Exact and heuristic algorithms for the Indel Maximum Likelihood Problem.

Given a multiple alignment of orthologous DNA sequences and a phylogenetic tree for these sequences, we investigate the problem of reconstructing the most likely scenario of insertions and deletions capable of explaining the gaps observed in the alignment. This problem, that we called the Indel Maximum Likelihood Problem (IMLP), is an important step toward the reconstruction of ancestral genomics sequences, and is important for studying evolutionary processes, genome function, adaptation and convergence. We solve the IMLP using a new type of tree hidden Markov model whose states correspond to single-base evolutionary scenarios and where transitions model dependencies between neighboring columns. The standard Viterbi and Forward-backward algorithms are optimized to produce the most likely ancestral reconstruction and to compute the level of confidence associated to specific regions of the reconstruction. A heuristic is presented to make the method practical for large data sets, while retaining an extremely high degree of accuracy. The methods are illustrated on a 1-Mb alignment of the CFTR regions from 12 mammals.     

Glocal alignment: finding rearrangements during alignment

MOTIVATION: To compare entire genomes from different species, biologists increasingly need alignment methods that are efficient enough to handle long sequences, and accurate enough to correctly align the conserved biological features between distant species. The two main classes of pairwise alignments are global alignment, where one string is transformed into the other, and local alignment, where all locations of similarity between the two strings are returned. Global alignments are less prone to demonstrating false homology as each letter of one sequence is constrained to being aligned to only one letter of the other. Local alignments, on the other hand, can cope with rearrangements between non-syntenic, orthologous sequences by identifying similar regions in sequences; this, however, comes at the expense of a higher false positive rate due to the inability of local aligners to take into account overall conservation maps. RESULTS: In this paper we introduce the notion of glocal alignment, a combination of global and local methods, where one creates a map that transforms one sequence into the other while allowing for rearrangement events. We present Shuffle-LAGAN, a glocal alignment algorithm that is based on the CHAOS local alignment algorithm and the LAGAN global aligner, and is able to align long genomic sequences. To test Shuffle-LAGAN we split the mouse genome into BAC-sized pieces, and aligned these pieces to the human genome. We demonstrate that Shuffle-LAGAN compares favorably in terms of sensitivity and specificity with standard local and global aligners. From the alignments we conclude that about 9% of human/mouse homology may be attributed to small rearrangements, 63% of which are duplications.     

Assignment of orthologous genes via genome rearrangement

The assignment of orthologous genes between a pair of genomes is a fundamental and challenging problem in comparative genomics. Existing methods that assign orthologs based on the similarity between DNA or protein sequences may make erroneous assignments when sequence similarity does not clearly delineate the evolutionary relationship among genes of the same families. In this paper, we present a new approach to ortholog assignment that takes into account both sequence similarity and evolutionary events at a genome level, where orthologous genes are assumed to correspond to each other in the most parsimonious evolving scenario under genome rearrangement. First, the problem is formulated as that of computing the signed reversal distance with duplicates between the two genomes of interest. Then, the problem is decomposed into two new optimization problems, called minimum common partition and maximum cycle decomposition, for which efficient heuristic algorithms are given. Following this approach, we have implemented a high-throughput system for assigning orthologs on a genome scale, called SOAR, and tested it on both simulated data and real genome sequence data. Compared to a recent ortholog assignment method based entirely on homology search (called INPARANOID), SOAR shows a marginally better performance in terms of sensitivity on the real data set because it is able to identify several correct orthologous pairs that are missed by INPARANOID. The simulation results demonstrate that SOAR, in general, performs better than the iterated exemplar algorithm in terms of computing the reversal distance and assigning correct orthologs.     

Pair stochastic tree adjoining grammars for aligning and predicting pseudoknot RNA structures

MOTIVATION: Since the whole genome sequences of many species have been determined, computational prediction of RNA secondary structures and computational identification of those non-coding RNA regions by comparative genomics become important. Therefore, more advanced alignment methods are required. Recently, an approach of structural alignment for RNA sequences has been introduced to solve these problems. Pair hidden Markov models on tree structures (PHMMTSs) proposed by Sakakibara are efficient automata-theoretic models for structural alignment of RNA secondary structures, although PHMMTSs are incapable of handling pseudoknots. On the other hand, tree adjoining grammars (TAGs), a subclass of context-sensitive grammars, are suitable for modeling pseudoknots. Our goal is to extend PHMMTSs by incorporating TAGs to be able to handle pseudoknots. RESULTS: We propose pair stochastic TAGs (PSTAGs) for aligning and predicting RNA secondary structures including a simple type of pseudoknot which can represent most known pseudoknot structures. First, we extend PHMMTSs defined on alignment of 'trees' to PSTAGs defined on alignment of 'TAG trees' which represent derivation processes of TAGs and are functionally equivalent to derived trees of TAGs. Then, we develop an efficient dynamic programming algorithm of PSTAGs for obtaining an optimal structural alignment including pseudoknots. We implement the PSTAG algorithm and demonstrate the properties of the algorithm by using it to align and predict several small pseudoknot structures. We believe that our implemented program based on PSTAGs is the first grammar-based and practically executable software for comparative analyses of RNA pseudoknot structures, and, further, non-coding RNAs.     

Annotating regulatory DNA based on man-mouse genomic comparison

Non-coding DNA segments that are conserved between the human and mouse genomic sequence are good indicators of possible regulatory sequences. Here we report on a systematic approach to delineate such conserved elements from upstream regions of orthologous gene pairs from man and mouse. We focus on orthologous genes in order to maximize our chances to find functionally similar regulatory elements. The identification of conserved elements is effected using the Waterman-Eggert local suboptimal alignment algorithm. We have modified an implementation of this algorithm such that it integrates the determination of statistical significance for the local suboptimal alignments. This has the effect of outputting a dynamically determined number of suboptimal alignments that are deemed statistically significant. Comparison with experimentally determined annotation shows a striking enrichement of regulatory sites among the conserved regions. Furthermore, the conserved regions tend to cover the promotor region described in the EPD database.     

AuberGene--a sensitive genome alignment tool

MOTIVATION: The accumulation of genome sequences will only accelerate in the coming years. We aim to use this abundance of data to improve the quality of genomic alignments and devise a method which is capable of detecting regions evolving under weak or no evolutionary constraints. RESULTS: We describe a genome alignment program AuberGene, which explores the idea of transitivity of local alignments. Assessment of the program was done based on a 2 Mbp genomic region containing the CFTR gene of 13 species. In this region, we can identify 53% of human sequence sharing common ancestry with mouse, as compared with 44% found using the usual pairwise alignment. Between human and tetraodon 93 orthologous exons are found, as compared with 77 detected by the pairwise human-tetraodon comparison. AuberGene allows the user to (1) identify distant, previously undetected, conserved orthogonal regions such as ORFs or regulatory regions; (2) identify neutrally evolving regions in related species which are often overlooked by other alignment programs; (3) recognize false orthologous genomic regions. The increased sensitivity of the method is not obtained at the cost of reduced specificity. Our results suggest that, over the CFTR region, human shares 10% more sequence with mouse than previously thought ( approximately 50%, instead of 40% found with the pairwise alignment).     

Sequence alignment with an appropriate substitution matrix.

A widely used algorithm for computing an optimal local alignment between two sequences requires a parameter set with a substitution matrix and gap penalties. It is recognized that a proper parameter set should be selected to suit the level of conservation between sequences. We describe an algorithm for selecting an appropriate substitution matrix at given gap penalties for computing an optimal local alignment between two sequences. In the algorithm, a substitution matrix that leads to the maximum alignment similarity score is selected among substitution matrices at various evolutionary distances. The evolutionary distance of the selected substitution matrix is defined as the distance of the computed alignment. To show the effects of gap penalties on alignments and their distances and help select appropriate gap penalties, alignments and their distances are computed at various gap penalties. The algorithm has been implemented as a computer program named SimDist. The SimDist program was compared with an existing local alignment program named SIM for finding reciprocally best-matching pairs (RBPs) of sequences in each of 100 protein families, where RBPs are commonly used as an operational definition of orthologous sequences. SimDist produced more accurate results than SIM on 50 of the 100 families, whereas both programs produced the same results on the other 50 families. SimDist was also used to compare three types of substitution matrices in scoring 444,461 pairs of homologous sequences from the 100 families.     

An Eulerian path approach to global multiple alignment for DNA sequences.

With the rapid increase in the dataset of genome sequences, the multiple sequence alignment problem is increasingly important and frequently involves the alignment of a large number of sequences. Many heuristic algorithms have been proposed to improve the speed of computation and the quality of alignment. We introduce a novel approach that is fundamentally different from all currently available methods. Our motivation comes from the Eulerian method for fragment assembly in DNA sequencing that transforms all DNA fragments into a de Bruijn graph and then reduces sequence assembly to a Eulerian path problem. The paper focuses on global multiple alignment of DNA sequences, where entire sequences are aligned into one configuration. Our main result is an algorithm with almost linear computational speed with respect to the total size (number of letters) of sequences to be aligned. Five hundred simulated sequences (averaging 500 bases per sequence and as low as 70% pairwise identity) have been aligned within three minutes on a personal computer, and the quality of alignment is satisfactory. As a result, accurate and simultaneous alignment of thousands of long sequences within a reasonable amount of time becomes possible. Data from an Arabidopsis sequencing project is used to demonstrate the performance.     

Faster algorithms for optimal multiple sequence alignment based on pairwise comparisons

Multiple sequence alignment (MSA) is one of the most fundamental problems in computational molecular biology. The running time of the best known scheme for finding an optimal alignment, based on dynamic programming, increases exponentially with the number of input sequences. Hence, many heuristics were suggested for the problem. We consider a version of the MSA problem where the goal is to find an optimal alignment in which matches are restricted to positions in predefined matching segments. We present several techniques for making the dynamic programming algorithm more efficient, while still finding an optimal solution under these restrictions. We prove that it suffices to find an optimal alignment of the predefined sequence segments, rather than single letters, thereby reducing the input size and thus improving the running time. We also identify "shortcuts" that expedite the dynamic programming scheme. Empirical study shows that, taken together, these observations lead to an improved running time over the basic dynamic programming algorithm by 4 to 12 orders of magnitude, while still obtaining an optimal solution. Under the additional assumption that matches between segments are transitive, we further improve the running time for finding the optimal solution by restricting the search space of the dynamic programming algorithm     

Algorithms for phylogenetic footprinting.

Phylogenetic footprinting is a technique that identifies regulatory elements by finding unusually well conserved regions in a set of orthologous noncoding DNA sequences from multiple species. We introduce a new motif-finding problem, the Substring Parsimony Problem, which is a formalization of the ideas behind phylogenetic footprinting, and we present an exact dynamic programming algorithm to solve it. We then present a number of algorithmic optimizations that allow our program to run quickly on most biologically interesting datasets. We show how to handle data sets in which only an unknown subset of the sequences contains the regulatory element. Finally, we describe how to empirically assess the statistical significance of the motifs found. Each technique is implemented and successfully identifies a number of known binding sites, as well as several highly conserved but uncharacterized regions. The program is available at http://bio.cs.washington.edu/software.html.     

Differences between pair-wise and multi-sequence alignment methods affect vertebrate genome comparisons

Producing complete and accurate alignments of multiple genomic sequences is complex and prone to errors, especially with sequences generated from highly diverged species. In this article, we show that multi-sequence (as opposed to pair-wise) alignment methods are substantially better at aligning (or 'capturing') all of the available orthologous sequence from phylogenetically diverse vertebrates (i.e. those separated by relatively long branch lengths). Maximum gains are obtained only when sequences from many species are aligned. Such multi-sequence alignments contain significant amounts of exonic and highly conserved non-exonic sequences that are not captured in pair-wise alignments, thus illustrating the importance of the alignment method used for performing comparative genome analyses.     

An Efficient Algorithm for Mapping of Reads to a Genome Graph Using an Index Based on Hash Tables and Dynamic Programming

The problem of storage of the sequences of a number of closely related genomes and analysis of genome variations is considered. A genome graph with the structure of an acyclic directed graph is used to store matching sections of sequences and known variants. An algorithm for rapid mapping of reads to the genome graph is developed to align the individual nucleotide sequence fragments to the genome graph. The algorithm combines rapid searching using hash tables with the algorithm of dynamic programming and solves the problem of exponential growth in the number of paths on the graph. The implementation of the genome graph and the algorithm of the alignment of reads is developed. A comparison with the best-known programs with similar functionality is made.     

MSOAR: a high-throughput ortholog assignment system based on genome rearrangement.

The assignment of orthologous genes between a pair of genomes is a fundamental and challenging problem in comparative genomics, since many computational methods for solving various biological problems critically rely on bona fide orthologs as input. While it is usually done using sequence similarity search, we recently proposed a new combinatorial approach that combines sequence similarity and genome rearrangement. This paper continues the development of the approach and unites genome rearrangement events and (post-speciation) duplication events in a single framework under the parsimony principle. In this framework, orthologous genes are assumed to correspond to each other in the most parsimonious evolutionary scenario involving both genome rearrangement and (post-speciation) gene duplication. Besides several original algorithmic contributions, the enhanced method allows for the detection of inparalogs. Following this approach, we have implemented a high-throughput system for ortholog assignment on a genome scale, called MSOAR, and applied it to human and mouse genomes. As the result will show, MSOAR is able to find 99 more true orthologs than the INPARANOID program did. In comparison to the iterated exemplar algorithm on simulated data, MSOAR performed favorably in terms of assignment accuracy. We also validated our predicted main ortholog pairs between human and mouse using public ortholog assignment datasets, synteny information, and gene function classification. These test results indicate that our approach is very promising for genome-wide ortholog assignment. Supplemental material and MSOAR program are available at http://msoar.cs.ucr.edu.     

A memory-efficient algorithm for multiple sequence alignment with constraints

MOTIVATION: Recently, the concept of the constrained sequence alignment was proposed to incorporate the knowledge of biologists about structures/functionalities/consensuses of their datasets into sequence alignment such that the user-specified residues/nucleotides are aligned together in the computed alignment. The currently developed programs use the so-called progressive approach to efficiently obtain a constrained alignment of several sequences. However, the kernels of these programs, the dynamic programming algorithms for computing an optimal constrained alignment between two sequences, run in (gamman2) memory, where gamma is the number of the constraints and n is the maximum of the lengths of sequences. As a result, such a high memory requirement limits the overall programs to align short sequences only. RESULTS: We adopt the divide-and-conquer approach to design a memory-efficient algorithm for computing an optimal constrained alignment between two sequences, which greatly reduces the memory requirement of the dynamic programming approaches at the expense of a small constant factor in CPU time. This new algorithm consumes only O(alphan) space, where alpha is the sum of the lengths of constraints and usually alpha < n in practical applications. Based on this algorithm, we have developed a memory-efficient tool for multiple sequence alignment with constraints. AVAILABILITY: http://genome.life.nctu.edu.tw/MUSICME.     

Inferring horizontal transfers in the presence of rearrangements by the minimum evolution criterion

MOTIVATION: The evolution of viruses is very rapid and in addition to local point mutations (insertion, deletion, substitution) it also includes frequent recombinations, genome rearrangements and horizontal transfer of genetic materials (HGTS). Evolutionary analysis of viral sequences is therefore a complicated matter for two main reasons: First, due to HGTs and recombinations, the right model of evolution is a network and not a tree. Second, due to genome rearrangements, an alignment of the input sequences is not guaranteed. These facts encourage developing methods for inferring phylogenetic networks that do not require aligned sequences as input. RESULTS: In this work, we present the first computational approach which deals with both genome rearrangements and horizontal gene transfers and does not require a multiple alignment as input. We formalize a new set of computational problems which involve analyzing such complex models of evolution. We investigate their computational complexity, and devise algorithms for solving them. Moreover, we demonstrate the viability of our methods on several synthetic datasets as well as four biological datasets. AVAILABILITY: The code is available from the authors upon request.