SUMMARY: With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies often include characterizations of the genomic landscape as it varies along chromosomes, commonly termed genome scans. While traditional summary statistics like FST and dXY between pre-assigned populations remain integral to characterizing the genomic divergence profile, PCA differs by providing single-sample resolution, thereby supporting the identification of polymorphic inversions, introgression and other types of divergent sequence that may not be fully aligned with global population structure. Here, we introduce WinPCA, a user-friendly package to compute, polarize and visualize genetic principal components in windows along the genome. To accommodate low-coverage whole genome-sequencing datasets, WinPCA can optionally make use of PCAngsd methods to compute principal components in a genotype likelihood framework. WinPCA accepts variant data in either VCF or BEAGLE format and can generate rich plots for interactive data exploration and downstream presentation. AVAILABILITY AND IMPLEMENTATION: WinPCA is implemented in Python and freely available at https://github.com/MoritzBlumer/winpca and https://doi.org/10.5281/zenodo.15614979.

SUMMARY: We present YaHS, a user-friendly command-line tool for the construction of chromosome-scale scaffolds from Hi-C data. It can be run with a single-line command, requires minimal input from users (an assembly file and an alignment file) which is compatible with similar tools and provides assembly results in multiple formats, thereby enabling rapid, robust and scalable construction of high-quality genome assemblies with high accuracy and contiguity. AVAILABILITY AND IMPLEMENTATION: YaHS is implemented in C and licensed under the MIT License. The source code, documentation and tutorial are available at https://github.com/sanger-tol/yahs. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: PacBio high fidelity (HiFi) sequencing reads are both long (15-20 kb) and highly accurate (> Q20). Because of these properties, they have revolutionised genome assembly leading to more accurate and contiguous genomes. In eukaryotes the mitochondrial genome is sequenced alongside the nuclear genome often at very high coverage. A dedicated tool for mitochondrial genome assembly using HiFi reads is still missing. RESULTS: MitoHiFi was developed within the Darwin Tree of Life Project to assemble mitochondrial genomes from the HiFi reads generated for target species. The input for MitoHiFi is either the raw reads or the assembled contigs, and the tool outputs a mitochondrial genome sequence fasta file along with annotation of protein and RNA genes. Variants arising from heteroplasmy are assembled independently, and nuclear insertions of mitochondrial sequences are identified and not used in organellar genome assembly. MitoHiFi has been used to assemble 374 mitochondrial genomes (368 Metazoa and 6 Fungi species) for the Darwin Tree of Life Project, the Vertebrate Genomes Project and the Aquatic Symbiosis Genome Project. Inspection of 60 mitochondrial genomes assembled with MitoHiFi for species that already have reference sequences in public databases showed the widespread presence of previously unreported repeats. CONCLUSIONS: MitoHiFi is able to assemble mitochondrial genomes from a wide phylogenetic range of taxa from Pacbio HiFi data. MitoHiFi is written in python and is freely available on GitHub ( https://github.com/marcelauliano/MitoHiFi ). MitoHiFi is available with its dependencies as a Docker container on GitHub (ghcr.io/marcelauliano/mitohifi:master).

BACKGROUND: Efficient and effective genome scaffolding tools are still in high demand for generating reference-quality assemblies. While long read data itself is unlikely to create a chromosome-scale assembly for most eukaryotic species, the inexpensive Hi-C sequencing technology, capable of capturing the chromosomal profile of a genome, is now widely used to complete the task. However, the existing Hi-C based scaffolding tools either require a priori chromosome number as input, or lack the ability to build highly continuous scaffolds. RESULTS: We design and develop a novel Hi-C based scaffolding tool, pin_hic, which takes advantage of contact information from Hi-C reads to construct a scaffolding graph iteratively based on N-best neighbors of contigs. Subsequent to scaffolding, it identifies potential misjoins and breaks them to keep the scaffolding accuracy. Through our tests on three long read based de novo assemblies from three different species, we demonstrate that pin_hic is more efficient than current standard state-of-art tools, and it can generate much more continuous scaffolds, while achieving a higher or comparable accuracy. CONCLUSIONS: Pin_hic is an efficient Hi-C based scaffolding tool, which can be useful for building chromosome-scale assemblies. As many sequencing projects have been launched in the recent years, we believe pin_hic has potential to be applied in these projects and makes a meaningful contribution.

MOTIVATION: Reconstructing high-quality haplotype-resolved assemblies for related individuals has important applications in Mendelian diseases and population genomics. Through major genomics sequencing efforts such as the Personal Genome Project, the Vertebrate Genome Project (VGP) and the Genome in a Bottle project (GIAB), a variety of sequencing datasets from trios of diploid genomes are becoming available. Current trio assembly approaches are not designed to incorporate long- and short-read data from mother-father-child trios, and therefore require relatively high coverages of costly long-read data to produce high-quality assemblies. Thus, building a trio-aware assembler capable of producing accurate and chromosomal-scale diploid genomes of all individuals in a pedigree, while being cost-effective in terms of sequencing costs, is a pressing need of the genomics community. RESULTS: We present a novel pedigree sequence graph based approach to diploid assembly using accurate Illumina data and long-read Pacific Biosciences (PacBio) data from all related individuals, thereby generalizing our previous work on single individuals. We demonstrate the effectiveness of our pedigree approach on a simulated trio of pseudo-diploid yeast genomes with different heterozygosity rates, and real data from human chromosome. We show that we require as little as 30× coverage Illumina data and 15× PacBio data from each individual in a trio to generate chromosomal-scale phased assemblies. Additionally, we show that we can detect and phase variants from generated phased assemblies. AVAILABILITY AND IMPLEMENTATION: https://github.com/shilpagarg/WHdenovo.

MOTIVATION: Rapid development in long-read sequencing and scaffolding technologies is accelerating the production of reference-quality assemblies for large eukaryotic genomes. However, haplotype divergence in regions of high heterozygosity often results in assemblers creating two copies rather than one copy of a region, leading to breaks in contiguity and compromising downstream steps such as gene annotation. Several tools have been developed to resolve this problem. However, they either focus only on removing contained duplicate regions, also known as haplotigs, or fail to use all the relevant information and hence make errors. RESULTS: Here we present a novel tool, purge_dups, that uses sequence similarity and read depth to automatically identify and remove both haplotigs and heterozygous overlaps. In comparison with current tools, we demonstrate that purge_dups can reduce heterozygous duplication and increase assembly continuity while maintaining completeness of the primary assembly. Moreover, purge_dups is fully automatic and can easily be integrated into assembly pipelines. AVAILABILITY AND IMPLEMENTATION: The source code is written in C and is available at https://github.com/dfguan/purge_dups. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The variation graph toolkit (VG) represents genetic variation as a graph. Although each path in the graph is a potential haplotype, most paths are non-biological, unlikely recombinations of true haplotypes. RESULTS: We augment the VG model with haplotype information to identify which paths are more likely to exist in nature. For this purpose, we develop a scalable implementation of the graph extension of the positional Burrows-Wheeler transform. We demonstrate the scalability of the new implementation by building a whole-genome index of the 5008 haplotypes of the 1000 Genomes Project, and an index of all 108 070 Trans-Omics for Precision Medicine Freeze 5 chromosome 17 haplotypes. We also develop an algorithm for simplifying variation graphs for k-mer indexing without losing any k-mers in the haplotypes. AVAILABILITY AND IMPLEMENTATION: Our software is available at https://github.com/vgteam/vg, https://github.com/jltsiren/gbwt and https://github.com/jltsiren/gcsa2. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: The bulk of space taken up by NGS sequencing CRAM files consists of per-base quality values. Most of these are unnecessary for variant calling, offering an opportunity for space saving. Results: On the Syndip test set, a 17 fold reduction in the quality storage portion of a CRAM file can be achieved while maintaining variant calling accuracy. The size reduction of an entire CRAM file varied from 2.2 to 7.4 fold, depending on the non-quality content of the original file (see Supplementary Material S6 for details). Availability and implementation: Crumble is OpenSource and can be obtained from https://github.com/jkbonfield/crumble. Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Human papillomavirus (HPV) is a common sexually transmitted infection associated with cervical cancer that frequently occurs as a coinfection of types and subtypes. Highly similar sublineages that show over 100-fold differences in cancer risk are not distinguishable in coinfections with current typing methods. RESULTS: We describe an efficient set of computational tools, rkmh, for analyzing complex mixed infections of related viruses based on sequence data. rkmh makes extensive use of MinHash similarity measures, and includes utilities for removing host DNA and classifying reads by type, lineage, and sublineage. We show that rkmh is capable of assigning reads to their HPV type as well as HPV16 lineage and sublineages. CONCLUSIONS: Accurate read classification enables estimates of percent composition when there are multiple infecting lineages or sublineages. While we demonstrate rkmh for HPV with multiple sequencing technologies, it is also applicable to other mixtures of related sequences.

Motivation: Constructing high-quality haplotype-resolved de novo assemblies of diploid genomes is important for revealing the full extent of structural variation and its role in health and disease. Current assembly approaches often collapse the two sequences into one haploid consensus sequence and, therefore, fail to capture the diploid nature of the organism under study. Thus, building an assembler capable of producing accurate and complete diploid assemblies, while being resource-efficient with respect to sequencing costs, is a key challenge to be addressed by the bioinformatics community. Results: We present a novel graph-based approach to diploid assembly, which combines accurate Illumina data and long-read Pacific Biosciences (PacBio) data. We demonstrate the effectiveness of our method on a pseudo-diploid yeast genome and show that we require as little as 50× coverage Illumina data and 10× PacBio data to generate accurate and complete assemblies. Additionally, we show that our approach has the ability to detect and phase structural variants. Availability and implementation: https://github.com/whatshap/whatshap. Supplementary information: Supplementary data are available at Bioinformatics online.

UNLABELLED: Runs of homozygosity (RoHs) are genomic stretches of a diploid genome that show identical alleles on both chromosomes. Longer RoHs are unlikely to have arisen by chance but are likely to denote autozygosity, whereby both copies of the genome descend from the same recent ancestor. Early tools to detect RoH used genotype array data, but substantially more information is available from sequencing data. Here, we present and evaluate BCFtools/RoH, an extension to the BCFtools software package, that detects regions of autozygosity in sequencing data, in particular exome data, using a hidden Markov model. By applying it to simulated data and real data from the 1000 Genomes Project we estimate its accuracy and show that it has higher sensitivity and specificity than existing methods under a range of sequencing error rates and levels of autozygosity. AVAILABILITY AND IMPLEMENTATION: BCFtools/RoH and its associated binary/source files are freely available from https://github.com/samtools/BCFtools CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Over the last few years, methods based on suffix arrays using the Burrows-Wheeler Transform have been widely used for DNA sequence read matching and assembly. These provide very fast search algorithms, linear in the search pattern size, on a highly compressible representation of the dataset being searched. Meanwhile, algorithmic development for genotype data has concentrated on statistical methods for phasing and imputation, based on probabilistic matching to hidden Markov model representations of the reference data, which while powerful are much less computationally efficient. Here a theory of haplotype matching using suffix array ideas is developed, which should scale too much larger datasets than those currently handled by genotype algorithms. RESULTS: Given M sequences with N bi-allelic variable sites, an O(NM) algorithm to derive a representation of the data based on positional prefix arrays is given, which is termed the positional Burrows-Wheeler transform (PBWT). On large datasets this compresses with run-length encoding by more than a factor of a hundred smaller than using gzip on the raw data. Using this representation a method is given to find all maximal haplotype matches within the set in O(NM) time rather than O(NM(2)) as expected from naive pairwise comparison, and also a fast algorithm, empirically independent of M given sufficient memory for indexes, to find maximal matches between a new sequence and the set. The discussion includes some proposals about how these approaches could be used for imputation and phasing.

SUMMARY: The variant call format (VCF) is a generic format for storing DNA polymorphism data such as SNPs, insertions, deletions and structural variants, together with rich annotations. VCF is usually stored in a compressed manner and can be indexed for fast data retrieval of variants from a range of positions on the reference genome. The format was developed for the 1000 Genomes Project, and has also been adopted by other projects such as UK10K, dbSNP and the NHLBI Exome Project. VCFtools is a software suite that implements various utilities for processing VCF files, including validation, merging, comparing and also provides a general Perl API. AVAILABILITY: http://vcftools.sourceforge.net

Abstract Motivation: Many programs for aligning short sequencing reads to a reference genome have been developed in the last 2 years. Most of them are very efficient for short reads but inefficient or not applicable for reads >200 bp because the algorithms are heavily and specifically tuned for short queries with low sequencing error rate. However, some sequencing platforms already produce longer reads and others are expected to become available soon. For longer reads, hashing-based software such as BLAT and SSAHA2 remain the only choices. Nonetheless, these methods are substantially slower than short-read aligners in terms of aligned bases per unit time. Results: We designed and implemented a new algorithm, Burrows-Wheeler Aligner's Smith-Waterman Alignment (BWA-SW), to align long sequences up to 1 Mb against a large sequence database (e.g. the human genome) with a few gigabytes of memory. The algorithm is as accurate as SSAHA2, more accurate than BLAT, and is several to tens of times faster than both. Availability: http://bio-bwa.sourceforge.net Contact: [email protected]

MOTIVATION: Sequence assembly is a difficult problem whose importance has grown again recently as the cost of sequencing has dramatically dropped. Most new sequence assembly software has started by building a de Bruijn graph, avoiding the overlap-based methods used previously because of the computational cost and complexity of these with very large numbers of short reads. Here, we show how to use suffix array-based methods that have formed the basis of recent very fast sequence mapping algorithms to find overlaps and generate assembly string graphs asymptotically faster than previously described algorithms. RESULTS: Standard overlap assembly methods have time complexity O(N(2)), where N is the sum of the lengths of the reads. We use the Ferragina-Manzini index (FM-index) derived from the Burrows-Wheeler transform to find overlaps of length at least tau among a set of reads. As well as an approach that finds all overlaps then implements transitive reduction to produce a string graph, we show how to output directly only the irreducible overlaps, significantly shrinking memory requirements and reducing compute time to O(N), independent of depth. Overlap-based assembly methods naturally handle mixed length read sets, including capillary reads or long reads promised by the third generation sequencing technologies. The algorithms we present here pave the way for overlap-based assembly approaches to be developed that scale to whole vertebrate genome de novo assembly.

Abstract Summary: We have developed an algorithm to detect copy number variants (CNVs) in homozygous organisms, such as inbred laboratory strains of mice, from short read sequence data. Our novel approach exploits the fact that inbred mice are homozygous at virtually every position in the genome to detect CNVs using a hidden Markov model (HMM). This HMM uses both the density of sequence reads mapped to the genome, and the rate of apparent heterozygous single nucleotide polymorphisms, to determine genomic copy number. We tested our algorithm on short read sequence data generated from re-sequencing chromosome 17 of the mouse strains A/J and CAST/EiJ with the Illumina platform. In total, we identified 118 copy number variants (43 for A/J and 75 for CAST/EiJ). We investigated the performance of our algorithm through comparison to CNVs previously identified by array-comparative genomic hybridization (array CGH). We performed quantitative-PCR validation on a subset of the calls that differed from the array CGH data sets. Availability: The software described in this manuscript, named cnD for copy number detector, is free and released under the GPL. The program is implemented in the D programming language using the Tango library. Source code and pre-compiled binaries are available at http://www.sanger.ac.uk/resources/software/cnd.html Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

Gene expression measurements are influenced by a wide range of factors, such as the state of the cell, experimental conditions and variants in the sequence of regulatory regions. To understand the effect of a variable of interest, such as the genotype of a locus, it is important to account for variation that is due to confounding causes. Here, we present VBQTL, a probabilistic approach for mapping expression quantitative trait loci (eQTLs) that jointly models contributions from genotype as well as known and hidden confounding factors. VBQTL is implemented within an efficient and flexible inference framework, making it fast and tractable on large-scale problems. We compare the performance of VBQTL with alternative methods for dealing with confounding variability on eQTL mapping datasets from simulations, yeast, mouse, and human. Employing Bayesian complexity control and joint modelling is shown to result in more precise estimates of the contribution of different confounding factors resulting in additional associations to measured transcript levels compared to alternative approaches. We present a threefold larger collection of cis eQTLs than previously found in a whole-genome eQTL scan of an outbred human population. Altogether, 27% of the tested probes show a significant genetic association in cis, and we validate that the additional eQTLs are likely to be real by replicating them in different sets of individuals. Our method is the next step in the analysis of high-dimensional phenotype data, and its application has revealed insights into genetic regulation of gene expression by demonstrating more abundant cis-acting eQTLs in human than previously shown. Our software is freely available online at http://www.sanger.ac.uk/resources/software/peer/.

MOTIVATION: The enormous amount of short reads generated by the new DNA sequencing technologies call for the development of fast and accurate read alignment programs. A first generation of hash table-based methods has been developed, including MAQ, which is accurate, feature rich and fast enough to align short reads from a single individual. However, MAQ does not support gapped alignment for single-end reads, which makes it unsuitable for alignment of longer reads where indels may occur frequently. The speed of MAQ is also a concern when the alignment is scaled up to the resequencing of hundreds of individuals. RESULTS: We implemented Burrows-Wheeler Alignment tool (BWA), a new read alignment package that is based on backward search with Burrows-Wheeler Transform (BWT), to efficiently align short sequencing reads against a large reference sequence such as the human genome, allowing mismatches and gaps. BWA supports both base space reads, e.g. from Illumina sequencing machines, and color space reads from AB SOLiD machines. Evaluations on both simulated and real data suggest that BWA is approximately 10-20x faster than MAQ, while achieving similar accuracy. In addition, BWA outputs alignment in the new standard SAM (Sequence Alignment/Map) format. Variant calling and other downstream analyses after the alignment can be achieved with the open source SAMtools software package. AVAILABILITY: http://maq.sourceforge.net.

SUMMARY: The Sequence Alignment/Map (SAM) format is a generic alignment format for storing read alignments against reference sequences, supporting short and long reads (up to 128 Mbp) produced by different sequencing platforms. It is flexible in style, compact in size, efficient in random access and is the format in which alignments from the 1000 Genomes Project are released. SAMtools implements various utilities for post-processing alignments in the SAM format, such as indexing, variant caller and alignment viewer, and thus provides universal tools for processing read alignments. AVAILABILITY: http://samtools.sourceforge.net.

MOTIVATION: Correct gene predictions are crucial for most analyses of genomes. However, in the absence of transcript data, gene prediction is still challenging. One way to improve gene-finding accuracy in such genomes is to combine the exons predicted by several gene-finders, so that gene-finders that make uncorrelated errors can correct each other. RESULTS: We present a method for combining gene-finders called Genomix. Genomix selects the predicted exons that are best conserved within and/or between species in terms of sequence and intron-exon structure, and combines them into a gene structure. Genomix was used to combine predictions from four gene-finders for Caenorhabditis elegans, by selecting the predicted exons that are best conserved with C.briggsae and C.remanei. On a set of approximately 1500 confirmed C.elegans genes, Genomix increased the exon-level specificity by 10.1% and sensitivity by 2.7% compared to the best input gene-finder. AVAILABILITY: Scripts and Supplementary Material can be found at http://www.sanger.ac.uk/Software/analysis/genomix

BACKGROUND: It is well known that different species have different protein domain repertoires, and indeed that some protein domains are kingdom specific. This information has not yet been incorporated into statistical methods for finding domains in sequences of amino acids. RESULTS: We show that by incorporating our understanding of the taxonomic distribution of specific protein domains, we can enhance domain recognition in protein sequences. We identify 4447 new instances of Pfam domains in the SP-TREMBL database using this technique, equivalent to the coverage increase given by the last 8.3% of Pfam families and to a 0.7% increase in the number of domain predictions. We use PSI-BLAST to cross-validate our new predictions. We also benchmark our approach using a SCOP test set of proteins of known structure, and demonstrate improvements relative to standard Hidden Markov model techniques. CONCLUSIONS: Explicitly including knowledge about the taxonomic distribution of protein domains can enhance protein domain recognition. Our method can also incorporate other context-specific domain distributions - such as domain co-occurrence and protein localisation.

The exponential increase in the submission of nucleotide sequences to the nucleotide sequence database by genome sequencing centres has resulted in a need for rapid, automatic methods for classification of the resulting protein sequences. There are several signature and sequence cluster-based methods for protein classification, each resource having distinct areas of optimum application owing to the differences in the underlying analysis methods. In recognition of this, InterPro was developed as an integrated documentation resource for protein families, domains and functional sites, to rationalise the complementary efforts of the individual protein signature database projects. The member databases - PRINTS, PROSITE, Pfam, ProDom, SMART and TIGRFAMs - form the InterPro core. Related signatures from each member database are unified into single InterPro entries. Each InterPro entry includes a unique accession number, functional descriptions and literature references, and links are made back to the relevant member database(s). Release 4.0 of InterPro (November 2001) contains 4,691 entries, representing 3,532 families, 1,068 domains, 74 repeats and 15 sites of post-translational modification (PTMs) encoded by different regular expressions, profiles, fingerprints and hidden Markov models (HMMs). Each InterPro entry lists all the matches against SWISS-PROT and TrEMBL (2,141,621 InterPro hits from 586,124 SWISS-PROT and TrEMBL protein sequences). The database is freely accessible for text- and sequence-based searches.

Abstract Summary: We have written a fast implementation of the popular Neighbor-Joining tree building algorithm. QuickTree allows the reconstruction of phylogenies for very large protein families (including the largest Pfam alignment containing 27000 HIV GP120 glycoprotein sequences) that would be infeasible using other popular methods. Availability: The source-code for QuickTree, written in ANSI~C, is freely available via the world wide web at http://www.sanger.ac.uk/Software/analysis/quicktree Contact: [email protected] * To whom correspondence should be addressed.

We present a novel comparative method for the ab initio prediction of protein coding genes in eukaryotic genomes. The method simultaneously predicts the gene structures of two un-annotated input DNA sequences which are homologous to each other and retrieves the subsequences which are conserved between the two DNA sequences. It is capable of predicting partial, complete and multiple genes and can align pairs of genes which differ by events of exon-fusion or exon-splitting. The method employs a probabilistic pair hidden Markov model. We generate annotations using our model with two different algorithms: the Viterbi algorithm in its linear memory implementation and a new heuristic algorithm, called the stepping stone, for which both memory and time requirements scale linearly with the sequence length. We have implemented the model in a computer program called DOUBLESCAN. In this article, we introduce the method and confirm the validity of the approach on a test set of 80 pairs of orthologous DNA sequences from mouse and human. More information can be found at: http://www.sanger.ac.uk/Software/analysis/doublescan/

The 3 billion base pair sequence of the human genome is now available, and attention is focusing on annotating it to extract biological meaning. I will discuss what we have obtained, and the methods that are being used to analyse biological sequences. In particular I will discuss approaches using stochastic grammars analogous to those used in computational linguistics, both for gene finding and protein family classification.

MOTIVATION: InterPro is a new integrated documentation resource for protein families, domains and functional sites, developed initially as a means of rationalising the complementary efforts of the PROSITE, PRINTS, Pfam and ProDom database projects. RESULTS: Merged annotations from PRINTS, PROSITE and Pfam form the InterPro core. Each combined InterPro entry includes functional descriptions and literature references, and links are made back to the relevant parent database(s), allowing users to see at a glance whether a particular family or domain has associated patterns, profiles, fingerprints, etc. Merged and individual entries (i.e. those that have no counterpart in the companion resources) are assigned unique accession numbers. Release 1.2 of InterPro (June 2000) contains over 3000 entries, representing families, domains, repeats and sites of post-translational modification (PTMs) encoded by 6581 different regular expressions, profiles, fingerprints and Hidden Markov Models (HMMs). Each InterPro entry lists all the matches against SWISS-PROT and TrEMBL (more than 1000000 hits from 264333 different proteins out of 384572 in SWISS-PROT and TrEMBL).

Algorithms for generating alignments of biological sequences have inherent statistical limitations when it comes to the accuracy of the alignments they produce. Using simulations, we measure the accuracy of the standard global dynamic programming method and show that it can be reasonably well modelled by an "edge wander" approximation to the distribution of the optimal scoring path around the correct path in the vicinity of a gap. We also give a table from which accuracy values can be predicted for commonly used scoring schemes and sequence divergences (the PAM and BLOSUM series). Finally we describe how to calculate the expected accuracy of a given alignment, and show how this can be used to construct an optimal accuracy alignment algorithm which generates significantly more accurate alignments than standard dynamic programming methods in simulated experiments. 2 Introduction Alignments of biological sequences generated by computational algorithms are routinely used as a basis for ...

When routinely analysing very long stretches of DNA sequences produced by genome sequencing projects, detailed analysis of database search results becomes exceedingly time consuming. To reduce the tedious browsing of large quantities of protein similarities, two programs, MSPcrunch and Blixem, were developed, which assist in processing the results from the database search programs in the BLAST suite. MSPcrunch removes biased composition and redundant matches while keeping weak matches that are consistent with a larger gapped alignment. This makes BLAST searching in practice more sensitive and reduces the risk of overlooking distant similarities. Blixem is a multiple sequence alignment viewer for X-windows which makes it significantly easier to scan and evaluate the matches ratified by MSPcrunch. In Blixem, matches to the translated DNA query sequence are simultaneously aligned in three frames. Also, the distribution of matches over the whole DNA query is displayed. Examples of usage are drawn from 36 C. elegans cosmid clones totalling 1.2 megabases, to which these tools were applied.

A genome mapping system has been developed that reads and assembles data from clones analysed by restriction enzyme fragmentation and polyacrylamide gel electrophoresis. Input data for the system can be most effectively obtained by the use of a scanning densitometer and image-processing package, such as that described in this article. The image-processing procedure involves preliminary location of bands, cooperative tracking of lanes by correlation of adjacent bands, a precise densitometric pass, alignment of the marker bands with the standard, optional interactive editing, and normalization of the accepted bands.

We introduce a new form of computational unit for feedforward learning networks of the backpropagation type. Instead of calculating a weighted sum this unit calculates a weighted product, where each input is raised to a power determined by a variable weight. Such a unit can learn an arbitrary polynomial term, which would then feed into higher level standard summing units. We show how learning operates with product units, provide examples to show their efficiency for various types of problems, and argue that they naturally extend the family of theoretical feedforward net structures. There is a plausible neurobiological interpretation for one interesting configuration of product and summing units.

This paper analyzes the elastic net approach (Durbin and Willshaw 1987) to the traveling salesman problem of finding the shortest path through a set of cities. The elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities. The tradeoff between these two requirements is controlled by a scale parameter K. A global minimum is found for large K, and is then tracked to a small value. In this paper, we show that (1) in the small K limit the elastic path passes arbitrarily close to all the cities, but that only one path point is attracted to each city, (2) in the large K limit the net lies at the center of the set of cities, and (3) at a critical value of K the energy function bifurcates. We also show that this method can be interpreted in terms of extremizing a probability distribution controlled by K. The minimum at a given K corresponds to the maximum a posteriori (MAP) Bayesian estimate of the tour under a natural statistical interpretation. The analysis presented in this paper gives us a better understanding of the behavior of the elastic net, allows us to better choose the parameters for the optimization, and suggests how to extend the underlying ideas to other domains.

A genome mapping package has been developed for reading and assembling data from clones analysed by restriction enzyme fragmentation and polyacrylamide gel electrophoresis. The package comprises: data entry; matching; assembly; statistical analysis; modelling. Data entry can be either manual or by a semiautomatic system based on a scanning densitometer. The primary emphasis in the analytical routines is on flexibility and interactive convenience, so that the operator has full knowledge of and control over the growing map, but a variety of automatic options are included. The package continually grows to meet the needs of the Caenorhabditis project.