilities by taking the expectation over Θx. For θx, we obtain a base-pairing probability Px that the i-th and the j-th positions form a base pair:The McCaskill algorithm defines a probability distribution Lx(i), Rx(i), Ux(i)}, we obtain three kinds of probability that the i-th position is paired with one of the downstream/upstream positions, or unpaired, respectively:For {Sxy by taking the expectation of (3) over Θx and Θy:We design a scoring function The proposed method is obtained by combining the normalized LA kernel (2) with the scoring function (4).O(|x|3 + |y|3) time, thanks to the McCaskill algorithm. Just as in all possible sequence alignments, the exact Sankoff algorithm results in O(|x|3|y|3) time, and the existing methods cannot incorporate all possible secondary structures. Our method requires O(|x||y|) + O(|x|3 + |y|3) time in total, which is more efficient than the exact Sankoff algorithm. Therefore, our strategy that combines the SW algorithm and the McCaskil algorithm allows to utilize the ensemble information with the reasonable computational cost.It should be noted that our method can take into account all possible secondary structures in The scoring function (4) proposed in this study is similar to the scoring function used in BPLA kernel ,19. BPLALC, RC, and UC. These coefficients take large values when the probabilities where α = 1.0, β = 0.1, g = –27, and d = –0.1Because of the resemblance between the scoring functions, (4) and (5), we set the parameters of the proposed method as used in BPLA kernel: In this section, we examine the performance of the proposed method in the hierarchical clustering of ncRNAs.We compared our method with the state-of-the-art methods developed for the hierarchical clustering of ncRNAs: LocARNA v1.5.2 , FOLDALIall possible sequence alignments and all possible secondary structures. LocARNA and FOLDALIGN only use one optimal sequence alignment and one optimal secondary structures. Stem kernel utilizes a subset of all possible sequence alignments and a subset of all possible secondary structures. CLUSTALW and LA kernel ignore secondary structures; CLUSTALW only uses one optimal sequence alignment, while LA kernel utilizes all possible sequence alignments.We can summarize our method and the existing methods as follows. Our method utilizes We created a dataset as summarized in Table We produced three versions of dataset. First, we used ncRNA sequences without modification, and named them the “normal” dataset. Second, we concatenated random sequences to both ends of ncRNA sequences, and named them the “plus flanking regions” dataset. This dataset was intended to simulate the situation where we do not know the exact boundaries of unannotated transcripts. A random sequence was generated from a ncRNA sequence so that it had the quarter length and the same dinucleotide contents. Third, we added false reference clusters, each of which contains one random sequence, and named them the “plus unrelated sequences” dataset. This dataset was intended to simulate the situation where non-functional ncRNAs arise from transcriptional noises. Therefore, we evaluated whether a false reference cluster could be a resultant cluster with a single member. We used a quarter number of false reference clusters compared to true reference clusters. A random sequence was generated from a ncRNA sequence so that it had the same length and the same dinucleotide contents.TP) was defined as the number of sequence pairs that belong to the same reference cluster and are correctly assigned to the same resultant cluster. Analogously, the numbers of false positives (FP), true negatives (TN), and false negatives (FN) are defined, respectively, by counting the pairs from different reference clusters but the same resultant cluster, the pairs from different reference clusters and different resultant clusters, and the pairs from the same reference cluster but different resultant clusters. The ROC analysis was performed by plotting true positive rates TP/(TP + FN) versus false positive rates FP/(TN + FP) for different distance thresholds. The quality of the clustering was measured by the area under the ROC curve (AUC). We measured the total time for computing similarity matrices on a 2.53 GHz Intel Xeon processor.We evaluated the overall quality of the cluster tree by the ROC analysis proposed in .  because these methods only use Figure Next, we evaluated the quality of the clustering for the “plus flanking regions” dataset Figure , and theAs described in Methods, the proposed method has the theoretical advantage compared to BPLA kernel, which can be regarded as a variation of our method. To verify this point experimentally, we compare the proposed method and BPLA kernel using the scoring functions (4) and (5), respectively.Figure Finally, we evaluated the computational cost of the similarity measures using three version of the dataset Table . Our metone optimal solution in their approximate Sankoff-style algorithms, there was a trade-off that LocARNA was faster but less accurate than FOLDALIGN (Figure subset of solutions in the more approximate Sankoff-style algorithm, partly improved this problem, being faster and more accurate than LocARNA. Our method, which utilizes all possible solutions in the combination of the Smith-Waterman algorithm and the McCaskill algorithm, successfully overcome the trade-off. These results suggest that our strategy is essential to enable fast and accurate clustering of ncRNAs.In the design of the proposed method, our idea was to improve the reliability of approximate algorithms by the information of suboptimal solutions in their dynamic programming frameworks. Among LocARNA and FOLDALIGN, which only use N Figure . Stem keWe have described a new method for the hierarchical clustering of ncRNAs, which can be applied to the identification of novel ncRNA families. Our method can achieve the best balance between the computational cost and the quality of the clustering compared to the existing methods.one optimal structural alignment, suffer from the trade-off between time-consuming accurate algorithms and fast approximate algorithms. Our similarity measure, which is designed to utilize all possible sequence alignments and all possible secondary structures, have overcome this problem. The improvement is especially remarkable when the similarity among family members is not detectable at the primary sequence level.The performance of the clustering is determined by similarity measures based on the scores of structural alignment. The existing similarity measures, which only use In conclusion, our method enables fast and accurate clustering of ncRNAs, providing a promising way to explore the functional diversity of ncRNAs.The authors declare that they have no competing interests.Y Saito and KS developed the algorithm and wrote the code. Y Saito performed the experiments and drafted the manuscript. Y Sakakibara initiated and coordinated the project. All authors have read and approved the final manuscript.


Multiobjective sequence alignment brings the advantage of providing a set of alignments that represent the trade-off between performing insertion/deletions and matching symbols from both sequences. Each of these alignments provide a potential explanation of the relationship between the sequences. We introduce MOSAL, a software tool that provides an open-source implementation and an on-line application for multiobjective pairwise sequence alignment. Sequence alignment is in the core of many bioinformatics applications. It aims to identify regions of similarity in sequences of biological data, such as nucleotide and amino acid residues. The procedure consists of inserting gaps between the residues so that similar symbols from several sequences become aligned. For two sequences, dynamic programming algorithms can compute the optimal alignment in an efficient manner . HoweverAny of these approaches rely on the a priori definition of coefficients that are assigned to the components of the score function. These weights are usually defined by default in most of the software packages for sequence alignment and are usually not modified by the practitioner. However, there is a considerable disagreement about how to weight each coefficient. A small change in the weights can lead to a completely different alignment.the Pareto optimal alignment set.One way of overcoming the problem of setting weights is to consider a multiobjective formulation, where the practitioner is provided a set of optimal alignments representing the trade-off between components of the score function, for instance, substitution score given by a substitution matrix and the number of gaps; in this case, an alignment is optimal if there is no other alignment with better substitution score value and lesser number of gaps. Usually, there is not only one optimal alignment but several for which this notion of optimality holds; such set of all optimal alignments is called Under a multiobjective formulation, no weights are needed to be set up. Moreover, according to a classical result in the multiobjective optimization field , this opA multiobjective approach to pairwise sequence alignment has been explored by several researchers, both from a problem formulation and algorithmic point of view -11. Recehttp://mosal.dei.uc.pt and physically located at the Department of Informatics Engineering, University of Coimbra, and is one of the outcomes of a national funded research project on multiobjective sequence alignment.MOSAL is a software tool that results from the problem formulation given in  with theC and provided under a GNU General Public License. A makefile is available for compilation under GNU/Linux. The implementation can be setup for several multiobjective score functions as described in [The code is written in ribed in : maximizSpeed-up techniques described in  are alsoThe command line options available are described in Table The web-server provides also an on-line application, written in PHP, that is available for sequences up to 2000 symbols. Four steps are needed to produce the set of Pareto optimal alignments: •Insertion of each sequence in FASTA format in a text box. The user can choose either Protein or DNA type of sequence in a switch button.•Choice of the score function with switch buttons. The user can choose either matches or substitution score for the first score function component and either indels or gaps for the second score function component. If substitution score is chosen, the user can choose a substitution score matrix  or can even provide one in a predefined text format.•Choice of the sequence alignment options: with or without the alignments and with or without pruning technique. If pruning is chosen, the number of bounds must be provided (10 is given by default). The option without alignment provides only the score function values of the alignments.•Submit to the server, with the option of sending an e-mail to the user with the output files.Once the Pareto optimal alignment set is computed, the score function values are shown in an iterative plot; the user can zoom and choose a given point to see the corresponding alignment, see Figure http://www.bioinformatics.org/sms2/) is also applied here to allow the identification of potential regions of interest in the several alignments.A visualization tool in the on-line application allows to visualize all the alignments and the corresponding score function values produced by the implementation or by the on-line application. The coloring scheme used in the Sequence Manipulation Suite (see MOSAL provides a set of tools for the practitioner to perform a more in-depth analysis on the relation between a pair of biological sequences. The multiobjective formulation that is explored by the framework provides further insight into the confidence of the alignments obtained by common methods; for instance, a large number of optimal scores suggests that a single alignment may be insufficient to understand the relation between the sequences and that further investigation is required. Moreover, the output can be used to construct phylogenetic trees as suggested in .The authors declare that they have no competing interests.LP is the principal investigator of the project, PM implemented the application in the web-server, MA developed the problem formulation and algorithms, MP tested and suggested improvements in the framework. All authors read and approved the final manuscript.


The importance of pairwise protein structural comparison in biomedical research is fueling the search for algorithms capable of finding more accurate structural match of two input proteins in a timely manner. In recent years, we have witnessed rapid advances in the development of methods for approximate and optimal solutions to the protein structure matching problem. Albeit slow, these methods can be extremely useful in assessing the accuracy of more efficient, heuristic algorithms. We utilize a recently developed approximation algorithm for protein structure matching to demonstrate that a deep search of the protein superposition space leads to increased alignment accuracy with respect to many well-established measures of alignment quality. The results of our study suggest that a large and important part of the protein superposition space remains unexplored by current techniques for protein structure alignment. Pairwise protein structure alignment is one of the most important problems in computational molecular biology. At the same time, protein structure alignment is a very difficult problem, due to an infinite number of possible ways to position a pair of proteins in the three-dimensional space. Because of the enormous size of the search space, the research into protein structure alignment has been traditionally focused on the development of methods with better objective functions, that explore a relatively small but representative set of proteins' spatial superpositions.In this paper, we take a different approach and study the benefits of searching proteins' superpositions in a more detailed manner. We demonstrate significant increase in the alignment accuracy of several well-known distance-based alignment methods, obtained by utilizing the superpositions that rigorously optimize a very simple and intuitive alignment metric, defined as the largest number of residues from the input proteins that can be fit under a predefined distance cutoff. The size of gap between the accuracy of current heuristic solutions and optimal solutions, observed in this study, suggests that the protein structure alignment problem will likely remain a hot topic in years to come.Sisyphus and FSSP. In both benchmarks, an in-house algorithm, MaxPairs [CA ≤ d, which is defined as the largest number of pairs of residues from the input proteins that can be fit under d Ångströms. MaxPairs algorithm is based on the approximation algorithm EPSILON-OPTIMAL [d + ε as an optimal superposition fits under the distance d, for any accuracy threshold ε > 0. As an approximation algorithm, EPSILON-OPTIMAL suffers from high computational complexity. The algorithm's run time is a high degree polynomial in the lengths of the structures being compared. To circumvent high computational cost, the present study utilizes MaxPairs—a heuristic version of EPSILON-OPTIMAL that searches through a relatively small subset of the space of all superpositions of the input proteins inspected by EPSILON-OPTIMAL. While still not practical, as demonstrated in [d = 3 Å and the accuracy threshold to ε = 1. Going below ε = 1 proves to be computationally prohibitive with our computing infrastructure.Our study is carried out using two protein structure alignment benchmarks: MaxPairs , is appl-OPTIMAL , which irated in , MaxPairCA ≤ d. We evaluated the performance of three well-known methods for protein structure comparison, STRUCTAL –4, TM-alIt is important to emphasize that our experiment is not designed to compare these three methods head-to-head, but rather to assess the extent of improvements in the accuracy of each method that can be made by exploring the search space in a more thorough manner. In choosing the methods for our study, we only considered the availability of software and the simplicity of implementing the alignment scoring functions (see the Results section). An overview of the three algorithms is given below.cRMS score with the lengths of aligned regions. In each iteration, the algorithm computes an optimal residue-residue correspondence  of the input proteins a =  and b =  and then finds a superposition that minimizes cRMS of the aligned subchains  and . The cRMS score is given byThe STRUCTAL algorithm –4 employp of a and q of b, along with the rigidly transformed protein b, denoted by Gp,q denotes the total number of gaps in the alignment. The STRUCTAL program used in our analysis was downloaded from http://csb.stanford.edu/levitt/Structal/.The alignment step in STRUCTAL is carried out using a dynamic programming routine, which implements the following recurrence formula:L is the length of the shorter structure [http://zhanglab.ccmb.med.umich.edu/TM-align/.TM-align is another popular protein structure alignment program, widely used in many applications, in particular for assessing the quality of protein models generated by comparative modeling or abinitio techniques. The score matrix in TM-align is protein-length specific and is defined asS=11S=11RMSD between aligned subchains of the input proteins, using the threshold distance of 3 Å for atomic superposition. Rigid body motions for RMSD minimization are realized using quaternion transformations [LOCK2  is an imrmations , 10.air are bir each other's nearest neighbors. More specifically, for every r ∈ {1,…, k}, the point bir is the closest point in protein b to the point air and vice versa. The final alignment is generated through a two-step process. First, for every atom ai from protein a, the algorithm finds the nearest atom from protein b that is at distance ≤3 Å from ai. In the second step, the algorithm selects the maximum number of aligned pairs in sequential order, by removing pairs that violate colinearity.The alignment returned by LOCK2 is a sequence of pairs of pointshttp://lock2.stanford.edu.The LOCK2 software can be downloaded from Sisyphus test [http://sisyphus.mrc-cpe.cam.ac.uk. The hus test  is frequhus test , 12. ThiSisyphus test set, containing 106 alignments between single-chain proteins. The two-step process is illustrated in Sisyphus set. These alignments are then compared to the reference (“gold-standard”) alignments to compute the percentage of correctly aligned residue pairs [In present study, we  utilizeue pairs .In the second step, the MaxPairs algorithm is run to compute the set of (near-)optimal superpositions, namely, the superpositions that rigorously maximize the number of pairs of atoms that can be fit under 3 Å. We used our own implementations of the STRUCTAL, TM-align, and LOCK2 alignment procedures to compute optimal residue-residue correspondence  between the newly superimposed proteins. The percentage agreement with reference alignments is recorded again and compared to the agreement obtained in the first step.Sisyphus test is defined as a function of the magnitude of the alignment error. More specifically, for the alignment tolerance shift s, the agreement is defined as Is/Lref, where Is is the number of aligned residues that are shifted by no more than s positions in the reference alignment and Lref is the length of the reference alignment [s = 0).The agreement with reference alignments in the lignment . The perThe dashed lines in Figures The increase in number of correctly aligned residues, obtained by switching to MaxPairs superpositions, varies from one pair of structures to another Figures , and 7. A more detailed analysis shows that, when MaxPairs superpositions are used, the number of residue pairs correctly aligned by STRUCTAL increases by more than 10 for 31 out of 106 test pairs. The corresponding number of test pairs for which the same magnitude of increase is observed for TM-align and LOCK is 14 and 13, respectively. For comparison, original STRUCTAL superpositions have such an advantage only in 3 out of 106 test pairs. For TM-align and LOCK, the corresponding numbers are 5 and 4.Sisyphus test. A slight accuracy advantage of algorithms such as Matt [The value added by the deep search of superposition space makes some of the methods analyzed here comparable to the best to date methods evaluated in the  as Matt , PPM [14 as Matt  is due tOur second benchmarking set utilizes 183 representative pairs of proteins, related at various levels according to FSSP structural classification . This teSisyphus benchmark, which compares alignments returned by automated methods to those generated by human experts, the alignment precision in the FSSP benchmark is assessed using a set of well-known alignment quality measures:d Ångströms from each other. We note that, unlike CA ≤ d, which is a globally optimal metric, representing the maximum number of pairs of residues in the superimposed structures that can be placed under d Ångströms, NumPairs(d) represents the method specific count of pairs of aligned residues at distance ≤d.NumPairs(d) represents the number of aligned pairs of residues in two proteins that are at distance ≤Similarity Index, denoted by SI, is defined as cRMS × min{L(a), L(b)}/Nmat, where Nmat is the number of aligned residues in proteins a and b and L(a) and L(b) are the lengths of a and b, respectively [cRMS score, used in the formula for SI, is computed based upon the method specific alignments.ectively . The cRMThe Percentage of Structural Similarity, PSI(d), is defined as NumPairs(d)/min{L(a), L(b)} .In contrast to As seen in The FSSP level-specific results of our benchmarking analysis are summarized in Tables The data used in Several examples illustrating the advantage of the deep search of superposition space are given in Figures While examples in Figures c · d as an optimal alignment fits under the distance d, for every fixed c > 1 [O(n8), where n denotes the protein length. An improved running time procedure for the same problem has also been published [d + ε as an optimal superposition places under the distance d. The asymptotic cost of EPSILON-OPTIMAL is O(n4) for globular and O(n8) for nonglobular proteins [Resent years have witnessed advances in the development of methods for approximate and exact solution to protein structure alignment problem. One of the first such methods is the Umeyama's algorithm for finding the transformation that gives the least mean squared error between two point patterns . Since ted c > 1 . This alublished . The EPSThe polynomial time approximation schemes (PTASs) have been designed for selected nonsequential protein structure alignment measures  as well Sisyphus benchmark, these superpositions increase the accuracy of alignments generated by STRUCTAL, TM-align, and LOCK2 by 11%, 7%, and 6%, respectively. An improvement of similar magnitude is seen after allowing for alignment errors (residue shifts). In the FSSP benchmark, the new superpositions increase NumPairs and PSI scores for STRUCTAL, TM-align, and LOCK2 by ~7%, ~5%, and ~13%, respectively. A particularly noticeable improvement is seen in the Similarity Index scores of alignments generated by LOCK2 (from 8.35 to 5.69). Although inefficient for large scale analysis, the algorithms for exact solution are indispensable tools for assessing the accuracy of more commonly used heuristic methods. The present study utilizes a set of precomputed superpositions to evaluate the improvements in accuracy of three well-known protein structure alignment algorithms, obtained by the deep search of the superposition space. In the We emphasize that our analysis provides an estimate of the lower bound on the difference between optimal and heuristic solution, since alignments generated by MaxPairs are not always optimal (in the strict sense).Finally, it is reasonable to expect that a more thorough exploration of the superposition space, coupled with the fragment-based alignment techniques, can be used to further improve the precision of methods based on sequences of local transformations, such as Matt , PPM 1414, and PA typical distance-based protein structure alignment method explores the space of proteins' spatial superpositions, computing an optimal residue-residue correspondence  each time a new superposition is generated. Because of the large search space, current methods for protein structure alignment must trade precision for speed and explore only a small but representative set of superpositions. We utilize an algorithm capable of finding an alignment of any specified accuracy to demonstrate significant increase in the alignment quality of solutions generated by three popular protein structure alignment methods, obtained through the deep search of the superposition space. The large lower bound on the size of gap between optimal and heuristic solutions, observed in this study, suggests that the protein structure alignment problem will likely remain an attractive research area throughout the next decade. ftp://ftp.ebi.ac.uk/pub/databases/fssp/).FSSP benchmark consisting of as set of 183 representative pairs of proteins extracted from the FSSP database (Click here for additional data file.


The Pharmacophore Alignment Search Tool (PhAST) is a string-based approach to virtual screening. Molecules are represented by linear sequences which describe their respective pattern of interaction possibilities. The problem of molecule linearization is tackled by applying Minimum Volume Embedding in combination with a Diffusion Kernel to the molecular graph ,2. LineaSignificance of chemical similarity was determined in form of p-values of global alignment scores, calculated in an approach that was adapted from its original application to local sequence alignments of protein sequences utilizing Marcov chain Monte Carlo simulation . BonferrPhAST was employed in two prospective applications: A screening for non-nucleoside analogue inhibitors of bacterial thymidine kinase yielded a hit with a distinct structural framework but only weak activity. Screenings for drugs that are not members of the NSAID  class as modulators of gamma secretase resulted in a potent modulator with clear structural distinction from the reference compound.