Statistical Alignment with a Sequence Evolution Model Allowing Rate Heterogeneity along the Sequence

We present a stochastic sequence evolution model to obtain alignments and estimate mutation rates between two homologous sequences. The model allows two possible evolutionary behaviors along a DNA sequence in order to determine conserved regions and take its heterogeneity into account. In our model, the sequence is divided into slow and fast evolution regions. The boundaries between these sections are not known. It is our aim to detect them. The evolution model is based on a fragment insertion and deletion process working on fast regions only and on a substitution process working on fast and slow regions with different rates. This model induces a pair hidden Markov structure at the level of alignments, thus making efficient statistical alignment algorithms possible. We propose two complementary estimation methods, namely, a Gibbs sampler for Bayesian estimation and a stochastic version of the EM algorithm for maximum likelihood estimation. Both algorithms involve the sampling of alignments. We propose a partial alignment sampler, which is computationally less expensive than the typical whole alignment sampler. We show the convergence of the two estimation algorithms when used with this partial sampler. Our algorithms provide consistent estimates for the mutation rates and plausible alignments and sequence segmentations on both simulated and real data.     

A context dependent pair hidden Markov model for statistical alignment

This article proposes a novel approach to statistical alignment of nucleotide sequences by introducing a context dependent structure on the substitution process in the underlying evolutionary model. We propose to estimate alignments and context dependent mutation rates relying on the observation of two homologous sequences. The procedure is based on a generalized pair-hidden Markov structure, where conditional on the alignment path, the nucleotide sequences follow a Markov distribution. We use a stochastic approximation expectation maximization (saem) algorithm to give accurate estimators of parameters and alignments. We provide results both on simulated data and vertebrate genomes, which are known to have a high mutation rate from CG dinucleotide. In particular, we establish that the method improves the accuracy of the alignment of a human pseudogene and its functional gene.     

Joint Bayesian estimation of alignment and phylogeny

We describe a novel model and algorithm for simultaneously estimating multiple molecular sequence alignments and the phylogenetic trees that relate the sequences. Unlike current techniques that base phylogeny estimates on a single estimate of the alignment, we take alignment uncertainty into account by considering all possible alignments. Furthermore, because the alignment and phylogeny are constructed simultaneously, a guide tree is not needed. This sidesteps the problem in which alignments created by progressive alignment are biased toward the guide tree used to generate them. Joint estimation also allows us to model rate variation between sites when estimating the alignment and to use the evidence in shared insertion/deletions (indels) to group sister taxa in the phylogeny. Our indel model makes use of affine gap penalties and considers indels of multiple letters. We make the simplifying assumption that the indel process is identical on all branches. As a result, the probability of a gap is independent of branch length. We use a Markov chain Monte Carlo (MCMC) method to sample from the posterior of the joint model, estimating the most probable alignment and tree and their support simultaneously. We describe a new MCMC transition kernel that improves our algorithm's mixing efficiency, allowing the MCMC chains to converge even when started from arbitrary alignments. Our software implementation can estimate alignment uncertainty and we describe a method for summarizing this uncertainty in a single plot.     

Evolutionary HMMs: a Bayesian approach to multiple alignment

MOTIVATION: We review proposed syntheses of probabilistic sequence alignment, profiling and phylogeny. We develop a multiple alignment algorithm for Bayesian inference in the links model proposed by Thorne et al. (1991, J. Mol. Evol., 33, 114-124). The algorithm, described in detail in Section 3, samples from and/or maximizes the posterior distribution over multiple alignments for any number of DNA or protein sequences, conditioned on a phylogenetic tree. The individual sampling and maximization steps of the algorithm require no more computational resources than pairwise alignment. METHODS: We present a software implementation (Handel) of our algorithm and report test results on (i) simulated data sets and (ii) the structurally informed protein alignments of BAliBASE (Thompson et al., 1999, Nucleic Acids Res., 27, 2682-2690). RESULTS: We find that the mean sum-of-pairs score (a measure of residue-pair correspondence) for the BAliBASE alignments is only 13% lower for Handelthan for CLUSTALW(Thompson et al., 1994, Nucleic Acids Res., 22, 4673-4680), despite the relative simplicity of the links model (CLUSTALW uses affine gap scores and increased penalties for indels in hydrophobic regions). With reference to these benchmarks, we discuss potential improvements to the links model and implications for Bayesian multiple alignment and phylogenetic profiling. AVAILABILITY: The source code to Handelis freely distributed on the Internet at http://www.biowiki.org/Handel under the terms of the GNU Public License (GPL, 2000, http://www.fsf.org./copyleft/gpl.html).     

Using evolutionary Expectation Maximization to estimate indel rates

MOTIVATION: The Expectation Maximization (EM) algorithm, in the form of the Baum-Welch algorithm (for hidden Markov models) or the Inside-Outside algorithm (for stochastic context-free grammars), is a powerful way to estimate the parameters of stochastic grammars for biological sequence analysis. To use this algorithm for multiple-sequence evolutionary modelling, it would be useful to apply the EM algorithm to estimate not only the probability parameters of the stochastic grammar, but also the instantaneous mutation rates of the underlying evolutionary model (to facilitate the development of stochastic grammars based on phylogenetic trees, also known as Statistical Alignment). Recently, we showed how to do this for the point substitution component of the evolutionary process; here, we extend these results to the indel process. RESULTS: We present an algorithm for maximum-likelihood estimation of insertion and deletion rates from multiple sequence alignments, using EM, under the single-residue indel model owing to Thorne, Kishino and Felsenstein (the 'TKF91' model). The algorithm converges extremely rapidly, gives accurate results on simulated data that are an improvement over parsimonious estimates (which are shown to underestimate the true indel rate), and gives plausible results on experimental data (coronavirus envelope domains). Owing to the algorithm's close similarity to the Baum-Welch algorithm for training hidden Markov models, it can be used in an 'unsupervised' fashion to estimate rates for unaligned sequences, or estimate several sets of rates for sequences with heterogenous rates. AVAILABILITY: Software implementing the algorithm and the benchmark is available under GPL from http://www.biowiki.org/     

Probabilistic phylogenetic inference with insertions and deletions

A fundamental task in sequence analysis is to calculate the probability of a multiple alignment given a phylogenetic tree relating the sequences and an evolutionary model describing how sequences change over time. However, the most widely used phylogenetic models only account for residue substitution events. We describe a probabilistic model of a multiple sequence alignment that accounts for insertion and deletion events in addition to substitutions, given a phylogenetic tree, using a rate matrix augmented by the gap character. Starting from a continuous Markov process, we construct a non-reversible generative (birth-death) evolutionary model for insertions and deletions. The model assumes that insertion and deletion events occur one residue at a time. We apply this model to phylogenetic tree inference by extending the program dnaml in phylip. Using standard benchmarking methods on simulated data and a new "concordance test" benchmark on real ribosomal RNA alignments, we show that the extended program dnamlepsilon improves accuracy relative to the usual approach of ignoring gaps, while retaining the computational efficiency of the Felsenstein peeling algorithm.     

Assessing Variability by Joint Sampling of Alignments and Mutation Rates

When two sequences are aligned with a single set of alignment parameters, or when mutation parameters are estimated on the basis of a single ``optimal' sequence alignment, the variability of both the alignment and the estimated parameters can be seriously underestimated. To obtain a more realistic impression of the actual uncertainty, we propose sampling sequence alignments and mutation parameters simultaneously from their joint posterior distribution given the two original sequences. We illustrate our method with human and orangutan sequences from the hyper variable region I and with gene–pseudogene pairs. Received: 16 November 2000 / Accepted: 15 May 2001     

Simultaneous statistical multiple alignment and phylogeny reconstruction

Although the reconstruction of phylogenetic trees and the computation of multiple sequence alignments are highly interdependent, these two areas of research lead quite separate lives, the former often making use of stochastic modeling, whereas the latter normally does not. Despite the fact that reasonable insertion and deletion models for sequence pairs were already introduced more than 10 years ago, they have only recently been applied to multiple alignment and only in their simplest version. In this paper we present and discuss a strategy based on simulated annealing, which makes use of these models to infer a phylogenetic tree for a set of DNA or protein sequences together with the sequences'indel history, i.e., their multiple alignment augmented with information about the positioning of insertion and deletion events in the tree. Our method is also the first application of the TKF2 model in the context of multiple sequence alignment. We validate the method via simulations and illustrate it using a data set of primate mtDNA.     

SATe-II: very fast and accurate simultaneous estimation of multiple sequence alignments and phylogenetic trees

Highly accurate estimation of phylogenetic trees for large data sets is difficult, in part because multiple sequence alignments must be accurate for phylogeny estimation methods to be accurate. Coestimation of alignments and trees has been attempted but currently only SATé estimates reasonably accurate trees and alignments for large data sets in practical time frames (Liu K., Raghavan S., Nelesen S., Linder C.R., Warnow T. 2009b. Rapid and accurate large-scale coestimation of sequence alignments and phylogenetic trees. Science. 324:1561-1564). Here, we present a modification to the original SATé algorithm that improves upon SATé (which we now call SATé-I) in terms of speed and of phylogenetic and alignment accuracy. SATé-II uses a different divide-and-conquer strategy than SATé-I and so produces smaller more closely related subsets than SATé-I; as a result, SATé-II produces more accurate alignments and trees, can analyze larger data sets, and runs more efficiently than SATé-I. Generally, SATé is a metamethod that takes an existing multiple sequence alignment method as an input parameter and boosts the quality of that alignment method. SATé-II-boosted alignment methods are significantly more accurate than their unboosted versions, and trees based upon these improved alignments are more accurate than trees based upon the original alignments. Because SATé-I used maximum likelihood (ML) methods that treat gaps as missing data to estimate trees and because we found a correlation between the quality of tree/alignment pairs and ML scores, we explored the degree to which SATé's performance depends on using ML with gaps treated as missing data to determine the best tree/alignment pair. We present two lines of evidence that using ML with gaps treated as missing data to optimize the alignment and tree produces very poor results. First, we show that the optimization problem where a set of unaligned DNA sequences is given and the output is the tree and alignment of those sequences that maximize likelihood under the Jukes-Cantor model is uninformative in the worst possible sense. For all inputs, all trees optimize the likelihood score. Second, we show that a greedy heuristic that uses GTR+Gamma ML to optimize the alignment and the tree can produce very poor alignments and trees. Therefore, the excellent performance of SATé-II and SATé-I is not because ML is used as an optimization criterion for choosing the best tree/alignment pair but rather due to the particular divide-and-conquer realignment techniques employed.     

Fast Statistical Alignment

We describe a new program for the alignment of multiple biological sequences that is both statistically motivated and fast enough for problem sizes that arise in practice. Our Fast Statistical Alignment program is based on pair hidden Markov models which approximate an insertion/deletion process on a tree and uses a sequence annealing algorithm to combine the posterior probabilities estimated from these models into a multiple alignment. FSA uses its explicit statistical model to produce multiple alignments which are accompanied by estimates of the alignment accuracy and uncertainty for every column and character of the alignment—previously available only with alignment programs which use computationally-expensive Markov Chain Monte Carlo approaches—yet can align thousands of long sequences. Moreover, FSA utilizes an unsupervised query-specific learning procedure for parameter estimation which leads to improved accuracy on benchmark reference alignments in comparison to existing programs. The centroid alignment approach taken by FSA, in combination with its learning procedure, drastically reduces the amount of false-positive alignment on biological data in comparison to that given by other methods. The FSA program and a companion visualization tool for exploring uncertainty in alignments can be used via a web interface at http://orangutan.math.berkeley.edu/fsa/, and the source code is available at http://fsa.sourceforge.net/.     

Benchmarking tools for the alignment of functional noncoding DNA

Background

Numerous tools have been developed to align genomic sequences. However, their relative performance in specific applications remains poorly characterized. Alignments of protein-coding sequences typically have been benchmarked against "correct" alignments inferred from structural data. For noncoding sequences, where such independent validation is lacking, simulation provides an effective means to generate "correct" alignments with which to benchmark alignment tools.

Results

Using rates of noncoding sequence evolution estimated from the genus Drosophila, we simulated alignments over a range of divergence times under varying models incorporating point substitution, insertion/deletion events, and short blocks of constrained sequences such as those found in cis-regulatory regions. We then compared "correct" alignments generated by a modified version of the ROSE simulation platform to alignments of the simulated derived sequences produced by eight pairwise alignment tools (Avid, BlastZ, Chaos, ClustalW, DiAlign, Lagan, Needle, and WABA) to determine the off-the-shelf performance of each tool. As expected, the ability to align noncoding sequences accurately decreases with increasing divergence for all tools, and declines faster in the presence of insertion/deletion evolution. Global alignment tools (Avid, ClustalW, Lagan, and Needle) typically have higher sensitivity over entire noncoding sequences as well as in constrained sequences. Local tools (BlastZ, Chaos, and WABA) have lower overall sensitivity as a consequence of incomplete coverage, but have high specificity to detect constrained sequences as well as high sensitivity within the subset of sequences they align. Tools such as DiAlign, which generate both local and global outputs, produce alignments of constrained sequences with both high sensitivity and specificity for divergence distances in the range of 1.25–3.0 substitutions per site.

Conclusion

For species with genomic properties similar to Drosophila, we conclude that a single pair of optimally diverged species analyzed with a high performance alignment tool can yield accurate and specific alignments of functionally constrained noncoding sequences. Further algorithm development, optimization of alignment parameters, and benchmarking studies will be necessary to extract the maximal biological information from alignments of functional noncoding DNA.

     

An improved general amino acid replacement matrix

Amino acid replacement matrices are an essential basis of protein phylogenetics. They are used to compute substitution probabilities along phylogeny branches and thus the likelihood of the data. They are also essential in protein alignment. A number of replacement matrices and methods to estimate these matrices from protein alignments have been proposed since the seminal work of Dayhoff et al. (1972). An important advance was achieved by Whelan and Goldman (2001) and their WAG matrix, thanks to an efficient maximum likelihood estimation approach that accounts for the phylogenies of sequences within each training alignment. We further refine this method by incorporating the variability of evolutionary rates across sites in the matrix estimation and using a much larger and diverse database than BRKALN, which was used to estimate WAG. To estimate our new matrix (called LG after the authors), we use an adaptation of the XRATE software and 3,912 alignments from Pfam, comprising approximately 50,000 sequences and approximately 6.5 million residues overall. To evaluate the LG performance, we use an independent sample consisting of 59 alignments from TreeBase and randomly divide Pfam alignments into 3,412 training and 500 test alignments. The comparison with WAG and JTT shows a clear likelihood improvement. With TreeBase, we find that 1) the average Akaike information criterion gain per site is 0.25 and 0.42, when compared with WAG and JTT, respectively; 2) LG is significantly better than WAG for 38 alignments (among 59), and significantly worse with 2 alignments only; and 3) tree topologies inferred with LG, WAG, and JTT frequently differ, indicating that using LG impacts not only the likelihood value but also the output tree. Results with the test alignments from Pfam are analogous. LG and a PHYML implementation can be downloaded from http://atgc.lirmm.fr/LG.     

Incorporating indel information into phylogeny estimation for rapidly emerging pathogens

Background  

Phylogenies of rapidly evolving pathogens can be difficult to resolve because of the small number of substitutions that accumulate in the short times since divergence. To improve resolution of such phylogenies we propose using insertion and deletion (indel) information in addition to substitution information. We accomplish this through joint estimation of alignment and phylogeny in a Bayesian framework, drawing inference using Markov chain Monte Carlo. Joint estimation of alignment and phylogeny sidesteps biases that stem from conditioning on a single alignment by taking into account the ensemble of near-optimal alignments.     

Comparison of minisatellites.

In the class of repeated sequences that occur in DNA, minisatellites have been found polymorphic and became useful tools in genetic mapping and forensic studies. They consist of a heterogeneous tandem array of a short repeat unit. The slightly different units along the array are called variants. Minisatellites evolve mainly through tandem duplications and tandem deletions of variants. Jeffreys et al. (1997) devised a method to obtain the sequence of variants along the array in a digital code and called such sequences maps. Minisatellite maps give access to the detail of mutation processes at work on such loci. In this paper, we design an algorithm to compare two maps under an evolutionary model that includes deletion, insertion, mutation, tandem duplication, and tandem deletion of a variant. Our method computes an optimal alignment in reasonable time; and the alignment score, i.e., the weighted sum of its elementary operations, is a distance metric between maps. The main difficulty is that the optimal sequence of operations depends on the order in which they are applied to the map. Taking the maps of the minisatellite MSY1 of 609 men, we computed all pairwise distances and reconstructed an evolutionary tree of these individuals. MSY1 (DYF155S1) is a hypervariable locus on the Y chromosome. In our tree, the populations of some haplogroups are monophyletic, showing that one can decipher a microevolutionary signal using minisatellite maps comparison.     

Alignment and topological accuracy of the direct optimization approach via POY and traditional phylogenetics via ClustalW + PAUP*

Direct optimization frameworks for simultaneously estimating alignments and phylogenies have recently been developed. One such method, implemented in the program POY, is becoming more common for analyses of variable length sequences (e.g., analyses using ribosomal genes) and for combined evidence analyses (morphology + multiple genes). Simulation of sequences containing insertion and deletion events was performed in order to directly compare a widely used method of multiple sequence alignment (ClustalW) and subsequent parsimony analysis in PAUP* with direct optimization via POY. Data sets were simulated for pectinate, balanced, and random tree shapes under different conditions (clocklike, non-clocklike, and ultrametric). Alignment accuracy scores for the implied alignments from POY and the multiple sequence alignments from ClustalW were calculated and compared. In almost all cases (99.95%), ClustalW produced more accurate alignments than POY-implied alignments, judged by the proportion of correctly identified homologous sites. Topological accuracy (distance to the true tree) for POY topologies and topologies generated under parsimony in PAUP* from the ClustalW alignments were also compared. In 44.94% of the cases, Clustal alignment tree reconstructions via PAUP* were more accurate than POY, whereas in 16.71% of the cases POY reconstructions were more topologically accurate (38.38% of the time they were equally accurate). Comparisons between POY hypothesized alignments and the true alignments indicated that, on average, as alignment error increased, topological accuracy decreased.     

Phylogenetic inference under varying proportions of indel-induced alignment gaps

Background  

The effect of alignment gaps on phylogenetic accuracy has been the subject of numerous studies. In this study, we investigated the relationship between the total number of gapped sites and phylogenetic accuracy, when the gaps were introduced (by means of computer simulation) to reflect indel (insertion/deletion) events during the evolution of DNA sequences. The resulting (true) alignments were subjected to commonly used gap treatment and phylogenetic inference methods.     

A deletion/insertion leading to the generation of a direct repeat as a result of slipped mispairing and intragenic recombination in the factor VIII gene

A deletion/insertion in the human factor VIII gene was found in a patient with severe hemophilia A; 316 bp were removed, viz., those enclosing part of intron 15 and the first 7 bp of exon 16. In addition to the deletion, 6 bp were added to the deletion breakpoints; this resulted in the duplication of an existing 13-bp unit. Thus, an overlapping 13-bp direct repeat was generated at the deletion junction. Moreover, the deleted fragment itself was flanked by two homologous 6-bp sequences, one unit being lost by the deletion. A combination of slipped mispairing during replication and an intragenic recombination is discussed to describe this deletion/insertion process. Received: 4 January 1999 / Accepted: 22 March 1999     

Frequency of insertion-deletion,transversion, and transition in the evolution of 5S ribosomal RNA

Summary The problem of choosing an alignment of two or more nucleotide sequences is particularly difficult for nucleic acids, such as 5S ribosomal RNA, which do not code for protein and for which secondary structure is unknown. Given a set of costs for the various types of replacement mutations and for base insertion or deletion, we present a dynamic programming algorithm which finds the optimal (least costly) alignment for a set of N sequences simultaneously, where each sequence is associated with one of the N tips of a given evolutionary tree. Concurrently, protosequences are constructed corresponding to the ancestral nodes of the tree. A version of this algorithm, modified to be computationally feasible, is implemented to align the sequences of 5S RNA from nine organisms. Complete sets of alignments and proto-sequence reconstructions are done for a large number of different con-figurations of mutation costs. Examination of the family of curves of total replacements inferred versus the ratio of transitions/trans-versions inferred, each curve corresponding to a given number of in-sertions-deletions inferred, provides a method for estimating relative costs and relative frequencies for these different types of mutation.     

Identifying DNA and protein patterns with statistically significant alignments of multiple sequences.

MOTIVATION: Molecular biologists frequently can obtain interesting insight by aligning a set of related DNA, RNA or protein sequences. Such alignments can be used to determine either evolutionary or functional relationships. Our interest is in identifying functional relationships. Unless the sequences are very similar, it is necessary to have a specific strategy for measuring-or scoring-the relatedness of the aligned sequences. If the alignment is not known, one can be determined by finding an alignment that optimizes the scoring scheme. RESULTS: We describe four components to our approach for determining alignments of multiple sequences. First, we review a log-likelihood scoring scheme we call information content. Second, we describe two methods for estimating the P value of an individual information content score: (i) a method that combines a technique from large-deviation statistics with numerical calculations; (ii) a method that is exclusively numerical. Third, we describe how we count the number of possible alignments given the overall amount of sequence data. This count is multiplied by the P value to determine the expected frequency of an information content score and, thus, the statistical significance of the corresponding alignment. Statistical significance can be used to compare alignments having differing widths and containing differing numbers of sequences. Fourth, we describe a greedy algorithm for determining alignments of functionally related sequences. Finally, we test the accuracy of our P value calculations, and give an example of using our algorithm to identify binding sites for the Escherichia coli CRP protein. AVAILABILITY: Programs were developed under the UNIX operating system and are available by anonymous ftp from ftp://beagle.colorado.edu/pub/consensus.