A few models have appeared in recent years that consider not only the way substitutions occur through evolutionary history at each site of a genome, but also the way the process changes from one site to the next. These models combine phylogenetic models of molecular evolution, which apply to individual sites, and hidden Markov models, which allow for changes from site to site. Besides improving the realism of ordinary phylogenetic models, they are potentially very powerful tools for inference and prediction—for gene finding, for example, or prediction of secondary structure. In this paper, we review progress on combined phylogenetic and hidden Markov models and present some extensions to previous work. Our main result is a simple and efficient method for accommodating higher-order states in the HMM, which allows for context-sensitive models of substitution— that is, models that consider the effects of neighboring bases on the pattern of substitution. We present experimental results indicating that higher-order states, autocorrelated rates, and multiple functional categories all lead to significant improvements in the fit of a combined phylogenetic and hidden Markov model, with the effect of higher-order states being particularly pronounced.

To date, few attempts have been made to benchmark the alignment algorithms upon nucleic acid sequences. Frequently, sophisticated PAM or BLOSUM like models are used to align proteins, yet equivalents are not considered for nucleic acids; instead, rather ad hoc models are generally favoured. Here, we systematically test the performance of existing alignment algorithms on structural RNAs. This work was aimed at achieving the following goals: (i) to determine conditions where it is appropriate to apply common sequence alignment methods to the structuralRNAalignmentproblem.Thisindicates where and when researchers should consider augmenting the alignment process with auxiliary information, such as secondary structure and (ii) to determine which sequence alignment algorithms perform well under the broadest range of conditions. We find that sequence alignment alone, using the current algorithms, is generally inappropriate,50–60 % sequence identity. Second, we note that the probabilistic method ProAlign and the aging Clustal algorithms generally outperform other sequence-based algorithms, under the broadest range of applications.

ABSTRACT Multiple sequence alignment is one of the cornerstones of modern molecular biology. It is used to identify conserved motifs, to determine protein domains, in 2D/3D structure prediction by homology and in evolutionary studies. Recently, high-throughput technologies such as genome sequencing and structural proteomics have lead to an explosion in the amount of sequence and structure information available. In response, several new multiple alignment methods have been developed that improve both the efficiency and the quality of protein alignments. Consequently, the benchmarks used to evaluate and compare these methods must also evolve. We present here the latest release of the most widely used multiple alignment benchmark, BAliBASE, which provides high quality, manually refined, reference alignments based on 3D structural superpositions. Version 3.0 of BAliBASE includes new, more challenging test cases, representing the real problems encountered when aligning large sets of complex sequences. Using a novel, semiautomatic update protocol, the number of protein families in the benchmark has been increased and representative test cases are now available that cover most of the protein fold space. The total number of proteins in BAliBASE has also been significantly increased from 1444 to 6255 sequences. In addition, full-length sequences are now provided for all test cases, which represent difficult cases for both global and local alignment programs. Finally, the BAliBASE Web site

We present an efficient algorithm for statistical multiple alignment based on the TKF91 model of Thorne, Kishino, and Felsenstein (1991) on an arbitrary k-leaved phylogenetic tree. The existing algorithms use a hidden Markov model approach, which requires at least O. p 5 k / states and leads to a time complexity of O.5 k L k /, where L is the geometric mean sequence length. Using a combinatorial technique reminiscent of inclusion/exclusion, we are able to sum away the states, thus improving the time complexity to O.2 k L k / and considerably reducing memory requirements. This makes statistical multiple alignment under the TKF91 model a definite practical possibility in the case of a phylogenetic tree with a modest number of leaves.

Phylogenetic hidden Markov models, or phylo-HMMs, are probabilistic models that consider not only the way substitutions occur through evolutionary history at each site of a genome, but also the way this process changes from one site to the next. By treating molecular evolution as a combination of two Markov processes—one that operates in the dimension of space (along a genome) and one that operates in the dimension of time (along the branches of a phylogenetic tree)—these models allow aspects of both sequence structure and sequence evolution to be captured. Moreover, as we will discuss, they permit key computations to be performed exactly and efficiently. Phylo-HMMs allow evolutionary information to be brought to bear on a wide variety of problems of sequence “segmentation, ” such as gene prediction and the identification of conserved elements. Phylo-HMMs were first proposed as a way of improving phylogenetic models that allow for variation among sites in the rate of substitution [8, 52]. Soon afterward, they were adapted for the problem of secondary structure

Phylogenies are often thought to be more dependent upon the specifics of the sequence alignment rather than on the method of reconstruction. Simulation of sequences containing insertion and deletion events was performed in order to determine the role that alignment accuracy plays during phylogenetic inference. Data sets were simulated for pectinate, balanced, and random tree shapes under different conditions (ultrametric equal branch length, ultrametric random branch length, nonultrametric random branch length). Comparisons between hypothesized alignments and true alignments enabled determination of two measures of alignment accuracy, that of the total data set and that of individual branches. In general, our results indicate that as alignment error increases, topological accuracy decreases. This trend was much more pronounced for data sets derived from more pectinate topologies. In contrast, for balanced, ultrametric, equal branch length tree shapes, alignment inaccuracy had little average effect on tree reconstruction. These conclusions are based on average trends of many analyses under different conditions, and any one specific analysis, independent of the alignment accuracy, may recover very accurate or inaccurate topologies. Maximum likelihood and Bayesian, in general, outperformed neighbor joining and maximum parsimony in terms of tree reconstruction accuracy. Results also indicated that as the length of the branch and of the neighboring branches increase, alignment accuracy decreases, and the length of the neighboring branches is the major factor in topological accuracy. Thus, multiple-sequence alignment can be an important factor in downstream effects on topological reconstruction. [Bayesian; maximum likelihood; maximum parsimony; multiple sequence alignment; neighbor

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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 multiplesequence 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

Abstract: For a set of sequences, related by a binary tree, that have evolved according to the Thorne-Kishino-Felsenstein model, a Gibbs sampler is presented for simulating the ancestral sequences and their alignments. The updating step consists in updating the ancestral sequence and its three alignments within a 3-star tree. We compare the Gibbs sampler with the algorithm suggested recently by Holmes and Bruno. Key words and phrases: 3-star tree, EM-algorithm, evolutionary model, hidden

Motivation: Bayesian analysis is one of the most popular methods in phylogenetic inference. The most commonly used methods fix a single multiple alignment and consider only substitutions as phylogenetically informative mutations, though alignments and phylogenies should be inferred jointly as insertions and deletions also carry informative signals. Methods addressing these issues have been developed only recently and there has not been so far a userfriendly program with a graphical interface that implements these methods. Results: We have developed an extendable software package in the Java programming language that samples from the joint posterior distribution of phylogenies, alignments and evolutionary parameters by applying the Markov chain Monte Carlo method. The package also offers tools for efficient on-the-fly summarisation of the results. It has a graphical interface to configure, start and supervise the analysis, to track the status of the Markov chain and to save the results. The background model for insertions and deletions can be combined with any substitution model. It is easy to add new substitution models to the software package as plugins. The samples from the Markov chain can be summarised in several ways, and new postprocessing plugins may also be installed. Availability: The code is available from