Sequence Comparison Tools Research Articles

Graph-based analysis of DNA sequence comparison in closed cotton species: A generalized method to unveil genetic connections.

Graph theory provides a systematic method for modeling and analysing complicated biological data as an effective bioinformatics tool. Based on current trends, the number of DNA sequences in the DNA database is growing quickly. To determine the origin of a species and identify homologous sequences, it is crucial to detect similarities in DNA sequences. Alignment-free techniques are required for accurate measures of sequence similarity, which has been one of the main issues facing computational biologists. The current study provides a mathematical technique for comparing DNA sequences that are constructed in graph theory. The sequences of each DNA were divided into pairs of nucleotides, from which weighted loop digraphs and corresponding weighted vectors were computed. To check the sequence similarity, distance measures like Cosine, Correlation, and Jaccard were employed. To verify the method, DNA segments from the genomes of ten species of cotton were tested. Furthermore, to evaluate the efficacy of the proposed methodology, a K-means clustering method was performed. This study proposes a proof-of-model that utilises a distance matrix approach that promises impressive outcomes with future optimisations to be made to the suggested solution to get the hundred percent accurate result. In the realm of bioinformatics, this paper highlights the use of graph theory as an effective tool for biological data study and sequence comparison. It's expected that further optimization in the proposed solution can bring remarkable results, as this paper presents a proof-of-concept implementation for a given set of data using the proposed distance matrix technique.

Family-Free Genome Comparison.

The comparison of large-scale genome structures across distinct species offers valuable insights into the species' phylogeny, genome organization, and gene associations. In this chapter, we review the family-free genome comparison tool FFGC that, relying on built-in interfaces with a sequence comparison tool (either BLAST+ or DIAMOND) and with an ILP solver (either CPLEX or Gurobi), provides several methods for analyses that do not require prior classification of genes across the studied genomes. Taking annotated genome sequences as input, FFGC is a complete workflow for genome comparison allowing not only the computation of measures of similarity and dissimilarity but also the inference of gene families, simultaneously based on sequence similarities and large-scale genomic features.

Fast and robust metagenomic sequence comparison through sparse chaining with skani

Sequence comparison tools for metagenome-assembled genomes (MAGs) struggle with high-volume or low-quality data. We present skani (https://github.com/bluenote-1577/skani), a method for determining average nucleotide identity (ANI) via sparse approximate alignments. skani outperforms FastANI in accuracy and speed (>20× faster) for fragmented, incomplete MAGs. skani can query genomes against >65,000 prokaryotic genomes in seconds and 6 GB memory. skani unlocks higher-resolution insights for extensive, noisy metagenomic datasets.

UniAligner: a parameter-free framework for fast sequence alignment.

Even though the recent advances in 'complete genomics' revealed the previously inaccessible genomic regions, analysis of variations in centromeres and other extra-long tandem repeats (ETRs) faces an algorithmic challenge since there are currently no tools for accurate sequence comparison of ETRs. Counterintuitively, the classical alignment approaches, such as the Smith-Waterman algorithm, fail to construct biologically adequate alignments of ETRs. We present UniAligner-the parameter-free sequence alignment algorithm with sequence-dependent alignment scoring that automatically changes for any pair of compared sequences. UniAligner prioritizes matches of rare substrings that are more likely to be relevant to the evolutionary relationship between two sequences. We apply UniAligner to estimate the mutation rates in human centromeres, and quantify the extremely high rate of large duplications and deletions in centromeres. This high rate suggests that centromeres may represent some of the most rapidly evolving regions of the human genome with respect to their structural organization.

Development of a Sequence Searchable Database of Celiac Disease-Associated Peptides and Proteins for Risk Assessment of Novel Food Proteins.

Celiac disease (CeD) is an autoimmune enteropathy induced by prolamin and glutelin proteins in wheat, barley, rye, and triticale recognized by genetically restricted major histocompatibility (MHC) receptors. Patients with CeD must avoid consuming these proteins. Regulators in Europe and the United States expect an evaluation of CeD risks from proteins in genetically modified (GM) crops or novel foods for wheat-related proteins. Our database includes evidence-based causative peptides and proteins and two amino acid sequence comparison tools for CeD risk assessment. Sequence entries are based on the review of published studies of specific gluten-reactive T cell activation or intestinal epithelial toxicity. The initial database in 2012 was updated in 2018 and 2022. The current database holds 1,041 causative peptides and 76 representative proteins. The FASTA sequence comparison of 76 representative CeD proteins provides an insurance for possible unreported epitopes. Validation was conducted using protein homologs from Pooideae and non-Pooideae monocots, dicots, and non-plant proteins. Criteria for minimum percent identity and maximum E-scores are guidelines. Exact matches to any of the 1,041 peptides suggest risks, while FASTA alignment to the 76 CeD proteins suggests possible risks. Matched proteins should be tested further by CeD-specific CD4/8+ T cell assays or in vivo challenges before their use in foods.

Parallel Fine-Grained Comparison of Long DNA Sequences in Homogeneous and Heterogeneous GPU Platforms With Pruning

The parallelization of Smith-Waterman (SW) sequence comparison tools for long DNA sequences has been a big challenge over the years, requesting the use of several devices and sophisticated optimizations. Pruning is one of these optimizations, which can reduce considerably the amount of computation. This article proposes MultiBP, a sequence comparison solution in multiple GPUs with block pruning. Two MultiBP strategies are proposed. In static score-sharing, workload is statically distributed to the GPUs, and the best score is sent to neighbor GPUs to simulate a global view. In the dynamic strategy, execution is divided into cycles and workload is dynamically assigned, according to the GPUs processing rate. MultiBP was integrated to MASA-CUDAlign and tested in homogeneous and heterogeneous platforms, with different NVidia GPU architectures. The best results in our homogeneous and heterogeneous platforms were mostly obtained by the static and dynamic approaches, respectively. We also show that our decision module is able to select the best strategy in most cases. Finally, the comparison of the human and chimpanzee chromosomes 1 in a cluster with 512 V100 NVidia GPUs took 11 minutes and obtained the impressive rate of 82,822 GCUPS (Billions of Cells Updated per Second) which is, to our knowledge, the best performance for SW tools in GPUs.

ADACT: a tool for analysing (dis)similarity among nucleotide and protein sequences using minimal and relative absent words.

Researchers and practitioners use a number of popular sequence comparison tools that use many alignment-based techniques. Due to high time and space complexity and length-related restrictions, researchers often seek alignment-free tools. Recently, some interesting ideas, namely, Minimal Absent Words (MAW) and Relative Absent Words (RAW), have received much interest among the scientific community as distance measures that can give us alignment-free alternatives. This drives us to structure a framework for analysing biological sequences in an alignment-free manner. In this application note, we present Alignment-free Dissimilarity Analysis & Comparison Tool (ADACT), a simple web-based tool that computes the analogy among sequences using a varied number of indexes through the distance matrix, species relation list and phylogenetic tree. This tool basically combines absent word (MAW or RAW) computation, dissimilarity measures, species relationship and thus brings all required software in one platform for the ease of researchers and practitioners alike in the field of bioinformatics. We have also developed a restful API. ADACT has been hosted at http://research.buet.ac.bd/ADACT/. Supplementary data are available at Bioinformatics online.

Using Multiple Fickett Bands to Accelerate Biological Sequence Comparisons

Most of the exact algorithms for biological sequence comparison obtain the optimal result by calculating dynamic programming (DP) matrices with quadratic time and space complexity. Fickett prunes the DP matrices by only computing values inside a band of size k, thus reducing time and space complexity to [Formula: see text]. Myers and Miller (MM) proposed a linear space algorithm that splits a sequence comparison into multiple comparisons of subsequences, using a divide-and-conquer approach. In this article, we propose a parallel strategy that combines the Fickett and MM algorithms, thus adding pruning capability to the MM algorithm. By using an appropriate Fickett band in each subsequence comparison, we can significantly reduce the number of cells computed in the DP matrices. Our strategy was integrated to stages 3 and 4 of CUDAlign, a state-of-the-art parallel tool for optimal biological sequence comparison, generating two implementations: Fickett-MM-4 and Fickett-MM-3-4. These implementations were used to compare real DNA sequences, reaching a speedup of 101.19 × in the 10 × 10 millions of base pairs comparison when compared with CUDAlign stages 3 and 4. In this case, the execution time was reduced from 71.42 to 0.7 seconds.

Porcine reproductive and respiratory syndrome virus: web-based interactive tools to support surveillance and control initiatives

BackgroundControl of porcine reproductive and respiratory syndrome (PRRS) represents a tremendous challenge. The trend is now toward managing the disease collectively. In Quebec, area and regional control and elimination (ARC&E) initiatives started in 2011; diagnostic testing, including ORF5 sequencing, and sharing of information among stakeholders are largely promoted. At the provincial level, a data-sharing agreement was signed by Quebec swine practitioners allowing PRRS virus (PRRSV) sequences to be transferred to a database maintained by the Laboratoire d’épidémiologie et de médecine porcine (LEMP-DB). Several interactive tools were developed and are available to veterinarians to allow comparison of PRRSV ORF5 sequences within ARC&E projects or provincially while managing confidentiality issues.ResultsBetween January 1st 2010 and December 31st 2018, 4346 PRRSV ORF5 sequences were gathered into the LEMP-DB, involving 1254 sites and 43 practicing veterinarians. Approximately 34% of the submissions were from ARC&E projects. Using a novel web-based sequence comparison tool, each veterinarian has access to information on his/her client sequences and can compare each sequence with 1) commercial vaccine strains, 2) historical samples from the same site, and 3) all sequences submitted to the database over the last 4 years. Newly introduced PRRSV into breeding herds can be monitored using a new sequence comparison tool based on comparison of sequences at the provincial level. Each month, graphs providing the number of introductions per month and the yearly cumulative are updated. Between August 1st 2014 and December 31st 2018, 233 introductions were detected on 180 different breeding sites. Following a data-sharing agreement, veterinarians involved in ARC&E projects have access to an interactive mapping tool to locate pig sites, compare sequence similarity between participating sites and visualize the results on the map.ConclusionsThe structure developed in Quebec to collect, analyse and share sequencing data was efficient to provide useful information to the swine industry at both provincial and regional levels while dealing with confidentiality issues.

BASTA – Taxonomic classification of sequences and sequence bins using last common ancestor estimations

Abstract Identification of the taxonomic origin of a DNA sequence is crucial for many sequencing projects, e.g. metagenomics studies, identification of contaminations in whole genome sequencing projects and filtering of organisms of interest in marker‐gene based community analyses. Last common ancestor algorithms are powerful approaches to estimate the taxonomy of a given sequence and have been widely used for classification of next‐generation sequencing (NGS) reads, also known as 2nd generation sequencing reads. Here, we present BASTA (https://github.com/timkahlke/BASTA), a basic sequence taxonomy annotator, which extends last common ancestor estimations from sequencing reads to any kind of nucleotide or amino acid sequence utilizing NCBI taxonomies of user‐defined best hits. BASTA can be configured to use the output of many common sequence comparison tools, e.g. BLAST and Diamond, in conjunction with either provided or user‐defined target sequence databases.

Clustering of multi-domain protein sequences.

The overall function of a multi-domain protein is determined by the functional and structural interplay of its constituent domains. Traditional sequence alignment-based methods commonly utilize domain-level information and provide classification only at the level of domains. Such methods are not capable of taking into account the contributions of other domains in the proteins, and domain-linker regions and classify multi-domain proteins. An alignment-free protein sequence comparison tool, CLAP (CLAssification of Proteins) was previously developed in our laboratory to especially handle multi-domain protein sequences without a requirement of defining domain boundaries and sequential order of domains. Through this method we aim to achieve a biologically meaningful classification scheme for multi-domain protein sequences. In this article, CLAP-based classification has been explored on 5 datasets of multi-domain proteins and we present detailed analysis for proteins containing (1) Tyrosine phosphatase and (2) SH3 domain. At the domain-level CLAP-based classification scheme resulted in a clustering similar to that obtained from an alignment-based method. CLAP-based clusters obtained for full-length datasets were shown to comprise of proteins with similar functions and domain architectures. Our study demonstrates that multi-domain proteins could be classified effectively by considering full-length sequences without a requirement of identification of domains in the sequence.

Quantifying the Number of Independent Organelle DNA Insertions in Genome Evolution and Human Health.

Fragments of organelle genomes are often found as insertions in nuclear DNA. These fragments of mitochondrial DNA (numts) and plastid DNA (nupts) are ubiquitous components of eukaryotic genomes. They are, however, often edited out during the genome assembly process, leading to systematic underestimation of their frequency. Numts and nupts, once inserted, can become further fragmented through subsequent insertion of mobile elements or other recombinational events that disrupt the continuity of the inserted sequence relative to the genuine organelle DNA copy. Because numts and nupts are typically identified through sequence comparison tools such as BLAST, disruption of insertions into smaller fragments can lead to systematic overestimation of numt and nupt frequencies. Accurate identification of numts and nupts is important, however, both for better understanding of their role during evolution, and for monitoring their increasingly evident role in human disease. Human populations are polymorphic for 141 numt loci, five numts are causal to genetic disease, and cancer genomic studies are revealing an abundance of numts associated with tumor progression. Here, we report investigation of salient parameters involved in obtaining accurate estimates of numt and nupt numbers in genome sequence data. Numts and nupts from 44 sequenced eukaryotic genomes reveal lineage-specific differences in the number, relative age and frequency of insertional events as well as lineage-specific dynamics of their postinsertional fragmentation. Our findings outline the main technical parameters influencing accurate identification and frequency estimation of numts in genomic studies pertinent to both evolution and human health.

Sequence-, structure-, and dynamics-based comparisons of structurally homologous CheY-like proteins

We recently introduced a physically based approach to sequence comparison, the property factor method (PFM). In the present work, we apply the PFM approach to the study of a challenging set of sequences-the bacterial chemotaxis protein CheY, the N-terminal receiver domain of the nitrogen regulation protein NT-NtrC, and the sporulation response regulator Spo0F. These are all response regulators involved in signal transduction. Despite functional similarity and structural homology, they exhibit low sequence identity. PFM sequence comparison demonstrates a statistically significant qualitative difference between the sequence of CheY and those of the other two proteins that is not found using conventional alignment methods. This difference is shown to be consonant with structural characteristics, using distance matrix comparisons. We also demonstrate that residues participating strongly in native contacts during unfolding are distributed differently in CheY than in the other two proteins. The PFM result is also in accord with dynamic simulation results of several types. Molecular dynamics simulations of all three proteins were carried out at several temperatures, and it is shown that the dynamics of CheY are predicted to differ from those of NT-NtrC and Spo0F. The predicted dynamic properties of the three proteins are in good agreement with experimentally determined B factors and with fluctuations predicted by the Gaussian network model. We pinpoint the differences between the PFM and traditional sequence comparisons and discuss the informatic basis for the ability of the PFM approach to detect physical differences between these sequences that are not apparent from traditional alignment-based comparison.

20D-dynamic Representation of Protein Sequences

A new method of comparison of protein sequences called by us Representation of Protein Sequences is presented [1]. This method belongs to the group of alignment-free methods . This class of methods constitute fast developing branch of bioinformatics. The alignment-free methods reveal different aspects of similarity with low computational effort. They offer both numerical and graphical tools for sequence comparisons. In the 20D-dynamic Representation of Protein Sequences, the sequences of amino acids are represented by set of point masses in 20D space. The distribution of points in the space is obtained by applying the method of a walk in the 20D space. As consequence 20D-dynamic graph is obtained which is mathematical representation of the protein sequence. The 3D and 2D projections of this graph are convenient graphical tools for sequence comparison. The descriptors, i. e. the numerical values characterizing the 20D-dynamic graphs, are designed using the ideas coming from the classical dynamics (moments of inertia of rigid bodies). Some numerical examples of this method, using NADH dehydrogenase subunit 5 (ND5) protein sequences of nine species and subunit 6 (ND6) of eight species, are presented. [1] A. Czerniecka, D. Bielinska-Waz, P. Waz, T. Clark, 20D-dynamic representation of protein sequences , Genomics 107 (2016) 16--23.

When Whole-Genome Alignments Just Won't Work: kSNP v2 Software for Alignment-Free SNP Discovery and Phylogenetics of Hundreds of Microbial Genomes

Effective use of rapid and inexpensive whole genome sequencing for microbes requires fast, memory efficient bioinformatics tools for sequence comparison. The kSNP v2 software finds single nucleotide polymorphisms (SNPs) in whole genome data. kSNP v2 has numerous improvements over kSNP v1 including SNP gene annotation; better scaling for draft genomes available as assembled contigs or raw, unassembled reads; a tool to identify the optimal value of k; distribution of packages of executables for Linux and Mac OS X for ease of installation and user-friendly use; and a detailed User Guide. SNP discovery is based on k-mer analysis, and requires no multiple sequence alignment or the selection of a single reference genome. Most target sets with hundreds of genomes complete in minutes to hours. SNP phylogenies are built by maximum likelihood, parsimony, and distance, based on all SNPs, only core SNPs, or SNPs present in some intermediate user-specified fraction of targets. The SNP-based trees that result are consistent with known taxonomy. kSNP v2 can handle many gigabases of sequence in a single run, and if one or more annotated genomes are included in the target set, SNPs are annotated with protein coding and other information (UTRs, etc.) from Genbank file(s). We demonstrate application of kSNP v2 on sets of viral and bacterial genomes, and discuss in detail analysis of a set of 68 finished E. coli and Shigella genomes and a set of the same genomes to which have been added 47 assemblies and four “raw read” genomes of H104:H4 strains from the recent European E. coli outbreak that resulted in both bloody diarrhea and hemolytic uremic syndrome (HUS), and caused at least 50 deaths.

A Small-Group Activity Introducing the Use and Interpretation of BLAST

As biological sequence data are generated at an ever increasing rate, the role of bioinformatics in biological research also grows. Students must be trained to complete and interpret bioinformatic searches to enable them to effectively utilize the trove of sequence data available. A key bioinformatic tool for sequence comparison and genome database searching is BLAST (Basic Local Alignment Search Tool). BLAST identifies sequences in a database that are similar to the entered query sequence, and ranks them based on the length and quality of the alignment. Our goal was to introduce sophomore and junior level undergraduate students to the basic functions and uses of BLAST with a small group activity lasting a single class period. The activity provides students an opportunity to perform a BLAST search, interpret the data output, and use the data to make inferences about bacterial cell envelope structure. The activity consists of two parts. Part 1 is a handout to be completed prior to class, complete with video tutorial, that reviews cell envelope structure, introduces key terms, and allows students to familiarize themselves with the mechanics of a BLAST search. Part 2 consists of a hands-on, web-based small group activity to be completed during the class period. Evaluation of the activity through student performance assessments suggests that students who complete the activity can better interpret the BLAST output parameters % query coverage and % max identity. While the topic of the activity is bacterial cell wall structure, it could be adapted to address other biological concepts.

Genome-scale NCRNA homology search using a Hamming distance-based filtration strategy.

BackgroundNCRNAs (noncoding RNAs) play important roles in many biological processes. Existing genome-scale ncRNA search tools identify ncRNAs in local sequence alignments generated by conventional sequence comparison methods. However, some types of ncRNA lack strong sequence conservation and tend to be missed or mis-aligned by conventional sequence comparison.ResultsIn this paper, we propose an ncRNA identification framework that is complementary to existing sequence comparison tools. By integrating a filtration step based on Hamming distance and ncRNA alignment programs such as FOLDALIGN or PLAST-ncRNA, the proposed ncRNA search framework can identify ncRNAs that lack strong sequence conservation. In addition, as the ratio of transition and transversion mutation is often used as a discriminative feature for functional ncRNA identification, we incorporate this feature into the filtration step using a coding strategy. We apply Hamming distance seeds to ncRNA search in the intergenic regions of human and mouse genomes and between the Burkholderia cenocepacia J2315 genome and the Ralstonia solanacearum genome. The experimental results demonstrate that a carefully designed Hamming distance seed can achieve better sensitivity in searching for poorly conserved ncRNAs than conventional sequence comparison tools.ConclusionsHamming distance seeds provide better sensitivity as a filtration strategy for genome-wide ncRNA homology search than the existing seeding strategies used in BLAST-like tools. By combining Hamming distance seeds matching and ncRNA alignment, we are able to find ncRNAs with sequence similarities below 60%.

Consensus Decision for Protein Structure Classification

The fundamental aim of protein classification is to recognize the family of a given protein and determine its biological function. In the literature, the most common approaches are based on sequence or structure similarity comparisons. Other methods use evolutionary distances between proteins. In order to increase classification performance, this work proposes a novel method, namely Consensus, which combines the decisions of several sequence and structure comparison tools to classify a given structure. Additionally, Consensus uses the evolutionary information of the compared structures. Our method is tested on three databases and evaluated based on different criteria. Performance evaluation of our method shows that it outperforms the different classifiers used separately and gives higher classification perfor-mance than a free-alignment method, namely ProtClass.

Comparative analysis of a cryptic thienamycin-like gene cluster identified in Streptomyces flavogriseus by genome mining

In silico database searches allowed the identification in the S. flavogriseus ATCC 33331 genome of a carbapenem gene cluster highly related to the S. cattleya thienamycin one. This is the second cluster found for a complex highly substituted carbapenem. Comparative analysis revealed that both gene clusters display a high degree of synteny in gene organization and in protein conservation. Although the cluster appears to be silent under our laboratory conditions, the putative metabolic product was predicted from bioinformatics analyses using sequence comparison tools. These data, together with previous reports concerning epithienamycins production by S. flavogriseus strains, suggest that the cluster metabolic product might be a thienamycin-like carbapenem, possibly the epimeric epithienamycin. This finding might help in understanding the biosynthetic pathway to thienamycin and other highly substituted carbapenems. It also provides another example of genome mining in Streptomyces sequenced genomes as a powerful approach for novel antibiotic discovery.

Weighted k-word matches: a sequence comparison tool for proteins

The use of $k$-word matches was developed as a fast alignment-free comparison method for DNA sequences in cases where long range contiguity has been compromised, for example, by shuffling, duplication, deletion or inversion of extended blocks of sequence. Here we extend the algorithm to amino acid sequences. We define a new statistic, the weighted word match, which reflects the varying degrees of similarity between pairs of amino acids. We computed the mean and variance, and simulated the distribution function for various forms of this statistic for sequences of identically and independently distributed letters. We present these results and a method for choosing an optimal word size. The efficiency of the method is tested by using simulated evolutionary sequences, and the results compared with BLAST. References R. A. Lippert, H. Huang, and M. S. Waterman. Distributional regimes for the number of $k$-word matches between two random sequences. Proc. Natl. Acad. Sci. USA, 99(22):13980--9, 2002. doi:10.1073/pnas.202468099 J. Jing, C. J. Burden, S. Foret, and S. R. Wilson. Statistical considerations underpinning an alignment-free sequence comparison method. J. Korean Stat. Soc., 39:325--335, 2010. doi:10.1016/j.jkss.2010.02.009 S. F. Altschul, T. L. Madden, A. A. Schaffer, J. Zhang, Z. Zhang, W. Miller, and D. J. Lipman. Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res., 25(17):3389--402, 1997. doi:10.1093/nar/25.17.3389 W. J. Ewens and G. R. Grant. Statistical Methods in Bioinformatics: an Introduction. Springer, 2nd edition, 2005. S. Foret, M. R. Kantorovitz, and C. J. Burden. Asymptotic behaviour and optimal word size for exact and approximate word matches between random sequences. BMC Bioinformatics, 7 Suppl 5:S21, 2006. doi:10.1186/1471-2105-7-S5-S21 S. Henikoff and J. G. Henikoff. Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. USA, 89:10915--10919, 1992. doi:10.1073/pnas.89.22.10915 http://bioinfo.lifl.fr/reblosum/ [31 May 2011] G. Reinert, D. Chew, F. Sun, and M. S. Waterman. Alignment-free sequence comparison (i): statistics and power. J. Comput. Biol., 16(12):1615--1634, 2009. doi:10.1089/cmb.2009.0198 S. Foret, S. R. Wilson, and C. J. Burden. Empirical distribution of $k$-word matches in biological sequences. Pattern Recogn., 42:539--548, 2009. doi:10.1016/j.patcog.2008.06.026 S. Foret, S. R. Wilson, and C. J. Burden. Characterizing the $D2$ statistic: Word matches in biological sequences. Stat. Appl. Genet. Mo. B., 8(1):Article 43, 2009. doi:10.2202/1544-6115.1447 M. R. Kantorovitz, H. S. Booth, C. J. Burden, and S. R. Wilson. Asymptotic behavior of $k$-word matches between two uniformly distributed sequences. J. Appl. Probab., 44:788--805, 2006. doi:10.1239/jap/1189717545 T. J. Wu, Y. H. Huang, and L. A. Li. Optimal word sizes for dissimilarity measures and estimation of the degree of dissimilarity between DNA sequences. Bioinformatics, 21(22):4125--32, 2005. doi:10.1093/bioinformatics/bti658 S. Q. Le and O. Gascuel. An improved general amino acid replacement marix. Mol. Biol. Evol., 25:1307--1320, 2008. doi:10.1093/molbev/msn067 E. Gazave, P. Lapebi, G. S. Richards, F. Brunet, A. V. Ereskovsky, B. M. Degnan, C. Borchiellini, M. Vervoort, and E. Renard. Origin and evolution of the Notch signalling pathway: an overview from eukaryotic genomes. BMC Evol. Biol., 9:249, 2009. doi:10.1186/1471-2148-9-249 S. Q. Schneider, J. R. Finnerty, and M. Q. Martindale. Protein evolution: structure-function relationships of the oncogene Beta-catenin in the evolution of multicellular animals. J. Exptl. Zool. (Mol. Dev. Evol.), 295B:25--44, 2003. doi:10.1002/jez.b.00006