Sequence alignment is one of the first steps in many modern genomic analyses, such as variant detection, transcript abundance estimation and metagenomic profiling. Unfortunately, it is often a computationally expensive procedure. As the quantity of data and wealth of different assays and applications continue to grow, the need for accurate and fast alignment tools that scale to large collections of reference sequences persists.In this article, we introduce PuffAligner, a fast, accurate and versatile aligner built on top of the Pufferfish index. PuffAligner is able to produce highly sensitive alignments, similar to those of Bowtie2, but much more quickly. While exhibiting similar speed to the ultrafast STAR aligner, PuffAligner requires considerably less memory to construct its index and align reads. PuffAligner strikes a desirable balance with respect to the time, space and accuracy tradeoffs made by different alignment tools and provides a promising foundation on which to test new alignment ideas over large collections of sequences.https://github.com/COMBINE-lab/pufferfish/tree/cigar-strings.All the data used for preparing the results of this paper can be found with 10.5281/zenodo.4902332. PuffAligner is a free and open-source software. It is implemented in C++14 and can be obtained from Bioinformatics online. Since its introduction, next generation sequencing (NGS) has been widely used as a low-cost and accessible technology to produce high-throughput sequencing reads for many important biological assays.The sequencing data that is generated in the form of short reads, drawn from longer molecular fragments, and finding the optimal alignments of these short reads to some reference is a necessary first step for many downstream biological analyses. The process of finding the segment on the reference that is most similar to the query read, and therefore most likely to be the source of the fragment from which the read was drawn, is known as read mapping or read alignment.The main goal in read alignment is to find alignments of contiguous sub-string of the underlying reference that yields a minimum edit distance  between the read and the reference sequence at the alignment position. If the reads are paired-end, characteristics other than the alignment score can be used to filter spurious alignment locations, such as orientation of each end of the alignment pair (forward or reverse) or distance between the alignments corresponding to reads that are ends of the same fragment.Short-read aligners are a major workhorse of modern genomics. Given the importance of the alignment problem, a tremendous number of different tools have been developed to tackle this problem. Some widely used examples are BWA , Bowtie2Existing alignment tools use a variety of indexing methods. Some tools, such as BWA, Bowtie2 and STAR use a full-text index over the reference sequences; BWA and Bowtie2 use variants of the FM-index, while STAR uses a suffix array.k (k-mers) from the reference sequence. Trading off index size for potential sensitivity, such indices can either index all of the k-mers present in the underlying reference, or some uniform or intelligently chosen sampling of k-mers. There are a large variety of k-mer-based aligners, including tools like the Subread aligner (k-mers based on a winnowing (or minimizer) scheme. This approach has been particularly common in tools designed for long-read sequence alignment like mashmap . A de Bruijn graph is a graph over a set of distinct k-mers where each edge connects two neighboring k-mers that appear consequently in a reference sequence and therefore, overlap on ‘k—1’ bases. Kallisto  have very large memory requirements for indexing, and make some sacrifices in sensitivity to obtain their speed. On the other hand, the most sensitive aligners (like Bowtie2) have very moderate memory requirements but obtain their sensitivity at the cost of a higher runtime. Maintaining the balance between time and memory is especially more critical while aligning to a large set of references, like a large collection of microbial and viral genomes which may be used as an index in microbiome or metagenomic studies. As both the collection of reference genomes and the amount of sequencing data grows quickly, it is import for alignment tools to scale to such large collections of data and references with reasonable resource requirements while remaining fast and sensitive.Based on the compact Pufferfish  where this k-mer appears in the colored compacted de Bruijn graph . This match between the query and the graph can then be easily ‘unpacked’ into the implied list of matches with the underlying references by finding all of the places that the matched unitig appears in the reference sequences.PuffAligner is an aligner built on top of the Pufferfish indexing data structure. Pufferfish is a space-efficient and fast index for the colored compacted de Bruijn graph (ccdBg). A colored compacted de Bruijn graph is a graph whose vertices (strings) are the compacted non-branching paths of the underlying de Bruijn graph, with the restriction that each node also have the same color set (set of reference sequences in which it appears). The nodes in the colored compacted de Bruijn graph are referred to as unitigs. Each unitig can exist in multiple references and be mapped to a list of <reference ID, position orientation > tuples. The tuple describes the position and orientation with which the unitig subsequence appears in each reference. The basic query operation in the Pufferfish index is to query a k-mer query is the basic operation performed by Pufferfish index, we actually do not query for all the k-mer matches directly in PuffAligner. Instead, starting from k-mer k0, we extend the initial k-mer match into a unique maximal exact match [uni-MEMs, as introduced k0. This uni-MEM is later used to construct a Maximal Exact Matches (MEM), which is a Maximal Exact Match shared between the read and the reference. We utilize the uniqueness property of unitigs to reduce the operational overhead of MEM extension per each reference to only once for a unitig. We expand a uni-MEM to different MEMs by assigning the reference information of the uni-MEM’s underlying unitig to the uni-MEM. Using this approach, a uni-MEM can be a part of multiple MEMs, just as a unitig can be a part of multiple references. During MEM assembly, we merge overlapping consequent uni-MEMs that are only separated because of small branched unitigs. In this way, we guarantee the accuracy, performance of later mapping steps, and obtain similar behavior that is expected from dealing with chains of MEMs in more traditional alignment approaches. Finally, rather than fully aligning each query sequence to the anchored position on the reference, only the sub-sequences from the query that are not part of the MEMs (exact matches) appearing within the current high-scoring MEM chain are aligned to the reference; we call this procedure between-MEM alignment. Each of these steps are explained in detail in the following sections.The main advantage of an aligner based on a compacted sequence graph, such as PuffAligner, offers compared to aligners based on linear full-text indices such as the FM-index, is the reduction of overhead related to computations for repeated subsequences within or across multiple references. This benefit results by performing the basic matching and mapping preprocessing steps on the graph itself, and annotating the results with respect to each reference, rather than performing these operations on all reference sequences individually. While k-mer lookup within a list of references such as a collection of transcripts, genes or genomes. Specifically, the core components of the index are (i) a minimal perfect hash function (MPHF), (ii) a unitig sequence vector, (iii) a unitig -to-reference table and (iv) a vector storing the position associated with each k-mer in the unitig sequence vector. The unitig sequence vector contains all the unitigs in the ccdBg. In the Pufferfish index, a unitig is a monochromatic path in the colored compacted de Bruijn graph, where a color corresponds to a set of reference identifiers. Hence, each unitig is a substring of some set of reference sequences. Each unitig is annotated with the list of references that contain the unitig’s sequence. In this design, a unitig can belong to multiple references and a reference can contain multiple unitigs.The Pufferfish index provides PuffAligner with an efficient index for k-mers, as well as longer matches that are unique in both the query string and colored compacted de Bruijn graph. These matches, called uni-MEM, were originally defined in deBGA  and the reference. In PuffAligner, this is accomplished by collecting the set of uni-MEMs that co-occur between the query and reference. PuffAligner starts processing the read from the left-end and looks up each k-mer that is encountered until a match to the index is found. Once a match is discovered, it is extended in both query and the reference until one of these termination conditions occur: (i) a mismatch is encountered, (ii) the end of the query is reached or (iii) the end of the unitig is reached. This process results in a uni-MEM match shared between the query and reference. uni-MEMs where extension is terminated as a result of reaching the end of a unitig must later be examined and potentially ‘collpased’ together to form MEMs with respect to the references on which they appear. If the uni-MEM extension is not terminated as a result of reaching the end of the query, then the position in the read is incremented by a small value and the same procedure is repeated for the next k-mer on the read. This process continues until either the uni-MEM extension terminates because the end of the query is reached, or because the last k-mer of the query is searched in the index. Here, we recall an important property of uni-MEM extension that is different from e.g. MEM extension or maximum mappable prefix (MMP) extension . Furthermore, we also provide a flag –allowHighMultiMappers that mitigates the effect of this filter for a slight tradeoff on the alignment performance.uni-MEM compaction: For paired-end reads, PuffAligner aligns each end of the read pairs individually. For each end, all the uni-MEMs are sorted on the basis of their positions on the reference. First the uni-MEMs are ‘unpacked’ to their corresponding unitig’s reference list and assigned a reference position by adding the unitig’s relative position in the reference to the uni-MEM’s position in the unitig. After mapping the uni-MEMs to the references, it is now possible to construct the <read end, reference > MEMs. Each MEM is defined as either a single uni-MEM or a combination of those consecutive uni-MEMs that have an overlap of k—1 on both the query and reference .The compactable uni-MEMs result from terminating the extension process due to reaching the end of a unitig. After the compaction of uni-MEMs, there is a list of MEMs which are shared sequences between the query and a set of reference positions, that are sorted based on the reference positions.k-mer once per read and simply using the extended subsequence in MEMs of the read to difference references. However, the shorter the unitigs, the shorter the uni-MEMs. Therefore, the more k-mers per read need to be queried. This will affect the performance of MEM construction which, in the worst-case scenario, is required to query for each k-mer in the read. However, the k-mer queries still only happen once per each read and not once per each pair of read and reference.Generally, a MEM is calculated for each pair of read and reference. This means that, in the case of highly similar references, the process of finding the same MEM of the read has to be repeated for each reference. Through the indirect construction of MEMs from uni-MEMs we gain a performance boost by extending the k shared between a read and the reference sequences. As shown in Via the procedures described above, we have enumerated all of the possible MEMs of length at least r to the reference t, are sorted by the ending position of the MEMs on the reference. Then, this algorithm computes a score for each set of MEMs based on the number of unique covered bases in the read, the coverage score is also penalized by the length of the gaps, both in the read and reference sequence, between each consecutive pair of MEMs.To accomplish this, we adopt the dynamic programming approach used in minimap2  for findm1 and m2, on the read and the reference is rd and td respectively, these two MEMs should not be chained together if C is the maximum allowed gap. So, the penalization term, the β value in  which match exactly to the reference. While the optimal alignment of the read to the reference at the position being considered is not guaranteed to contain these exact matches as alignments of the corresponding substrings, this is almost always the case in practice.After finding the high-scoring MEM chains for each reference sequence, a base-to-base alignment of the read to each of the candidate reference sequences is computed. Each selected chain implies a position on the reference sequence where the read might exhibit a high quality alignment. Thus, we can attempt to compute an optimal alignment of the read to the reference at this implied position, potentially allowing a small bit of padding on each side of the read. This approach utilizes the positional information provided by the MEM chains. However, the starting position of the alignments is not the only piece of information embedded in the chains. Rather each chain of MEMs consists of sub-sequences of the read .PuffAligner uses KSW2  for compFinally, once alignments have been computed for the individual ends of a read, they must be paired together to produce valid alignments for the entire fragment. At this point in the process, on each reference sequence, there are a number of locations where the left end of each read or the right end of each read, or both, are mapped to the reference. For the purpose of determining which mappings will be reported as a valid pair, the mappings are joined together only if they occur on opposite strands of the reference, and if they are within a maximum allowed fragment length. There are two different types of paired-end alignments that can be reported by PuffAligner; concordant and discordant. If PuffAligner is disallowed from reporting discordant alignments, then the mapping orientation of the left and right end should agree with the library preparation protocols of the reads. PuffAligner first tries to find concordant mapping pairs on a reference sequence, and if no concordant mapping is discovered and the tool is being run in a mode where discordant mappings are allowed, then PuffAligner reports pairs that map discordantly. Here, discordant pairs may be pairs that do not, for example, obey the requirement of originating from opposite strands. While this is not expected to happen frequently, it may occur if there has been an inversion in the sequenced genome with respect to the reference.For measuring the performance of PuffAligner and comparing it to other aligners, we have designed a series of experiments using both simulated and experimental data from different sequencing assays. We compare PuffAligner with Bowtie2 , STAR , to situations where each fragment is expected to align to many loci with similar quality (RNA-seq and metagenomic sequencing), and spanning the range of index sizes from small transcriptomes to large collections of genomes.k-mer lookups take longer. However, in the alignment process described here, since the steps after the initial lookup are the main bottleneck in alignment time , we recommend the sparse Pufferfish index to be the choice. This is the index version we have used for all experiments in this manuscript.PuffAligner’s underlying index, Pufferfish supports two index variants, ‘dense’, and ‘sparse’ (Dense is the default index and sparse is activated using the ‘-s’ option in the index build step). The ‘sparse’ version trades off lookup time for index size, and provides a smaller index in which First, we show PuffAligner exhibits similar accuracy for aligning DNA-seq reads to Bowtie2, but it is considerably faster. In the case of experimental reads, since the true origin of the read is unknown, we use measures such as mapping rate and concordance of alignments to compare the methods. Furthermore, in https://www.internationalgenome.org/data-portal/sample/HG00190). There are 18 297 585 paired-end reads, each of length 108 nucleotides in this sample. Using fastp (https://www.gencodegenes.org/human/release_33.html). All the tool, if possible, are run in the concordant-mode in this experiment.First, we evaluate the performance of PuffAligner with a whole genome sequencing (WGS) sample from the 1000 Genomes project  are mapped by all three aligners. The next largest set (∼400K reads) represents the reads which are only mapped by Bowtie2 and PuffAligner. All the other sets are much smaller compared to the first two sets. This fact illustrates that the highest agreement in the aligners is between Bowtie2 and PuffAligner. We have also visualized the results in an upset plot in Exploring a series of individual reads from the smaller sets in the upset plot, suggests that some of these differences happen as a result of small differences in the scoring configuration, while some result from different search heuristics adopted by the different tools. Mapping sequencing reads to target transcriptomes is the initial step in many pipelines for reference-based transcript abundance estimation. While lightweight mapping approaches . Thus, tIn One main property of metagenomic samples is that they contain reads from a variety of genomes. Some of these genomes are highly similar and some are not even assembled yet—and hence unknown. To demonstrate the performance and accuracy of PuffAligner for metagenomic samples, we design two different experiments. The first which we call ‘Single-strain’ experiment is designed to specifically evaluate issues related to the similarity challenge and the second, the ‘bulk’ experiment, evaluates aligners in the presence of a high variety of species in the sample in addition to the high similarity of references. We discuss the results of the ‘bulk’ experiment which is a more comprehensive one, in the following paragraphs. The ‘single-strain’ experiment is described in We construct the indices of PuffAligner, Bowtie2, STAR and deBGA on a random set of 4000 complete bacterial genomes downloaded from the NCBI microbial database. We select three Illumina WGS samples with accession IDs SRR10948222 , SRR1128Spearman Correlation, Mean Absolute Relative Difference (MARD), Mean Absolute Error (MAE) and Mean Squared Log Error (MSLE). The metrics have been chosen to be similar to previous work such as in Bracken  rather than by comparing the read alignments directly. In  Bracken . The defThis experiment leads to three main observations. First, regardless of the alignment mode, quantifications derived from the deBGA alignments seem to lead to systematic underestimation of abundance. However, PuffAligner, STAR and Bowtie2, show very similar behavior with respect to accuracy. STAR is the best in primary mode as well as when allowing 20 alignments, closely followed by PuffAligner. When allowing up to 200 alignments per read, Bowtie2 tends to yield the most accurate abundances, again with PuffAligner being the close runner-up. These results demonstrate that PuffAligner is a reliable alignment tool showing a stable pattern of being comparable to the best aligner under all the scenarios tested. That is, the good performance of PuffAligner is robust across a variety of different parameter settings.bestStrata mode compared to when we allow up to 200 alignments per read. This observation is also consistent across the other two simulated samples in Moreover, due to the nature of the metagenomic data—the high degree of ambiguity and multi-mapping—we expect to see improvement in the accuracy metrics as more alignments are reported per read, as this leads to a higher recall. While STAR’s accuracy changes only slightly from 20 alignments to 200 alignments (only improving MAE) the results for PuffAligner and Bowtie2 improve considerably when allowing more alignments per read. However, this higher accuracy comes in the cost of alignment time for Bowtie2 as shown in Overall, these results along with other similar experiments in k-mers from the read in the Pufferfish index. The aligner then chains together the collected uni-MEMs using a dynamic programming approach, choosing the chains with the highest coverage as potential alignment positions for the reads. Finally, PuffAligner is able to efficiently compute alignment, exploiting information from long matches in the chains and making use of an alignment cache to avoid redundant work.In this article, we introduce PuffAligner, an aligner suitable for the contiguous alignment of short-read sequencing data. We demonstrate its use in aligning DNA-seq reads to the genome of a single species, aligning RNA-seq reads to the transcriptome, and aligning DNA-seq reads from metagenomic samples to a large collection of references. It is built on top of the Pufferfish index, which constructs a colored compacted de Bruijn graph using the input reference sequences. PuffAligner begins read alignment by collecting unique maximal exact matches, querying We compared the accuracy and efficiency of PuffAligner against two widely used alignment tools, Bowtie2 and STAR, that perform unspliced and  spliced alignments of reads, respectively. We also compare the results against deBGA, an aligner that also utilizes an index built over the compacted de Bruijn graph.We analyze the performance of these tools on both simulated and experimental DNA and RNA sequencing datasets. The accuracy of PuffAligner is comparable to Bowtie2, which exhibits very high alignment. PuffAligner generally performs better than STAR and deBGA . In terms of speed and memory, PuffAligner reaches a tradeoff between the relatively high memory usage of STAR and deBGA and the slower speed of Bowtie2. Hence, while the memory requirement of PuffAligner is more than that of Bowtie2, the speed gain is significant. In the tests performed in this manuscript, PuffAligner is almost always the fastest tool .et al., 2020). The analysis shows that specificity of alignments in such a case can be improved by filtering from quantification reads that are better aligned to some genomic locus that is not present in the transcriptome.An additional advantage of the Pufferfish index used in PuffAligner is that it can scale well to a collection of genomes, transcriptomes, or both, especially when the reference sequences being indexed exhibit a high degree of sequence similarity. This feature is already utilized in a specific pipeline for RNA-seq quantification that makes use of a joint index over the genome and transcriptome  alignment procedure of PuffAligner makes it a particularly useful for indexing and aligning to a highly similar collection of sequences. This potentially makes it a good match for metagenomic analyses.We have provided a proof of concept for such a PuffAligner-based metagenomic analysis pipeline, and plan to build a more sophisticated and fully featured metagenomic analysis framework around PuffAligner in the future.btab408_Supplementary_DataClick here for additional data file.


Sequence alignment is an excellent way to visualize the similarities and differences between DNA, RNA or protein sequences, yet it is currently difficult to jointly view sequence alignment data with genetic variations, modifications such as post-translational modifications and annotations (i.e. protein domains). Here, we present the MSABrowser tool that makes it easy to co-visualize genetic variations, modifications and annotations on the respective positions of amino acids or nucleotides in pairwise or multiple sequence alignments. MSABrowser is developed entirely in JavaScript and works on any modern web browser at any platform, including Linux, Mac OS X and Windows systems without any installation. MSABrowser is also freely available for the benefit of the scientific community.https://thekaplanlab.github.io/ and GitHub repository https://github.com/thekaplanlab/msabrowser.MSABrowser is released as open-source and web-based software under MIT License. The visualizer, documentation, all source codes and examples are available at Bioinformatics Advances online. Caenorhabditis elegans, Alliance of Genome Resources and Ensembl  would facilitate comparison of human variants and variant-specific annotations with variants and variant-specific annotations from non-human species , variant ID, etc.] to the corresponding positions (e.g. p. C4957Y in human RYR2 and p. C4956Y in mice Ryr2) . MSABrowC. elegans FARS-3 . These OrthoVars were inserted into the PSA of human FARSB and C. elegans FARS-3 at their respective sequence locations , OrthoVars, nonsense variants (a stop codon) or PTMs  into the respective sequence positions on the PSA and MSA   into the corresponding positions, it is difficult or impossible for other MSA visualization tools . While sPSAs and MSAs are the fundamental methods for the alignment of any sequences of DNA, RNA and protein . The MSAThe MSABrowser has multiple ways of navigating the alignment. Firstly, by scrolling through the sequence alignment and secondly, by specifying either amino acid or nucleotide position and the species in the bottom panel. Users can hide sequences from the alignment by selection. Additionally, a cross-reference link is automatically generated based on the sequence identifiers from the imported FASTA file. Therefore, users may click the species names to jump to the sequence database . For visualizing the alignments, users might choose between 13 predefined colour schemes. The MSABrowser is capable of exporting alignment as a FASTA file format and the visualization as a publication-quality figure in Portable Network Graphics (PNG). Furthermore, we provide a detailed comparison of features among other visualization tools .MSABrowser is the most recently created tool that allows the visualization of MSAs, genetic variations, PTMs and protein domains at the same time. MSABrowser makes it much easier to display orthologous variants between different species (vbab009_Supplementary_DataClick here for additional data file.


Alternative splicing is a ubiquitous process in eukaryotes that allows distinct transcripts to be produced from the same gene. Yet, the study of transcript evolution within a gene family is still in its infancy. One prerequisite for this study is the availability of methods to compare sets of transcripts while accounting for their splicing structure. In this context, we generalize the concept of pairwise spliced alignments (PSpAs) to multiple spliced alignments (MSpAs). MSpAs have several important purposes in addition to empowering the study of the evolution of transcripts. For instance, it is a key to improving the prediction of gene models, which is important to solve the growing problem of genome annotation. Despite its essentialness, a formal definition of the concept and methods to compute MSpAs are still lacking.We introduce the MSpA problem and the SplicedFamAlignMulti (SFAM) method, to compute the MSpA of a gene family. Like most multiple sequence alignment (MSA) methods that are generally greedy heuristic methods assembling pairwise alignments, SFAM combines all PSpAs of coding DNA sequences and gene sequences of a gene family into an MSpA. It produces a single structure that represents the superstructure and models of the gene family. Using real vertebrate and simulated gene family data, we illustrate the utility of SFAM for computing accurate gene family superstructures, MSAs, inferring splicing orthologous groups and improving gene-model annotations.https://github.com/UdeS-CoBIUS/SpliceFamAlignMulti.The supporting data and implementation of SFAM are freely available at Bioinformatics Advances online. Alternative splicing is one of the most important mechanisms revealed in the postgenomic era , which is a spliced alignment of a set of spliced RNA sequences with a set of unspliced genomic sequences. Contrary to classic multiple sequence alignment (MSA), MSpA accounts for the splicing structure and the exonic structure of the input gene sequences. Like MSA that has been instrumental in better understanding the mechanisms of sequence evolution, MSpA is expected to shed light on important questions about the evolution of alternative splicing and of sets of alternative spliced RNA. For instance, the question about the conservation of the function of conserved transcripts between homologous genes remains open. MSpA will allow us to directly compare the exon architecture of alternative splicing in multiple genes and species at once, in order to answer questions about the evolution of transcripts as in  such that gene model of g is a representation of a CDS c of g as a chain of exons of g, ia, ib) and c, we have ith exon of a CDS c is denoted by g. The set of all exons of g composing its CDS is denoted by gene structure of g, denoted by g obtained by merging all overlapping exons of g  such that c1] = ATGCAAGCAGGTCTGGGGTGA has a length of 21 with a set of exons m and a location k such that g corresponding to the location k on The sequence of a CDS Definition 1ith multiblock of A. Each multiblock x represented by the pair For any multiblock x in x in For any CDS or gene c induced by A, c.For any CDS c and g in For any multiblock [multiple spliced alignment (MSpA)] An MSpA of a set of CDSs A PSpA is an alignment of a CDS and a gene sequence that accounts for the splicing structure of sequences and allows identification of homologous exon sequences. In Each multiblock a is consistent with b, if one of the following conditions is satisfied:Given two multiblocks a is located before b orfor any a is located after b orfor any a overlaps b.for any A of a on a is consistent with A if for any multiblock A, a is consistent with Definition 2[pairwise spliced alignment (PSpA)] A PSpA is an MSpA of a single CDS and a single gene. In this case, the multiblocks of the alignment are called blocks  uses a consistency-based progressive alignment that relies on the use of the T-Coffee alignment package  also uses a greedy approach that consists in first precomputing a set of candidate multiblocks by assembling aligned pairwise blocks that share identical segment. The candidate multiblocks are then sorted according to their size, including multiblocks one-by-one into a growing consistent set of multiblocks. We call this approach the greedy multiblock approach. The rationale behind this approach is that a candidate multiblock of large size is supported by a high number of pair blocks, and is less likely to be a random artifact than a multiblock containing a small number of segments. Like the consistency-based progressive alignment, the greedy multiblock approach also takes into account the information of all pairwise alignments at each stage of the alignment by considering candidate multiblocks instead of pair blocks.The two algorithms SFAM_tcoffee and SFAM_mblock make use of a spliced alignment graph, denoted by Definition 3g = h, then  Let A fully detailed description of each step of the algorithms is provided in the The SFAM_tcoffee algorithm follows a consistency-based progressive alignment strategy that relies on the use of the T-Coffee alignment package (Generate the primary library of residue pairs: SFAM_tcoffee provides two ways to generate the primary library of residue pairs.1. • The first method named SFAM_tcoffee_p (p for pairwise) makes direct use of the blocks of the PSpAs given as input to SFAM_tcoffee to extract the pairs of aligned residues between gene sequences.cc of cc, and pairs of aligned residues between gene sequences are extracted from the MSA.• The second method named SFAM_tcoffee_m (m for multiple) makes use of the alignment graph Compute anMSAM of2. Compute anMSpAofgiven theMSAM of3. The SFAM_mblock is based on the alignment graph Compute the alignment graphWeight the edges ofPID(e) and connect(e) are assigned to each edge e of PID(e) is the percent sequence identity (PID) of the pairwise sequence alignment represented by e. connect(e) evaluates the strength of the connectivity between the two vertices connected by e. The two scores serve as confidence scores for the segment alignment represented by e.Split connected components ofcc of cc contains two vertices corresponding to two nonoverlapping segments of a sequence x, then cc cannot correspond to a multiblock, since a multiblock contains at most one segment from each sequence cc to disconnect the two vertices.Build theMSpAin a progressive manner: The connected components of cc of cc is built. The resulting set A is initialized to an empty chain, and candidate multiblocks that are consistent with A are progressively added to A as follows:Let Computing anMSAofComputing CDS orthology groups: Given two CDSs c1 and c2 of c1 and c2 as orthologous CDS if:for any multiblock if c1 and c2 are orthologs if they have segments in the same multiblocks, and the lengths of each pair of segments of c1 and c2 that belong to the same multiblock are congruent modulo 3. These conditions ensure that c1 and c2 have the same splicing structure, and are translated in the same reading frame in order to yield similar protein sequences. For instance, in the MSpA depicted in g[c1] and h[c3] are orthologs. Given the orthology relation defined on the set of CDSs In other terms, Predicting gene models by homology: Let c1 be a CDS of a gene g. A putative CDS c2 can be predicted for h if:for any multiblock if c2 is obtained by concatenating the set of segments of h contained in multiblocks that contains segments of c1, c2 is a predicted CDS for h, if it is not already a CDS of h, and it does not contain any STOP codons. It is easy to see that c1 and the predicted CDS c2 will then be orthologs according to the definition provided above. For instance, in the MSpA depicted in AAGCAGGTCTGGGGTGATTGA orthologous to The putative CDS To evaluate the performance and show the utility of SFAM, we used three datasets of 20 simulated gene families, and a dataset of 20 real gene families from the Ensembl database . The second set of results was obtained by aligning the gene sequences and the CDSs using the other alignment methods , and then computing the CDS alignments induced by these whole MSAs. The precision, recall, F-score and computing time were computed for each of these sets of results. For SFAM, the computing time for PSpAs is included.Based on the true MSAs of the CDS of each family of the simulated datasets, the precision, recall, Based on the true splicing orthologous groups of the CDS for each family of the simulated datasets, the Rand index (RI) and the computing time for each method and each gene family were calculated. The RI is the fraction of CDS pairs that have the same relation in the estimated clustering and the true clustering, either in the same cluster or in different clusters.T (for true) of dog CDSs present in release 98 of the Ensembl database, but absent in release 97, and the set P (for predicted) of dog CDSs predicted by SpliceFamAlignMulti (SFAM_mblock) based on data from release 97. We computed the precision, recall and F-score of the prediction. The precision is the fraction of CDSs in P that correspond to CDS T. The recall is the fraction of CDS in T that corresponds to CDS in P, and the F-score is again the harmonic mean of precision and recall. For each gene family, we considered two methods to define the correspondence between CDSs of T and P. The more stringent method defines two CDSs of T and P as matching if they are 100% identical. The second less stringent method defines two CDSs of T and P as matching if they are >90% identical and reciprocal best hits. For this second method, the PID is computed based on a pairwise alignment of the CDS that is computed using a global alignment method, FsePSA  and the spliced alignment graph that makes it possible to consistently group conserved exon blocks of PSpAs in MSpA blocks without relying on sequence alignment. This shows the accuracy of the underlying MSpAs. This also illustrates that it is possible to obtain high-quality MSpAs in a reasonable amount of time by focusing on the splicing structure information. Some MSA methods that are agnostic to splicing structure information such as Mirage, PRANK and MACSE performed comparably to SFAM_mblock for MSA. In contrast, their performance either decreased faster when the sequence similarity increased or they were much more computationally intensive. Even if some MSA methods performed as well as SFAM_mblock and might be preferred if the splicing structure information is not available or splicing structure conservation is not important, the accurate MSAs provided by SFAM_mblock constitute robust foundations for its other applications: CDS orthology groups inference and gene-model prediction.Small, Medium and Large). Cluss had the lowest running time, because, unlike the other methods, it does not rely on any computationally intensive sequence or structure alignment step. Rather it relies on an alignment-free sequence similarity measure.As for the execution times, SFA, SFAM_mblock, SFAM_tcoffee_p, SFAM_tcoffee_m and OrthoFinder had comparable running times for all classes of sequence similarity , a recall rate up to 100% (for ENSGT00390000004965 and ENSGT00390000005532) and an F-score rate up to 67% (for ENSGT00390000004965). With the second less stringent method which defines two CDSs as matching if they have a PID higher than 90% and are reciprocal best hits, SFAM_mblock succeeds to predict true new CDS in 15 out of the 20 gene families . With the less stringent method, it predicted 29 out of the 106 new dog CDS . This can be attributed to the comparison with homologous genes from only five other species. It is important to indicate that the new CDSs were findable by SFAM_mblock only if they had conserved counterparts (splicing orthologs) in homologous genes in release 97 of Ensembl. Thus, there was a proportion of new CDSs that lack splicing orthologs in homologous genes that were not targeted by SFAM_mblock, and which should be predicted using complementary methods. Yet, SFAM_mblock’s ability to predict up to 27% of the new CDSs is remarkable. It demonstrates the usefulness of SFAM_mblock predicting gene models by homology in order to improve existing genome annotations. Moreover, the number of newly annotated exons and alternative splicing transcripts is constantly increasing in databases. This indicates that there is a proportion of CDSs yet to be found. These CDSs might not be currently annotated because they contain exons that have not yet been annotated. Thus, the set of true CDSs might be larger in reality, and so would the intersection of the true and predicted CDS sets. Therefore, the predictions underestimated the precision and recall rates.The ability to identify conserved gene transcripts in gene families is a fundamental step for studying the evolution of alternative transcripts. This will help identify which alternative transcripts are conserved across genes and species, and thus are the probable main functional isoforms of a gene. It will also make it possible to study the impact that new alternative transcripts have upon the function of a gene. It will offer a broader picture of the timing of gain and loss of alternative transcripts and help refine hypotheses concerning these evolutionary events.Moreover, several ongoing projects aim to fully sequence thousands of eukaryote genomes (This paper introduced the MSpA problems and describes the SFAM method that computes MSpAs and provides for effectively identifying conserved gene transcripts by performing CDS orthology group inference. Compared with popular MSA methods and sequence clustering methods, SFAM_mblock achieved comparable or higher performance than other methods with more robustness to changes in the sequence similarities. SFAM_mblock was also effective at predicting gene models by homology based on the computation of MSpAs. Applying SFAM_mblock to 20 real gene families from the Ensembl database revealed that up to 27% of the true new dog CDSs in release 98 could be predicted based on data from release 97.The SFAM method takes into account both evolutionary rate and changes in the splicing structure, but does not include other events commonly discussed in gene orthology inference and evolutionary biology: duplication and losses of genes. These events are commonly the target of orthology inference methods such as OrthoFinder. Future work will define spliced homology groups in this context as proposed in vbab044_Supplementary_DataClick here for additional data file.


In a few cases, we have split the superfamily as per the clusters predicted and provided complete data for each cluster. A new feature included in this update is absolutely conserved interactions (ACIs) between residue backbones and side chains, which are obtained by aligning protein structure networks using structure-guided sequence alignments of superfamilies. ACIs provide valuable information about functionally important residues and the structure–function relationships of proteins. The ACIs and the corresponding conserved networks for backbone and sidechain have been marked on the superimposed structure separately.Sequence alignments are models that capture the structural, functional and evolutionary relationships between proteins. Structure-guided sequence alignments are helpful in the case of distantly related proteins with poor sequence identity, thus rendering routine sequence alignment methods ineffective. Protein Alignment organized as Structural Superfamilies or PASS2 database provides such sequence alignments of protein domains within a superfamily as per the Structural Classification of Proteins extended (SCOPe) database. The current update of PASS2 (i.e. PASS2.7) is following the latest release of SCOPe (2.07) and we provide data for 14 323 protein domains that are <40% identical and are organized into 2024 superfamilies. Several useful features derived from the alignments, such as conserved secondary structural motifs, HMMs and residues conserved across the superfamily, are also reported. Protein domains that are deviant from the rest of the members of a superfamily may compromise the quality of the alignment, and we found this to be the case in ∼7% of the total superfamilies we considered. To improve the alignment by objectively identifying such ‘outliers’, in this update, we have used a http://caps.ncbs.res.in/pass2/.The updated version of the PASS2 database is available at  Studying the protein sequence and structure space and understanding their link to protein function has been one of the key questions in the field of biology. In the case of proteins that resemble each other in terms of structure, but are sequentially distant, a comparison of the mere structures may not reveal much. Therefore, sequence alignments of such proteins serve as a useful evolutionary model. Unfortunately, the alignment of proteins with common evolutionary descent is not easy through routine multiple sequence alignment methods owing to poor sequence identity. For alignment of members of a superfamily—evolutionarily related, structurally similar yet sequentially divergent proteins—structure-based sequence alignment methods are more appropriate. These structure-guided sequence alignments may be used to perform rigid-body superposition of the proteins, which in turn may be used for structural identification of newly discovered proteins that are yet to find membership in a structural fold. The alignments themselves may be converted into hidden Markov models (HMMs) , which cProtein Alignment organized as Structural Superfamilies (PASS2) is a database that provides structure-based sequence alignments of protein domains within a SCOPe superfamily . With eaα-root-mean-square deviation (RMSD)] and using an unsupervised machine learning method, handled such domains on a case-by-case basis, to improve the quality of the alignment. An improved alignment results in higher confidence in the HMMs and other features derived out of it.Within a superfamily, there may be members that have structural elements unique to themselves. This could be due to insertions within the protein domain resulting in a sequence longer than other members, and the additional residues may constitute secondary structural elements, which make the domain deviant from other members in the superfamily. In our last update, we had treated such structurally highly deviant members as outliers and not included these in the alignment . In thisIn addition to the existing features, in this update, we have included absolutely conserved interactions (ACIs) for each superfamily. Protein structure networks (PSNs) constructed for each member of the superfamily considering backbone and side chain atoms are aligned using structure-guided sequence alignment of the superfamily members, and common edges are identified as ACIs for that particular superfamily. These ACIs are plotted on superimposed structures of all members of the superfamily and interactive 3D visualization is available for each type of interaction ; the PyMol session files are also available for download from the database.α backbones of the protein domain structures using the MNYFIT program, within JOY (The ASTRAL compendium within the SCOPe database provides Protein Data Bank (PDB) files of protein domains within a superfamily that share no >40% sequence identity with each other . This dathin JOY , 12, 13.k-means) for clustering with the elbow method to estimate the optimal number of clusters in a superfamily. The features given for clustering include the percentage of gaps contributed by each domain to the alignment, the Cα RMSD calculated by JOY and the length of the domain. Scikit-learn (a Python machine learning library) was used to implement the machine learning methods for each alignment, and the optimal numbers of clusters predicted and features used were plotted for each superfamily. The outliers could be recognized automatically using this approach, and hence, alignments were thus improved either by trimming the giant member or removing a dwarf domain or a structural outlier domain or by splitting the superfamily into two or more split superfamilies, as per the clusters realized. The quality of the alignment was assessed in two ways: identification of secondary structural content using an in-house program, ASSALIMAV  at a distance cut-off of 4.5 Å. Similar to backbone networks, residues were considered as nodes and interactions represented by edges. Networks thus constructed were aligned as per the COMPARER alignment, by inserting dummy nodes at the positions of gaps  backbone and (b) side chain. For the backbone networks, two residues were marked as interacting, when their C of gaps . An edgeThe data were organized as ASCII files, images and database tables. Python scripts were used to prepare the organized collection of the files. The database tables are implemented in the MySQL5.2 database engine. Python, BioPython and Flask micro frameworks have been used as the backend engine interacting with the web interface, database and data file collection. The web interface was implemented with the support of CSS, JavaScript, Ajax and JQuery along with HTML and Bootstrap framework. Alignment visualization panels were implemented using the in-house custom-made plug-in. JSmol, Raphael and jsPhyloSVG were used for implementing the visualization panels for displaying the molecular structure (including conserved interactions), phylogenetic tree. Various Python scripts, working at the backend, use Restful API calls to fetch details such as the GO annotations from external sources dynamically.In the latest version of the PASS2 database, PASS2.7, a total of 2024 superfamilies have been considered, of which 1219 are MMSs and 805 are SMSs. These superfamilies contained a total of 14 323 SCOPe domains. SCOPe groups superfamilies into 12 classes, of which 7 are available for download from the ASTRAL compendium. The numbers of superfamilies (both SMS and MMS) from each of these seven classes were counted and have been represented in The alignment of protein domains within MMS in PASS2 consists of several steps that can be grouped into four main phases: organization of data, initial alignment, final alignment and annotation of the final alignment with several features . In thisThe final alignment produced by COMPARER may retain a large number of gaps that may have been incorporated while trying to align one or more member(s) that are different from the remaining members. Such difference may be brought about by structural dissimilarity  or length of the domain (dwarf or giant domain). We identified 87 MMSs that had >50% gaps contributed by at least one member in the alignment and conserved secondary structural content of <30%. For these MMSs, an unsupervised machine learning-based clustering method was used to identify the best possible way to improve the alignment.α-RMSD or both—could be identified, this member was inspected for its domain length. If it was found to be a dwarf domain, the member was removed and the remaining members re-aligned to obtain a lower number of gaps and a higher number of conserved secondary structural elements. If the domain was found to be a giant member, the domain was ‘trimmed’ guided by the COMPARER alignment, albeit a ‘gappy’ (containing a large number of gaps) one, and re-alignment was performed for the MMS  in the alignment and the conserved secondary structural content before and after the improvement of alignment for about 80 superfamilies, as described above, have been plotted in –Figure 5G–For each of the superfamily, ACIs were identified for backbone and side chain separately using PSNs as explained in the ‘Methods’ section. More details about the method of obtaining ACIs are available in the Help tab of the database. ACIs, common to both backbone and side chains, have also been computed and presented in the database. Figure 5AApart from the conserved interactions between backbone and side chains of residues of MMS members, several other useful features are provided within PASS2.7 for download. The statistics of the alignment (ALISTAT), information regarding length variation among MMS members due to insertions or deletions (CUSP) and conservation of secondary structural elements (ASSALIMAV) were provided alongside structural motifs (SMotif), conserved residues (ACR and HCR) for each alignment. The structure-based sequence alignments can be used to construct PSSMs, which can further be used for sensitive sequence searches, and the HMMs created out of these alignments provided in the database also serve this purpose. GO terms, PCA based on structural dissimilarity, as well as dissimilarity-based tree, provide information regarding the individual members of the MMS. For both SMS and MMS, structure and sequence information are amalgamated using JOY, which provides hydrogen bonding, solvent accessibility and secondary structural information for both the alignment (in case of MMS) and the domains (in both SMS and MMS).The availability of structure-based sequence alignments of 2024 protein domain superfamilies permits bioinformatic analyses, such as the construction of mathematical models for sensitive detection of additional members in the vast and ever-increasing space of protein sequences. They also serve as reliable evolutionary models for the comparison of incoming members, to design biochemical experiments and to appreciate structurally conserved/weak regions, insertions and deletions. The provision of accessory structural data, such as conserved structural blocks, structure-annotated derived files and the brand new feature of networks of conserved residues for the superfamilies, organized within this PASS2 database, should be useful for further structural and biochemical analyses. The identification of structural outliers using machine learning techniques, as introduced in this update, should enable rapid updates in future.baac025_SuppClick here for additional data file.


Bio-sequence comparators are one of the most basic and significant methods for assessing biological data, and so, due to the importance of proteins, protein sequence comparators are particularly crucial. On the other hand, the complexity of the problem, the growing number of extracted protein sequences, and the growth of studies and data analysis applications addressing protein sequences have necessitated the development of a rapid and accurate approach to account for the complexities in this field. As a result, we propose a protein sequence comparison approach, called PCV, which improves comparison accuracy by producing vectors that encode sequence data as well as physicochemical properties of the amino acids. At the same time, by partitioning the long protein sequences into fix-length blocks and providing encoding vector for each block, this method allows for parallel and fast implementation. To evaluate the performance of PCV, like other alignment-free methods, we used 12 benchmark datasets including classes with homologous sequences which may require a simple preprocessing search tool to select the homologous data. And then, we compared the protein sequence comparison outcomes to those of alternative alignment-based and alignment-free methods, using various evaluation criteria. These results indicate that our method provides significant improvement in sequence classification accuracy, compared to the alternative alignment-free methods and has an average correlation of about 94% with the ClustalW method as our reference method, while considerably reduces the processing time. Furthermore, accurate classification of a protein sequence among large protein sequence database is critical while developing pharmaceutical products3, such as vaccines, which is becoming increasingly important, particularly in the wake of the coronavirus epidemic. Without current redundancy, the protein sequence database contains over 190 million inputs, and the number of unique functional domains is much larger4. Any attempt to annotate protein function has many issues due to the huge amount of data connected with these proteins. In this manner, protein classification into sequence and structural classes has long been used as a means of simplifying the challenge. As a result, a variety of approaches are used, as explored below.One of the most important disciplines in bioinformatics is protein classification, which is used to discover phylogenetic and evolutionary relationships amongst species7. As a result, comparing and phylogenetic analysis of these biological sequences becomes a new issue, posing challenges in a variety of areas, including processing time and resource management, due to the large number of data to be considered5. Various methods have been proposed up to this point, which can be divided into two categories: alignment-based methods and alignment-free methods8. For a clear description, Table 9, FASTA10), multiple sequence aligners , sequences’ profile search programs , and whole-genome aligners . Although these methods achieve up-to-scratch results in evolutionary relationships discovery, they are generally time and resource consuming and rely on multiple assumptions about the evolution of the sequences to be compared 2. As a consequence, several alignment-free methods have been presented to prevail over these drawbacks. Alignment-free approaches include any method for evaluating sequence similarity/dissimilarity that does not apply or produce sequence alignment at any step of the algorithm; instead, they use feature extraction to extract the required information from the query sequences5. As mentioned before, the alignment-based methods provide high accuracy at the cost of being time-consuming and expensive in memory usage. In contrast, alignment-free methods are fast in computational speed and have been introduced to overcome the complication of sequence alignment5. However, they confront the obstacle of accurate comparison and classification. In other words, one of the outstanding concerns in this field is to develop an accurate alignment-free approach that can be utilized in practice, and hence, studies in the field of developing alignment-free methods are mostly focused on this.The process of obtaining a large number of protein sequences has been made easier for researchers because of advances in sequencing technologies25: (1) the protein's amino acid composition, which includes the frequencies of the 20 distinct amino acids within the sequence as well as their physicochemical qualities, or (2) the order and positional information of amino acids within the sequence. So, the physicochemical properties of amino acids can be used to derive features from a protein sequence. As is obvious, a protein sequence is made up of amino acids, each of which has its own set of physicochemical properties that influence protein structures, functions, folding, protein–protein interactions, and evolutionary patterns27. As a result, amino acid physicochemical properties play an essential role in protein sequence similarity analysis, protein subcellular localization prediction, and protein structural class prediction. Another aspect to consider is that relying solely on the amino acids’ physical qualities results in the loss of various information, such as the number of amino acids, their location in a string, and so forth25. This positional information, on the other hand, can significantly affect the accuracy of similarity analysis between two sequences. As a result, by relying simply on either physicochemical characteristic or positional information, some data is lost, and the information embedded within a protein sequence is not fully utilized.Feature extraction from a protein sequence is the challenging part of protein classification studies in any of the approaches discussed above; as a result, various alignment-free methods have been developed in this area. These techniques can extract features in one of two ways27, for example, is built upon the chaos game model based on the physicochemical features of amino acids. The Energy matrix approach2 is another study that is based on physicochemical properties and the position-feature Energy Matrix. Apart from these two studies, methods28, and many others have utilized the physicochemical features in various ways in their methods. The main drawback of these studies is that they just use the value of physicochemical properties of amino acids in an indirect manner, which results in some information loss. Moreover, there are other concerns, such as the high complexity and increasing volume of calculations in these methods, such as DCGR.In this regard, many studies have been conducted in this area, each of which has used one of these two methodologies or a combination of them. One of these state-of-the-art methods, DCGR29 that is based on the k-mer natural vector, fuzzy integral (FI) based method5 that is based on the fuzzy integral and Markov chain, and7 method, and many more, do not consider physicochemical properties of the amino acids. Even though these properties provide essential factors for predicting the function and structure of protein sequences.On the other hand, other studies, such as natural vector based method27. After retrieving the attributes of the protein sequences, numerous methods have been proposed to leverage these features to complete the target tasks and perform the desired calculations. These approaches either require large memories or are not optimal in terms of algorithm execution time, although they achieve acceptable accuracy among various alignment-free methods27. To build an efficient algorithm for protein classification, several tradeoffs between memory requirement, time consumption, and high accuracy, must be evaluated, which necessitates effective feature extraction.As a consequence, based on the previous studies, it appears that combining physicochemical properties of amino acids with other properties of protein sequences can assist to enrich the features derived from the sequencesGiven aforementioned challenges of the available alignment-free methods, including clustering accuracy, accuracy of the resultant similarity/dissimilarity scores in comparison to the alignment-based methods, computation speed, considering each protein sequence as a single unit to be processed, and thus, ignoring individual indels' effect, and finally, not involving the physicochemical properties of the amino acids, we propose a simple but efficient vector-based method named PCV  to numerically characterize a protein sequence, utilizing the value of the amino acids' physicochemical properties, as well as the positional information of the letters. In more details, we utilize all physicochemical properties of the amino acids, we split each protein sequence into fixed-size blocks, and encode each block of protein applying the proposed encoding method. As a result, PCV takes into account both the influential amino acids' physicochemical properties and the local sequence comparisons, none of which have been considered by most of the existing alignment-free methods. In this work, we also attempt to incorporate the key advantages of the alignment-free methods, including increased processing speed and reduced resource utilization, in comparison to the alternative alignment-based and alignment-free methods.Extract physicochemical properties from the AAindex.Cluster properties into 110 items.Split a sequence into fixed-length blocks.Calculate statistical or positional characteristics and produce vectors based on the physicochemical properties.Calculate the distance metric between different spices vectors to perform the evolutionary analysis.The steps of our approach are as follows:Going through above steps, PCV offers several key advantages: (1) simple feature extraction by using the value of the amino acids’ physicochemical properties, and (2) preserving more sequence information by using the amino acids’ physicochemical properties and moment values as a combination of protein composition and positional information, (3) incorporating locational information of amino acids to fully utilize all information embedded within a protein sequence, (4) providing computational parallelism as the result of sequence partitioning into fixed-length blocks, which facilitates parallel operation on various blocks through iterative steps, (5) capable of handling numerous mutations in compared sequence, (6) reduced runtime, compared to alternative methods.5 and ClustalW as the reference method11. The results confirm that PCV offers higher accuracy, provides correct evolutionary relationships of different kinds of species, and offers high speed comparison. The rest of the paper is organized as follows. Details of the proposed method, i.e. PCV, are introduced in “As a comparative study, we evaluate PCV on a variety of datasets with diverse sequence lengths and numbers of sequences. Also several comparison metrics (e.g. Correlation Coefficient and Robinson Foulds distance) are applied to compare our results with those of alternative methods, such as fuzzy integral based methodClustering unit categorizes physicochemical features of the amino acids. This unit categorizes 566 amino acid features into 110 classes. As a result, although all features are utilized, the amount of data fed to the comparison algorithm is reduced.Splitting unit splits protein sequences into fixed-size blocks: Splitting sequences preserves local information, while enables indel modeling.Calculation unit generates statistical information vector for each block: In this unit, statistical information of the amino acids and their order are calculated based on the corresponding physicochemical features.Comparison unit computes dissimilarity/similarity metric. This unit computes Euclidean distance of physicochemical and statistical information vectors for each pair of blocks of two sequences, and so, utilizes the extracted distance to compute the dissimilarity metric between input sequences.As the main target of this paper, we attempt to develop an accurate alignment-free approach to boost the speed of protein comparison, while preserving resource efficiency. In this case, we utilize two different types of data: 1) physical and chemical characteristics of amino acids, and (2) statistical information of the amino acids, such as their spatial frequency within the sequences. For this purpose, as shown in Fig.  physicalThe process of PCV algorithm is such that first of all, its Splitting unit elongates the input sequences to a specific length and splits them into pieces of fixed length. Afterwards, the Calculation unit encodes these components using the physicochemical properties clustered by the Clustering unit. Finally, the PCV algorithm calculates a score as the degree of similarity / dissimilarity between each two sequences. To clarify these functionalities, Fig. 26. This database consists of three sections: (1) AAindex1 for the amino acid indices, as we require in this paper, (2) AAindex2 for the amino acid substitution matrices, and (3) AAindex3 for the amino acid contact potentials.The physicochemical properties of amino acids demonstrate the characteristics of biochemical reactions and have been widely used in bioinformatics research. AAindex is a database of numerical indices representing diverse physicochemical and biochemical properties of amino acids26. Although it can be used in various applications, such as sequence comparison involving high number of sequences, this massive volume of data arises resource consumption and computational complexity concerns. In this manner, we propose grouping them together to overcome these challenges. For this purpose, we first calculate the correlation between each pair of 566 properties to obtain a 566 × 566 correlation matrix. Then, we use this matrix to calculate a pairwise Euclidean distance in a 566-dimensional space to achieve a 1-d array. This array is then used to feed the “linkage method” 31, as is discussed in more details in the supplementary materials section "AAindex1 clustering". Finally, we form flat clusters from the hierarchical clustering defined by the given linkage matrix, provided that each flat cluster has a cophenetic distance not greater than 0.2 × max_distance (maximum Euclidean distance from the 1-d array). The details of clustering these 566 properties into 110 groups can be seen in Table AAindex1 includes 566 properties for amino acidsOnce the physicochemical properties are clustered, to use each class, a representative value of all the attributes in that class should be determined. In this paper, we employ the average values of all attributes of each class for each amino acid, resulting in a 110 × 20 matrix, which replaces the 566 × 20 matrix used by AAindex1 to feed the PCV. In addition, these values are normalized by Studentized residual to unify the impact of the physicochemical properties. This clustered 110 × 20 matrix is called “level-1 categorization”, which is still a significant amount of data to be used through the sequence comparison process. To resolve the issue, we also partition the numerical range of each of these 110 classes into four equal ranges, and allocate each amino acid to one of the four ranges at which its corresponding numerical value is located. This categorization scheme, called as quadruple classification, is utilized in other parts of the PCV as well. It is worth noting that the number of amino acids in each of the four categories might be different. Figure Splitting unit partitions protein sequences into blocks of constant length. This partitioning preserves the locality information of protein sequences through the comparison process, which is also empowered by the physicochemical characteristics of amino acids. However, due to the different lengths of input sequences, first of all, lengths of all sequences are made equal to the length of the longest sequence by appending a meaningless substring to their tails.The occurrence of indels within the sequences and their diagnosis raises some challenges since sequence partitioning into fixed length blocks might prevent their appearances. To resolve this issue, as shown in Fig. Once the sequences have been split into blocks, they must be encoded and compared with each other. For this purpose, the Calculation unit performs the encoding and the comparison unit compares the sequences. Each block is encoded as a vector, consisting of two parts: (1) physicochemical vector, representing values of the block's physicochemical attributes collected and preprocessed from AAindex1, and (2) statistical vector, representing statistical information of the block's amino acid groups. In the following, we describe these two parts of the vector in more details.As described in the clustering unit, the 566 properties provided for each amino acid in AAindex1 are clustered into 110 classes. As a result, for each amino acid in the split block, the calculating unit allocates a vector of length 110 to represent its physicochemical properties. In this manner, for a block of length |S|, a matrix of size 110 ×|S| is generated. As the next step for each block, the values of each physicochemical property for various amino acids are added up. It should be noted that this process is performed for all possible shifts of each block. Figure s is the number of repetitions of each quadruple classification group for each property in block S, fN is a binary function calculated for each group of quadruple classification of each of 110 property classes and assumes that all members (amino acids) of each group are similar. Therefore, for each group of quadruple classification, fN equals one if its input character (each amino acid of block S) belongs to the intended group, and its zero otherwise, μS is the mean position of each group of quadruple classification for each property in block S, As described in the introduction, in order to extract the most information from a protein strand, the statistical and spatial information of amino acids must be analyzed, alongside their physicochemical properties. Specifically, quadruple classification as defined in the clustering unit is employed to produce statistical vectors for each block. For this purpose, 2nd moment of position of each group of quadruple classification is used for each block as statistical vector which is derived from the other two concepts as follow: 1) the number of repetitions of each quadruple classification group for each property in the block, and (2) the mean position of each group for each property in the block. This statistical information can be calculated by Eqs.  the numb, respectThe vectors produced by the computation unit for each block, as well as their corresponding shifts, are compared in this unit. To accomplish so, it compares ith blocks of two sequences using the Euclidean distance, as addressed in Eq. .4\docume29. Our datasets include 9 ND5, 8 ND6, 24 TFs, Coronavirus in two versions, i.e. a) 24 sequences and b) 50 sequences, Betaglobin in three versions, i.e. a) 9 sequences, b) 50 sequences, and c) 88 sequences, 27 AFPs, 114 HRV,1163 influenza, and 20 xylanases protein sequences. The detailed information of each dataset is provided in Table The proposed algorithm is tested on 12 different datasets, available at The National Center for Biotechnology Information (NCBI), F10 and G11 protein datasets, and other public databases5. The qualitative analysis of trees can assess the clustering ability and topology of the resultant trees, demonstrating the method's capacity to appropriately categorize the input data. Analyzing the RF distance and CC similarity metric for the two phylogenetic trees or the distance matrices determines their topological dissimilarity/similarity, considering the corresponding similarity ratios, by investigating the linear relationship between the corresponding branch lengths of the trees (or the distance matrices) produced by the two methods. Finally, the ROC diagram and AUC are primarily used to qualify data classification, and do not assess an exact numerical relationship between similarity scores supplied by the compared methods.As mentioned in the data section, we utilized 12 datasets  and some others by NJ (Neighbor-Joining), we have used both methods to produce the trees. All trees produced by these methods are accessible in the supplemental materials, however to avoid overlength paper, depending on the method being compared with PCV, either UPGMA or NJ is reported in the following section. Finally, it should be mentioned that we use MEGAX software version 10.1.7 to produce the trees.28. This dataset includes 9 protein sequences of ND5, which approximately has 600 amino acids. The phylogenetic tree (produced by UPGMA method) constructed by our method, PCV, is shown in Fig. 5 for this dataset, which is shown in Figure 11 . This protein is a section of a large enzyme complex, known as complex I, which is active in mitochondria. This enzyme is the largest of the respiratory complexes, and is responsible for the first step of the electron transport process, i.e. the transfer of electrons from a molecule called NADH to another molecule called ubiquinone5. This dataset includes 8 protein sequences of ND6, which approximately has 175 amino acids. The phylogenetic tree constructed by our method is shown in Fig. 5, which put wallaroo in the same clade with , as shown in Figure 11, generates a phylogenetic tree with the same topology as that of PCV. Hence, we can conclude that PCV can be as accurate as the alignment-based methods.MT-ND6, the only protein-coding gene located on the L-strand of the human mitogenome, is one of seven mitochondrial genes encoding subunits of the enzyme NADH dehydrogenase (ubiquinone)8. For PCV, both UPGMA and Neighbor-Joining tree construction methods show the precise categorization. Figure 5  from vertebrates, with approximately 700 amino acids, are glycoproteins found in vertebrates that bind to iron (Fe), and consequently, they mediate the transport of iron (Fe) through blood plasma. The liver is the main site of transferrin synthesis, but other tissues and organs, including the brain, also produce transferrin. Transferrin is also associated with the innate immune system. It is found in the mucosa and binds iron, thus creates an environment with low level of free iron that impedes bacterial survival in a process called iron withholding5 Figure  clusters5 Figure  does not32. Coronaviruses can be classified into four types based on their spike proteins and host types. This dataset contains 24 coronavirus protein sequences divided into four classes5: classes I , II , III (avian coronaviruses), and IV (SARS-CoV samples). As shown in Fig. 11 method for comparison. Similar to our method, as shown in Figure 7. While this method has not created a phylogenetic tree for this dataset, it uses UPGMA for phylogenetics tree construction for two other datasets (i.e. ND 5 and betaglobin). The intensity-based technique merely presented the average and standard deviation of the produced intensity vectors  are a group of proteins that bind to macromolecular ice and prevent it from accumulating. Spruce budworm , yellow mealworm , Hypogastrura harveyi (HH), Dorcus curvidens binodulosus (DCB), Microdera dzhungarica punctipennis (MDP), and Dendroides canadensis (DC) are the six species that makeup AFPsW Figure  provide s Figure , the Ene29. The phylogenetic tree constructed by PCV, based on UPGMA method, is shown in Fig. 11  Hominidae, including Chimpanzee, Gorilla, Human, (2) Rodentia, including Rat, mouse, (3) Didelphidae, including Oppossum, and (4) Anatidae, including Duck, Gutta, Gallus5, these 50 beta-globin protein sequences, from various species taken from GenBank, can be divided into four categories: mammals, birds, reptiles, and aquatic animals. However, the categorization does not end here; there are more details, while each of these classes encompasses multiple subclasses. Specifically, Primates, Proboscidea, Ungulate, Carnivora, Rodentia, Chiroptera, and Cetacea are all mammals; birds or Aves are both categorized as birds; and, Aquatics consist of Actinopterygii and Chondrichthyes5. As shown in Fig. 5 . As a result, a classifier strategy with a strong performance is expected to bring these categories closer together. This database is created using the natural vector approach, and the findings are presented in the form of a phylogenetic tree created by NJ. So, for a fair comparison, outputs of PCV for this dataset are used to produce a phylogenetic tree based on the NJ approach. PCV clusters all 20 categories appropriately, as well as groups related categories closer together at the order level, as shown in Fig. 11  is one of the most prevalent causes of respiratory infections and is often associated with the common cold. The HRV dataset29. As a result, subtypes of influenza A viruses are identified by two numbers H and N, where H represents the hemagglutinin type, which currently has 18 variants, and N represents the type of neuraminidase, for which currently there are 11 variants. Thus, diversity of this dataset emphasizes its key role for evaluating classification methods, including PCV. For this purpose, we used 1163 influenza A viruses NA protein sequences which are divided into 13 subtypes: H5N6, H5N1, H7N9, H1N1, H6N2, H3N8, H3N2, H4N6, H5N5, H10N3, and H7N3. As shown in Fig. 11  and neuraminidase (NA), varies substantially across influenza viruses5. As presented in this section, we built phylogenetic trees using both the UPGMA and NJ methods, and for each method, we reported RF distance between the phylogenetic trees produced by our method (i.e. PCV) and three alignment-based method, the ClustalW11, Clustal Omega18, and Muscle12, as the reference method. Furthermore, while some other studies, such as the fuzzy integral-based technique5, provide RF distances for their proposed methods, we have also included those information in Table The Robinson–Foulds (RF) distance is a commonly used comparison metric for analyzing the linear relation between two phylogenetic trees. The RF distance of zero indicates that the trees are identical; as the distance increases, the trees become less similar28. The value of this metric is in the range of , where the greater the linear relationship between two vectors, the closer CC value is to 1 or − 1, and the weaker the relationship, the closer it is to zero. The direct and indirect connection of the two vectors, respectively, is presented by positive and negative values. In this manner, for each of the 12 datasets, we utilized CC to examine the linear relationship between the distance matrix of PCV and three alignment-based methods ClustalW11, Clustal Omega18, and Muscle12; Table 5 for the given datasets and also outperforms ED for most of datasets. More detailed discussions of this table are provided in the "Another well-known metric for measurement of linear relationships between two vectors is the Correlation Coefficient (CC)35. More information about this curve can be found in the "ROC" section of the supplementary materials.The ROC (Receiver Operating Characteristic) curve is a graphical representation of the diagnostic capabilities of a binary classifier system when its discrimination threshold varies. It can, however, be used for a multi-class classifier as well. The ROC curve is produced by the true positive rate (TPR), also known as sensitivity, recall, or probability of detection, against the false positive rate (FPR), also known as the probability of false alarm and computed as (1—specificity). In addition, the AUC (Area under the ROC Curve) measure is one of the most prevalent interpretations based on the ROC curve. AUC is in the range of , while the closer value to 1 indicates the classification approach with the greater accuracy. Generally, an approach with an AUC above 0.9 is considered as a high accurate classifier, while AUC between 0.7 and 0.9, and between 0.5 and 0.7 represent classifiers with average and low accuracy, respectively34, and three alignment-based methods ClustalW11, Clustal Omega18 and Muscle12. Moreover, all ROC curves and AUC values reported for fuzzy integral based method5 are also considered in Table 5. Based on all information reported in Fig. 5, which in most datasets is greater than the AUC values of ClustalW and PCV methods, should be discussed. As a key point to be noticed in this section is that the classification matrix used to calculate AUC has a high impact on its value, while these matrices are identical for both ClustalW and PCV methods. As a result, their AUC values confirm the trend of other metrics, such as the CC between PCV and ClustalW, as expected. However, the classification matrix of fuzzy integral based approach is ambiguous, and it most likely differs from the matrix we utilize, resulting in a higher AUC score, compared to the ClustalW method, while other metrics indicate that it is inferior to ClustalW.To evaluate the proposed algorithm, for all 12 datasets, we generated ROC curves and computed their AUC values for PCV, ED5, we constructed ROC curves for this method using our classification matrix. In this manner, we achieved two ROC curves for the fuzzy integral approach (the one published at5 and the other one we generated from the provided matrix). As reported in Table 5 is still used for the other five alignment-free methods. Given the ROC curves and the repetition of the ROCs production for the fuzzy integral based method and their AUC values, we can conclude that our classification matrices are more rigid and reliable, and hence, it is possible that the computed AUC values based on our classification matrix for five alternative alignment-free methods be lower than the corresponding reported values at5. Finally, as a key advantage of our proposed method, it should be noted that PCV provides better classification results for large datasets, such as influenza A and betaglobin (88), and HRV, compared to the alternative alignment-free methods as well as alignment-based methods, ClustalW, Clustal Omega, and Muscle. As analysis of quantitative metrics confirm this superiority, the latter achievement is also obvious from qualitative study of the corresponding phylogenetic trees. More detailed discussions of this table are provided in the "To resolve the aforementioned issue, considering the distance matrix provided by the fuzzy integral based method at11, as an alignment-based algorithm, and the fuzzy integral based approach5, as a free-alignment method, have been presented as well. The corresponding execution times are listed in Table 5, and so, the execution times for the datasets not examined by FI tool are not applied. It should be mentioned that, in addition to the method's execution time, the system’s specifications executing the algorithm should be presented as well. Saw et al. 5 uses a Linux server with 24 dual-core processors, 384 GB RAM, and two threads to run its fuzzy integral based technique. While execution times of PCV and ClustalW are measured on a Windows system with a 4-core CPU running at 3.6 GHz and 12 GB of RAM. Considering above specifications, assuming execution of fuzzy integral based technique on a similar system implementing PCV and ClustalW methods, its runtime would be several times higher. Moreover, it should be noted that in order to report the ClustalW's execution time, we ran it 20 times on the system and averaged their results. According to Table 36, is depicted in this diagram for a various numbers of input sequences. As depicted in this figure, the priority of PCV in terms of execution time for a large number of sequences is crystal clear. For example, PCV can compare around 5000 input sequences in about 28 h, while the other two approaches take more than 84 h to accomplish this comparison. It should be noted that the sequences in this database are around 330 characters long, and execution times are measured on a system with a 4-core CPU running at 2.4 GHz and 12 GB of RAM. Finally, in section "time estimates" of the supplementary materials, we provided a runtime estimation formula of PCV, based on the implementing system’s specification and maximum sequence length.Considering 12 aforementioned datasets with different number of sequences and varying sequence lengths, in this section, we evaluate the execution time of PCV. For a comparative study, the implementations of ClustalW27. As a result, effective physicochemical qualities combined with sequence information can be utilized to increase the accuracy of comparison tools and form the basis for their application in other tools, such as predicting the second and third structures and the protein function. PCV is created and developed with these scenarios in mind.As discussed in this paper, it is critical to provide an accurate and high-speed tool, as a means of protein sequence comparison, which provides sequence categorization, particularly for large datasets with a significant number of sequences. Proteins are sequences whose folded structures have a direct effect on their functions, and their structures are influenced by physicochemical qualities on the one hand34, the phylogenetic trees of PCV offer substantially much similarity with those of ClustalW11, Clustal Omega18, and Muscle12 based on the RF distance. For this comparison, the topology and branch lengths of the trees are addressed for similarity measurement of phylogenetic trees, assuming that the reference tree is completely correct. On the other hand, since alignment-based metrics are still being studied, it is not definitive to choose an alignment-based method as the reference one. As a result, for some datasets, such as Influenza A and HRV, due to the large number of samples and the less likely exact similarity of the phylogenetic tree of PCV to the reference one, PCV results in large values of RF distance for some datasets. Since no other approach has supplied RF distance for these challenging datasets, PCV evaluation for these datasets is impossible.As previously stated, evaluations and comparisons with current acceptable tools are required to assure PCV’s performance, and these are carried out at several levels. We employed numerous comparison methods, since each method offers a distinct comparison approach. In comparison to the fuzzy integral based technique and ED5, PCV is improved greatly in terms of this parameter, with an average CC value of 95%. Another measure for evaluating classification capability of a method is the ROC curve. Regarding this measurement, PCV showed to be an accurate classification approach for most datasets. In addition to all these achievements in accuracy comparison, our method is also able to determine the local similarity for each pair of blocks, as well as the overall similarity of the sequences indicated by the final dissimilarity score.We performed a comparative study of PCV and three alignment-based methods, ClustalW, Clustal Omega, and Muscle using the CC similarity metric. For this purpose, we eased the similarity conditions of phylogenetic trees by examining the linear relationship between our method's distance matrix and that of the reference method. In comparison to the fuzzy integral-based method5, with no explicit statement, involve customized datasets containing a number of sequences from specific categories, often at the taxonomy levels of family, genus, or species. In other words, to prepare a customized dataset, an extensive search is performed within a large database to select the proper sequences and create the required datasets. It should be mentioned that for the alignment-free methods, the initial assumption is that the input sequences do not include large structural variations; in other words, they are homologous, so that a one-way comparison can be performed from the beginning to the end of the sequences. Moreover, the assumption can be equated with the proposition that along with the alignment-free methods, a simple sequence search method is required to detect the homologous data. Therefore, we can conclude that generally, the alignment-free methods can process the datasets of homologous sequences, unless joined with some preprocessing tools. To validate the aforementioned statement, for each alignment-free comparison tool, we determined its best response assuming the least identity of the input sequences and the minimum degree of sequence alignment. In this manner, we obtained Table It should be noted that most studies addressing the protein sequence alignment-free comparison5, we can conclude that in the case of large datasets, either in terms of sequence lengths or number of sequences, we can offer a higher processing speed.In addition to the issue of accuracy, high speed processing is one of our main goals in designing a suitable method for comparing protein sequences. Examining the speed of our method compared to those of ClustalW, ClustalW2, Muscle and fuzzy integral based methodFinally it should be mentioned that the alignment-based methods, such as ClustalW, are known as the accurate comparison tools, and have been used for many years. Therefore, in this study, ClustalW was chosen as a reference method to assess the accuracy of the PCV and the alternative alignment-free methods. ClustalW, as mentioned in "11 as the reference method, in addition to improving the comparison speed compared to the other methods, Correlation Coefficient (CC) metric, RF distance, ROC curve, and the corresponding AUC metric indicate greater improvement for PCV method than the alternative alignment-free methods. Specifically, we reported an average CC of 94% between PCV and ClustalW methods, as well as more accurate classifications at the different levels of evolution. In this way, we can conclude that PCV is accurate and fast, while providing local similarity information which is not considered by other alignment-free methods. As the future works, PCV can be developed to display pseudo-dot plots and reduce the required amount of memory. Furthermore, due to its structure, employing repetitive operational units, PCV method can be implemented on widely available hardware platforms, such as FPGA, which can assist speeding up this approach, compared to its current CPU-based version. In addition, we would like to make PCV method available as a public online tool.Due to the growing need for development of sequence comparison tools, especially protein sequences, in this work, we presented an alignment-free method that uses sequence information and physicochemical properties of amino acids. This method estimates the similarity of the protein sequence in whole by determining local similarity of fixed length blocks. As a result, although it is an alignment-free method, it can resemble the behavior of alignment-based methods for protein comparison. We compared this method, known as PCV, to some well-known alignment-based and alignment-free methods in a variety of ways. Specifically, we evaluated the PCV approach for 12 benchmark datasets considering various conditions, which is a superior of datasets compared to alternative studies. It should be mentioned that like other alignment-free methods, these datasets include classes with homologous sequences which may require a simple preprocessing search tool to select the homologous data. Assuming ClustalWSupplementary Information.