Protein sequence profile-profile alignment is an important approach to recognizing remote homologs and generating accurate pairwise alignments. It plays an important role in protein sequence database search, protein structure prediction, protein function prediction, and phylogenetic analysis.In this work, we integrate predicted solvent accessibility, torsion angles and evolutionary residue coupling information with the pairwise Hidden Markov Model (HMM) based profile alignment method to improve profile-profile alignments. The evaluation results demonstrate that adding predicted relative solvent accessibility and torsion angle information improves the accuracy of profile-profile alignments. The evolutionary residue coupling information is helpful in some cases, but its contribution to the improvement is not consistent.Incorporating the new structural information such as predicted solvent accessibility and torsion angles into the profile-profile alignment is a useful way to improve pairwise profile-profile alignment methods. Pairwise protein sequence alignment methods have been essential tools for many important bioinformatics tasks, such as sequence database search, homology recognition, protein structure prediction and protein function prediction –5. FolloDue to their relatively high sensitivity in recognizing remote protein homologs, profile-profile alignment methods have become the default structural template identification method for many template-based protein structure modeling methods and servers –14. For In order to more accurately align the structurally equivalent residues in a target protein and a template protein together, secondary structure information was incorporated into profile-profile sequence alignment methods, yielding the better sensitivity and accuracy , 17. AimSpecifically, we add the additional scoring terms for solvent accessibility, torsion angles, and evolutionary residue coupling information into the scoring function of HHsuite  in orderWe extended an existing profile-profile alignment method within the standard five-step alignment framework of HHsuite  shown inq and a template profile t) in HHsuite was calculated according to Equation  and tj(a) denote the probability of amino acid at position i in the query profile and at position j the template profile, respectively, and f(a) is the background frequency of residue a . The best alignment between two profile HMMs was obtained by maximizing the log-sum-odds score SLSO according to Equation  and j(k) are the respective columns in q and t, Ptr is the product of all transition probabilities for the path through q and t. The latest version of HHsuite has included the secondary structure information into the calculation of the score. In this work, we further augment the calculation of the score by adding the terms to account for the solvent accessibility, and torsion angles.where SAB  representing matching different states  in two SIM and SGD are calculated similarly as SMI and SDG.Ssa, Stors) were added to utilize the solvent accessibility and torsion angle information. In Equation  is the secondary structure score between column i in query HMM (qi) and column j in template HMM (tj), which was the same as the one originally used in HHsuite. Ssa is the solvent accessibility score between qi and tj, and Stors is the torsion angle score between qi and tj, which are the new terms introduced in this work. wss, wsa, and wtors are weights for the secondary structure score, solvent accessibility score and torsion angle score respectively. Sshift is the score offset for match-match states. Three weights wss, wsa, wtors and shift score Sshift are set to 0.11, 0.72, 0.4 and −0.03 by default, and can be adjusted by users as well. qi − 1 is the transition probability from state M at column i-1 to next state M of in the query HMM, and tj − 1 is the transition probability from state M at column j-1 to next state M in the template HMM.The difference between Equation  above anEquation , Sss of the query protein and the jth residue (yj) of the template protein are sa(xi) and sa(yj), the solvent accessibility score between the two residues Ssa is defined as:Here we denote this extension of the HHsuite method as HMMsato. HMMsato allows for scoring predicted (or known) solvent accessibilities of one protein against predicted (or known) ones of another protein. DSSP  is used δ, which equals to 1 if a = b, 0 otherwise.The score is calculated by the kronecker-delta function φ) and psi angle (ψ) can be automatically predicted by SPINE-X [φ and ψ is . Given the query sequence X and template sequence Y, the predicted phi angle and psi angle of the i-th residue xi in the query are denoted as φ(xi) and ψ(xi), and those of the j-th residue yj in the template as φ(yj) and ψ(yj). The torsion angle score Stors between the two residues is calculated as:Similarly as the solvent accessibility, the torsion angles including both phi angle  algorithm can generally create a more accurate alignment than the Viterbi algorithm, while the latter can generate better alignment scores, e-values and probabilities , 24. Conmact)  to very precise, short local alignments (mact ≈ 1). The default value of mact is set to 0.3501 in HMMsato as in HHsuite. To find the best MAC alignment path, an optimal sub-alignment score matrix AS is calculated recursively using the posterior probability The maximum accuracy algorithm , 24 creaFMM and Backward partition function BMM are introduced to calculate the posterior probability for pair state . FIM and FGD are calculated similarly as FMI and FDG. Solvent accessibility score Ssa and torsion angle score Stors are calculated as in the Viterbi alignment.where BMM are calculated recursively as follows:In analogy to the Forward partition function, the Backward partition function matrix BIM and BGD are calculated similarly as BMI and BDG.i, j) of each profile according to Equation (The Evolutionary Coupling (EC) stands for the correlation between two positions or columns in a multiple protein sequence alignment or a protein profile , 20. It Equation .12N is 21, standing for 20 amino acids plus gap. The joint probability of two residues Xi and Xj ) and the probability of residue Xi (Fi(Xi)) are calculated in the same way as in [ECij is calculated as the mutual information (MI) instead of the direct information (DI) based on the global probability model [ay as in . Howeverty model  in orderAS (see Equation (i in query q as kq(i), and the coupled position of position j in template t as kt(j). Moreover, Mq(i) denotes the position in template t matched with position i in query q when tracing back the original AS matrix, Mt(j) denotes the position in query q matched with position j in template t when tracing back the original AS matrix, and wec is the weight for the evolutionary coupling information. The new AS' matrix integrating the evolutionary coupling information is recalculated as follows during the track back process.Based on the calculated EC value matrices for both the query and template profiles, top highly correlated position pairs with higher EC values for each profile are selected. The evolutionary residue coupling information is then applied to check the counterpart pairs during the process of tracing back through the sub-alignment score matrix Equation ) of the Figure th Critical Assessment of Techniques for Protein Structure Prediction (CASP9) [We evaluated HMMsato along with HHSearch  and HHsu (CASP9) , 16 and  (CASP9)  to align (CASP9) . The quaThe SP score is the number of correctly aligned pairs of residue in the predicted alignment divided by the total number of aligned pairs of residues in the core blocks  of the true alignment . The TC wsa = 0.72) for solvent accessibility. Then, we identified the best weight value (wtors = 0.4) for torsion angles while keeping the weight for solvent accessibility fixed. Finally, we found the best parameter value (wec = 0.1) for the evolutionary residue coupling information by keeping wsa and wtors at their optimum values. HHsearch and HHsuite were both evaluated with and without secondary structure information. The default parameter values were used with HHsearch and HHsuite.We estimated the weights of the solvent accessibility, torsion angles and evolutionary residue coupling information on the training alignments step by step. Firstly, we found the best weight value . The highest accuracy is achieved when wsa is set to 0.72. Figure sa. Red curve represents the SP scores and blue represents the TC scores.We studied the effect of the solvent accessibility information by solely adjusting the value of its weight wtors (weight for torsion angle information) while keeping wsa as 0.72. The SP scores and TC scores of the alignments generated by HMMsato with different wtors values on the training data set are shown in Table tors is set to 0.4. Figures tors values.We studied the effect of torsion angles on alignments by solely adjusting the value of wwec was 0.1. However, the evolutionary coupling information did not improve the overall alignment accuracy on the training data set, probably due to lack of a large number of diverse sequences in many cases required by the evolutionary coupling calculation to obtain the sufficient discriminative power. Specifically speaking, the alignment quality increased in 57 alignments, stayed the same in 1363 alignments, but decreased in 61 alignments. Similarly, on the test data set, the alignment quality increased in 59 alignments, stayed the same in 1024 alignments, but decreased in 55 alignments. Generally speaking, the evolutionary coupling information contributed to the improvement of alignment accuracy in some cases, but its effect was rather inconsistent.We studied the effect of the evolutionary residue coupling information on alignment accuracy in a similar way. HMMsato worked the best when We studied the SP score differences between HMMsato and HHSearch with secondary structure for all the 1138 testing pairs. The plot of the SP score difference (SP score of HMMsato minus SP score of HHSearch) for these pairs is shown in Figure We designed a method to incorporate relative solvent accessibility, torsion angles and evolutionary residue coupling information into HMM-based pairwise profile-profile protein alignments. Our experiments on the large CASP9 alignment data set showed that utilizing solvent accessibility and torsion angles improved the accuracy of HMM-based pairwise profile-profile alignments. However, the effect of the evolutionary residue coupling information on alignments is less consistent according to our current experimental setting, even though it may still be a valuable source of information to explore in the future. Particularly, we will use the latest method  of calculating evolutionary coupling information to guide the profile alignment process. Furthermore, we will carry out more extensive search of optimal weights for solvent accessibility, torsion angle, secondary structure, and evolutionary coupling information to improve alignment accuracy.


Accurate multiple sequence alignment is central to bioinformatics and molecular evolutionary analyses. Although sophisticated sequence alignment programs are available, manual adjustments are often required to improve alignment quality. Unfortunately, few programs offer a simple and intuitive way to edit sequence alignments.We present Seqotron, a sequence editor that reads and writes files in a wide variety of sequence formats. Sequences can be easily aligned and manually edited using the mouse and keyboard. The program also allows the user to estimate both phylogenetic trees and distance matrices.https://github.com/4ment/seqotron/.Seqotron will benefit researchers who need to manipulate and align complex sequence data. Seqotron is a Mac OS X compatible open source project and is available from Github  State-of-the-art methods of multiple sequence alignment such as MUSCLE  and MAFFHerein, we present a user-friendly application for visualizing, aligning, and manually editing genomic and protein sequences, and for converting between a variety of file formats. Alignments can be generated automatically using the MUSCLE  and MAFFSeqotron is written in Objective-C and uses Cocoa, the native application programming interface for the Mac OS X operating system.Seqotron is designed for visualizing, aligning, and editing nucleotide and amino acid sequences Fig. . UnalignGiven an accurate alignment of homologous sequences, it is natural to investigate the evolutionary history of the underlying organisms using phylogenetic methods. Seqotron allows the inference of phylogenetic trees using Physher  from botFinally, Seqotron supports natively the Quick Look technology that enables the Finder to display a quick preview of an alignment file and other useful information such as the number of sequences and the alignment length.A comparison of the features available in Seqotron and other editors is provided in Table We have presented an open source, memory efficient, and user-friendly desktop application to automatically or manually align and edit multiple nucleotide and amino acid sequences. Seqotron also provides the option to estimate phylogenetic trees and distance matrices. We aim to add more functionalities in the future, such as creating a plugin mechanism and algorithms for searching sequence motifs.Project name: Seqotron.https://github.com/4ment/seqotron/.Project home page: Operating system: Macintosh OS X (Intel) version 10.8 and higher.Programming language: Objective-C/Cocoa.License: GNU GPL version 3.Any restrictions to use by non-academics: None.


Markov chain Monte Carlo (MCMC) sampling, which is widely recognized as the most effective approach for characterizing a complex, high dimensional distribution. Other routines then map correlated residue patterns to available structures with a view to hypothesis generation. When applied to N-acetyltransferases, this reveals sequence and structural features indicative of functionally important, yet generally unknown biochemical properties. Even for sets of proteins for which nothing is known beyond unannotated sequences and structures, this can lead to helpful insights. We describe, for example, a putative coenzyme-A-induced-fit substrate binding mechanism mediated by arginine residue switching between salt bridge and π-π stacking interactions. A suite of programs implementing this approach is available (psed.igs.umaryland.edu).Over evolutionary time, members of a superfamily of homologous proteins sharing a common structural core diverge into subgroups filling various functional niches. At the sequence level, such divergence appears as correlations that arise from residue patterns distinct to each subgroup. Such a superfamily may be viewed as a population of sequences corresponding to a complex, high-dimensional probability distribution. Here we model this distribution as hierarchical interrelated hidden Markov models (hiHMMs), which describe these sequence correlations implicitly. By characterizing such correlations one may hope to obtain information regarding functionally-relevant properties that have thus far evaded detection. To do so, we infer a hiHMM distribution from sequence data using Bayes’ theorem and  Protein sequence data, when gathered in great quantity, contain important but implicit biological information manifest as statistical correlations. Here we describe an approach to access this information by comprehensively modeling and characterizing the distribution of sequences belonging to a major protein superfamily. This approach takes as input a large set of unaligned sequences belonging to the superfamily. By applying the minimum description length principle, it seeks the statistical model that best explains the sequences while avoiding over-fitting the data. It concurrently aligns the sequences and, to model evolutionary divergence, partitions them into subgroups that are hierarchically-arranged based upon correlated residue patterns. Auxiliary routines create PyMOL scripts to visualize the locations of correlated residues within available structures. Because these correlations likely arise from structural and biochemical constraints, they can help elucidate protein properties important for functional specificity. Comparing and contrasting sequence and structural features in this way may therefore suggest, in the light of published studies, plausible biological hypotheses for experimental investigation. We illustrate this approach with N-acetyltransferases. Fig 1)  bits. For example, if c = 200, t = 10, and we choose p = 0.1, this comes to about 160 bits per node. For n = 250 nodes, the description length of all discriminating columns and their associated patterns is about 40,000 bits. In practice, we limit the number of discriminating columns for each node to ≤ m, where m = 25 by default, and place decreasing prior probabilities on progressively larger residue sets, as previously described  ≡ Aj − {ak,j} to denote the set Aj without ak,j and define {A} ≡ {ak,j: k = 1,..,K, j = 1,…,w} to denote the set of residues indices for the alignment variable A. We represent the collection of residues indexed by elements in a set C as RC. For instance, RA}{ = {ak,j: k = 1,…,K; j = 1,…w} represents the set of residues in the alignment defined by A.X defines a w column alignment; R specifies the sequences; j of the alignment and outside of aligned columns, respectively; and βj and β0 specify the numbers of pseudocounts in each column j and in the background, respectively. We model indels based on the hidden Markov model (HMM) shown in S1.1 Fig. The sampler infers position-specific gap penalties, as follows: For a given alignment, each sequence is associated with a “path” through the HMM indicating its alignment against the model. We denote the collection of these paths by Λ, the total number of HMM transitions of type M→M, M→I, …, D→D at position j by Nmm[j], Nmi[j], …, Ndd[j], and corresponding prior pseudocounts by nmm,…,ndd. The contribution of implicit gap penalties to the overall probability, after integrating out position-specific transition probabilities (Ignoring insertions and deletions (indels), the MSA posterior distribution –71 is deThis gives rise to a new posterior distributionnce data , 71.BPPS sampling. A hierarchical alignment consists of a MSA, a tree—each node of which corresponds to a contrast alignment —and a set of labels assigning each aligned sequence to one of the nodes. Each contrast alignment consists of a pattern and a foreground or a background partition corresponding, respectively, to the subtree rooted at that node and to the rest of the subtree rooted at the parent of that node. By sampling over alternative sequence and pattern assignments, our BPPS sampler seeks to optimally partition the sequences into subgroups where the foreground sequences conserve a pattern that the background sequences do not [a priori, we know neither which sequences belong to each node, nor which positions are pattern positions, nor which residues are conserved at each pattern position. The sampler also seeks to optimize the number of nodes and the relationships between nodes . Thus the sampler favors convergence on a hierarchy where the pattern and partitioning for each node best distinguishes its foreground from its background. The probability of the data given the parameters of the BPPS statistical model is defined  as:X defines a sequence alignment of k columns, the probability of which is defined by Eq  and from which the BPPS sampler infers H,S,A,α, and Θ; H defines the hierarchy with h foreground and background node sets, respectively; S specifies assigned sequence sets for each node; A defines foreground pattern residue sets where α specifies the fraction of background ‘contamination’ at pattern positions in the foreground; Θ specifies residue compositions with θh,j the background. See [s do not . MCMC saund. See –24 for dFig 2A are accomplished using our recently described MSA [w-column alignment, the sequences of which are partitioned into hierarchically-arranged subgroups. Converting this into a hiMSA  involves the following: (i) Applying MSA sampling to refine the alignment of each set of subgroup sequences, starting with the root node’s child subtrees and recursively progressing to descendant subtrees. This will extend sub-alignments into subgroup-specific insert regions and will remove regions from each sub-alignment that are deleted relative to its corresponding super-alignment . To improve speed, all but one among each set of highly similar sequences  may be removed. (ii) The lineage-specific alignments are aligned to each other (based on the hierarchy) to construct a set of template alignments, as illustrated schematically in S1.2C Fig. These templates define how each of the subtrees is aligned to its parent node, which is important for defining BPPS foreground and background frequencies (see Eq ((iii) Apply BPPS sampling to find additional pattern positions within subgroup-specific insert regions. Because these insert regions are absent from the background alignment, standard amino acid residue frequencies are used as the background. (iv) Finally, BPPS sampling is performed to further refine the hiMSA and thus the hiHMM.Steps 1 and 2 in ibed MSA  and BPPSibed MSA , 24 sampFig 2D. The hiHMM defined by this process can be used to search the protein database using MAPGAPS [This process creates a hierarchical alignment, for which the sequences assigned to each subtree in the hierarchy are more or less optimally aligned for that subtree. In other words, only those regions that are conserved across each subtree’s sequence set are aligned—as is illustrated schematically in  MAPGAPS .Fig 2B) are created. This is illustrated in S2.2, S2.3 and , which show the set of contrast alignments corresponding to the lineages from the root to various leaf nodes, with one contrast alignment for each node along the lineage. In essence, each lineage-contrast-alignment decomposes the constraints imposed on the sequences assigned to that leaf node. This is perhaps the most important information obtained from the analysis. These lineages, one for each of the leaf nodes, are concatenated into a single rich text format (rtf) file as output. Another previously-described [Since the focus of our analysis is on large, functionally diverse protein superfamilies, hiHMM sampling produces a large amount of output. To make this output intelligible, several procedures are used to summarize the results. First, for each leaf node hierarchical contrast alignments  were implemented in the following C++ programs: MAPGAPS [The key steps of hiMSA analysis Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 FigThe sequences used for the acetylase analysis are available at psed.igs.umaryland.edu.(PDF)Click here for additional data file.S5 FigThese figures were adapted from .(PDF)Click here for additional data file.


The ever-increasing size of sequence databases caused by the development of high throughput sequencing, poses to multiple alignment algorithms one of the greatest challenges yet. As we show, well-established techniques employed for increasing alignment quality, i.e., refinement and consistency, are ineffective when large protein families are investigated. We present QuickProbs 2, an algorithm for multiple sequence alignment. Based on probabilistic models, equipped with novel column-oriented refinement and selective consistency, it offers outstanding accuracy. When analysing hundreds of sequences, Quick-Probs 2 is noticeably better than ClustalΩ and MAFFT, the previous leaders for processing numerous protein families. In the case of smaller sets, for which consistency-based methods are the best performing, QuickProbs 2 is also superior to the competitors. Due to low computational requirements of selective consistency and utilization of massively parallel architectures, presented algorithm has similar execution times to ClustalΩ, and is orders of magnitude faster than full consistency approaches, like MSAProbs or PicXAA. All these make QuickProbs 2 an excellent tool for aligning families ranging from few, to hundreds of proteins. Multiple sequence alignment (MSA) is of crucial importance in life sciences. The ability to reveal evolutionary and structural relationships between sequences makes MSA the basic tool in a number of biological analyses, including phylogeny, structure prediction, gene finding, and many others. Rapid dissemination of high throughput sequencing technologies causes sequence databases to grow exponentiallyAmong many proposed heuristics for finding multiple sequence alignments, progressive scheme has become the most popular. It consists of three steps: (I) estimating evolutionary distances between sequences, (II) building a guide tree based on the distances, (III) greedy alignment of sequences in the order described by the tree. The classic representative of progressive aligners with more than 50 thousand citations  is ClustalWIn this article, we give a new insight into the effect of refinement and consistency on the progressive alignment. We investigated large sequence sets showing that accuracy of the aforementioned techniques scales unsatisfactorily with the number of sequences. In particular, when sets of hundreds or thousands of sequences are of interest, existing refinement variants have little effect on alignment quality, while consistency decreases it by introducing more noise than relevant information. We present new ideas to overcome those issues. i.e., column-oriented refinement and selective consistency.The research was based on QuickProbs algorithmIn this paper, we introduce QuickProbs 2, a novel algorithm for multiple sequence alignment. It consists of four stages: (I) calculation of posterior probability matrices, (II) construction of the guide tree, (III) consistency transformation, (IV) construction of the final alignment followed by the iterative refinement. Posterior probability matrices are calculated for all sequence pairs on the basis of hidden Markov modelThe most important advances with respect to existing methods were achieved at stages III and IV. QuickProbs 2 has been equipped with a novel column-oriented refinement and selective consistency, which are described further in following subsections. A separate subsection concerns other algorithmic improvements and new facilities introduced in the presented algorithm. Finally, we describe in detail benchmark datasets and measures used for quality assessment.Refinement was designed to overcome the most important disadvantage of progressive algorithms–misalignments caused by the propagation of errors from early progressive steps up the guide tree. Usually, the procedure employs an iterative scheme of alternate splits and realignments and incorporates an objective function for results evaluation. A number of refinement strategies were investigated in the literature2122First revision of QuickProbs, similarly to ProbCons or MSAProbs, employs the former idea: each refinement iteration splits an alignment randomly into two horizontal profiles and realigns them after removing columns containing only gaps. No objective function is incorporated. The substantial drawback of the procedure is that the larger the number of sequences, the smaller the chance of producing profiles with gap-only columns. As a result, no columns are removed in the majority of cases and the realigned profile is likely to be the same as the input one. Therefore, for numerous sets, consecutive random refinements give no improvement in accuracy. An alternative approach, incorporated e.g. by MUSCLE or MAFFT, is tree-guided refinement. It splits the alignment by breaking randomly selected branch in the guide tree. As gap-only columns are more likely to occur due to gathering phylogenetically related sequences in subprofiles, this approach can potentially be more successful when large protein families are investigated.column-oriented and, as experiments show, it is superior to the random and tree-guided approaches, especially for large sequence sets. We present a new approach to the refinement which considers columns containing at least one gap. The algorithm selects randomly one of those columns and splits the alignment into two profiles depending on the gap presence in this column. As a result, at each refinement iteration at least one profile is shortened increasing significantly the chance of rearranging the alignment and producing a higher quality outcome. This type of refinement will be referred to as g in a column, according to which an alignment is divided, affects the sizes of the resulting profiles. The closer is g to the half of the sequence set size N, the more balanced is the division. To investigate the effect of imbalance in profile splitting on alignment quality columns were sorted with respect to An important observation is that the number of gaps unsupervised SP score under assumed substitution matrix and gap penalty model  is amongst the most popular522The refinement is often facilitated by introducing an objective function. The usage of trident score , with L being the sequence length, makes this stage very time consuming. Precisely, posterior matrices are represented in a sparse form with a sparsity coefficient β < 1. As presented in O(β2N3L3) to O(βN3L3). Nevertheless, as QuickProbs comes with a fast relaxation algorithm suited for graphics processors, we were able to investigate the effect of consistency on sets exceeding one thousand sequences. As presented in the experimental section, the procedure decreased alignment quality for protein families of such sizes.The time complexity of selective consistency. Given x, y, z sequences and dxz, dyz distances, posterior matrix Sxy is relaxed over sequence z if an aggregation function α fulfills given condition. In the research we investigated two different dxy measures:score-based distance calculated at stage I, ranked and normalized to  interval,x and y.tree-guided distance defined as a number of nodes in a minimal subtree containing both The challenge which naturally arises, is to apply consistency only on sequences carrying most of the information. Particularly, we examined whether there is a correlation between information content and evolutionary relationship of sequences involved in the consistency. For this purpose we introduce α. Selectivity was applied either by:α on arbitrary value T,deterministically thresholding applying stochastic filtering.Maximum, minimum, or sum can be used as examples of aggregation function filter function F which maps the value of the aggregation function α to the probability of performing relaxation over sequence z, i.e.: F(α): α → . Shape of the filter function determines which sequences are preferred in the consistency procedure (e.g. closely or distantly related). The procedure of stochastic selectivity for matrix Sxy over sequence z works according to the following steps:α0 = α according to the assumed distance measure d and aggregation function α,calculate the value of F(α0),determine the value of the filter function p from the uniform distribution ,sample a random number F(α0) ≤ p, perform relaxation of Sxy over z.if The latter requires defining a As combination of tree-based distances and deterministic thresholding rendered superior results, we explain this variant of selectivity in Sxy compared to the matrices it is multiplied by. E.g., a matrix relaxed by thirty sequences contributes to the transformation ten times less than that relaxed by three. To overcome this, we additionally analysed the effect of multiplication of Sxy elements by a coefficient hxy. The value of hxy is set individually for each matrix and varies linearly from 1, when no relaxations of Sxy are performed, to user-defined value h, when maximum number of relaxations under chosen selectivity settings is done (200 in our case). This allows sets of different sizes to be handled properly.The side effect of selectivity is the variability in the number of relaxations performed for different posterior matrices. Consequently, the larger the number of sequences undergoing consistency transformation, the weaker is the information from the original In spite of focusing QuickProbs 2 research on extending refinement and consistency stages, calculation of posterior matrices was also a subject to some modifications. Quality improvements include replacing Gonnet160 matrix for partition function calculation by VTML200, which was proven to be more accurateThe presented algorithm is equipped with a nucleotide mode in which HOXD substitution matrixN < 50, 1 otherwise). It was also discovered that for two consistency transformations, 30 iterations of refinement instead of default 200 is sufficient to get satisfactory convergence.Due to different behaviour of consistency depending on the set size, the number of transformations is adjusted to the number of sequences  and total column (TC) scores defined as a fraction of correctly aligned symbol pairs and columns, respectively. When a single quality measure was needed, e.g., for visualization, a geometric mean In the initial experiments, we investigated random and tree-guided refinements together with different variants of novel column-oriented procedure. As refinement was acquired by alignment algorithms formerly to consistency, the latter was disabled in this experimental part. BaliFam-800 × 2 benchmark was selected as a representative of large protein families instead of BaliFam because it contains twice as many sets which reduces results variability. The effect of consecutive refinement iterations is presented in As charts show, for numerous protein families such as those in BaliFam-800 × 2, consecutive random refinements gave no gain in the accuracy. Moreover, random procedure was profitable only for BAliBASE and starting from BaliFam-200 × 16 it had no effect on the results. The performance of tree-guided refinement was noticeably better, however the improvement declined with the increasing number of sequences. The opposite situation occured in the case of column-oriented refinement. Not only it was superior to the competing approaches, but the advance over non-refined output was characterized by perfect scalability. Namely, it increased from 2% on BAliBASE to almost 7% on BaliFam, confirming the selection of gap-only columns to be the choice for large protein families. When analysing the effect of split imbalance on alignment quality, it is visible that narrowing the subset of columns considered in the selection to 50% or 20% of most balanced/imbalanced positions caused accuracy decay. Consequently, the version without preference was chosen for further investigation.The final refinement experiments concerned the effect of different acceptance rules. Those were non-increasing alignment length and non-decreasing entropy score. As presented in To investigate the accuracy of column-oriented refinement in different classes of alignment problems, all BaliFam subsets were analysed independently. They correspond to BAliBASE 3 reference sets representing: equidistant sequences of 0–20% ref.  and 20–4α. z was performed when sum or maximum of tree-based distances dxz and dyz was smaller than assumed threshold T. The comparison of selectivity strategies  which is a noticeable improvement over full consistency variant. The comparison of execution times . Software packages suited for parallel processing were run with 12 processing threads to fully utilize multi-core architecture of the CPU.The comparison of alignment software on benchmark datasets is given in 1K), consistency methods became inapplicable due to hardware limitations. Moreover, the accuracy of consistency was often unsatisfactory, as in the MSAProbs case. For these reasons, ClustalΩ became the choice when numerous alignments were of interest. Nevertheless, thanks to the column-oriented refinement and selective consistency, QuickProbs 2 was noticeably more accurate than ClustalΩ on both large sets. E.g., the greatest advantage observed on BaliFam in TC score corresponds to almost 25% more successfully aligned columns. When one considers ClustalΩ with two combined iterations enabled, QuickProbs 2 was still superior by a fair margin. 1K benchmarks. For all families in a benchmark, absolute advantages of QuickProbs over competing software in SP and TC measures were determined. For each measure, the differences were sorted and plotted on a chart as two independent series. The points above the horizontal axis represent sets on which QuickProbs 2 was superior, the ones below correspond to the opposite situation. This way one can asses on what portion of the dataset and to what extent one algorithm performed better than the other. The advance of QuickProbs 2 over default variant of ClustalΩ is clear: on both analysed benchmarks our algorithm was superior to the competitor on approximately 3/4 families. This was also the case for ClustalΩ-iter2 on HomFam1K. A bit different situation was for BaliFam, where enabling combined iterations noticeably improved ClustalΩ results. Though, it was still clearly inferior to QuickProbs 2.For small sets of sequences  QuickProbs 2 competes with other consistency-based algorithms. Experiments show QuickProbs 2 to overcome them by a small margin (the distance to the second best does not exceed one percentage point on both SP and TC) with an exception of SABmark where GLProbsα=0.05, the Bonferroni-Holm correction was applied. Low p-values for BaliFam and HomFam1K give strong evidence that QuickProbs 2 is currently the best algorithm for alignment of large sets of sequences also when compared to ClustalΩ-iter2 and MAFFT-L-INS-i. The lack of significance was observed in few cases concerning small sets only (including the advantage of GLProbs over QuickProbs 2).The effect of presented algorithm being worse than ClustalΩ on several test cases is natural and is visible also when comparing other algorithms. For instance, combined iterations were reported to significantly elevate the quality of ClustalΩ7Superior accuracy of QuickProbs 2 on large protein families coincides with reasonable computational requirements. QuickProbs 2 is comparable to default mode of ClustalΩ in terms of execution times and orders of magnitude faster than consistency-based methods . As QuickProbs 2 employs OpenCL, it can be executed on different massively parallel devices like NVidia and AMD GPUs. Moreover, presented software has also the ability to be run on central processor without OpenCL. As experiments on different hardware platforms show , CPU varThe bottleneck of QuickProbs 2 are the memory requirements, particularly the neccessity to store posterior matrices for all pairs of sequences. E.g. 8 GB of RAM was needed to process 1,000 sequences of length 100 or 300 sequences of length 500. When 64 GB was available, presented algorithm successfully aligned familes of 1,300 proteins with 500 amino acids.N < 100), when methods based on full consistency like MAFFT-L-INS-i, MSAProbs, or PicXAA are applicable, QuickProbs 2 is still superior to the competitors. What is important, outstanding accuracy is obtained in a short time thanks to the utilization of massively parallel architectures.Constantly growing availability of genomic and proteomic data opens new opportunities in life sciences. Yet, it is a major challenge facing algorithms for sequence analyses, including multiple sequence alignment. Increasing number of sequences is one of the most important factors determining the difficulty of the MSA problem. In our research we have confirmed refinement and consistency, two most popular quality-aimed techniques employed by progressive aligners, to be ineffective or even harmful for sets of hundreds and more sequences. We present QuickProbs 2, a multiple alignment algorithm equipped with novel column-oriented refinement and selective consistency. It scales well with the number of sequences offering significantly better accuracy than ClustalΩ—the previous leader for analysing large sets of sequences. For less numerous sets .Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


A profile-comparison method with position-specific scoring matrix (PSSM) is among the most accurate alignment methods. Currently, cosine similarity and correlation coefficients are used as scoring functions of dynamic programming to calculate similarity between PSSMs. However, it is unclear whether these functions are optimal for profile alignment methods. By definition, these functions cannot capture nonlinear relationships between profiles. Therefore, we attempted to discover a novel scoring function, which was more suitable for the profile-comparison method than existing functions, using neural networks.Although neural networks required derivative-of-cost functions, the problem being addressed in this study lacked them. Therefore, we implemented a novel derivative-free neural network by combining a conventional neural network with an evolutionary strategy optimization method used as a solver. Using this novel neural network system, we optimized the scoring function to align remote sequence pairs. Our results showed that the pairwise-profile aligner using the novel scoring function significantly improved both alignment sensitivity and precision relative to aligners using existing functions.We developed and implemented a novel derivative-free neural network and aligner  for optimizing sequence alignments. Nepal improved alignment quality by adapting to remote sequence alignments and increasing the expressiveness of similarity scores. Additionally, this novel scoring function can be realized using a simple matrix operation and easily incorporated into other aligners. Moreover our scoring function could potentially improve the performance of homology detection and/or multiple-sequence alignment of remote homologous sequences. The goal of the study was to provide a novel scoring function for profile alignment method and develop a novel learning system capable of addressing derivative-free problems. Our system is capable of optimizing the performance of other sophisticated methods and solving problems without derivative-of-cost functions, which do not always exist in practical problems. Our results demonstrated the usefulness of this optimization method for derivative-free problems. The profile-comparison alignment method with a position-specific scoring matrix (PSSM)  is a higThe expression of nonlinear functions can be realized by neural networks. A neural network is a computing system that mimics biological nervous systems. Theoretically, if a proper activation function is set on middle layer(s) of a network, it can approximate any function including nonlinear functions . Neural Since neural networks are capable of implementing nonlinear functions, they are suitable for developing novel scoring functions for PSSV comparison. Therefore, in this study we used a neural network to optimize a nonlinear scoring function associated with PSSV comparison by combining two PSSVs as an input vector. Since we lacked a target vector normally required to implement supervised learning, we calculated the entire DP table for the input sequences, and the difference between the resultant alignment and the correct alignment was used to calculate cost of learning. Due to the nature of the problem, we could not use the backpropagation method as a solver for optimal weight and bias searches, because we lacked the derivative-of-cost function normally required. These issues are common when applying such methods to real-world problems. It is impossible to calculate a derivative for problems where the output vectors are not directly used for computation of cost function such as cross entropy or square error . In thisHere, we used a covariance matrix adaptation-evolution strategy (CMA-ES)  as a solclass, fold, superfamily, and family. To guarantee independence between a learning and test dataset, all notations of superfamily in the dataset were sorted in alphabetical order, and all superfamilies, the ordered numbers of which were multiples of three, were classified into a learning dataset, whereas the others were classified into a test dataset. This procedure is often used in existing studies for protein sequence analysis [superfamily to negate a bias induced by different volumes of each superfamily and used these sequence pairs for subsequence construction of a PSSM. We confirmed that sequences in each pair were from the same family in order to obtain decent reference alignments. We ultimately obtained 1721 and 3195 sequence pairs in the learning and test datasets, respectively. These datasets are provided at https://github.com/yamada-kd/nepal.We downloaded the non-redundant subset of SCOP40 (release 1.75) , in whicanalysis , 9, in oWe constructed PSSMs for all sequences in the learning and test datasets using DELTA-BLAST version 2.2.30+ with the Conserved Domain Database for DELTA-BLAST version 3.12 . Referenxa (PSSV A) and Wa1, xb (PSSV B) and Wb,1 and 1 (bias) and b1 in the neural network were calculated. Here, xa and xb were 20-element vector calculated from a DELTA-BLAST search, where each element of the vector represented the likelihood of existence of each amino acid, and Wa1, Wb,1 1, and b1 were weight and bias parameters of the neural network. The resultant vector was transformed by an activating function, φ(u). The rectified linear unit [Figure ear unit  was utilφ(u) and w2, and 1 and b2 was calculated, where u was a vector representing the middle layer, and w2, 1, and b2 were parameters of the neural network. The resultant value was used as the similarity score for the two sites. Namely, the forward calculation was computed by the equation:The summation of the dot products between the transformed vector, y, a scalar value, is the similarity score.The complete DP table was calculated using the similarity score, and a final pairwise alignment was produced. The pairwise alignment and its corresponding reference alignment were compared to each other, and an alignment sensitivity score was calculated. Subtraction of the alignment-sensitivity score from 1 was used as the cost for searching the optimal weight using the neural network with CMA-ES.Wa1 and Wb1 equal to each other (shared weight) in order to apply the same value to the network outputs, even though the input order of the two PSSVs was opposite one another:We set the weights https://github.com/yamada-kd/nepal.The number of units of the middle layer was set to 144. To compute backward calculations for the network, we used CMA-ES. As hyperparameters for CMA-ES, we set σ, λ, and μ to 0.032, 70, and 35, respectively. Here, σ is almost equivalent to the step size (learning rate) of the normal gradient-descent method, and λ and μ indicate the number of descendant and survival individuals in the evolutionary process, respectively. We input training datasets into the learning system in a batch manner. The maximum number of epochs was set to a relatively small number (150) to accommodate our computational environment. During learning, the performance of the scoring function was evaluated on the validation dataset starting from the 50th epoch to the final epoch in five steps, and a scoring function that maximized the validation score was selected as the final product of the learning process. The initial weight and bias were derived from parameters that mimicked the correlation coefficient. To generate the initial weight, we randomly generated 200,000 PSSV pairs and learned them using multilayer perceptron with hyperparameters (the dimensions of the weight and activating function) identical to those already described. In addition to the parameters, we simultaneously optimized the open- and extension-gap penalties, the initial values of which were set to − 1.5 and − 0.1, respectively. The source code for our learning method is provided at In this study, we implemented the semi-global alignment method  , 28.Alignment quality was evaluated using alignment sensitivity and precision . The aliThe relative accessible surface area (rASA) for residues of all proteins in the learning and test datasets was calculated by areaimol in the CCP4 package version 6.5.0 . The reshttps://cran.r-project.org/), respectively.Statistical tests, including Wilcoxon signed-rank test with Bonferroni correction and Spearman’s rank correlation, were computed using the functions pairwise.wilcox.test and cor.test from R version 2.15.3  and observed training and validation curves to confirm overfitting did not occur. The learning and validation dataset included 1536 and 160 pairwise PSSM sets and the corresponding reference alignments as targets, respectively. Because calculation of learning using our parameter settings requires > 100,000 × DP (the size of the training dataset × λ) per epoch, the consumption of computer resources was large, and calculation time was long, even when 24 threads were used with the C++ program. Therefore, we set the maximum limit for epoch to a relatively small number (150). To maximize the learning within the finite learning time, we monitored the performance of intermediate scoring functions on the validation dataset every fifth epoch. According to the validation scores, we ultimately selected a scoring function derived from the 145th epoch, which maximized the validation score, as the final product of learning. In addition to the scoring function, open- and extension-gap penalties are also vital parameters for DP, which outputs optimal alignments against four parameters, including the pairwise sequences, a scoring function, and open- and extension-gap penalties. We optimized the gap penalties along with other parameters, and simultaneously optimized gap penalties using a scoring function to obtain final weight and bias matrices representing the substance of a novel scoring function and optimal gap-penalty combinations, respectively. Our results allowed realization of an optimal combination of open- and extension-gap penalties for the final weight and bias matrices .y, between two PSSVs (xa and xb) is calculated using Eq. Wa1, Wb1, and w2) and two bias (b1 and b2) matrices the final products of learning. Our aligner and scoring function (weight and bias matrices) can be downloaded from https://github.com/yamada-kd/nepal.We implemented a pairwise-profile aligner with the weight and bias matrices as a novel scoring function and named it Neural network Enhanced Profile Alignment Library . Nepal accepts pairwise sequences and their corresponding PSSM as an input and outputs a pairwise alignment for the input sequences. The scoring function is performed by a neural network, and the similarity score, We then conducted a benchmark test of Nepal and other aligners using an existing function on the test dataset. In addition to profile-comparison methods, we examined the performance of sequence-comparison aligners with different substitution matrices, such as BLOSUM62  and MIQSTable We calculated the importance of 20 attributes of input vectors using the connection-weight method , where aBased on these results, the connection weights of hydrophobic residues, such as Leu, Ile, and Val, were of higher value. These residues are located mostly inside the hydrophobic cores of proteins. Additionally, as shown in Fig. a) and B (b), resulting in 0.488207 and 0.387911 when calculated using the correlation coefficient and Nepal methods, respectively (Fig. Additionally, although the connection weight consisted of various values, it contributed to increases in the expressive power of the novel scoring function. We calculated the similarity score between PSSV A (In this study, we optimized a scoring function for pairwise-profile alignment using a machine-learning method mimicking a nonlinear function. Our method enabled computational optimization, regardless of whether given problem involved a derivative-of-cost function, given that this scenario is not always present in real-world problems. In this study, we developed a novel derivative-free neural network with CMA-ES and successfully applied this learning system to optimize a scoring function for pairwise-profile alignment. Nepal significantly improved the alignment quality of profile alignments, especially for alignments based on remote relationships, as compared with existing scoring functions. Moreover, Nepal improved alignment quality based on the adaptation to remote sequence alignment and the increasing expressiveness of the similarity score. This method alone is not practical as a standalone pairwise-profile aligner; however, because the novel scoring function involves a simple matrix operation using parameters provided on the website, the performance of distant homology detection or multiple-sequence-alignment methods for remote homologous sequences might be further improved by incorporation of our scoring function. Finally, the goal of the study was not only to provide an alternative alignment method but also to provide a novel learning system capable of addressing derivative-free problems. Our system will be useful for optimizing the scoring functions of other sophisticated methods such as similarity search, multiple-sequence alignment and etc.


Transmembrane proteins are estimated to constitute approximately 30% of proteins at genomic scale. It has been a difficult task to develop specific alignment tools for transmembrane proteins due to limited number of experimentally validated protein structures. Alignment tools based on homology modeling provide fairly good result by recapitulating 70–80% residues in reference alignment provided all input sequences should have known template structures. However, homology modeling tools took substantial amount of time, thus aligning large numbers of sequences becomes computationally demanding. Here we present TM-Aligner, a new tool for transmembrane protein sequence alignment. TM-Aligner is based on Wu-Manber and dynamic string matching algorithm which has significantly improved its accuracy and speed of multiple sequence alignment. We compared TM-Aligner with prevailing other popular tools and performed benchmarking using three separate reference sets, BaliBASE3.0 reference set7 of alpha-helical transmembrane proteins, structure based alignment of transmembrane proteins from Pfam database and structure alignment from GPCRDB. Benchmarking against reference datasets indicated that TM-Aligner is more advanced method having least turnaround time with significant improvements over the most accurate methods such as PROMALS, MAFFT, TM-Coffee, Kalign, ClustalW, Muscle and PRALINE. TM-Aligner is freely available through  Interestingly, half of the drug molecules produce some effect on transmembrane proteins, another reason transmembrane proteins are so critical. Transmembrane proteins also participate in variety of cellular processes such as cell adhesion, immune-protection, metabolism and signal transduction2. Besides, transmembrane proteins are potential drug target candidates due to their essential roles as transporters, receptors and structural proteins as well as their effect on downstream intracellular processes3. Complex nature and involvement of transmembrane proteins in wide variety of biological processes makes them an imperative research subject. Transmembrane proteins are well known for their complexities in determining their structures experimentally4. Only 3099 transmembrane protein structures are available till date with Protein Data Bank of transmembrane proteins version 2017.02.10 5. This lack of data inspired many research groups towards predicting structures of transmembrane proteins by homology modeling. In homology modeling, unknown structure of a target sequence is modeled on a known (template) structure of a distantly-related protein, in order to gain insights into membrane protein function. Such studies rely on methods for detecting relationships between two proteins, by subsequently, aligning their protein sequences. Moreover, wide variations can be detected at the sequence level within a transmembrane protein family, thereby increasing complexity and error in the alignment.Transmembrane proteins or integral proteins are known for the variety of role they play inside the cellular system like communication, metabolism and regulation. Approximately 30% of proteins encoded by the mammalian genome are transmembrane proteins6 followed by Bahr7, and over the years, a few more methods and tools were developed for transmembrane protein sequence alignment. Multiple sequence alignment (MSA) methods, like Kalign8, MAFFT9, Muscle10, and ClustalW derives their accuracy from a ‘consistency’ criterion and/or iterative optimization. Consistency-based approaches aim to generate a multiple sequence alignment that accords best with a library of pairwise alignments between the sequences being aligned. TM-Coffee11, PRALINETM12 and Promals13 are based on homology modelling14 that has been found to perform well on alignments of transmembrane proteins from the BALiBASE2.07 benchmark. Dearth of known transmembrane proteins structures in PDB often leads to low sequence identity in best templates, which is often under 30%. Despite availability of homology based tools for multiple sequence alignment of transmembrane proteins, it is likely that a significant number of transmembrane regions remain undetected or unaligned because of limitations of the available methods like number of input sequences, turnaround time and dependency on structures. On the other hand, TM-Aligner is not working on structural homology based approaches neither it has limitation over number of sequences and took very less turnaround time. TM-Aligner can perform multiple sequence alignment of unlimited number of transmembrane proteins of any length.Multiple sequence alignment of transmembrane proteins was first addressed by Cserzo15 method to create an initial guide tree that describes sequence relatedness. To predict transmembrane regions, TMHMM16 was used and alignments were made using dynamic programming and Wu-Manber string matching algorithm17 to stitch different regions together.As biological membrane proteins have a transmembrane between cytoplasmic and non-cytoplasmic regions, so even at low sequence similarity, accurate alignment is possible by dividing the sequence into different regions and aligning them separately. These alignments are then stitched together precisely so that transmembrane regions were not disrupted and important residues within protein family are conserved throughout the alignment process. TM-Aligner is an unconditional (in terms of length and number of sequences) tool which can align transmembrane proteins accurately and responsively. TM-Aligner has been designed as a unique global, progressive alignment method for aligning transmembrane proteins. Progressive or tree-based method align most similar sequences first and then successively add less similar sequences to alignment until all sequences are aligned. TM-Aligner uses UPGMA3), however, time complexity has been reduced to O(N2) by maintaining an array of references to the minimum value in each row of the distance matrix10. TMHMM is used to predict transmembrane regions within the protein sequence. The input protein sequences are divided into cytoplasmic, non-cytoplasmic and transmembrane regions. For aligning divergent sequences, dynamic programming has been found exceptionally superior over K-tuple method therefore, all regions are aligned independently using dynamic programming. The Wu-Manber string matching algorithm is used in stitching transmembrane regions with cytoplasmic and non-cytoplasmic regions. Wu-Manber string matching algorithm sieve through thousands of matches that are found in sequences (or profiles) and determine the largest set of consistent matches that can be included in final alignment. The workflow for alignment process is outlined in Fig. TM-Aligner (Transmembrane Membrane proteins - Aligner) is a protein sequence alignment tool developed in C, Perl (version 5.20) and PHP (version 5.6). The web interface of TM-Aligner is written in PHP and JavaScript under XAMPP web server running on a Linux system. TM-Aligner uses the progressive alignment strategy for aligning protein sequences. The UPGMA method is used to find similar sequences which guide the alignment process. Time complexity of UPGMA is O * (n + 1)  has been introduced, called branch matrix which stores transitions occurring in every cell of dynamic programming matrix. Therefore, optimal alignment is obtained from branch matrix. Since TM-Aligner breaks input sequence into short sequences, memory optimization is not required. All these steps reduce the processing time in Dynamic programming.Dynamic programming19 multi-pattern matching algorithm, which uses text in blocks of size S  for comparison. Wu-Manber algorithm has two core mechanisms, filtering based on hashing and blocking based on bad—shift mechanism.Wu-Manber is a high performanceWu-Manber works in two phases, preprocessing phase and scanning phase.Preprocessing phase speed up process of pattern matching, by determining the size of match window which is equal to the smallest length pattern (say ‘m’) and creating three important tables, SHIFT table, HASH table and PREFIX table. Wu-Manber algorithm uses patterns of a size S to create a SHIFT table, when SHIFT is 0. HASH and PREFIX tables are used to identify candidate pattern.Locating match window at the start of the sequence.Compare last S characters of the window against character blocks in SHIFT table. If corresponding value in SHIFT table is greater than zero than window is shifted according to value and process is repeated. Otherwise, HASH table is used for a match within matching window.If HASH table consists multiple entries than match prefix of a pattern from prefix table, if it is matched, complete pattern were matched.Continue the process till end of the text.Pattern search works as:In TM-Aligner transmembrane, cytoplasmic and non-cytoplasmic regions are predicted and aligned using dynamic programming. All regions are aligned independently. 3 substitution matrix  are provided for multiple sequence alignment, default is PHAT with gap insertion penalty of 8 and gap extension penalty of 1.20 and structure based alignment from GPCRDB 21 has been used.To compare TM- Aligner to other alignment programs, eight transmembrane protein families of BAliBASE3.0 reference set7 , multiple datasets from Pfam database 22 test sets are a collection of alignments derived from structural databases and/or manual alignment from literature. In BAliBASE, alignment of transmembrane proteins was constructed from alignment of known proteins families and new sequences were added, based on score obtained in profile search7. References set 7 of BAliBASE version- 3.0 has been implemented for benchmarking which contains 435 alpha-helical transmembrane proteins, classified into eight super-families, namely 7tm, acr, photo, dtd, ion, msl, Nat and ptga, each multiply aligned. The accuracy of the method was assessed by sum of pairs score (SP), which reflects the percentage of correctly aligned residues with respect to reference alignment. Total Column score (TC) were not considered for scoring purpose because this score did not reflect the biological correctness of alignments. For example, consider a sequence alignment where the most of the sequences were correctly aligned, the total column score can end up noticeably zero because of a single misaligned sequence8.BAliBASE20 is a database of conserved protein families, containing collection of multiple sequence alignment and profile hidden markov models. In Pfam, seed alignment was constructed from representative protein sequences of family, to accurately identify the position-specific amino acid frequency, gap penalty and length parameter in profile hidden markov model. Other sequences were added on the basic of profile alignment score. For TM-Aligner, alignments from multiple TM families containing 9735 distant sequences were used for benchmarking.PfamTM-Aligner is very quick and exclusively well suited for aligning large numbers of sequences.TM-Aligner was compared with seven most accurate alignment methods: i. PRALINETM one of the most widely used alignment tool for aligning transmembrane proteins; ii. TM-Coffee, which has the best average SP score on BAliBASE, reported till date; iii. Promals uses progressive alignment strategy for MSA of protein sequences by incorporating profile information from known structure databases and secondary structure prediction methods, iv. Muscle, v. ClustalW, vi. MAFFT and vii. Kalign. These all are based on dynamic programming method, progressive alignment and iterative refinement . For TM- Aligner benchmarking BAliBASE3.0 reference set-7 has been used, which is the only reference set for transmembrane proteins in BAliBASE. For comparison, Sum-of -Pair (SP) score and processing time were considered for each family in BAliBASE3.0 reference set – 7 Table . P-valueTM-Aligner outperforms Praline by 3.8% on the basis of SP- score. TM-Aligner and Promals have similar accuracy, however, Promals is computationally very demanding. On average Promals takes several thousand fold more CPU time than TM-Aligner , Table As BAliBASE alignments are relatively small, large alignments from Pfam database has been used for examining the performance of TM-Aligner. For that, multiple test sets from Pfam database were used. Here, the comparative analysis is limited to tools which works on the basis of homology modeling. The result in Table Another benchmarking approach has been used against structural based alignment from GPCRDB  for evaluating performance of TM-Aligner details and result is provided in Table Detailed comparison of TM-Aligner with the available transmembrane alignment tools is shown in Table In this work, we have shown how 2D structure prediction and string matching algorithms can increase alignment quality for transmembrane proteins. Our results in Table , 2 and 3Tables Web server for TM-Aligner is simple and interactive; TM-Aligner accepts input in FASTA format. The user can directly paste protein sequence in the text-area provided or upload sequence file in FASTA format. The proposed maximum number of sequences that should be submitted to the server is set to 5000, but this is mainly to limit the server load and is not a program limitation.http://lms.snu.edu.in/TM-Aligner/.TM-Aligner is fast and robust alignment tool and provides instant result for alignment. An optional email notification can be requested that is delivered upon the completion of job and has the link to the results. Gap opening and gap extension penalties and the amino acid substitution matrix can be manually set if required  for any of the alignment strategies as given in Fig.


Our findings suggest that the network captures not only key aspects of microbial genome evolution as inferred from a tree, but also features that are not treelike. The method is highly scalable, allowing for investigation of genome evolution across a large number of genomes. Instead of using specific regions or sequences from genome sequences, or indeed Haeckel’s idea of ontogeny, we argue that genome phylogenies can be inferred usingk-mers from whole-genome sequences. Representing these networks dynamically allows biological questions of interest to be formulated and addressed quickly and in a visually intuitive manner.Ernst Haeckel based his landmark Tree of Life on the supposed ontogenic recapitulation of phylogeny, i.e. that successive embryonic stages during the development of an organism re-trace the morphological forms of its ancestors over the course of evolution. Much of this idea has since been discredited. Today, phylogenies are often based on families of molecular sequences. The standard approach starts with a multiple sequence alignment, in which the sequences are arranged relative to each other in a way that maximises a measure of similarity position-by-position along their entire length. A tree (or sometimes a network) is then inferred. Rigorous multiple sequence alignment is computationally demanding, and evolutionary processes that shape the genomes of many microbes  can add further complications. In particular, recombination, genome rearrangement and lateral genetic transfer undermine the assumptions that underlie multiple sequence alignment, and imply that a tree-like structure may be too simplistic. Here, using genome sequences of 143 bacterial and archaeal genomes, we construct a network of phylogenetic relatedness based on the number of shared Phylogenie to describe the series of morphological stages in the evolutionary history of an organism or group of organisms1. In his Tree of Life published 150 years ago2, Haeckel postulated that living organisms trace their evolutionary origin(s) along three distinct lineages  to a “common Moneran root of autogonous organisms”. In some  later works (e.g. in 18683) he allowed that different Monera may have arisen independently by spontaneous generation. Either way, these views accord with the Larmackian notion of a built-in direction of evolution from morphologically simple “lower” organisms to more-complex “higher” forms4.Ernst Haeckel coined the term2: that the embryonic series of an organism is a record of its evolutionary history. Under this view, morphologies observed at different developmental stages of an organism resemble and represent the successive stages (including adult stages) of its ancestors over the course of evolution. Of course, he worked before the advent of genetics and the modern synthesis, and before it was appreciated that information on hereditary is carried by DNA and can be recovered by sequencing and statistical analysis. He could not have foreseen that these DNA sequences code for other biomolecules and control life processes, including his beloved developmental series and organismal phenotype, through vastly complex molecular webs of interactions. Nor could Haeckel have envisaged the scale of phylogenetic analysis that can be carried out today using these DNA sequences across multiple genomes, made possible by the advent of high-throughput sequencing and computing technologies.Haeckel through his “Biogenetic Law” advocated that “ontogeny recapitulates phylogeny”6, i.e. that they share a common ancestry. From the earliest days of molecular phylogenetics, multiple sequences have been aligned8 to display this homology position-by-position along the length of the sequences. That is, the residues are arranged relative to each other such that the best available hypothesis of homology is achieved at every position (column) of the alignment. By default, it is assumed that the best alignment can be achieved simply by displaying the sequences in the same direction, and inserting gaps where needed (to represent insertions and deletions). This assumption is largely valid when working with highly conserved orthologs of any source, and with exons or proteins of morphologically complex eukaryotes. However, microbial genomes are often affected by recombination and rearrangement9, undermining the assumption of homology along adjacent positions, while lateral genetic transfer would not be represented by a common treelike process13. As Haeckel observed when he drew his Tree2, biological evolution can be anything but straightforward, and these complications have become ever more-complicated15.Fast-forwarding 150 years, phylogenetic inference based on comparative analysis of biological sequences is now a common practice. The similarity among sequences is commonly interpreted as evidence of homologyk-mers (short sub-sequences of a fixed lengthk) that they share. Such approaches avoid multiple sequence alignment, and for this reason are termedalignment-free. As opposed to heuristics in multiple sequence alignment, these methods provide exact solutions. Various modifications are available, e.g. the use of degeneratek-mers, scoring match lengths rather thank-mer composition, and grammar-based techniques; see recent reviews17 for more detail. Methods for inferring lateral genetic transfer have also been developed19. Importantly, evolutionary relationships can also be depicted as a network, with taxa and relationships represented respectively as nodes and edges24, rather than as a strictly bifurcating tree. Using simulated and empirical sequence data, we recently demonstrated that alignment-free approaches can yield phylogenetic trees that are biologically meaningful27. We find that these approaches are more robust to genome rearrangement and lateral genetic transfer, and are highly scalable26, a much-desired feature given the current deluge of sequence data facing the research community28. Here we extend the alignment-free phylogenetic approaches on 143 bacterial and archaeal genomes to generate a network of phylogenetic relatedness, and assess biological implications of this network relative to the phylogenetic tree. The phylogenetic relationships among these genomes have been carefully studied using the standard approach based on multiple sequence alignment10 and an alignment-free approach25; this dataset thus provides a good reference for comparison.Alternative approaches for inferring and representing phylogenies are available. An attractive strategy that addresses the issue of full-length alignability is to compute relatedness among a set of sequences based on the number or extent of25, we inferred the relatedness of these genome sequences using an alignment-free method based on theD2S statistic30. We computed aD2S distance,d for each possible pair of 143 genomes based on the presence of shared 25-mers using jD2Stat version 1.0 (http://bioinformatics.org.au/tools/jD2Stat/)26 and following Bernardet al.25. Here the distanced is normalised based on genome sizes and the probabilities that correspondingk-mers occur in the compared sequences30;d ranges between 0.0  and 15.5 (< 0.0001% 25-mers are shared between the two genomes). For a pair of genomesa andb, we transformedabd into a similarity measureabS, in whichabS = 10 –abd. We ignore instances ofd >10, as these pairs of sequences share ≤ 0.01% of 25-mers (i.e. there is little evidence of homology). To visualise the phylogenetic relatedness of these genomes, we adopted the D3 JavaScript library for data-driven documents (https://d3js.org/). In this network, each node represents a genome, and an edge connecting two nodes represents the qualitative evidence of sharedk-mers between them. We set a threshold functiont for which only edges withS ≥t are displayed on the screen. Changingt dynamically changes the network structure. The resulting dynamic network is available athttp://bioinformatics.org.au/tools/AFnetwork/.Using 143 complete genomes of Bacteria and ArchaeaD2S statistic30. In an earlier study10, a supertree was generated for these genomes, summarising 22,432 protein phylogenies. Incongruence between the two trees was observed in 42% of the bipartitions, most of which are at terminal branches25. The alignment-free tree  linked to the bacterial groups Thermotogales and Aquificales25. Upon reachingt = 3, most of the 14 phyla have formed distinct densely connected subgraphs in our network, i.e. Cyanobacteria and Chlamydiales form cliques att = 1.5 and all subgroups of Proteobacteria form a large paraclique with the Firmicutes att = 2. FourEscherichia coli and twoShigella isolates, known to be closely related, form a clique up tot = 8.5. Interestingly, this network also showcases the extent that genomic regions are shared among diverse phyla, e.g. the high extent of genetic similarity among Proteobacteriaversus the low extent between Chlamydiales and Cyanobacteria. Our observations largely agree with published studies25, but also highlight the inadequacy of representing microbial phylogeny as a tree. For instance, in the treeCoxiella burnetii, a member of the gamma-Proteobacteria, is grouped withNitrosomonas europaea of the alpha-Proteobacteria  is highly reduced31 and theC. burnetii genome (2 Mbp) is proposed to be undergoing reduction32. As both the tree , second only toW. glossinidia (S = 2.05), and because it shares little or no similarity with other genomes of gamma-Proteobacteria that are closely related toW. glossinidia, i.e.Buchnera aphidicola isolates (averageS = 0.63) and “Candidatus Blochmannia floridanus” (S = 0).ur tree , Archaeahe tree  and netwt, we can dynamically visualise changes in the network structure. These changes are not random, but appear to correlate to the evolutionary history of the species. Att = 0, Archaea and Bacteria form two distinct paracliques, linked only by two edges, and the Planctomycetes isolate forms a singleton. When we increaset from 1 to 2, the Archaea and Bacteria paracliques quickly dissociate from each other; within the Bacteria, cliques of Chlamydiales and Cyanobacteria are formed and the Spirochaetales become isolated. Going fromt = 2 tot = 3 we observe a scission between Firmicutes and Proteobacteria, and att > 3 all classes of Proteobacteria start to form respective paracliques. The separation (ast is incremented) of a densely connected subgraph involving all representatives of a phylum, from the rest of the network mimics the divergence of this phylum from a common ancestor. Because the similarity measures do not have a unit (such as number of substitutions per site), it is not straightforward to interpretS as an evolutionary rate or divergence time. A comprehensive comparative analysis between our network here and one that is generated using multiple sequence alignment is beyond the scope of this work. However, our findings suggest that our alignment-free network yields snapshots of biologically meaningful evolutionary relationship among these genomes, and that increasing the threshold based on the proportion of sharedk-mers recapitulates the progressive separation of genomic lineages in evolution.By changing the threshold33. One can imagine inferring a network of thousands of microbial genomes in a few hours using distributed computing. More importantly, the network can be visualised dynamically, explored interactively and shared.The alignment-free network reconstructed using whole-genome sequences thus recovers phylogenetic signals that cannot be captured in a binary tree. Using this approach, we generated the network in < 30 minutes; a whole-genome alignment of 143 sequences would have taken days, and even then, the alignment would be difficult to interpret given the genome dynamics in Bacteria and Archaeak-mers to their genomic locations and annotated genome features, e.g. in a relational database34. For instance, we could use such a database to compare thousands of isolates and identify core gene functions for a specific phylum or genus, or exclusiveversus non-exclusive functions in bacterial pathogens, in a matter of seconds. We can also usek-mers to quickly search for biological information e.g. functions relevant to lateral genetic transfer, recombination or duplications.Other biological questions could be addressed by linking thek-mers used in this way recapitulate phylogenetic signal, not ontogeny. Alignment-free approaches generate a biologically meaningful phylogenetic inference, and are highly scalable. More importantly, representing alignment-free phylogenetic relationships using a network captures aspects of evolutionary histories that are not possible in a tree. As more genome data become available, Haeckel’s goal of depicting the History of Life is closer to reality.In contrast to Haeckel’s “Biogenetic Law”,The data referenced by this article are under copyright with the following copyright statement: Copyright: © 2016 Bernard G et al.25, available athttp://dx.doi.org/10.14264/uql.2016.90835. The dynamic phylogenetic network of these genomes is available athttp://bioinformatics.org.au/tools/AFnetwork, with the source code available athttp://dx.doi.org/10.14264/uql.2016.95236The 143 Bacteria and Archaea genomes used in this work are the same dataset used in an earlier study The authors' responses are acceptable.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. k-mers from whole-genome sequences to recapitulate phylogenetic relationships from trees to networks. The analyses seemed to be convincing, and of general interest. I just have some comments on the manuscript structure and some other minor suggestions.The manuscript usesk-mers was not made strong in the current version of the manuscript. The authors used Ernst Haeckel’s phylogeny and Biogenetic Law to start their manuscript. Although it is fun to read all these historical pieces, the link between Haeckel’s ideas and the construction of networks usingk-mers can tackle them all. I suggest the authors to rather stay closer to their data and make more specific statements. The authors compared alignment-free data against sequence alignments, and stated that the sequence alignment approach “ignores important evolutionary processes that are known to shape the genomes of microbes” followed by mentioning recombination, genome rearrangement, and lateral gene transfer. This is not accurate, as sequence alignments can also be used to reconstruct web-like phylogenetic relationships, which are sometimes called phylogenetic networks . I think it is important to carefully define and compare the networks mentioned in this manuscript and the phylogenetic networks mentioned by Huson and Bryant. Along this line, approaches based on sequence alignments might not all assume tree-like relationship. Furthermore, the authors mentioned evolutionary events, such as recombination, genome rearrangement, and lateral gene transfer, that are difficult to study using sequence alignments, but did not provide detailed evidence on whether In the third introduction paragraph, “By default, it is assumed that the best alignment can be achieved simply by displaying the sequences in the same direction and inserting gaps where needed. This assumption is largely valid when working with exons or proteins of morphologically complex eukaryotes. However, in microbes this assumption is violated...” I feel the meaning of “assumption” in each of these sentences is a moving target. If they are talking about orthologous sequences, the analysis of orthologs should hold for both eukaryotes and prokaryotes. The key here, I guess, is the comparison of ortholgs, versus, the comparison of exenologs even non-homologs. Another minor point is the use of “microbes”, which can mean, bacteria, archaea, and small-eukaryotes. I don’t think it is a good word to use here. The authors did not justify the use of the 143 genomes. It seemed that they were inherited from their previous study conducted some time ago, and likely skewed in terms of taxon-sampling. Since taxon-samping is important for tree-like phylogenetic analysis, it would be nice to address how the improved  taxon-sampling can benefit the network analyses. The authors wrote “... in agreement with previously published studies; as such, this tree represents reality as presently understood, i.e., is biologically correct”. The use of words such as reality, biologically correct here, is inappropriate. The data of Wigglesworthia, Coxiella and others are of potential interest. The readers would definitely appreciate some real data analyses to address them, which are currently lacking. The cited references are relatively recent and skewed. Some of the older and more influential papers need to be added .I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. k-mers was not made strong in the current version of the manuscript.The link between Haeckel’s ideas and the construction of networks using The work we present here is a proof-of-concept for a biologically informative network based onk-mers extracted from whole-genome sequences. We hope to convince readers that dynamic visualization of such a network is intuitive for exploring and addressing biological questions, aiding discovery. The paper is part of a special collection of F1000Research articles in phylogenetics, commemorating the 150th anniversary of Ernst Haeckel’s Tree of Life published in 1866. Here we argue that by usingk-mers we can recapitulate phylogenetic signal, somewhat in the same spirit as Haeckel famously argued that “ontogeny recapitulates phylogeny”. More precisely, our claim is that “increasing the threshold based on the proportion of sharedk-mers recapitulates the progressive separation of genomic lineages in evolution”. Full consideration of Haeckel’s work in the context of Darwinian evolution then and today is well beyond the scope of our brief paper, although we cite some key references.The authors … stated that the sequence alignment approach “ignores important evolutionary processes that are known to shape the genomes of microbes” followed by mentioning recombination, genome rearrangement, and lateral gene transfer. This is not accurate, as sequence alignments can also be used to reconstruct web-like phylogenetic relationships, which are sometimes called phylogenetic networks . I think it is important to carefully define and compare the networks mentioned in this manuscript and the phylogenetic networks mentioned by Huson and Bryant.Along this line, approaches based on sequence alignments might not all assume tree-like relationship. We agree and have now rewritten part of the Abstract to stage our argument more clearly: genomic processes in microbes can undermine the assumptions that underlie multiple sequence alignment, hence phylogenetic inference as usually practiced. We have now cited other articles on phylogenetic networks in the text where appropriate, specifically Huson and Bryant1 and Kuninet al.2. Comprehensive comparison ofk-mer-based and  phylogenetic networks is important but, due to its complexity, beyond the scope of this paper; we have now clarified this in the revised text.The authors mentioned evolutionary events, such as recombination, genome rearrangement, and lateral gene transfer … but did not provide detailed evidence on whether k-mers can tackle them all. I suggest the authors to rather stay closer to their data and make more specific statements. In Chanet al.3 and Bernardet al.4 we provided detailed evidence that alignment-free approaches based onk-mers, at multi-genome scale, can be robust to insertions/deletions, genome rearrangement and lateral genetic transfer; these articles are cited where appropriate.In the third introduction paragraph, “By default, it is assumed that the best alignment can be achieved simply by displaying the sequences in the same direction and inserting gaps where needed. This assumption is largely valid when working with exons or proteins of morphologically complex eukaryotes. However, in microbes this assumption is violated...” I feel the meaning of “assumption” in each of these sentences is a moving target. If they are talking about orthologous sequences, the analysis of orthologs should hold for both eukaryotes and prokaryotes.  We have now revised the text to make it clear that the main assumption underlying multiple sequence alignment, i.e. that the alignment columns display homology position-by-position along the length of the sequences, is largely valid when working with highly conserved orthologs of any source; and that the validity of this assumption is often undermined in the case of microbial genome sequences, due to recombination and rearrangement.Another minor point is the use of “microbes”, which can mean, bacteria, archaea, and small-eukaryotes. I don’t think it is a good word to use here. We used the word “microbes” here specifically to include archaea, bacteria and microbial eukaryotes. Genomes of many microbial eukaryotes are known to be impacted by lateral genetic transfer, at frequencies sometimes nearly as large as in bacteria and archaea.The authors did not justify the use of the 143 genomes. … Since taxon-sampling is important for tree-like phylogenetic analysis, it would be nice to address how the improved  taxon-sampling can benefit the network analyses. Here we used the 143-genome dataset because the phylogenetic relationships among these genomes have been studied using careful alignment-based methods5 and by alignment-free approaches4; it thus provides a good reference for comparison. We have now clarified this in the text. In our alignment-free network, each edge represents the qualitative evidence ofk-mers shared pairwise between two genomes. This evidence is not affected by other genomes present in (or absent from) the dataset. Therefore, our networks are not affected by taxon-sampling biases of the sort encountered in tree inference. Of course, the presence or absence of a critical node (genome) might affect the biological conclusion we draw from a network, but the same is true for any scientific analysis. We considered the effect of phyletic balance on the inference of lateral genetic transfer networks in another context6.  The authors wrote “... in agreement with previously published studies; as such, this tree represents reality as presently understood, i.e., is biologically correct”. The use of words such as reality, biologically correct here, is inappropriate. We agree and now state that “as such, this tree captures most of the major biological groupings of Bacteria and Archaea as presently understood”.Wigglesworthia,Coxiella and others are of potential interest. The readers would definitely appreciate some real data analyses to address them, which are currently lacking.The data of A follow-up analysis betweenWigglesworthia andCoxiella would indeed be interesting, but is beyond the scope of this Research Note, the aim of which is to present limited findings in hopes of inspiring and encouraging others to explore this research area.Some of the older and more influential papers need to be added . We have now cited older, relevant references in the text for both networks1, 2 and alignment-free methods7.Thank you for these comments.ReferencesMol Biol Evol. 2006;23(2): 254-67.Huson DH, Bryant D: Application of phylogenetic networks in evolutionary studies., et al.: The net of life: reconstructing the microbial phylogenetic network.Genome Res. 2005;15(7): 954-9.Kunin V, Goldovsky L, Darzentas N, et al.: Inferring phylogenies of evolving sequences without multiple sequence alignment.Sci Rep. 2014;4: 6504.Chan CX, Bernard G, Poirion OSci Rep. 2016;6: 28970.Bernard G, Chan CX, Ragan MA: Alignment-free microbial phylogenomics under scenarios of sequence divergence, genome rearrangement and lateral genetic transfer.Proc Natl Acad Sci U S A. 2005;102(40): 14332-7.Beiko RG, Harlow TJ, Ragan MA: Highways of gene sharing in prokaryotes.Sci Rep. 2016;6: 29319.Cong Y, Chan YB, Ragan MA: Exploring lateral genetic transfer among microbial genomes using TF-IDF.Bioinformatics. 2011;27(11): 1466-72.Domazet-Lošo M, Haubold B: Alignment-free detection of local similarity among viral and bacterial genomes. et al. aim for speed and use an established alignment-free measure, D_2, to reconstruct the phylogeny of 143 Bacteria and Archaea from full genome sequences. D_2 is based on the number of sharedk-mers, and the main contribution of the paper is the visualization of the D_2 distance matrix of the 143 taxa as a network rather than the traditional bifurcating tree. This visualization is dynamic in the sense that the user can choose a similarity threshold between 0 and 10, and watch as the taxa disintegrate from initially two clusters to essentially every taxon on its own. This is an innovative way of presenting large-scale evolutionary relationships, and the tool is fun to use. As the authors remark, it is unclear how the D_2 metric scales with more familiar measures of evolutionary time such as substitutions per site. It would thus be interesting to explored this in future work; for example by supplying a version of the visualization tool that allows users to upload their own sequences. I was also wondering how the networks generated by Bernardet al. compare to established methods of network-based evolutionary analysis such as SplitsTree and minimum spanning trees. I realize that these are both usually based on alignments, but it is always possible to analyze a given alignment using D_2, thereby allowing a direct assessment of the accuracy lost (if any) for the speed gained.Phylogeny reconstruction is a classical research topic in bioinformatics. In this context the standard trade-off between speed and accuracy becomes a choice between slow but accurate sequence alignment on the one hand and fast but less accurate alignment-free methods on the other. BernardI have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. k-mer-based network and a phylogenetic network based on multiple sequence alignment, although doable, is not straightforward. We believe the adoption of alignment-free methods in phylogenetic inference is still in its infancy, and we hope that this work will inspire and encourage other researchers to pursue this approach.Thank you for these comments. Indeed, the correlation between D2 metrics and evolutionary distances is an interesting area, and a tool that allows users to upload their own datasets would be useful. A comparative analysis between a