An evolutionary model for maximum likelihood alignment of DNA sequences

Summary Most algorithms for the alignment of biological sequences are not derived from an evolutionary model. Consequently, these alignment algorithms lack a strong statistical basis. A maximum likelihood method for the alignment of two DNA sequences is presented. This method is based upon a statistical model of DNA sequence evolution for which we have obtained explicit transition probabilities. The evolutionary model can also be used as the basis of procedures that estimate the evolutionary parameters relevant to a pair of unaligned DNA sequences. A parameter-estimation approach which takes into account all possible alignments between two sequences is introduced; the danger of estimating evolutionary parameters from a single alignment is discussed.     

Improving profile HMM discrimination by adapting transition probabilities

Profile hidden Markov models (HMMs) are used to model protein families and for detecting evolutionary relationships between proteins. Such a profile HMM is typically constructed from a multiple alignment of a set of related sequences. Transition probability parameters in an HMM are used to model insertions and deletions in the alignment. We show here that taking into account unrelated sequences when estimating the transition probability parameters helps to construct more discriminative models for the global/local alignment mode. After normal HMM training, a simple heuristic is employed that adjusts the transition probabilities between match and delete states according to observed transitions in the training set relative to the unrelated (noise) set. The method is called adaptive transition probabilities (ATP) and is based on the HMMER package implementation. It was benchmarked in two remote homology tests based on the Pfam and the SCOP classifications. Compared to the HMMER default procedure, the rate of misclassification was reduced significantly in both tests and across all levels of error rate.     

Tree-based maximal likelihood substitution matrices and hidden Markov models

There has been considerable interest in the problem of making maximum likelihood (ML) evolutionary trees which allow insertions and deletions. This problem is partly one of formulation: how does one define a probabilistic model for such trees which treats insertion and deletion in a biologically plausible manner? A possible answer to this question is proposed here by extending the concept of a hidden Markov model (HMM) to evolutionary trees. The model, called a tree-HMM, allows what may be loosely regarded as learnable affine-type gap penalties for alignments. These penalties are expressed in HMMs as probabilities of transitions between states. In the tree-HMM, this idea is given an evolutionary embodiment by defining trees of transitions. Just as the probability of a tree composed of ungapped sequences is computed, by Felsenstein's method, using matrices representing the probabilities of substitutions of residues along the edges of the tree, so the probabilities in a tree-HMM are computed by substitution matrices for both residues and transitions. How to define these matrices by a ML procedure using an algorithm that learns from a database of protein sequences is shown here. Given these matrices, one can define a tree-HMM likelihood for a set of sequences, assuming a particular tree topology and an alignment of the sequences to the model. If one could efficiently find the alignment which maximizes (or comes close to maximizing) this likelihood, then one could search for the optimal tree topology for the sequences. An alignment algorithm is defined here which, given a particular tree topology, is guaranteed to increase the likelihood of the model. Unfortunately, it fails to find global optima for realistic sequence sets. Thus further research is needed to turn the tree-HMM into a practical phylogenetic tool.     

Detection of recombination in DNA multiple alignments with hidden Markov models.

Conventional 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.     

Probabilistic alignments with quality scores: an application to short-read mapping toward accurate SNP/indel detection

MOTIVATION: Recent studies have revealed the importance of considering quality scores of reads generated by next-generation sequence (NGS) platforms in various downstream analyses. It is also known that probabilistic alignments based on marginal probabilities (e.g. aligned-column and/or gap probabilities) provide more accurate alignment than conventional maximum score-based alignment. There exists, however, no study about probabilistic alignment that considers quality scores explicitly, although the method is expected to be useful in SNP/indel callers and bisulfite mapping, because accurate estimation of aligned columns or gaps is important in those analyses. RESULTS: In this study, we propose methods of probabilistic alignment that consider quality scores of (one of) the sequences as well as a usual score matrix. The method is based on posterior decoding techniques in which various marginal probabilities are computed from a probabilistic model of alignments with quality scores, and can arbitrarily trade-off sensitivity and positive predictive value (PPV) of prediction (aligned columns and gaps). The method is directly applicable to read mapping (alignment) toward accurate detection of SNPs and indels. Several computational experiments indicated that probabilistic alignments can estimate aligned columns and gaps accurately, compared with other mapping algorithms e.g. SHRiMP2, Stampy, BWA and Novoalign. The study also suggested that our approach yields favorable precision for SNP/indel calling.     

transition priors for protein hidden Markov models: an empirical study towards maximum discrimination.

Insertions and deletions in a profile hidden Markov model (HMM) are modeled by transition probabilities between insert, delete and match states. These are estimated by combining observed data and prior probabilities. The transition prior probabilities can be defined either ad hoc or by maximum likelihood (ML) estimation. We show that the choice of transition prior greatly affects the HMM's ability to discriminate between true and false hits. HMM discrimination was measured using the HMMER 2.2 package applied to 373 families from Pfam. We measured the discrimination between true members and noise sequences employing various ML transition priors and also systematically scanned the parameter space of ad hoc transition priors. Our results indicate that ML priors produce far from optimal discrimination, and we present an empirically derived prior that considerably decreases the number of misclassifications compared to ML. Most of the difference stems from the probabilities for exiting a delete state. The ML prior, which is unaware of noise sequences, estimates a delete-to-delete probability that is relatively high and does not penalize noise sequences enough for optimal discrimination.     

Statistical alignment: computational properties, homology testing and goodness-of-fit

The model of insertions and deletions in biological sequences, first formulated by Thorne, Kishino, and Felsenstein in 1991 (the TKF91 model), provides a basis for performing alignment within a statistical framework. Here we investigate this model.Firstly, we show how to accelerate the statistical alignment algorithms several orders of magnitude. The main innovations are to confine likelihood calculations to a band close to the similarity based alignment, to get good initial guesses of the evolutionary parameters and to apply an efficient numerical optimisation algorithm for finding the maximum likelihood estimate. In addition, the recursions originally presented by Thorne, Kishino and Felsenstein can be simplified. Two proteins, about 1500 amino acids long, can be analysed with this method in less than five seconds on a fast desktop computer, which makes this method practical for actual data analysis.Secondly, we propose a new homology test based on this model, where homology means that an ancestor to a sequence pair can be found finitely far back in time. This test has statistical advantages relative to the traditional shuffle test for proteins.Finally, we describe a goodness-of-fit test, that allows testing the proposed insertion-deletion (indel) process inherent to this model and find that real sequences (here globins) probably experience indels longer than one, contrary to what is assumed by the model.     

Measuring the fit of sequence data to phylogenetic model: allowing for missing data

It is fundamentally important to assess the fit of data to model in phylogenetic and evolutionary studies. Phylogenetic methods using molecular sequences typically start with a multiple alignment. It is possible to measure the fit of data to model expectations of data, for example, via the likelihood-ratio (G) test or the X(2) test, if all sites in all sequences have an unambiguous residue. However, nearly all alignments of interest contain sites (columns of the alignment) with missing data, that is, ambiguous nucleotides, gaps, or unsequenced regions, which must presently be removed before using the above tests. Unfortunately, this is often either undesirable or impractical, as it will discard much of the data. Here, we show how iterative ML estimators may directly estimate the site-pattern probabilities for columns with missing data, given only standard i.i.d. assumptions. The optimization may use an EM or Newton algorithm, or any other hill-climbing approach. The resulting optimal likelihood under the unconstrained or multinomial model may be compared directly with the likelihood of the data coming from the model (a G statistic). Alternatively the modified observed and the expected frequencies of site patterns may be compared using a X(2) test. The distribution of such statistics is best assessed using appropriate simulations. The new method is applicable to models using codons or paired sites. The methods are also useful with Hadamard conjugations (spectral analysis) and are illustrated with these and with ML evolutionary models that allow site-rate variability.     

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.     

HMM-ModE – Improved classification using profile hidden Markov models by optimising the discrimination threshold and modifying emission probabilities with negative training sequences

Background  

Profile Hidden Markov Models (HMM) are statistical representations of protein families derived from patterns of sequence conservation in multiple alignments and have been used in identifying remote homologues with considerable success. These conservation patterns arise from fold specific signals, shared across multiple families, and function specific signals unique to the families. The availability of sequences pre-classified according to their function permits the use of negative training sequences to improve the specificity of the HMM, both by optimizing the threshold cutoff and by modifying emission probabilities to minimize the influence of fold-specific signals. A protocol to generate family specific HMMs is described that first constructs a profile HMM from an alignment of the family's sequences and then uses this model to identify sequences belonging to other classes that score above the default threshold (false positives). Ten-fold cross validation is used to optimise the discrimination threshold score for the model. The advent of fast multiple alignment methods enables the use of the profile alignments to align the true and false positive sequences, and the resulting alignments are used to modify the emission probabilities in the original model.     

Gene finding with a hidden Markov model of genome structure and evolution

Motivation: A growing number of genomes are sequenced. The differences in evolutionary pattern between functional regions can thus be observed genome-wide in a whole set of organisms. The diverse evolutionary pattern of different functional regions can be exploited in the process of genomic annotation. The modelling of evolution by the existing comparative gene finders leaves room for improvement. Results: A probabilistic model of both genome structure and evolution is designed. This type of model is called an Evolutionary Hidden Markov Model (EHMM), being composed of an HMM and a set of region-specific evolutionary models based on a phylogenetic tree. All parameters can be estimated by maximum likelihood, including the phylogenetic tree. It can handle any number of aligned genomes, using their phylogenetic tree to model the evolutionary correlations. The time complexity of all algorithms used for handling the model are linear in alignment length and genome number. The model is applied to the problem of gene finding. The benefit of modelling sequence evolution is demonstrated both in a range of simulations and on a set of orthologous human/mouse gene pairs. AVAILABILITY: Free availability over the Internet on www server: http://www.birc.dk/Software/evogene.     

A Probabilistic Model for Indel Evolution: Differentiating Insertions from Deletions

Insertions and deletions (indels) are common molecular evolutionary events. However, probabilistic models for indel evolution are under-developed due to their computational complexity. Here, we introduce several improvements to indel modeling: 1) While previous models for indel evolution assumed that the rates and length distributions of insertions and deletions are equal, here we propose a richer model that explicitly distinguishes between the two; 2) we introduce numerous summary statistics that allow approximate Bayesian computation-based parameter estimation; 3) we develop a method to correct for biases introduced by alignment programs, when inferring indel parameters from empirical data sets; and 4) using a model-selection scheme, we test whether the richer model better fits biological data compared with the simpler model. Our analyses suggest that both our inference scheme and the model-selection procedure achieve high accuracy on simulated data. We further demonstrate that our proposed richer model better fits a large number of empirical data sets and that, for the majority of these data sets, the deletion rate is higher than the insertion rate.     

A hidden Markov model for progressive multiple alignment

MOTIVATION: Progressive algorithms are widely used heuristics for the production of alignments among multiple nucleic-acid or protein sequences. Probabilistic approaches providing measures of global and/or local reliability of individual solutions would constitute valuable developments. RESULTS: We present here a new method for multiple sequence alignment that combines an HMM approach, a progressive alignment algorithm, and a probabilistic evolution model describing the character substitution process. Our method works by iterating pairwise alignments according to a guide tree and defining each ancestral sequence from the pairwise alignment of its child nodes, thus, progressively constructing a multiple alignment. Our method allows for the computation of each column minimum posterior probability and we show that this value correlates with the correctness of the result, hence, providing an efficient mean by which unreliably aligned columns can be filtered out from a multiple alignment.     

基因组水平的插入和缺失变异研究进展

插入和缺失(insertion and deletion)是DNA和蛋白质在进化过程中发生的序列长度上的改变,由于缺乏祖先序列的信息,不能肯定其到底是插入事件还是缺失事件,故统称之为增减(indel)。indel是分子水平进化变异的主要来源之一,近年来对这种进化事件的研究已经涵盖了其发生频率、大小、分布模式、序列进化模型及应用等各个方面。该文总结了基因组水平上插入和缺失的研究进展和发生机制;介绍了已经提出的插入和缺失进化模型,包括TKF91、TKF92、"Long Indel"模型和序列环境模型;讨论了插入和缺失作为分子标记在分子进化、基因分型和药物设计等方面的应用。     

Incorporating information from length-mutational events into phylogenetic analysis

With the growing number of phylogenetic studies that use length variable DNA sequences, incorporating information from length-mutational events into phylogenetic analysis is becoming increasingly important. A new method, modified complex indel coding is described that aims at maximizing the phylogenetic information retained from unambiguously aligned sequence regions or regions where the principal relative position of gaps to one another can be safely established. An algorithm is described that allows application of the method to all theoretically possible gap-nucleotide patterns. A platform-independent computer program is introduced that automates the new method as well as several previously published coding schemes. Differences to previously published indel coding approaches as well as to the integration of ambiguously aligned regions into phylogenetic analysis are discussed.     

Accurate reconstruction of insertion-deletion histories by statistical phylogenetics

The Multiple Sequence Alignment (MSA) is a computational abstraction that represents a partial summary either of indel history, or of structural similarity. Taking the former view (indel history), it is possible to use formal automata theory to generalize the phylogenetic likelihood framework for finite substitution models (Dayhoff's probability matrices and Felsenstein's pruning algorithm) to arbitrary-length sequences. In this paper, we report results of a simulation-based benchmark of several methods for reconstruction of indel history. The methods tested include a relatively new algorithm for statistical marginalization of MSAs that sums over a stochastically-sampled ensemble of the most probable evolutionary histories. For mammalian evolutionary parameters on several different trees, the single most likely history sampled by our algorithm appears less biased than histories reconstructed by other MSA methods. The algorithm can also be used for alignment-free inference, where the MSA is explicitly summed out of the analysis. As an illustration of our method, we discuss reconstruction of the evolutionary histories of human protein-coding genes.     

Characterization of pairwise and multiple sequence alignment errors

We characterize pairwise and multiple sequence alignment (MSA) errors by comparing true alignments from simulations of sequence evolution with reconstructed alignments. The vast majority of reconstructed alignments contain many errors. Error rates rapidly increase with sequence divergence, thus, for even intermediate degrees of sequence divergence, more than half of the columns of a reconstructed alignment may be expected to be erroneous. In closely related sequences, most errors consist of the erroneous positioning of a single indel event and their effect is local. As sequences diverge, errors become more complex as a result of the simultaneous mis-reconstruction of many indel events, and the lengths of the affected MSA segments increase dramatically. We found a systematic bias towards underestimation of the number of gaps, which leads to the reconstructed MSA being on average shorter than the true one. Alignment errors are unavoidable even when the evolutionary parameters are known in advance. Correct reconstruction can only be guaranteed when the likelihood of true alignment is uniquely optimal. However, true alignment features are very frequently sub-optimal or co-optimal, with the result that optimal albeit erroneous features are incorporated into the reconstructed MSA. Progressive MSA utilizes a guide-tree in the reconstruction of MSAs. The quality of the guide-tree was found to affect MSA error levels only marginally.     

Molecular phylogenetics of the lizard genus Microlophus (squamata:tropiduridae): aligning and retrieving indel signal from nuclear introns

We use a multigene data set (the mitochondrial locus and nine nuclear gene regions) to test phylogenetic relationships in the South American "lava lizards" (genus Microlophus) and describe a strategy for aligning noncoding sequences that accounts for differences in tempo and class of mutational events. We focus on seven nuclear introns that vary in size and frequency of multibase length mutations (i.e., indels) and present a manual alignment strategy that incorporates insertions and deletions (indels) for each intron. Our method is based on mechanistic explanations of intron evolution that does not require a guide tree. We also use a progressive alignment algorithm (Probabilistic Alignment Kit; PRANK) and distinguishes insertions from deletions and avoids the "gapcost" conundrum. We describe an approach to selecting a guide tree purged of ambiguously aligned regions and use this to refine PRANK performance. We show that although manual alignment is successful in finding repeat motifs and the most obvious indels, some regions can only be subjectively aligned, and there are limits to the size and complexity of a data matrix for which this approach can be taken. PRANK alignments identified more parsimony-informative indels while simultaneously increasing nucleotide identity in conserved sequence blocks flanking the indel regions. When comparing manual and PRANK with two widely used methods (CLUSTAL, MUSCLE) for the alignment of the most length-variable intron, only PRANK recovered a tree congruent at deeper nodes with the combined data tree inferred from all nuclear gene regions. We take this concordance as an objective function of alignment quality and present a strongly supported phylogenetic hypothesis for Microlophus relationships. From this hypothesis we show that (1) a coded indel data partition derived from the PRANK alignment contributed significantly to nodal support and (2) the indel data set permitted detection of significant conflict between mitochondrial and nuclear data partitions, which we hypothesize arose from secondary contact of distantly related taxa, followed by hybridization and mtDNA introgression.     

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.