Finding large deletions in genome sequences has become increasingly more useful in bioinformatics, such as in clinical research and diagnosis. Although there are a number of publically available next generation sequencing mapping and sequence alignment programs, these software packages do not correctly align fragments containing deletions larger than one kb. We present a fast alignment software package, BinaryPartialAlign, that can be used by wet lab scientists to find long structural variations in their experiments. For BinaryPartialAlign, we make use of the Smith-Waterman (SW) algorithm with a binary-search-based approach for alignment with large gaps that we called partial alignment. BinaryPartialAlign implementation is compared with other straight-forward applications of SW. Simulation results on mtDNA fragments demonstrate the effectiveness (runtime and accuracy) of the proposed method. In bioinformatics, sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences . Next GeIn the Smith-Waterman algorithm, to find the optimal local alignment between a query and a reference sequence, a scoring system including a set of specified gap penalties is used. However, when a sequence subjected to a large deletion is used as a query sequence, its alignment with the reference is problematic because the query sequence must be first divided into two parts: the one before the deletion that we will refer to as the “former part” and the one after the deletion that we will call the “latter part” of the query . OtherwiThe paper is organized as follows. The classical SW method is explained in The Smith-Waterman (SW) algorithm  is an allformer and llatter denote the lengths of the former and the latter parts of the query sequence. Also let  denote the fragment from base position a to the base position b in the reference that best aligns with the former part of the query . Similarly, let  denote the fragment from base position c to the base position d in the reference that best aligns with the latter part of the query (c < d). For the sake of simplicity, let us assume b < c (and in fact b ≪ c for the large deletions). Then, it follows that  is the part of the sequence subjected to the deletion (and thus not visible in the query sequence). The length of the deletion can be defined asLet In We aligned the query pattern with basic SW to find these two fragments and the location of the large deletion. We used BLOSUM 62  as the sTo alleviate this problem in a most basic manner, we used SW in an incremental approach and we named this method “IncrementalPartialAlign”. This method takes four input parameters, query sequence, reference sequence, similarity ratio threshold, and minimum sequence length. After aligning the query, if the similarity ratio is found to be below the given threshold, considering that this can be due to the presence of a large gap , we try splitting the query into a former and a latter part in all possible ways. We start with the shortest possible former part, the length of which is determined by the minimum sequence length. For example, if the minimum sequence length parameter is 20, we take the first 20 bases of the query pattern. Starting with such a short former part results in a high similarity ratio, but then, we repeatedly increase its length (one by one) until the similarity ratio becomes smaller than the threshold value, at which position we assume that the deletion starts. Then we align the remaining (latter) part of the query pattern with the reference  as the IncrementalPartialAlign method does. Again, similarly, BinaryPartialAlign is also based on repetitive use of SW. However, unlike IncrementalPartialAlign, it shifts the boundary between the former and latter parts by more than one base in every iteration based on an approach that resembles binary search.2n). Given n elements to search within, the binary search method takes at most log2n iterations .The binary search is a fast way to search a key within a sorted array. Firstly we check the element in the middle. If the key is equal to that, the search is finished. If the key is less than the middle element, we perform a binary search for the key within the first half. Otherwise (if it is greater), we perform a binary search within the second half. This procedure is demonstrated for searching 96 in a sample integer sequence in lquery be the total length of the query; we start with a former part and a latter part of length lquery/2.After aligning the query, if the similarity ratio is above the given threshold, similar to IncrementalPartialAlign, we conclude that there is no deletion in this query and terminate the algorithm. Otherwise, in contrast to the IncrementalPartialAlign, we divide the query pattern into two equal length parts: first half is called the former part and the second half is called the latter part of the query as before. In other words, let Then, we align both parts separately and get two similarity ratios to compare with the given similarity ratio threshold. If both of them are above the threshold, we assume that deletion position is found and terminate the algorithm with the current former and latter parts as the output.If only one of the similarity ratios is greater than the threshold, we lengthen the part with the bigger similarity ratio (and thus shorten the other one) byi is the number of the current iteration . Then, we increase the length of the former part as its similarity ratio is above the threshold and it is below for the latter part. We obtain 30–10 splits this time. Then, the former part has a similarity ratio below the threshold, which means that the latter part is lengthened. Thus, we obtain 25–15 splits. Then procedure is iterated similarly and stops at 27–13 splits, a perfect partial alignment with EDPE = 0.2n) algorithm.When we aligned the query pattern with IncrementalPartialAlign, the alignment time was 187 msecs, which improves to 109 msecs with BinaryPartialAlign. If the query pattern is long and a large deletion occurred towards the end of the query, the alignment would take much more time with IncrementalPartialAlign; however, the BinaryPartialAlign method is not badly affected by neither the position of deletion or the length of the query as it is an O, which are shown in Sequence database searching is among the most important and challenging tasks in bioinformatics. One special case of sequence searching is when large deletions are present in the query fragments, which is called partial or large-gap alignment. Partial alignment has become a need in bioinformatics as they are associated with developmental and malformation disorders, emergence of complex genetic traits, and genome evolution. Although the best choice of sequence search algorithm is Smith-Waterman's, if a sequence is subjected to a large deletion, to find the deletion location with the classical Smith-Waterman (SW) algorithm is inconclusive. In order to handle this problem, one basic approach is to use SW for various splits of the query pattern repeatedly in a systematic, incremental way. This approach that we called the IncrementalPartialAlign method works better, but, for longer query patterns , the procedure would take much longer time as it has many more iterations of SW that are used. Therefore, we proposed the BinaryPartialAlign method based on the binary search idea. 2n) algorithm, the proposed BinaryPartialAlign is more robust to these factors. Considering the  alignment time and error in estimated deletion position, the BinaryPartialAlign method gives better results than both IncrementalPartialAlign and the classical SW. Despite the runtime of the IncrementalPartialAlign method is badly affected by the query length and where the deletion occurs within the query, being an O(loghttp://ce.istanbul.edu.tr/bioinformatics/PartialAlignment/. These tools will be beneficial to researchers for finding large deletions in investigating their role in the genetics of complex traits and in genome evolution.The executable application, a short user-manual, and the query sequences used for simulations are made publicly available on the site


After aligning a substring of the reference sequence against the high-quality prefix of a short read--the seed--an important problem is to find the best possible alignment between a substring of the reference sequence succeeding and the remaining suffix of low quality of the read--extend. The fact that the reads are rather short and that the gap occurrence frequency observed in various studies is rather low suggest that aligning (parts of) those reads with a single gap is in fact desirable.A wide variety of short-read alignment programmes have been published recently to tackle the problem of mapping millions of short reads to a reference genome, focusing on different aspects of the procedure such as time and memory efficiency, sensitivity, and accuracy. These tools allow for a small number of mismatches in the alignment; however, their ability to allow for gaps varies greatly, with many performing poorly or not allowing them at all. The libgapmis, a library for extending pairwise short-read alignments. Apart from the standard CPU version, it includes ultrafast SSE- and GPU-based implementations. libgapmis is based on an algorithm computing a modified version of the traditional dynamic-programming matrix for sequence alignment. Extensive experimental results demonstrate that the functions of the CPU version provided in this library accelerate the computations by a factor of 20 compared to other programmes. The analogous SSE- and GPU-based implementations accelerate the computations by a factor of 6 and 11, respectively, compared to the CPU version. The library also provides the user the flexibility to split the read into fragments, based on the observed gap occurrence frequency and the length of the read, thereby allowing for a variable, but bounded, number of gaps in the alignment.In this article, we present libgapmis, a library for extending pairwise short-read alignments. We show that libgapmis is better-suited and more efficient than existing algorithms for this task. The importance of our contribution is underlined by the fact that the provided functions may be seamlessly integrated into any short-read alignment pipeline. The open-source code of libgapmis is available at http://www.exelixis-lab.org/gapmis.We present  The problem of finding substrings of a text similar to a given pattern has been intensively studied over the past decades, and it is a central problem in a wide range of applications, including signal processing , informat that are similar to a pattern x. It consists of producing the positions of the substrings of t that are at distance at most k from x, for a given natural number k. For the rest of this article, we assume that k <|x| ≤ |t|. We focus on online searching--the text cannot be preprocessed to build an index on it. There exist four main approaches to online approximate string matching: algorithms based on dynamic programming; algorithms based on automata; algorithms based on word-level parallelism; and algorithms based on filtering. We focus on algorithms based on dynamic programming. There mainly exist two different distances for measuring the approximation: the edit distance and the Hamming distance.Approximate string matching, in general, consists in locating all the occurrences of substrings inside a text The edit distance between two strings, not necessarily of the same length, is the minimum cost of a sequence of elementary edit operations between these two strings. A restricted notion of this distance is obtained by considering the minimum number of edit operations rather than the sum of their costs. The Hamming distance between two strings of the same length is the number of positions where mismatches occur between the two strings.Alignments are a commonly used technique to compare strings and are based on notions of distance  or of sigap is a sequence of consecutive insertions or deletions (indels) of letters in an alignment. The extensive use of alignments on biological sequences has shown that it can be desirable to penalise the formation of long gaps rather than penalising individual insertions or deletions of letters.A The notion of gap in a biological sequence can be described as the absence  of a fragment, which is  present in another sequence . Gaps ocA number of natural processes can cause gaps in DNA sequences: long pieces of DNA can be copied and inserted by a single mutational event; slippage during the replication of DNA may cause the same area to be repeated multiple times as the replication machinery loses its place on the template; an insertion in one sequence paired with a reciprocal deletion in one other may be caused by unequal cross-over in meiosis; insertion of transposable elements--jumping genes--into a DNA sequence; insertion of DNA by retroviruses; and translocations of DNA between chromosomes . The accre-sequencing--the assembly of a genome directed by a reference sequence. New developments in sequencing technologies .From Figure Example 1 (GapMis, aIn this section, we give a few definitions, generally following  and 7]..7].alphabet ∑ is a finite non-empty set whose elements are called letters. A string on an alphabet ∑ is a finite, possibly empty, sequence of elements of ∑. The zero-letter sequence is called the empty string, and is denoted by ε. The set of all the strings on the alphabet ∑ is denoted by ∑*. The length of a string x is defined as the length of the sequence associated with the string x, and is denoted by |x|. We denote by x[i], for all 1 ≤ i ≤ |x|, the letter at index i of x. Each index i, for all 1 ≤ i ≤ |x|, is a position in x when x ≠ ε. It follows that the ith letter of x is the letter at position i in x, and that x = x[1 .. |x|]. A string x is a substring of a string y if there exist two strings u and v, such that y = uxv. Let x, y, u, and v be strings, such that y = uxv holds. If u = ε, then x is a prefix of y. If v = ε, then x is a suffix of y.An x be a non-empty string and y be a string. We say that there exists an occurrence of x in y, or, more simply, that x occurs in y, when x is a substring of y. Every occurrence of x can be characterised by a position in y. Thus we say that x occurs at the starting position i in y when y[i .. i + |x| - 1] = x. It is sometimes more suitable to consider the ending position i + |x| - 1. The H Hamming distance δfor two strings of the same length, is defined as the number of positions where the two strings have different letters. A don't care letter is a special letter that does not belong to alphabet ∑, and matches with itself as well as with any letter of ∑. It is denoted by ★. A gap is a finite sequence of such don't care letters. A gap string is a finite, possibly empty, sequence of elements of the alphabet ∑ ∪ {★}. Two letters a and b of alphabet ∑ ∪ {★} are said to correspond (denoted by a ≈ b) if they are equal, or, if at least one of them is the don't care letter. The G-distance, denoted by Gδ, for two gap strings of the same length is defined as the number of positions in which the two strings possess letters that do not correspond. A gap string x is called single-gap string if there exist two strings u and v on alphabet ∑ and a gap g, such that x = ugv. Let conc(y') be an operation that, given a gap stringLet i y∈ ∑*, for all 0 ≤ i < n, and j g∈ {★}*, for all 0 ≤ j < n - 1, returns the string y = y0y1 ... yn-1, such that y ∈ ∑*.where approximate string matching with k-mismatches and a single gap problem can now be formally defined:The Problem 1 ( be a matrix, where G contains the minimum number of mismatches of the alignment between substring t[1 .. i] of t and substring x[1 .. j] of x allowing the insertion of a single gap either in t[1 .. i] or in x[1 .. j], for all 1 ≤ i ≤ n, 1 ≤ j ≤ m. For all 1 ≤ j ≤ m and 1 ≤ i ≤ n, we say that x[1 .. j] matches t[1 .. i] with at most k-mismatches and a single gap if and only if G ≤ k. Matrix G is defined by the following recurrence   , such thExample 3 ( , yields a solution since G ≤ 1 . Trivially, the inserted gap is in the pattern, and its length is 1. Finally, we can find the position of the inserted gap (position 5) using matrix H. Hence, a solution to this problem instance is the ending position 6 , since there exists a single-gap string x' = GGGT★A, with a gap g = ★, such that x = conc(GGGT★A), Gδ = 1, and |g| = 1.ample 4  Let t =cell H6,   by Proposition 1.Alternatively, we could compute matrix G and matrix H based on a simple ction or , for exalibgapmis was implemented in the C programming language. First, we start by describing the standard CPU version of the library. Thereafter, we discuss some technical issues regarding the SSE- and GPU-based implementations. Finally, we describe how the provided functions are extended to accommodate a variable, but bounded, number of gaps in the alignment.In this section, we give a brief description of the library implementation. APMIS was implemented as a function computing matrices G and H based on a simple alignment score scheme. The scheme uses the scoring matrix EDNAFULL gapmis isgapmis was able to complete the assignment up to 20× faster than needle. Although the asymptotic complexity of the two algorithms is the same, the number of arithmetic operations required by algorithm GAPMIS is substantially lower. This can be easily explained by examining the recurrence relations of the two algorithms. The version with the modifier -m 30 was always the fastest confirming our theoretical results. Note that, it only computes a narrow band in the dynamic-programming matrices ;• the SSE version with 4 threads  are 290 MCUP/s, 1.6 GCUP/s, 6.5 GCUP/s, and 1.2 GCUP/s, for the CPU, the SSE, the SSE -t 4, and the GPU versions, respectively.The same experiment was repeated with 150 and 200 bp-long sequences. As shown by the results in Figure gapmis_many_to_many were used, and the same experimental procedure was repeated with 150 and 200 bp-long sequences. As shown by the results in Figure -t 4 version by a factor of 20 compared to the CPU version; and the GPU version by a factor of 11 compared to the CPU version. The CUP/s are 190 MCUP/s, 1.1 GCUP/s, 4 GCUP/s, and 2.2 GCUP/s, for the CPU, the SSE, the SSE -t 4, and the GPU versions, respectively.As further experiment, we generated 1, 000, 000 75 bp-long DNA query sequences and 200 100 bp-long DNA target sequences. Similar to the above experiment, the four aforementioned versions of function gapmis_one_to_one_f, function gapmis_one_to_one_onf, and needle, under real conditions, we simulated 1, 000, 000 100 bp-long query sequences from the 30 Mbp chromosome 1 of Arabidopsis thaliana (AT) obtained from [-3and 2.4 × 10-5, respectively--the ones observed in AT [accuracy as the proportion of correct alignments in the dataset. Thus, we evaluated the accuracy of the aforementioned programmes in extending an alignment end-to-end, assuming that the seed part of the alignment is already performed by using a conventional indexing scheme, that is, a hash-based index [Beta vulgaris (BV) [Homo sapiens (HS) exome [As further experiment, in order to evaluate the performance of programme gapmis, function ned from , and insed in AT . Since, ed in AT . For theed in AT ,22,23). ed index  or an FMed index . We reperis (BV)  and HomoS) exome .libgapmis is demonstrated by the results shown in Table gm -onf 3 has the highest accuracy in all cases. It can increase the accuracy of extending short-read alignments end-to-end by 0.01% compared to needle. Given the observed gap occurrence frequencies, the increased accuracy of gap identification is significant. For instance, the proportion of pairs of sequences with gaps in the six datasets of Table The high accuracy of needle could be increased by the user, this would have a potentially fatal impact on accuracy because the high number of mismatches opted would be underestimated [needle, similar to the previous experiments. The gap opening penalty ranged from 10.0 to 20.0, and the gap extension penalty was set to 0.5. Our assumption is confirmed by the results shown in Table needle: the number of correct alignments decreases.Although the gap opening penalty in stimated . We checlibgapmis, an ultrafast and flexible library for extending pairwise short-read alignments end-to-end. Apart from the standard CPU version, it includes ultrafast SSE- and GPU-based implementations. libgapmis is based on GapMis, a tool that computes a different version of the traditional dynamic-programming matrix for sequence alignment.In this article, we presented libgapmis is more suitable and efficient than more traditional approaches for extending short-read alignments end-to-end. Adding the flexibility of bounding the number of gaps inserted in the alignment, strengthens the classical scheme of scoring matrices and affine gap penalty scores. The presented experimental results are very promising, both in terms of identifying gaps and efficiency.This work is directly motivated by the next-generation re-sequencing application. We demonstrated that libgapmis can be directly integrated into any short-read alignment programme. Our immediate target is to further optimise the code, and also integrate the functions of this library into a short-read alignment pipeline.By exploiting the potential of modern CPU and GPU architectures and applying multi-threading, we improved the performance of the purely sequential CPU version by more than one order of magnitude. More importantly, the functions provided in The authors declare that they have no competing interests.SPP and AS designed the study. NA, SB, TF, and SPP developed the library. TF and SPP conducted the experiments. SPP wrote the manuscript with the contribution of all authors. The final version of the manuscript is approved by all authors.APMISAlgorithm G. The algorithm GAPMIS computes matrices G and H. It takes as input the text t of length n, the pattern x of length m, and the threshold β. This algorithm was taken from [ken from .Click here for file


One major problem all TBM algorithms face, however, is their unsatisfactory performance when proteins under consideration are low-homology. To improve the performance of TBM methods for such targets, a novel model evaluation method was developed here, and named MEFTop. Our novel method focuses on evaluating the topology by using two novel groups of features. These novel features included secondary structure element (SSE) contact information and 3-dimensional topology information. By combining MEFTop algorithm with FR-t5, a threading program developed by our group, we found that this modified TBM program, which was named FR-t5-M, exhibited significant improvements in predictive abilities for low-homology protein targets. We further showed that the MEFTop could be a generalized method to improve threading programs for low-homology protein targets. The softwares (FR-t5-M and MEFTop) are available to non-commercial users at our website:  Template-based modeling is defined as modeling of protein structures based on already determined structure templates, and it is currently the most powerful prediction method. To build a structure model for a target sequence, the TBM method usually follows four steps: identification of structural templates, alignment of the target sequence to structural templates , model building, and model quality evaluation. In recent years, various TBM programs were developed for the first two steps Whilst TBM methods are now widely used for protein structure prediction and structure-function relationship studies, their low performance for low-homology proteins still presents a bottleneck. The underlying reasons behind the bottleneck can be complicated, and include issues like incorrect template selection and sequence-template alignment, modeling errors, or a biased scoring function, to name a few. All together, these errors ultimately result in the failure of generating high-quality models, even in the presence of good templates in the template library at use.st models in FR-t5 are always of native-unlike topology for the target sequence, even though native-like models exist in the searching space. These proteins in dawn region are low-confidence targets for FR-t5, which included a significant portion of low-homology proteins. In consideration of more conserved features derived directly from a structure model, model evaluation method could provide an avenue to improve the performance of TBM in the dawn region. Here we report a novel model evaluation method called MEFTop that combines traditional features with two groups of newly introduced structural features. The obtained testing results indicate that these novel structural features contribute significantly to the improvement of MEFTop performance in the dawn region. We further show that MEFTop could be combined with FR-t5 and other threading programs to improve the low-homology protein modeling.Our previously developed TBM method FR-t5 In this section, we will first show the performance improvement of MEFTop for protein targets in the dawn region. Then, we will analyze the contribution of newly introduced structural features in MEFTop. Thirdly, we will explore how the FR-t5-M, the combination of MEFTop with FR-t5, improves modeling for targets in the dawn region and test its performance on CASP10 targets. Finally, we will demonstrate the application of MEFTop to some other threading algorithms such as RaptorX To evaluate the robustness of MEFTop, a 5-fold cross-validation was carried out on the training set SCOP1.75-Z6. The average and standard deviation of the percentage of native-like Top1 models (Top1%) (see Methods section for details) was 46.84%±2.55%, which indicates stable performance of MEFTop for targets in the dawn region. The performance of MEFTop was further tested on the data set (SCOP1.75–500) which included 110 proteins in dawn region. The Top1% selected with the P-score of MEFTop was compared to that selected with the Z-score of FR-t5. As shown in To investigate the contribution of newly introduced structural features of MEFTop to the improvement of model evaluation for dawn region proteins, different combinations of features were trained on the SCOP1.75-Z6 set and tested on the SCOP1.75–500 set. As shown in As shown in To evaluate FR-t5-M, we compared the performance of M-score and Z-score for the 110 targets in the dawn region of SCOP1.75–500 . From thSince a significant portion of low-homology proteins were included in the dawn regions, we further compared FR-t5-M and FR-t5 on these low-homology proteins. Of 110 proteins in dawn region of SCOP1.75–500, 59 have sequence identity less than 40%. As shown in The FR-t5-M was also evaluated on the 390 targets of high confidence from the SCOP1.75–500 dataset . We founWe further tested the performance of FR-t5-M on targets of the recent CASP10. A comprehensive comparison between the performance of FR-t5-M (M-score) and FR-t5 (Z-score) on the 103 targets of CASP10 data set is shown in Here we would like to demonstrate that the MEFTop could offer a general approach to improve protein modeling by combining it with another two popular threading programs, RaptorX and SPARKS-X. These two integrated methods RaptorX-M and SPARKS-X-M were tested on the 110 targets in the dawn region of SCOP1.75–500. As shown in We further looked into the performance of the newly integrated methods (RaptorX-M and SPARKSX-M) on 59 low-homology targets (sequence identity less than 40%) in SCOP1.75–500. From the data presented in In order to improve low-homology protein modeling, we have developed a useful model evaluation method (MEFTop) by focusing on evaluating the native-likeness of topology. Further, by incorporating MEFTop with our previously developed threading method FR-t5, a new TBM method (FR-t5-M) was developed. We found that FR-t5-M significantly outperforms our previous threading method FR-t5, and displays a predictive performance for low-homology CASP10 targets that is comparable to most other popular protein structure prediction programs. Moreover, we observed significant improvements in predicting structures for low-homology proteins when combining the MEFTop with RaptorX and SPARKS-X. Taken together, we argue that MEFTop could offer a generalized method to improve threading algorithms for low-homology protein modeling.A wide range of earlier studies have demonstrated that traditional features of 1D and 2D information can be effectively utilized for high-quality model evaluation Whilst we have shown that the application of MEFTop or FR-t5-M brings significant improvements, both methods can be optimized further. First, models of FR-t5-M could be optimized with the introduction of side-chain packing and refinement in the future. Second, a systematic and complete programming code optimization should result in accelerating the program. As a case in point, a mutation in the transporter membrane protein SLC45A2, which is the genetic basis of the fur color of white tigers, was successfully predicted by using FR-t5-M http://predictioncenter.org/). The CASP10 data set was used as testing data, which includes 103 targets in total (http://predictioncenter.org/).The CASP7-8 data set was used as training data, which consists of 221 CASP7 and CASP8 targets  1-dimensional (1D) and (2) 2-dimentional (2D) contact map features, (3) Secondary Structural Element (SSE) contact features and (4) 3-dimensional topology features.1D features included secondary structure (SS) represented by helix, strand and coil and relative solvent accessibility (RSA) computed as exposed and buried states. For a target sequence, its SS state and RSA state for each residue were predicted by SCRATH ijC is the predicted contact probability from target sequence or extract contact information from structural models for residues i and j). Thus, the residues contact order of target sequence and its structural model can be regarded as two composition vectors. The cosine and correlation of the two composition vectors were calculated as two similarity scores at a distance threshold. Similarly, another 2 similarity scores were obtained for contact number.2D contact map features capture contact information between residues with separation ≥6 residues at two distance thresholds (<8Å and <12Å) between the side chain center of mass (SCM) fres) of the contact probability between target sequence and structural model was calculated as the following equation:In addition, the overall match score .Here, Therefore, to describe the extent of correspondence between a target sequence and its structural model, ten features including eight similarity scores for contact order and contact number and two overall match scores were derived at two distance thresholds. In total, 24 traditional 1D and 2D features were generated.fSSE) of the SSE contact strength between structural model and target sequence was calculated in the following equation:SSE contact features capture the information of SSE spatial relationship including the SSE pairs in contact, the distances between SSEs and the SSE lengths. Based on the SS states of residues calculated above, an SSE was identified as a segment consisting of at least 4 continuous residues with helix or strand state. n is the total number of corresponding SSEs between a structural model and target sequence. S(ij)C is the predicted contact strength of SSE i and j from target sequence divided by the length of SSE i, and S(ij)N is the contact strength between SSE i and j extracted from structural model divided by the length of SSE i.Here, MF =   and the target sequence TF =  (i in the target sequence) and then transformed into similarity scores using the cosine and correlation function.Two composition vectors of SSE contact numbers were generated, respectively, for the structural model The overall match of the distances of SSE pairs between the structural model and target sequence was also considered. First, the distance of an SSE pair in structural model was assigned with the minimum distance between residues of this SSE pair, and the distance of SSE pair for the target sequence was estimated from its residue predicted contact probability as follows:D is the predicted distance of a SSE pair, p is the maximum predicted contact probability between the residues of a SSE pair, mD is the distance threshold, k is a constant, and 0P and 0D denote ideal status values. Then, the similarity score of SSE pair distance between the structural model and target sequence was calculated as by following equation S3  of the SSE contact strength, two similarity scores for SSE contact numbers, one similarity score of SSE pair distance, and two different ratios of SSE lengths.The length of the corresponding SSEs between the structural model and target sequence was compared and transformed into two different ratios by equation S6 and S7 see . As seenAs shown in R is the predicted radius of gyration, L is the length of sequence, k and m are constant parameters. The radii of gyration predicted from the target sequence and extracted from the structural model were compared and transformed into two similarity scores by equation S8 and S9 , and the HC is a new structural descriptor . The radIn the FR-t5 program, the Z-score was applied for template ranking, and could also be used to assist in the selection of the optimal structural model. The raw score Here In MEFTop, a P-score was used to evaluate the quality of a structural model through a SVM regression function Here, the value computed by M-score was then used as follows:In order to form the new modeling program FR-t5-M, MEFTop was combined with FR-t5. A new metric called n is the weight for P-score.Here, F) as follows:MEFTop was firstly trained and evaluated as a general model evaluation method in our research. The training dataset was CASP7-8 set, which is generated from 221 targets of CASP7 and CASP8 with FR-t5. Furthermore, in order to adapt this method for targets in the dawn region, MEFTop was optimized using the SCOP1.75-Z6 set. First, the weight for the vector of this structural model was assigned according to its TM-score, and the weights and features were used as inputs for the software LIBSVM Z-scoreSVM) for training target, n is the weight of Z-scoreSVM and Here, After training of MEFTop using the above process, the performance of MEFTop was tested on the SCOP1.75–500, with particular focus on targets in the dawn region. Mostly, two criteria were used to evaluate the performance of evaluation method. They include the percentage of native-like Top1 models (Top1%) and the average rank of Top1 models. The Top1% is the fraction of native-like Top1 models for all targets. If the TM-score of a model is larger than 0.4, the model is usually defined as a native-like model, which has a similar topology when compared with its native structure Similar to MEFTop, our new method FR-t5-M (using M-score as a metric) was optimized on the SCOP1.75-Z6 dataset, and evaluated on both the SCOP1.75–500 and CASP10 datasets.Similar to the Z-score of FR-t5, a score of RaptorX and an energy score of SPARKS-X were used to rank templates, respectively. We integrated the P-score of MEFTop with the rank score of these threading programs into new metrics similar to the M-score of FR-t5-M. Then these new methods which combined MEFTop with threading programs (RaptorX and SPARKS-X) were evaluated for 110 targets in the dawn region of SCOP1.75–500. Among the 110 targets, 59 targets have sequence identity to templates less than 40%, and 25 targets less than 30%. For each protein in training and testing data, 100 structural models were generated by RaptorX and 80 structural models were generated by SPARKS-X.Table S1Performances of FR-t5-M and FR-t5 on targets of high confidence from the SCOP1.75–500 dataset.(DOC)Click here for additional data file.Methods S1Equations for Feature Extraction.(DOC)Click here for additional data file.


Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly. Alignment-free methods, on the other hand, are based on abstract string comparisons and avoid potential alignment problems. However, in general they are not biologically motivated and ignore our knowledge about the evolution of sequences. Thus, it is still a major open question how to define an evolutionary distance metric between divergent sequences that makes use of indel information and known substitution models without the need for a multiple alignment. Here we propose a new evolutionary distance metric to close this gap. It uses finite-state transducers to create a biologically motivated similarity score which models substitutions and indels, and does not depend on a multiple sequence alignment. The sequence similarity score is defined in analogy to pairwise alignments and additionally has the positive semi-definite property. We describe its derivation and show in simulation studies and real-world examples that it is more accurate in reconstructing phylogenies than competing methods. The result is a new and accurate way of determining evolutionary distances in and beyond the twilight zone of sequence alignments that is suitable for large datasets. For a long time, multiple sequence alignments followed by maximum-likelihood (ML) tree reconstruction have been seen as the computationally expensive gold standard for phylogenetic analyses In the light of these findings, alignment-free distance-based reconstruction methods deserve special attention, as they circumvent potential pitfalls of the multiple alignment approach, especially with respect to divergent sequences, and can be advantageous in speed possibly without sacrificing reconstruction accuracy. Unfortunately many purely alignment-free approaches kernel-trickSince there exists a one-to-one relationship between binary trees and additive metrics The kernel trick has been applied successfully in a variety of different fields, including natural language processing, face recognition, speech recognition and computational biology. Here we extend its use to the problem of phylogenetic reconstruction. The major challenge here is finding the right pd kernel. The pairwise similarity measure between sequences must map sequences to an evolutionary feature space ruled by the modification of sequences in terms of insertions, deletions and substitutions. The natural distance in this space should then come as close as possible to the true evolutionary distance on the sequences.In this article we derive such a kernel. Making use of classical results from global pairwise alignment we show how a different formulation of the alignment problem can map sequences to a feature space of insertions, deletions and substitutions and gives rise to a pd kernel. We study this similarity measure in its topological reconstruction accuracy of phylogenetic trees from simulated and real data. We show its superiority over conventional methods for phylogenetic studies with a broad range of sequence divergence in and beyond the twilight zone of remote homology. We further investigate possible benefits of including suboptimal alignments into the score.finite-state transducers (FST), for modeling the transformation of one sequence into another or describing joint distributions on two sequences semirings) to be used as weights. These include, for example: probabilities, logarithmic numbers ; and boolean values. In the following we use FSTs to create our kernel for evolutionary sequence comparison. We make use of two major observations: (i) The classical problem of pairwise alignment can be posed as a shortest-path problem on a log-weighted FST Hidden Markov Models (HMMs) have been extensively used for probabilistic modeling of sequence families, database searches and other tasks. Pair-HMMs work on two sequences simultaneously and are capable of probabilistic modeling of pairwise alignments real semiring, the final score for two sequences is the  sum of all possible paths generating those two sequences, where the weights in each path are  multiplied. Weights on the real semiring can be converted to the log semiring by the link function log semiring, multiplication is turned into summation and the sum is replaced by the logarithm of the sum. The tropical semiring is a special instance of the log semiring in that the log-sum over all paths is replaced by the minimum, and corresponds to the Viterbi approximation in conventional HMMs. For a more formal definition of semirings, see The different classes of weights that can be used for FSTs are the so-called semirings. They define two operations on a set, an abstract sum and multiplication. In the case of the tropical semiring tropical semiring, the alignment score is defined as Any edit-distance can be computed via a FST over the real semiring associates a real-valued number with every pair of sequences sum over all possible paths transforming multiplying instead of summing the weights along the path. This mapping from two-tuples of the space of sequences to the reals is called a rational kernel. If the transducer A FST It is our goal to modify the pairwise alignment problem in a way that we can prove the resulting alignment score to be pd. To achieve this we replace the min operation by the log-sum, thereby changing semirings from the tropical to the log. The resulting score includes all possible  alignments. By making use of the link function To see that this kernel is indeed pd we need to decompose it in to a feature space mapping FST and its inverse We can think of a feature space mapping where each position in a biological sequence can either be retained, substituted or deleted using some intermediate alphabet It can easily be seen how the composed FST again resembles the topology of a global alignment FSA In summary, reformulation of the classical global pairwise alignment paradigm allows for the interpretation of the alignment score as a shortest-path approximation of the kernel score of a pd rational kernel working on biological sequences.If the absolute difference between the summands of a logarithmic sum is large the sum is heavily dominated by its smaller summand. Therefore, in cases where the optimal alignment score is distinctively smaller than any suboptimal alignment the kernel score including all suboptimal alignments will be close to the shortest-path approximation. In cases where even the best alignment score is not significantly smaller than its closest suboptimal siblings the full score will differ. In order to be able to study the effect of the inclusion of suboptimal alignments in terms of reconstruction accuracy we project the exponential of the matrix of pairwise alignment scores to the next positive semi-definite We performed repeated simulation experiments to validate our distance measures using nucleotide and amino acid sequences over two different tree topologies and on each with increasing sequence divergence.MusclePhylipProbCons based on pair-HMMs RAxML maximum-likelihood tree reconstruction Amino acid and nucleotide sequences were generated according to two tree topologies with 18 and 52 taxa in realistic scenarios using INDELible column score (CS) is the proportion of columns from the true alignment that are present and correct in the test alignment. The sum-of-pairs score (SPS) is the proportion of aligned pairs of nucleotides/amino-acids from the true alignment that are also aligned together in the test alignment. The first is a very stringent measure as all nucleotides/amino-acids in a column must be correctly placed for that column to be deemed correct. The latter is a more lenient measure as it rewards correct alignment between some sequences even if other sequences in that column are mis-aligned To assess the impact of sequence divergence on multiple alignment accuracy we first compared the alignments from Muscle with the true INDELible alignments. We calculated two scores to quantify this accuracy : The colThe results show that the number of correctly aligned positions exponentially decreases with increasing sequence divergence for nucleotide sequences. Amino acid sequences showed a more linear trend, possibly due to the higher information content introduced by the larger alphabet size of amino acids as compared to nucleotides, but suffer from the same effect.ProbCons results showed that aligners specifically designed to address these issues indeed perform slightly better to moderately better across all experiments but still suffer from a rapid loss in reconstruction accuracy with increasing sequence divergence. The alignment-free methods generally performed worse than other methods tested on the 18 taxa tree but were close to the best alignment-based methods for the 52 taxa trees.Quartet distances between the estimated and true trees for nucleotide as well as amino acid sequences over all tree topologies  show thaDistance estimation using our proposed finite-state transducers (blue and green lines) came close to the performance of classical multiple alignment for closely related species. It showed only a gradual decrease in reconstruction accuracy with increasing evolutionary divergence, being significantly more accurate than any other method tested. This evidently shows that the classical approach of multiple alignment followed by tree reconstruction is superior only if the alignment is correct. From a certain distance on, multiple sequence alignments cannot be reconstructed accurately any more, leading to poor reconstruction power in the downstream phylogenetic analysis. This seems to hold for classical progressive multiple alignment as well as statistical consistency alignment.Paramecium tetraurelia. We showed that the kinome of P. tetraurelia is more than 5 times the size of the human kinome. In addition to whole genome duplications, further duplications lead to the expansion of specific subfamilies. More than 20 ciliate specific domain architectures were discovered When comparing both proposed kernel scores, one incorporating all suboptimal alignments into the score, the other only using the optimal alignment, we noticed differences between the two tree topologies: In the 18-taxa case both variants perform equally well. In the 52-taxa case the suboptimal alignments added more noise to the score than signal and the kernel using only the optimal score came out ahead. Even though the average branch length in the 52 taxa tree is moderate the variance of pairwise distances between sequences is higher when the tree contains more branches. When comparing sequences beyond the twilight zone the scores of the optimal and subsequent suboptimal alignments are similar, influencing the kernel score  sequences of the Chlorophyceae Sphaeroplea clade. The distance tree places the Sphaeroplea clade between the Hydrodictyon and Scenedesmus clades . The distances are meaningful in evolutionary terms and outperform other phylogenetic inference methods on divergent sequences in and beyond the so-called twilight zone of remote homologies. Thus, our methods complement traditional approaches for more closely related sequences. Future work will focus on assessing the robustness of the kernel score (bootstrapping) and the question of mapping sequences directly to an additive space, i.e. from which additive distances can be immediately derived, to remove the final approximation step when going from the matrix of pairwise distances to the tree.Text S1Supporting text.(PDF)Click here for additional data file.


Phylogenomics – the study of evolutionary relationships based on comparative analysis of genome-scale data – has so far been developed as industrial-scale molecular phylogenetics, proceeding in the two classical steps: multiple alignment of homologous sequences, followed by inference of a tree (or multiple trees). However, the algorithms typically employed for these steps scale poorly with number of sequences, such that for an increasing number of problems, high-quality phylogenomic analysis is (or soon will be) computationally infeasible. Moreover, next-generation data are often incomplete and error-prone, and analysis may be further complicated by genome rearrangement, gene fusion and deletion, lateral genetic transfer, and transcript variation. Here we argue that next-generation data require next-generation phylogenomics, including so-called alignment-free approaches.Thanks to advances in next-generation technologies, genome sequences are now being generated at breadth (Reviewed by Mr Alexander Panchin (nominated by Dr Mikhail Gelfand), Dr Eugene Koonin and Prof Peter Gogarten. For the full reviews, please go to the Reviewers’ comments section. Plans are afoot to sequence 100,000 human genomes  and 100,000 food-borne pathogens (100kgenome.vetmed.ucdavis.edu). Next-generation data offer particular promise in the study of population genomics and variation, and of the genetic mechanisms underlying how organisms respond to their environments.Next-generation sequencing technologies are yielding genome-scale data in immense quantities: genomes and transcriptomes of viruses, bacteria, archaea and eukaryotes; single-cell isolates and clonal cultures; diverse cell types under normal, stress and disease conditions; meta-genomes and meta-transcriptomes. With a steady decline in costs as new technologies are developed and/or refined, sequencing projects nowadays are not only taxonomically broad but increasingly deep, e.g. sequencing errors, contaminating DNA), regions of low information content  and among-individual heterogeneity. Given the technologies and services currently on offer, advanced centres (e.g. BGI in China and the Joint Genome Institute in USA) are simply sequencing to high coverage, even for prokaryotes, in the most-ambitious projects (e.g. Genomic Encyclopedia of Bacteria and Archaea: jgi.doe.gov/programs/GEBA/). The resulting unfinished data, replete with un-joined contigs, ambiguous assemblies and erroneous base calls, will be noisier, yet far more abundant, than the tidy closed circles that up to now have been iconic of microbial genomics.While prospects have never been brighter for data generation, genome projects may be limited by the supply of human and computational power for data analysis. Assembly (de-replication of overlapping reads to yield a single contiguous sequence) is computationally expensive even for a single large genome, and approaches impossibility against the backdrop of noise  of life. Relationships among taxa are inferred based on homology  across entire genomes, whether in a comparative gene-by-gene [Arabidopsis, Drosophila) were the first to be sequenced and until very recently predominated in public databases, although as cost per base has decreased, other factors  have begun to drive sequencing decisions. Where genome data are unavailable , it is not uncommon to utilise transcriptome data in phylogenomic analysis [e.g.[Phylogenomics, the study of evolutionary relationships based on comparative analysis of genome-scale data, is indispensible in assessing diverse biological hypotheses, -by-gene ,2, conca-by-gene ,4 or who-by-gene . Genomesanalysis -8, at sosis [e.g.,9,10) hasis [e.g.-13.These approaches, however, are not without limitations, especially when evolutionary histories are complicated ,15. LikeA comprehensive, sustainable strategy for phylogenomics should therefore transcend gene boundaries – whatever those may be – while capturing, or at least not being led astray by, the complex dynamics playing out both within genes  and in the vast intergenic regions. Current best-practice phylogenomics cannot do this adequately or at the necessary scale.sine qua non in phylogenetics [within genes as well, yielding regions that can be aligned only ambiguously, or not at all. Given the heuristic nature of key steps in standard phylogenomic workflows, the relevance of alignment scores to homology can be difficult to assess statistically [Multiple sequence alignment (MSA) has long been a genetics . The aimgenetics ,23. Locastically . All of e.g. proteolipids of ATPase [MSA of highly divergent homologous sequences, f ATPase  or aquapf ATPase , is knowf ATPase  estimatef ATPase , in whicf ATPase . The divf ATPase . These ak-mers or n-grams, offer an interesting alternative to MSA. A k-mer can be treated as a unit of information. This motivates so-called alignment-free approaches in which k-mers are extracted and their counts or frequency distributions (i.e. k-mer spectra) are computed; sequencing errors can appear as unexpected k-mers, while gene-regulatory regions, repetitive elements or laterally transferred regions can exhibit unexpected k-mer spectra  length, known variously as words, tra  evolutionary biologists, including signal transmission and information retrieval [In the same way, individual transfer ,33. Studd on MSA . By decog Figure . In learetrieval . Table 1e.g. k-mers) they share in common. This measure can be transformed (e.g. via logarithmic representation of the geometric mean) to estimate an evolutionary distance. A matrix of pairwise distances built on these statistics for a set of sequences can then be used to reconstruct a phylogeny. The measure of relatedness can be based on the frequency (number of occurrences) of k-mers, or can also take into account their relative positions within the sequences. Correlation among the common k-mer sets, sometimes adjusted by the value of k (length) relative to whole sequence, can be incorporated as an up- or down-weighting factor. This measure can alternatively be normalised by the probability at which corresponding k-mers occur in the sequences, or extended to include imperfect k-mer matches [k-mer distances have also been put forward [In one class of alignment-free approach, relatedness of two sequences is based on the number and value of sub-sequences  sequences can be used to infer the relatedness among these sequences, and the positions at which a particular subject sequence is most similar to the query can be used to infer genetic transfer ,39. In aher  are a good place to start; but beyond those, problems previously encountered in engineering or data-mining may not map precisely to evolutionary biology. Every attempt should be made to carry over into next-generation phylogenomics the generally quadratic to cubic time-complexity of phylogenetic distance methods on trees [e.g. genome, transcriptome, proteome and/or metabolome) in a one-stop inference of evolutionary relationships, hybrid approaches (e.g. applying k-mer- and model-based methods for more and less similar sequences respectively), or functional inference based on k-mer spectra.Before we can dispense altogether with MSA the scalability, robustness and efficiency of on trees  or netwoon trees . MoreoveLike molecular phylogenetics in the 1970s, alignment-free phylogenomics has just entered a period of development, refinement and application. Major aims can be articulated – reconstructing complex biological scenarios efficiently and well, based on unprecedented volumes of new data and data types – although the best algorithmic paths to those aims remain to be discovered and explored. To the extent that these paths prove to be scalable and robust, next-generation phylogenomics may be alignment-free.MSA: Multiple sequence alignment.The authors declare that they have no competing interests.CXC and MAR conceived and wrote the manuscript. Both authors read and approved the final manuscript.Reviewer’s report 1: Mr Alexander Panchin, Institute of Information Transmission Problems, Russian Academy of Sciences The article “Next-generation phylogenomics” by Cheong Xin Chan and Mark A. Ragan addresses the idea of alignment-free methods for phylogenetic analysis using abundant next generation genome-wide data. Although there is hardly anything in the article I could disagree with, and the ideas expressed are sound, I am unsure if this article brings anything new to the table. The article is about next-generation phylogenomics, yet no new phylogenetic algorithms, applications, comparisons or phylogenetic trees are presented. In my opinion the article is a well written mini-review; however the value of this contribution for Biology Direct is questionable.Authors’ response:We thank the reviewer for his comments. We wrote this Comment to encourage the research community to consider alternative approaches for phylogenomics in light of the recent (continuing) deluge of sequence data. A full research paper detailing how the alternatives work better than existing approaches is important, but is beyond the scope of this Comment. We have modified the text to incorporate a more-detailed discussion of standard phylogenetic approaches and the limitations of multiple sequence alignment . In agreement with Reviewers 2 and 3, we believe this Comment is timely and appropriate for the readership of Biology Direct.Reviewer’s report 2: Dr Eugene V. Koonin, National Center for Biotechnology Information, NIH, USAReview of “Next-generation phylogenomics” by Chan and Ragan.This is a timely Comment, indeed. I agree with the authors in that we (as a community) should seriously think about next generation phylogenomics. Doing phylogenomics with the current methods on many thousands of genomes is simply not a possibility. At the same time, not making full use of the new wealth of genomic data is unthinkable as this is the surest way to new insights.Authors’ response:We thank the reviewer for his endorsement of the issues we have raised.k-mer-based approaches. To my knowledge, the prospects of these particular methods are very limited. Certainly, alignment-free approaches are attractive but from an information-theoretical standpoint, I find it dubious that they promise much progress, at least when large phylogenetic depths are involved. At this juncture, I am more optimistic about clever algorithmic improvements on the “conventional” phylogenomic methods. The prime example is FastTree [e.g.[What I am less enthusiastic about, are the alignment-free methods the authors discuss, in particular the FastTree  that, inree [e.g..Authors’ response:We agree that better and/or faster phylogenetic techniques, such as FastTree  are important for the field to progress as more data become available. These methods, largely based on maximum likelihood, require the  assumption of a model under which the sequences evolve, and are computationally expensive. FastTree, for instance, implements heuristics approximating maximum likelihood in restricting tree search space, and while faster, it is less accurate than the standard maximum likelihood methods. These methods are largely based on MSA, which implicitly assumes full-length sequence contiguity. As the reviewer points out, the problem of MSA itself is more challenging. We have now incorporated a discussion of other phylogenetic alternatives in the main text . The application of alignment-free methods in large-scale phylogenomics is currently limited, and the scalability and robustness of these methods remain to be systematically investigated. This approach, however, represents an attractive strategy in handling key limitations of multiple sequence alignment (as summarised in Table 1). We argue here that next-generation phylogenomics should consider alignment-free methods as an alternative – but not the only one.Reviewer’s report 3: Prof J. Peter Gogarten e.g., [Chan and Ragan provide a concise review of the advantages of alignment free approaches in comparative genomics. They point out that the calculation of multiple sequence alignments often is unreliable and computationally expensive. They review alignment free approaches and provide examples of their usefulness. A more detailed discussion of techniques to detect horizontally transferred genes and to bin sequences from metagenomes based on compositional signals might have provided additional examples for the power of alignment free approaches already in widespread use today e.g., -46)..e.g., [4Authors’ response:We thank the reviewer for his comments. We have now incorporated in the text a discussion of the use of alignment-free methods for detecting lateral genetic transfer and for classifying metagenomic data, to highlight further the power of alignment-free approaches.I also would have liked an expansion of the discussion of the problems created through multiple sequence alignments for downstream analyses. Ever since I attempted to analyse the evolutionary history of ATPase proteolipids , I am awAuthors’ response:These issues are exactly why we think approaches independent of MSA could be a good strategy in next-generation phylogenomics. Approaches integrating MSA with phylogenetic reconstruction were proposed back in the 1980s[and 1990s[, but these methods are not scalable due to NP-hardness, e.g.[, and remain inevitably limited by the MSA framework. A thorough description of issues associated with MSA deserves a paper on its own[and is beyond the scope and limit of this Comment. We have expanded the text to highlight other methods developed to address some of the limitations of MSA, and how alignment-free methods could be an attractive alternative.the 1980sand 1990sand 1990s-51, but ess, e.g., and remn its own-23and is


The web server provides a streamlined and intuitive interface, input data validation and output that is more extensive and easier to read and interpret than related servers. The R3D Align web server offers a unique Gallery of Featured Alignments, providing immediate access to pre-computed alignments of large RNA 3D structures, including all ribosomal RNAs, as well as guidance on effective use of the server and interpretation of the output. By accessing the non-redundant lists of RNA 3D structures provided by the Bowling Green State University RNA group, R3D Align connects users to structure files in the same equivalence class and the best-modeled representative structure from each group. The R3D Align web server is freely accessible at  Sequence alignment of biological macromolecules provides important information regarding their evolutionary histories, functional similarities and differences, and mechanisms of adaptation to new environments . MethodsStructural alignment of biological macromolecules is not a trivial task. Homologous molecules accumulate differences in sequence over evolutionary time. Although the 3D structures tend to change more slowly, significant structural differences can also accumulate over time. Because of computational challenges posed by the inherent difficulties noted earlier in the text, all RNA 3D alignment methods currently implemented on web servers, including ARTS, DIAL, SARA, iPARTS, SETTER and RNA 3D Align (R3D Align) ,13,15–18In this article, we describe the features and use of the redesigned and enhanced R3D Align web server. The revamped R3D Align user interface includes weekly synchronization with the PDB database, more intuitive guidance for advanced parameter specification and integration with RNA 3D Hub for in-depth information about RNA 3D structures, chains and similar structures. The results page now features additional alignment summaries, including summary statistics and visual displays available for immediate viewing.p. Pairs of neighborhoods, one from each structure, are superposed, and their geometric similarity is quantified using the geometric discrepancy, a measure first described in (d) and whose sequence positions are closer than half the alignment bandwidth (parameter β). Edges are drawn between vertices in the local alignment graph, only when the local alignments they represent are compatible with each other. The global alignment is then constructed on the basis of a maximal clique of the local alignment graph. Further details regarding the setting of parameters p, d, and β are provided in next section.The R3D Align web server is built on the alignment algorithm described in . A briefribed in . This meThe input interface for R3D Align is shown in R3D Align uses the specified chain order and, as with sequence alignments, respects nucleotide order when producing an alignment; therefore, the order in which chains are requested for each file is important. The user may restrict attention to one or more ranges of nucleotide numbers within each chain, as desired. R3D Align is unique among RNA alignment servers in offering users the capability to align domains, motifs or other sub-structures comprising one or more non-contiguous segments of nucleotide sequence from one or more chains. Among other alignment servers, only DIAL allows for the specification of a subsequence, but this is limited to a single contiguous chain segment .As a learning aid, the web server provides one-click loading of example input parameters J. On selTo ensure that user-submitted input can be processed, extensive pre-submission input validation has been implemented, and users are informed of specific errors in their input. This includes nucleotide validation to avoid the server attempting queries specifying non-existent nucleotides.Escherichia coli 16S rRNA belong to one equivalence class, all structures of E. coli 23S rRNAs to another and all Thermus thermophilus 16S rRNA structures to a third. When a user enters an existing PDB ID (R3D Align has been integrated with RNA 3D Hub (in preparation), which provides users access to the equivalence classes of RNA PDB files described previously in . Each eqg PDB ID A, a listg PDB ID C, and thg PDB ID .d, p, β and the number of iterations to be carried out. The default values for these parameters have been optimized through a series of rigorous tests of thousands of alignments. The default parameters provided are suitable for structures of all sizes. Parameter values customized to the size of the structures selected by users can be accessed by clicking the ‘Suggest parameters’ button  is advised.The R3D Align web server has been designed to iteratively produce structural alignments to achieve more efficient processing and higher accuracy. In the iterative approach, the alignment produced in one iteration is used as a seed alignment for the subsequent iteration. With an iterative approach, structures larger than 150 nt can be aligned in a significantly shorter period, without compromising the quality of the alignment. R3D Align uses an iterative approach by default. The initial seed alignment is determined by a simple dynamic programming sequence alignment, which may be inadequate for significantly diverged homologues. In this case, increasing the bandwidth parameter . The applet displays aligned nucleotides in opaque colors, orange for structure 1 and blue for structure 2, which conform to the guidelines suggested in , the representative structures from each organism are aligned pairwise. The Gallery page features a table with images of the rigid-body superpositions for each pair of aligned molecules. Clicking an image takes users to the pre-computed R3D Align Results page for that pair of structures. The content of these pages is described under Description of Output.E. coli and T. thermophilus) and archaea   . The GalAn additional use case for R3D Align is the evaluation of results from RNA 3D structure prediction software by alignment of modeled structures to experimental structures. Comparison of predicted models with known structures using rigid-body superposition and calculation of RMSD can be misleading, owing to the inherent flexibility of RNA. Using R3D Align, one obtains locally optimized alignments, which can be visualized with the unique diagnostic tools provided by the R3D Align web server, which facilitates assessing 3D alignment quality. To provide a real-world example, we focus on Challenge 3 from the recent RNAPuzzles structure prediction competition—prediction of the 3D structure of a riboswitch domain solely from sequence .lowest RMSD (7.24 Å) model from the RNA Puzzles competition, the one submitted by the Chen group. The arcs indicate that the overall architecture is accurately captured and most Watson–Crick basepairs are identified, but some non-Watson–Crick basepairs are lacking. The colors of the line segments indicate there are several regions with high geometric discrepancy.Panel B shows the highest RMSD (22.99 Å) model, submitted by the Major group. Few nucleotides can be aligned properly, and the secondary structure is different in one part of the model structure.For purposes of illustration, Panel C shows the Supplementary Table S1 lists URLs to the alignments in http://codeigniter.com), jQuery (http://jquery.com) and Twitter Bootstrap (http://twitter.github.com/bootstrap). The source code for both the standalone R3D Align program and the web application can be found at https://github.com/BGSU-RNA/. The server runs on a Mac Pro with a 2.66 GHz Quad-Core Intel Xeon processor and 6 Gb of RAM. Up to four jobs can be processed simultaneously, but if an alignment takes longer than 30 min of CPU time, the job is terminated. R3D Align processed >1800 queries between November 2010 and April 2013. According to Google Analytics, the site had 377 unique visitors from 46 countries over the same period. The web interface has been tested on Chrome, Safari and Firefox browsers on Mac OS X and Firefox and Chrome on PC. R3D Align is hosted and maintained by the Bowling Green State University RNA Bioinformatics group. Questions or feedback can be directed using the form on the website or by submitting a bug report via GitHub.R3D Align computations are performed by a suite of programs written in Matlab. The web application uses PHP, Javascript, Perl and MySQL and is implemented using open-source industry-standard frameworks, including CodeIgniter (Supplementary Data are available at NAR Online: Supplementary Table S1.National Institutes of Health [5R01GM085328-03 to N.B.L. and C.L.Z.].Funding for open access charge: Conflict of interest statement. None declared.


Sculptor is described, with an analysis of the algorithms used.The molecular-replacement model-improvement program  Sculptor, together with well established methods that are in common use for model improvement. An analysis of the new algorithms has been performed by studying the effect of algorithm parameters on the quality of models. Benchmarking against existing techniques shows that models from Sculptor compare favourably, especially if the alignment is unreliable. Carrying out multiple trials using alternative models created from the same structure but using different algorithm parameters can significantly improve the success rate.In molecular replacement, the quality of models can be improved by transferring information contained in sequence alignment to the template structure. A family of algorithms has been developed that make use of the sequence-similarity score calculated from residue-substitution scores smoothed over nearby residues to delete or downweight parts of the model that are unreliable. These algorithms have been implemented in the program  Although some of these difficulties only apply in certain special cases, preparing the best model for a rigid unit  is of basic importance in all molecular-replacement searches. Usually structures of homologous proteins are used for this purpose, although et al.  in order to allow the input of model files containing ligands and solvent. Firstly, the chain type is established based on the residue content. Protein chains are identified by most residues being common amino acids, but a small number of unknown residues  are allowed. Incidentally, this also helps to minimize structural gaps in the processed model, since modified residues can be included as long as their backbone atoms are named consistently. This procedure may therefore be more robust than making a decision based on a record being ATOM or HETATM and also leads to slightly higher model completeness. Protein chains are then paired with a corresponding alignment  and undergo the requested modification steps. Hetero chains are processed by deleting everything except specifically named compounds, e.g. a haem can be retained for haem-binding proteins.2.1.Sculptor currently includes the identity, PAM250  a score around 0.0 and segments containing consecutive residues that align with gap positions a score around −1.0. These normalized matrices are used in all subsequent steps. To calculate sequence-similarity scores, each alignment position is scored with the selected matrix. Subsequently, these primary scores are combined into a moving average by taking into account a certain number of alignment positions (averaging window) on either side of the position in question with a simple triangular weighting scheme that gives maximum weight to the central position, linearly decreasing with the distance of the position from the centre Fig. 1.2.2.Sculptor implements a simple algorithm described by Shrake & Rupley  and may discard residues surrounded by numerous gap positions .Sculptor also provides simple functions to polish the resulting chain trace, e.g. resulting short main-chain fragments can be deleted and short deletions in regular secondary structure  can be reinstated. Similar functionality is available in MOLREP, which imposes secondary-structure constraints onto the alignment, but in Sculptor these corrections are made by analysing the resulting trace. Similar results can be obtained by using a medium-to-long averaging window, as the smoothing provided by averaging seems to be sufficient to correct for these errors.2.4.Sculptor supports truncations to two separate levels, namely to the Cβ atom and also to the Cγ atoms based on the value of the sequence similarity. Firstly, equivalent side-chain atoms are mapped  from the residue type found in the model to that in the target sequence using a simple two-dimensional graph-matching procedure. Atoms that have no counterpart are deleted , B factors calculated with a linear combination could be negative. This is avoided by adding a constant if necessary so that the minimum B value is 10 Å2. In Phaser  against the target structure were calculated for potential solutions using utilities in PHENIX  and used to explore the effect of algorithm parameters on the quality of the resulting models. The parameters were explored on one-dimensional or two-dimensional grids that were made sufficiently large to see all effects.Z score was then calculated from a random sample of 500 translations.In order to separate changes in model quality from other aspects of the search that may influence whether or not a solution is found, instead of performing molecular replacement the log-likelihood gain was calculated by substituting the model for a previously established solution and performing rigid-body refinement. The Parameter combinations for models yielding high log-likelihood gain scores were collected and analysed to see whether correlations could be found between the score and model or alignment properties. Optimal parameter combinations and established relationships were used in defining the protocols investigated in benchmark calculations.2.8.et al.  A structural alignment from LSQMAN but with more generous spatial tolerances (8.0 Å). This results in less fragmented alignments in which moderate structural deviations (e.g. a loop in a different conformation) are permitted. This can be regarded as the best alignment that might be possible using an ideal sequence-alignment tool without any structural information.(ii) A similar structural alignment was prepared with ClustalW  It has been established by Schwarzenbacher  al. 2004 that a c3.et al. (2004e.g. Tyr to Phe) are less disruptive to the main-chain conformation than others. Moreover, in the case of amino-acid substitutions involving highly homologous side chains one can also expect the positions of side-chain atoms to be fairly conserved, while in the case of other substitutions this approximation has only proved to be valid up to the Cγ atom. These differences can be captured with an appropriate scoring matrix.Sequence-similarity-based model-editing algorithms can be regarded as generalized versions of the algorithm introduced by Schwarzenbacher  al. 2004. In the Sequence-based alignments also tend to contain smaller errors in the form of misalignments. This may have a negative effect on the resulting molecular-replacement model. One way of handling the problem is to decrease the ‘resolution’ of the alignment and spread information contained in neighbouring positions. On one hand, this averaging procedure models the effect the substitution has on the structure, namely it perturbs neighbouring positions. On the other hand, this may act as a noise filter that converts the inherently discrete nature of sequence alignments to a smooth function, reduces large variations and identifies longer-range tendencies.3.1.Structural differences between homologous proteins include insertions, deletions and conformational changes. It was investigated whether sequence similarity could be used to locate and correct these. A high-precision structure-based alignment was prepared; sequence-similarity values were calculated and mapped onto the main chain. This calculation was repeated using a sequence-based alignment and differences between the two results were compared visually.a). When using a sequence-based alignment, good results can be achieved with the binary scoring matrix and slightly better results with BLOSUM62 . With both matrices, the accuracy of the results can be further improved if sequence-similarity scores are averaged over neighbouring positions .It was found that long insertions corresponding to extra domains were easily identified from sequence-similarity scores using both alignments. The results differed more with shorter  insertions, but results from sequence-based alignments still matched those from structural alignments relatively well. A typical scenario is shown in Fig. 3ns Fig. 3d.a). However, with an averaging window of zero no substitution matrices are able to identify the same regions . This asymmetry is caused by the lower precision of non-structure-based alignment algorithms, which are able to identify the presence of deletions but not conformational changes in nearby residues that result from the deletion. In this case, information about the proximity of deletions needs to be propagated to neighbouring residues. This can be achieved using longer averaging windows and the resulting sequence-similarity scores can indicate the deletions more accurately .Interestingly, more significant differences were found when deletions were studied. Structural alignments still clearly identify deviating residues Fig. 4a. Howevly Fig. 4d.Structural alignments also clearly indicate regions that deviate structurally. In favourable cases, structural deviations can also be detected using sequence-similarity scores calculated from sequence-based alignments. In this case, it is essential to use longer averaging windows in sequence-similarity calculations and the results are also significantly less accurate than those that could be calculated from structural alignments if structural alignments were available prior to structure solution.3.2.et al.  as there were aligned positions in the sequence alignment. It is interesting to note that the algorithm published by Schwarzenbacher  al. 2004 also arret al.  was used to calculate sequence similarity. For protocol 1, which corresponds to the algorithm in Schwarzenbacher  al. 2004, both thLSQMAN are employed a shorter averaging window is more advantageous; models generated by protocol 1 have on average 2–4% higher log-likelihood gain than those generated by protocols 3 and 2, respectively. This may be attributed to the alignment being so accurate that smearing out the signal is counterproductive. With less accurate  alignments (including that from LSQMAN with more tolerant settings), the differences are negligible. As expected from preliminary results, protocol 2 does not perform as well as protocol 3. On the other hand, all protocols occasionally lead to solutions that are not located by other protocols.Results indicate that when strict alignments from 3.3.et al. . These were determined from a small-scale study using the identity and BLOSUM62 matrices. The quality of the best models yielded by the algorithm with the two different scoring matrices showed only minor differences. However, short averaging windows gave better results in sequence-similarity calculations with BLOSUM62, while on the whole longer averaging windows were better with the identity matrix. The optimal pruning threshold was identical for both matrices.To enable the use of sequence-similarity scores in side-chain pruning similar to the algorithm of Schwarzenbacher  al. 2004, suitablLSQMAN were used (compared with results obtained with the respective basis protocols), but became progressively worse with decreasing alignment accuracy.To assess the performance on a larger benchmark, two protocols were formulated. Protocols 1 and 3 were modified so that side-chain pruning is performed using sequence-similarity scores calculated with the BLOSUM62 matrix, using an averaging window of one and the optimal pruning threshold (protocols 4 and 5). These protocols led to solutions with a slightly higher log-likelihood gain than those provided by protocol 1 when accurate alignments from 3.4.3.4.1.B factors with those calculated from sequence-similarity scores. It was established from calculations on a small sample that longer averaging windows were needed in sequence-similarity calculations for this to work well. Suitable values of the proportionality factor between sequence-similarity scores and B factors were also determined from this sample.It has been established that low values of sequence similarity correlate with large structural differences. This correlation could be exploited to weight the model structure according to expected coordinate errors. This was studied by replacing B factors from the scores, a proportionality constant of −80 (protocols 6 and 7) was used. The results indicate a strong dependence on alignment precision. The average log-likelihood gain increases by around 3% with respect to the corresponding basis protocol for structure-based alignments, but decreases by about 0.5% for alignments created with ClustalW. However, since sequence similarity is a property of alignment position only one B factor per residue could be used, which is a relatively simple B-factor model and may not be optimal.Two protocols were set up to test this method with models from the benchmark suite. As before, protocols 1 and 3 were modified to include main-chain weighting using sequence-similarity scores calculated with the BLOSUM62 matrix and an averaging window of five. To calculate atomic 3.4.2.et al. . Generally good results were achieved. When compared with the respective protocols that they were based on, both protocols 8 and 9 resulted in a 3–5% increase in log-likelihood gain. Interestingly, greater improvements were found with less precise alignments. This may be attributed to the frequent occurrence of incorrectly aligned residues on the surface.Two protocols were formulated to study the method on a larger sample. As before, protocols 1 and 3 were modified to reset atomic e.g. multimer models) and because of the selection criteria applied for the benchmark set the results may be biased. In difficult cases it is therefore worthwhile to try models generated with and without this step as well.It should be noted that inclusion of this procedure may lead to a worse model than the original in some circumstances  and it was studied whether a combination of the two would be more powerful. Firstly, optimal values for proportionality factors were determined for the combination . The obtained proportionality factors were similar to, although slightly lower than, the optimal values when the methods were used in isolation.B factors with values calculated using a combined protocol (protocols 10 and 11) and calculations were performed on the benchmark suite. Unexpectedly good results were obtained in terms of the number of solutions, number of identifiable solutions and log-likelihood gain. The increase in log-likelihood gain was about 8–9% when compared with the respective basis protocol, which is approximately twice as much as one would expect from adding up the gains achieved by the individual methods. It is likely that the combination is more tolerant to exact parameter choices and will perform optimally over a wider parameter range, since the two methods generate B-factor distributions that are similar and therefore one can compensate for errors in the other.To establish the performance of the combined method, protocols 1 and 3 were modified to replace atomic MOLREP may include an indirect contribution from sequence similarity, since accessible surface area will increase in low-sequence-similarity regions owing to many atoms being deleted from the model.It should be noted that accessible surface-area values as calculated in 3.5.B-factor calculation was revealed when a protocol based on protocol 11 but also containing side-chain pruning as in protocols 4 or 5 (protocol 12) was formulated and calculations were performed using the full benchmark suite. Minor or no improvements were expected based on the established performances of protocols 4 and 5, but significant improvements were observed. This may indicate a synergistic effect between side-chain pruning (performed using sequence-similarity scores) and B-factor calculation, potentially the part that is based on accessible surface area. The exact mechanism of this is not clear, although it is likely to emerge as a consequence of pruning being an extreme form of B-factor modification.The existence of further correlations between main-chain deletion, side-chain pruning and 3.6.The number of test cases that could be solved by any protocol was determined and was found to be significantly higher than the number of solutions obtained with any single protocol for all three alignments. Improvements in the number of solved cases were around 10% of the solutions found by the best protocol, while up to 20% more solutions could be identified from search statistics. This improvement is even more impressive when compared with the number of borderline cases, which is estimated by the number of cases that were not solved by all protocols: the multi-protocol strategy leads to 50–100% more borderline cases being solved.LSQMAN alignments, protocols 2, 6, 7, 8 and 11 or 2, 6, 7, 10 and 11 for tolerant LSQMAN alignments and protocols 2, 6, 7, 10, 11 and 12 or 2, 7, 5, 10, 11 and 12 for ClustalW. There are several common features in these combinations, as follows.LSQMAN alignments to 2/5 with tolerant LSQMAN alignments to 1/6–2/6 with ClustalW alignments.(i) All combinations contain at least one protocol with a short averaging window and one protocol with a long averaging window. Protocols with a short averaging window tend to perform better with a more accurate alignment, indicated by their share dropping from 3/6 with strict B-factor models used. In almost all combinations, identical models (in terms of atoms contained) are tested with three different B-factor protocols.(ii) There are usually several e.g. protocols 6 and 7).(iii) In every combination, there is at least one protocol that is among the best performers in terms of the average log-likelihood gain of models. However, certain protocols also appear in many combinations despite their seemingly low performance  usually indicates a correct solution. On the other hand, low values of the Z score do not exclude success and typically one has to make a judgement taking several parameters into account, such as the number of distinct solutions with similar quality and the absolute value of the log-likelihood gain. It frequently happens that a solution has been found but it is not possible to identify it from the search statistics. In such a case, automated rebuilding calculations may identify one of the candidates as a true solution  observed between the Z score and the log-likelihood gain in preliminary studies; notable exceptions were models that contained large incorrect segments owing to alignment errors. We could therefore assume that models that yield higher log-likelihood gains will also give better Z scores and would be more suitable for molecular replacement.Unfortunately, the translation-function LSQMAN and ClustalW, respectively). On the other hand, there is a relatively strong correlation between fractional log-likelihood gain and number of identifiable solutions . Therefore, protocols that yield models with higher log-likelihood gains are more likely to provide solutions that can be identified from search statistics. Exploring a range of protocols can be instrumental in covering model space and finding unique solutions.Analysis of Table 24.1.B factors should conform to: they have to match the B-factor distribution of the target structure and at the same time downweight structural regions that potentially differ between the target and the model. The original B factors of the model are therefore a good default choice since they provide a B-factor distribution that resembles a real protein structure. However, they are influenced by crystal packing, which is not a transferable property from one protein model onto another. It may therefore be advantageous to replace the original B factors with those calculated from other sources. It was found that a combination of B factors calculated from accessible surface-area and sequence-similarity values performs favourably and may be used as a default choice. An alternative method would be the combination of the original B factors with those calculated from sequence-similarity scores, in which case the original model B factors would be responsible for matching the B-factor distribution of the target, while those calculated from sequence similarity would downweight potentially different regions.There are multiple criteria that optimal 4.2.B-factor adjustment, the structures obtained are sufficiently diverse that they could be employed in molecular replacement as unique models although they are based on the same structural template. Similar behaviour can be observed on a set of ensemble models truncated to various r.m.s.d. cutoffs  Varying the averaging-window parameter for main-chain deletion can have a large effect on the resulting trace. Good results could be obtained when a combination of one short and one longer averaging window was used. This may be improved slightly by trying additional values. Longer averaging windows perform better for less accurate alignments.B factors according to simple B-factor models  works surprisingly well. It may therefore be beneficial to explore additional B-factor models. One possibility would be to employ original model B factors to estimate the B-factor distribution of the target in combination with predicted coordinate error weighting calculated from sequence-similarity and accessible surface-area values.(ii) Calculating atomic It is tempting to speculate on how the best coverage of accessible model space could be achieved. Based on observations made on best-performing protocol combinations, the following may be beneficial.et al.  as a structural alignment prepared using tolerant settings, which approximates the best that might be achieved by sequence-based alignments. This may indicate that smaller errors can be compensated efficiently by using a number of protocols. More accurate alignments still seem to be important in helping solutions stand out from the noise, as indicated by the number of identifiable solutions being higher for structure-based alignments.When cumulative results with models generated from a single template using several protocols are compared the differences are minute and 4.5.Sculptor has many options and their effects on the resulting structure are somewhat obscure. Therefore, an interface between Sculptor and Coot  to a larger extent. The combination of all these features makes Sculptor a powerful tool. A visual interface (utilizing the Coot toolkit) has also been developed to help users experiment with available options and define optimal protocols.The model-editing program Sculptor confirm that it can generate a diverse set of molecular-replacement models from a single template structure. Although some of these models may perform better than those that are in current use, significantly better results can be obtained if these are employed as alternatives in a molecular-replacement search. This strategy can increase the success rate by up to 30% in the 20–30% sequence-identity region and can also compensate for alignment inaccuracies. A selection of protocols that maximizes diversity would therefore enhance the success rate in molecular-replacement pipelines.Benchmarks performed with Sculptor (including the Sculptor–Coot interface) is currently available in the PHENIX suite (http://www.phenix-online.org). Work is ongoing on incorporating it into the CCP4 suite and the development of a ccp4i GUI is also in progress.