A reliable sequence alignment method based on probabilities of residue correspondences

Symmetric time warping, Boltzmann pair probabilities and functional genomics

Given two time series, possibly of different lengths, time warping is a method to construct an optimal alignment obtained by stretching or contracting time intervals. Unlike pairwise alignment of amino acid sequences, classical time warping, originally introduced for speech recognition, is not symmetric in the sense that the time warping distance between two time series is not necessarily equal to the time warping distance of the reversal of the time series. Here we design a new symmetric version of time warping, and present a formal proof of symmetry for our algorithm as well as for one of the variants of Aach and Church [1]. We additionally design quadratic time dynamic programming algorithms to compute both the forward and backward Boltzmann partition functions for symmetric time warping, and hence compute the Boltzmann probability that any two time series points are aligned. In the future, with the availability of increasingly long and accurate time series gene expression data, our algorithm can provide a sense of biological significance for aligned time points - e.g. our algorithm could be used to provide evidence that expression values of two genes have higher Boltzmann probability (say) in the G1 and S phase than in G2 and M phases. Algorithms, source code and web interface, developed by the first author, are made publicly available via the Boltzmann Time Warping web server at bioinformatics.bc.edu/clotelab/.

ProbCons: Probabilistic consistency-based multiple sequence alignment

To study gene evolution across a wide range of organisms, biologists need accurate tools for multiple sequence alignment of protein families. Obtaining accurate alignments, however, is a difficult computational problem because of not only the high computational cost but also the lack of proper objective functions for measuring alignment quality. In this paper, we introduce probabilistic consistency, a novel scoring function for multiple sequence comparisons. We present ProbCons, a practical tool for progressive protein multiple sequence alignment based on probabilistic consistency, and evaluate its performance on several standard alignment benchmark data sets. On the BAliBASE, SABmark, and PREFAB benchmark alignment databases, ProbCons achieves statistically significant improvement over other leading methods while maintaining practical speed. ProbCons is publicly available as a Web resource.

Probabilistic description of protein alignments for sequences and structures

A number of equally optimal alignments inherently exist in the sequence and structure comparisons among proteins. To represent the sub-optimal alignments systematically, we have developed a method of generating probabilistic alignments for sequences and structures, by which the correspondence between pairs of residues is evaluated in a probabilistic manner. Our method uses the periodic boundary condition to avoid the entropy artifact favoring full-length matches. In the structure comparison, the environmental effects are incorporated by the mean-field approximation. We applied this method in comparisons of two pairs of proteins with internal symmetry; the first set were proteins of TIM-barrel fold and the second were beta-trefoil fold. These pairs are expected to have distinct sub-optimal alignments suitable for probabilistic description with the periodic boundary. It was shown that the sequence and structure alignments are consistent with each other and that the alignments with the highest probability represent circular permutation.

Identifying sequence-structure pairs undetected by sequence alignments

We examine how effectively simple potential functions previously developed can identify compatibilities between sequences and structures of proteins for database searches. The potential function consists of pairwise contact energies, repulsive packing potentials of residues for overly dense arrangement and short-range potentials for secondary structures, all of which were estimated from statistical preferences observed in known protein structures. Each potential energy term was modified to represent compatibilities between sequences and structures for globular proteins. Pairwise contact interactions in a sequence-structure alignment are evaluated in a mean field approximation on the basis of probabilities of site pairs to be aligned. Gap penalties are assumed to be proportional to the number of contacts at each residue position, and as a result gaps will be more frequently placed on protein surfaces than in cores. In addition to minimum energy alignments, we use probability alignments made by successively aligning site pairs in order by pairwise alignment probabilities. The results show that the present energy function and alignment method can detect well both folds compatible with a given sequence and, inversely, sequences compatible with a given fold, and yield mostly similar alignments for these two types of sequence and structure pairs. Probability alignments consisting of most reliable site pairs only can yield extremely small root mean square deviations, and including less reliable pairs increases the deviations. Also, it is observed that secondary structure potentials are usefully complementary to yield improved alignments with this method. Remarkably, by this method some individual sequence-structure pairs are detected having only 5-20% sequence identity.

Multiple sequence alignment: algorithms and applications

Elucidation of interrelationships among sequence, structure, function, and evolution (FESS relationships) of a family of genes or gene products is a central theme of modern molecular biology. Multiple sequence alignment has been proven to be a powerful tool for many fields of studies such as phylogenetic reconstruction, illumination of functionally important regions, and prediction of higher order structures of proteins and RNAs. However, it is far too trivial to automatically construct a multiple alignment from a set of related sequences. A variety of methods for solving this computationally difficult problem are reviewed. Several important applications of multiple alignment for elucidation of the FESS relationships are also discussed. For a long period, progressive methods have been the only practical means to solve a multiple alignment problem of appreciable size. This situation is now changing with the development of new techniques including several classes of iterative methods. Today's progress in multiple sequence alignment methods has been made by the multidisciplinary endeavors of mathematicians, computer scientists, and biologists in various fields including biophysicists in particular. The ideas are also originated from various backgrounds, pure algorithmics, statistics, thermodynamics, and others. The outcomes are now enjoyed by researchers in many fields of biological sciences. In the near future, generalized multiple alignment may play a central role in studies of FESS relationships. The organized mixture of knowledge from multiple fields will ferment to develop fruitful results which would be hard to obtain within each area. I hope this review provides a useful information resource for future development of theory and practice in this rapidly expanding area of bioinformatics.

Dynamic programming alignment accuracy

Algorithms for generating alignments of biological sequences have inherent statistical limitations when it comes to the accuracy of the alignments they produce. Using simulations, we measure the accuracy of the standard global dynamic programming method and show that it can be reasonably well modelled by an "edge wander" approximation to the distribution of the optimal scoring path around the correct path in the vicinity of a gap. We also give a table from which accuracy values can be predicted for commonly used scoring schemes and sequence divergences (the PAM and BLOSUM series). Finally we describe how to calculate the expected accuracy of a given alignment, and show how this can be used to construct an optimal accuracy alignment algorithm which generates significantly more accurate alignments than standard dynamic programming methods in simulated experiments.

Amino acid similarity matrix for homology modeling derived from structural alignment and optimized by the Monte Carlo method

In this paper, we obtained a similarity matrix for homology modeling based on the structure of proteins in a structural alignment. The alignment procedure was executed within dynamic programming generally used in alignment methods. An initial matrix derived from the structural alignment was optimized by the Markov chain Monte Carlo method at low temperature to fit its sequence alignment to the structural alignment. Structural alignment was performed on the basis of the superposition of C alpha atoms for two protein structures. The objective function in the Monte Carlo procedure was defined by entropy in the information theory, allowing us to show that the amino acid similarity matrix aligned accurately. When compared with the structural alignment, the average number of incorrect amino acid residues in the sequence alignment was 22.6 for all residues and about 3.7 for residues in structurally conserved regions. The alignment with our matrix was more similar to structural alignment than to sequence alignments using other amino acid substitution matrices.

Near-optimal sequence alignment

Recent advances in algorithmic techniques and statistics of sequence alignment have helped to make near-optimal alignments an important tool in the delineation of biologically valid alignments. Near-optimal alignments serve to judge the reliability of portions of a sequence alignment. The statistical assessment of suboptimal alignment scores makes sequence alignments less dependent on gap-penalty choice.