A fast algorithm for the constrained multiple sequence alignment problem

Given n strings S1, S2, ..., Sn, and a pattern string P, the constrained multiple sequence alignment (CMSA) problem is to find an optimal multiple alignment of S1, S2, ..., Sn such that the alignment contains P, i.e. in the alignment matrix there exists a sequence of columns each entirely composed of symbol P[k] for every k, where P[k] is the kth symbol in P, 1 ≤ k ≤ |P|, and in the sequence, a column containing P[i] appears before the column containing P[j] for all i,j, i < j. The problem is motivated from the problem of comparing multiple sequences that share a common structure, or sequence pattern. There are O(2ns1s2...snr)-time dynamic programming algorithms for the problem, where s1,s2, ...,sn and r are, respectively, the lengths of the input strings and the pattern string. Feasibility of these algorithms in practice is limited when the number of sequences is large, or the sequences are long because of the impractically long time required by these algorithms. We present a new algorithm with worst-case time complexity also O(2ns1s2...snr), but the algorithm avoids redundant computations in existing dynamic programming solutions. Experiments on both randomly generated strings and real data show that this algorithm is much faster than the existing algorithms. We present an analysis that explains the speed-up obtained in our experiments by our algorithm over the naive dynamic programming algorithm for constrained multiple sequence alignment of protein sequences. The speed-up is more significant when pattern is long, or n is large. For example in the case of constrained pairwise sequence alignment (the CMSA problem with n=2) when the pattern is sufficiently long for strings S1 and S2, the asymptotic time complexity is observed to be O(s1s2) instead of O(s1s2r). Main ideas in our algorithm can also be used in other constrained sequence alignment problems

Detection of recombination in DNA multiple alignments with hidden markov models

CConventional phylogenetic tree estimation methods assume that all sites in a DNA multiple alignment have the same evolutionary history. This assumption is violated in data sets from certain bacteria and viruses due to recombination, a process that leads to the creation of mosaic sequences from different strains and, if undetected, causes systematic errors in phylogenetic tree estimation. In the current work, a hidden Markov model (HMM) is employed to detect recombination events in multiple alignments of DNA sequences. The emission probabilities in a given state are determined by the branching order (topology) and the branch lengths of the respective phylogenetic tree, while the transition probabilities depend on the global recombination probability. The present study improves on an earlier heuristic parameter optimization scheme and shows how the branch lengths and the recombination probability can be optimized in a maximum likelihood sense by applying the expectation maximization (EM) algorithm. The novel algorithm is tested on a synthetic benchmark problem and is found to clearly outperform the earlier heuristic approach. The paper concludes with an application of this scheme to a DNA sequence alignment of the argF gene from four Neisseria strains, where a likely recombination event is clearly detected

Parametric Alignment of Drosophila Genomes

The classic algorithms of Needleman--Wunsch and Smith--Waterman find a maximum a posteriori probability alignment for a pair hidden Markov model (PHMM). In order to process large genomes that have undergone complex genome rearrangements, almost all existing whole genome alignment methods apply fast heuristics to divide genomes into small pieces which are suitable for Needleman--Wunsch alignment. In these alignment methods, it is standard practice to fix the parameters and to produce a single alignment for subsequent analysis by biologists. Our main result is the construction of a whole genome parametric alignment of Drosophila melanogaster and Drosophila pseudoobscura. Parametric alignment resolves the issue of robustness to changes in parameters by finding all optimal alignments for all possible parameters in a PHMM. Our alignment draws on existing heuristics for dividing whole genomes into small pieces for alignment, and it relies on advances we have made in computing convex polytopes that allow us to parametrically align non-coding regions using biologically realistic models. We demonstrate the utility of our parametric alignment for biological inference by showing that cis-regulatory elements are more conserved between Drosophila melanogaster and Drosophila pseudoobscura than previously thought. We also show how whole genome parametric alignment can be used to quantitatively assess the dependence of branch length estimates on alignment parameters. The alignment polytopes, software, and supplementary material can be downloaded at http://bio.math.berkeley.edu/parametric/.Comment: 19 pages, 3 figure