An Integer Linear Programming Approach for Scaffolding Based on Exemplar Breakpoint Distance.

Reference-based scaffolding is an important process used in genomic sequencing to order and orient the contigs in a draft genome based on a reference genome. In this study, we utilize the concept of genome rearrangement to formulate this process as an exemplar breakpoint distance (EBD)-based scaffolding problem, whose aim is to scaffold the contigs of two given draft genomes, both containing duplicate genes (or sequence markers) and acting with each other as a reference, such that the EBD between the scaffolded genomes is minimized. The EBD-based scaffolding problem is difficult to solve because it is non-deterministic polynomial-time (NP)-hard.

Multi-CSAR: a web server for scaffolding contigs using multiple reference genomes.

Multi-CSAR is a web server that can efficiently and more accurately order and orient the contigs in the assembly of a target genome into larger scaffolds based on multiple reference genomes. Given a target genome and multiple reference genomes, Multi-CSAR first identifies sequence markers shared between the target genome and each reference genome, then utilizes these sequence markers to compute a scaffold for the target genome based on each single reference genome, and finally combines all the single reference-derived scaffolds into a multiple reference-derived scaffold. To run Multi-CSAR, the users need to upload a target genome to be scaffolded and one or more reference genomes in multi-FASTA format.

Clover: a clustering-oriented de novo assembler for Illumina sequences.

Background: Next-generation sequencing technologies revolutionized genomics by producing high-throughput reads at low cost, and this progress has prompted the recent development of de novo assemblers. Multiple assembly methods based on de Bruijn graph have been shown to be efficient for Illumina reads. However, the sequencing errors generated by the sequencer complicate analysis of de novo assembly and influence the quality of downstream genomic researches.

Multi-CSAR: a multiple reference-based contig scaffolder using algebraic rearrangements.

Background: One of the important steps in the process of assembling a genome sequence from short reads is scaffolding, in which the contigs in a draft genome are ordered and oriented into scaffolds. Currently, several scaffolding tools based on a single reference genome have been developed. However, a single reference genome may not be sufficient alone for a scaffolder to generate correct scaffolds of a target draft genome, especially when the evolutionary relationship between the target and reference genomes is distant or some rearrangements occur between them.

CSAR-web: a web server of contig scaffolding using algebraic rearrangements.

CSAR-web is a web-based tool that allows the users to efficiently and accurately scaffold (i.e. order and orient) the contigs of a target draft genome based on a complete or incomplete reference genome from a related organism.

R3D-BLAST2: an improved search tool for similar RNA 3D substructures.

Background: RNA molecules have been known to play a variety of significant roles in cells. In principle, the functions of RNAs are largely determined by their three-dimensional (3D) structures. As more and more RNA 3D structures are available in the Protein Data Bank (PDB), a bioinformatics tool, which is able to rapidly and accurately search the PDB database for similar RNA 3D structures or substructures, is helpful to understand the structural and functional relationships of RNAs.

CSAR: a contig scaffolding tool using algebraic rearrangements.

Summary: Advances in next generation sequencing have generated massive amounts of short reads. However, assembling genome sequences from short reads still remains a challenging task. Due to errors in reads and large repeats in the genome, many of current assembly tools usually produce just collections of contigs whose relative positions and orientations along the genome being sequenced are still unknown.

Multi-CAR: a tool of contig scaffolding using multiple references.

Background: A draft genome assembled by current next-generation sequencing techniques from short reads is just a collection of contigs, whose relative positions and orientations along the genome being sequenced are unknown. To further obtain its complete sequence, a contig scaffolding process is usually applied to order and orient the contigs in the draft genome. Although several single reference-based scaffolding tools have been proposed, they may produce erroneous scaffolds if there are rearrangements between the target and reference genomes or their phylogenetic relationship is distant.

iPARTS2: an improved tool for pairwise alignment of RNA tertiary structures, version 2.

Since its first release in 2010, iPARTS has become a valuable tool for globally or locally aligning two RNA 3D structures. It was implemented by a structural alphabet (SA)-based approach, which uses an SA of 23 letters to reduce RNA 3D structures into 1D sequences of SA letters and applies traditional sequence alignment to these SA-encoded sequences for determining their global or local similarity. In this version, we have re-implemented iPARTS into a new web server iPARTS2 by constructing a totally new SA, which consists of 92 elements with each carrying both information of base and backbone geometry for a representative nucleotide.

An efficient algorithm for the contig ordering problem under algebraic rearrangement distance.

Assembling a genome from short reads currently obtained by next-generation sequencing techniques often results in a collection of contigs, whose relative position and orientation along the genome being sequenced are unknown. Given two sets of contigs, the contig ordering problem is to order and orient the contigs in each set such that the genome rearrangement distance between the resulting sets of ordered and oriented contigs is minimized. In this article, we utilize the permutation groups in algebra to propose a near-linear time algorithm for solving the contig ordering problem under algebraic rearrangement distance, where the algebraic rearrangement distance between two sets of ordered and oriented contigs is the minimum weight of applicable rearrangement operations required to transform one set into the other.

CAR: contig assembly of prokaryotic draft genomes using rearrangements.

Background: Next generation sequencing technology has allowed efficient production of draft genomes for many organisms of interest. However, most draft genomes are just collections of independent contigs, whose relative positions and orientations along the genome being sequenced are unknown. Although several tools have been developed to order and orient the contigs of draft genomes, more accurate tools are still needed.

Assembling contigs in draft genomes using reversals and block-interchanges.

The techniques of next generation sequencing allow an increasing number of draft genomes to be produced rapidly in a decreasing cost. However, these draft genomes usually are just partially sequenced as collections of unassembled contigs, which cannot be used directly by currently existing algorithms for studying their genome rearrangements and phylogeny reconstruction. In this work, we study the one-sided block (or contig) ordering problem with weighted reversal and block-interchange distance.

Sorting permutations by cut-circularize-linearize-and-paste operations.

Background: Genome rearrangements are studied on the basis of genome-wide analysis of gene orders and important in the evolution of species. In the last two decades, a variety of rearrangement operations, such as reversals, transpositions, block-interchanges, translocations, fusions and fissions, have been proposed to evaluate the differences between gene orders in two or more genomes. Usually, the computational studies of genome rearrangements are formulated as problems of sorting permutations by rearrangement operations.

R3D-BLAST: a search tool for similar RNA 3D substructures.

R3D-BLAST is a BLAST-like search tool that allows the user to quickly and accurately search against the PDB for RNA structures sharing similar substructures with a specified query RNA structure. The basic idea behind R3D-BLAST is that all the RNA 3D structures deposited in the PDB are first encoded as 1D structural sequences using a structural alphabet of 23 distinct nucleotide conformations, and BLAST is then applied to these 1D structural sequences to search for those RNA substructures whose 1D structural sequences are similar to that of the query RNA substructure. R3D-BLAST takes as input an RNA 3D structure in the PDB format and outputs all substructures of the hits similar to that of the query with a graphical display to show their structural superposition.

SoRT2: a tool for sorting genomes and reconstructing phylogenetic trees by reversals, generalized transpositions and translocations.

SoRT(2) is a web server that allows the user to perform genome rearrangement analysis involving reversals, generalized transpositions and translocations (including fusions and fissions), and infer phylogenetic trees of genomes being considered based on their pairwise genome rearrangement distances. It takes as input two or more linear/circular multi-chromosomal gene (or synteny block) orders in FASTA-like format. When the input is two genomes, SoRT(2) will quickly calculate their rearrangement distance, as well as a corresponding optimal scenario by highlighting the genes involved in each rearrangement operation.

iPARTS: an improved tool of pairwise alignment of RNA tertiary structures.

iPARTS is an improved web server for aligning two RNA 3D structures based on a structural alphabet (SA)-based approach. In particular, we first derive a Ramachandran-like diagram of RNAs by plotting nucleotides on a 2D axis using their two pseudo-torsion angles eta and . Next, we apply the affinity propagation clustering algorithm to this eta- plot to obtain an SA of 23-nt conformations.

Sorting by reversals, generalized transpositions, and translocations using permutation groups.

In this article, we consider the problem of sorting a linear/circular, multi-chromosomal genome by reversals, block-interchanges (i.e., generalized transpositions), and translocations (including fusions and fissions) where the used operations can be weighted differently, which aims to find a sequence of reversal, block-interchange, and translocation operations such that the sum of these operation weights in the sequence is minimum.

Reconstructing genome trees of prokaryotes using overlapping genes.

Background: Overlapping genes (OGs) are defined as adjacent genes whose coding sequences overlap partially or entirely. In fact, they are ubiquitous in microbial genomes and more conserved between species than non-overlapping genes. Based on this property, we have previously implemented a web server, named OGtree, that allows the user to reconstruct genome trees of some prokaryotes according to their pairwise OG distances.

FASTR3D: a fast and accurate search tool for similar RNA 3D structures.

FASTR3D is a web-based search tool that allows the user to fast and accurately search the PDB database for structurally similar RNAs. Currently, it allows the user to input three types of queries: (i) a PDB code of an RNA tertiary structure (default), optionally with specified residue range, (ii) an RNA secondary structure, optionally with primary sequence, in the dot-bracket notation and (iii) an RNA primary sequence in the FASTA format. In addition, the user can run FASTR3D with specifying additional filtering options: (i) the released date of RNA structures in the PDB database, and (ii) the experimental methods used to determine RNA structures and their least resolutions.

SARSA: a web tool for structural alignment of RNA using a structural alphabet.

SARSA is a web tool that can be used to align two or more RNA tertiary structures. The basic idea behind SARSA is that we use the vector quantization approach to derive a structural alphabet (SA) of 23 nucleotide conformations, via which we transform RNA 3D structures into 1D sequences of SA letters and then utilize classical sequence alignment methods to compare these 1D SA-encoded sequences and determine their structural similarities. In SARSA, we provide two RNA structural alignment tools, PARTS for pairwise alignment of RNA tertiary structures and MARTS for multiple alignment of RNA tertiary structures.

OGtree: a tool for creating genome trees of prokaryotes based on overlapping genes.

OGtree is a web-based tool for constructing genome trees of prokaryotic species based on a measure of combining overlapping-gene content and overlapping-gene order in their whole genomes. The overlapping genes (OGs) are defined as adjacent genes whose coding sequences overlap partially or entirely. In fact, OGs are ubiquitous in microbial genomes and more conserved between species than non-OGs.

Analysis of genome rearrangement by block-interchanges.

Block-interchanges are a new kind of genome rearrangements that affect the gene order in a chromosome by swapping two nonintersecting blocks of genes of any length. More recently, the study of such rearrangements is becoming increasingly important because of its applications in molecular evolution. Usually, this kind of study requires to solve a combinatorial problem, called the block-interchange distance problem, which is to find a minimum number of block-interchanges between two given gene orders of linear/circular chromosomes to transform one gene order into another.

RE-MuSiC: a tool for multiple sequence alignment with regular expression constraints.

RE-MuSiC is a web-based multiple sequence alignment tool that can incorporate biological knowledge about structure, function, or conserved patterns regarding the sequences of interest. It accepts amino acid or nucleic acid sequences and a set of constraints as inputs. The constraints are pattern descriptions, instead of exact positions of fragments to be aligned together.

SPRING: a tool for the analysis of genome rearrangement using reversals and block-interchanges.

SPRING (http://algorithm.cs.nthu.

Analysis of circular genome rearrangement by fusions, fissions and block-interchanges.

Background: Analysis of genomes evolving via block-interchange events leads to a combinatorial problem of sorting by block-interchanges, which has been studied recently to evaluate the evolutionary relationship in distance between two biological species since block-interchange can be considered as a generalization of transposition. However, for genomes consisting of multiple chromosomes, their evolutionary history should also include events of chromosome fusions and fissions, where fusion merges two chromosomes into one and fission splits a chromosome into two.

Results: In this paper, we study the problem of genome rearrangement between two genomes of circular and multiple chromosomes by considering fusion, fission and block-interchange events altogether.