Explorer MCALIGN 2 : faster , accurate global pairwise alignment of non-coding DNA sequences based on explicit models of indel evolution

Background: Non-coding DNA sequences comprise a very large proportion of the total genomic content of mammals, most other vertebrates, many invertebrates, and most plants. Unraveling the functional significance of non-coding DNA depends on how well we are able to align non-coding DNA sequences. However, the alignment of non-coding DNA sequences is more difficult than aligning protein-coding sequences. Results: Here we present an improved pair-hidden-Markov-Model (pair HMM) based method for performing global pairwise alignment of non-coding DNA sequences. The method uses an explicit model of indel length frequency distribution which can be specified, and allows any time reversible model of nucleotide substitution. The method uses a deterministic global optimiser to find the alignment with the highest posterior probability. We test MCALIGN2 in simulations, and compare it to a previous Monte Carlo based method (MCALIGN), to the pair HMM method of Knudsen and Miyamoto, and to a heuristic method (AVID) that performed very well in a previous simulation study. We show that the pair HMM methods have excellent performance for all combinations of parameter values we have considered. MCALIGN2 is up to ten times faster than MCALIGN. MCALIGN2 is more accurate in resolving indels given an accurate explicit model than heuristic methods, but is computationally slower. Conclusion: MCALIGN2 produces better quality alignments by explicitly using biological knowledge about the indel length distribution and time reversible models of nucleotide substitution. As a result, it can outperform other available sequence alignment methods for the cases we have considered to align non-coding DNA sequences. Background The advent of automated DNA sequencing methods has resulted in an enormous growth in the volume of sequence data deposited in public databases. The increasing availability of genome sequence data for many related organisms offers great opportunities to study gene function and genome evolution, but it also presents new challenges for DNA sequence analysis, especially for noncoding DNA sequences. For much of the past two decades, research in DNA sequence analysis has focused on protein-coding Published: 08 June 2006 BMC Bioinformatics 2006, 7:292 doi:10.1186/1471-2105-7-292 Received: 07 November 2005 Accepted: 08 June 2006 This article is available from: http://www.biomedcentral. com/1471-2105/7/292 © 2006 Wang et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. BMC Bioinformatics 2006, 7:292 http://www.biomedcentral. com/1471-2105/7/292 Page 2 of 15 (page number not for citation purposes) sequences, which account for only a very small proportion of the total genomic content in mammals, most other vertebrates, many invertebrates, and most plants [1]. For example, protein-coding gene sequences comprise as little as 1–2% of the human and mouse genomes [2,3]. However, there is an increasing body of evidence showing that non-coding DNA sequences contain many functional sequences involved in gene regulation and potentially other unknown functions. For example, it has been estimated that ~50% of bases in intergenic and intronic sequences of Drosophila melanogaster are selectively constrained [4]. In rodents, it has been inferred that the total number of selectively constrained nucleotides in non-coding DNA adjacent to gene sequences is similar to that in coding DNA [5], Evidence for the presence of a large number of potentially functional non-coding sequences on human chromosome 21 has recently been obtained from a comparative genomics analysis [6]. Determining the fraction of non-coding DNA that is functional and establishing what that function is, is therefore a central problem in genome research. Accurate inferences about the function of non-coding DNA from comparative methods depends critically on correct alignments of non-coding sequences. However, the alignment of non-coding DNA sequences is more difficult than aligning protein-coding sequences. Proteincoding sequences tend to be highly evolutionarily conserved, so insertions and deletions (indels) are uncommon and rarely cross codon boundaries. However, indel events are common in non-coding DNA, and can occur at most nucleotide sites. Numerous advances in sequence alignment methods for noncoding DNA have been made. Many recently proposed methods are based on heuristic alignment algorithms that can be very fast and accurate in cases where sequences are similar, but perform less well when sequence divergence is high [7]. Furthermore, heuristic scoring functions are not guaranteed to use the correct relationship between the relative penalties for point substitution and indel events, as they have no evolutionary interpretation. Therefore, explicit evolutionary models are desired to address this problem. True evolutionary models of sequence evolution allow both multiple point substitutions and multiple indel events to affect any site in the sequence. The first true evolutionary model of indel evolution was introduced by Thorne, Kishino, and Felsenstein [8], the TKF91 model, and allows single-residue indel events. This method uses a maximum likelihood algorithm to estimate the evolutionary distance between two sequences, summing over all possible alignments in the likelihood calculations [8]. It was subsequently improved by allowing longer indel events with a geometric length distribution [9], by assuming that the sequence contains unbreakable fragments, and that only whole fragments are inserted and deleted. This assumption introduces hidden information in the form of fragment boundaries, and may potentially bias multiple alignment [10]. Knudsen and Miyamoto [11] presented a pairwise statistical alignment method based on an explicit evolutionary model of indel events. Indel length was assumed to be geometrically distributed, and up to two overlapping events were allowed for indels. A good approximation to such a model was then made using a pair HMM. The geometric distribution parameter, the indel rate, and the evolutionary time were estimated by maximum likelihood. A "long indel" evolutionary model has been introduced recently by Miklos et al. [12], which allows multiple-residue indels without hidden information such as fragment boundaries. They developed a finite trajectory approximation for computing the likelihood function, producing a method that has very good performance [12]. Previously, Keightley and Johnson [13] proposed a noncoding sequence alignment method called MCALIGN. This is based on a simplified evolutionary model that does not allow for any multiple hits or interaction between indel events. A key feature of their approach is that it uses additional data from "unambiguous" alignments (e.g. between sequences from closely related species) to infer the actual distribution of indel lengths, and the relative rate of indels to point substitutions. They used a Monte Carlo (MC) hill-climbing algorithm to search for the most probable alignments. This method has been successfully used for aligning real genomic sequences, such as Drosophila, rodent and hominid non-coding DNA [5,14,15]. In a simulation study, Keightley and Johnson [13] found that MCALTGN was generally superior to the other alignment methods that it was compared to. Here, we describe an improved non-coding sequence alignment algorithm based on a generalisation of the evolutionary model used by Keightley and Johnson [13]. We show how a combination of a dynamic programming (DP) algorithm and a one dimensional deterministic optimisation – algorithm can be used to find the most probable pairwise sequence alignment. Note that when we assume the Jukes-Cantor [16] model for nucleotide substitution, the present DP method and the previous MC method are essentially using two different optimisers to attempt to maximise the same "score" function: alignment probability. However, the new optimiser is expected to be better and faster. We have compared our method to the pair HMM method of Knudsen and Miyamoto (PairHMM_KM hereafter), which is quite similar to the present method in that it explicitly makes use of an evolutionary time parameter [11]. We have also compared our method to the heuristic BMC Bioinformatics 2006, 7:292 http://www.biomedcentral. com/1471-2105/7/292 Page 3 of 15 (page number not for citation purposes) alignment program AVID of Bray et al. [17] in simulations that assume a general-time-reversible (GTR) model [18] that had first been fitted to real Drosophila non-coding DNA sequence data. It has been shown that AVID performs very well compared to other heuristic methods [13,17], so here we only compare our method to AVID rather than other heuristic methods. In our tests, the new DP method (MCALIGN2) is up to ten times faster than the previous MC method (MCALIGN), and is also faster than the pairHMM_KM method [11], although none can compete in speed terms with heuristic methods. For cases of real non-coding sequence data, we also compared MCALIGN2 with AVID and CLUSTALW [19], and show that they perform differently for some specific cases. Implementation We use a Bayesian statistical framework [20,21] to make inference about the pairwise alignment. The aim is to compute the posterior probabilities of different possible alignments, using the observed sequences as data and eliminating other "nuisance" parameters from the analysis. Here we focus on finding the alignment with the highest posterior probability. Let t be the total divergence time between two sequences, a be an alignment of two sequences, and S be the observed data, which is two non-coding DNA sequences. In a Bayesian framework, the behaviours of all variables are modelled by probability distributions