Alignment with context dependent scoring function.

In the paper by Gambin et al. (2002) we introduced the model of contextual alignment of biological sequences. It is an extension of the classical alignment, in which the cost of a substitution depends on the surrounding symbols. Consequently, in this model the cost of transforming one sequence into another depends on the order of editing operations. In this paper, we strengthen some of our results which concern reconstructing (the representation of) all the orders of operations which yield this optimal cost. We also present a procedure to construct context-dependent substitution tables and discuss the distribution of scores of local contextual alignment, which is shown to follow the extreme value distribution in the gap-free, reduced context case. We also demonstrate a linear time algorithm to compute the optimal local and global alignment without gaps.     

Alignments of mitochondrial genome arrangements: applications to metazoan phylogeny

Mitochondrial genomes provide a valuable dataset for phylogenetic studies, in particular of metazoan phylogeny because of the extensive taxon sample that is available. Beyond the traditional sequence-based analysis it is possible to extract phylogenetic information from the gene order. Here we present a novel approach utilizing these data based on cyclic list alignments of the gene orders. A progressive alignment approach is used to combine pairwise list alignments into a multiple alignment of gene orders. Parsimony methods are used to reconstruct phylogenetic trees, ancestral gene orders, and consensus patterns in a straightforward approach. We apply this method to study the phylogeny of protostomes based exclusively on mitochondrial genome arrangements. We, furthermore, demonstrate that our approach is also applicable to the much larger genomes of chloroplasts.     

Clustalnet: the joining of Clustal and CORBA

MOTIVATION: Performing sequence alignment operations from a different program than the original sequence alignment code, and/or through a network connection, is often required. Interactive alignment editors and large-scale biological data analysis are common examples where such a flexibility is important. Interoperability between the alignment engine and the client should be obtained regardless of the architectures and programming languages of the server and client. RESULTS: Clustalnet, a Clustal alignment CORBA server is described, which was developed on the basis of Clustalw. This server brings the robustness of the algorithms and implementations of Clustal to a new level of reuse. A Clustalnet server object can be accessed from a program, transparently through the network. We present interfaces to perform the alignment operations and to control these operations via immutable contexts. The interfaces that select the contexts do not depend on the nature of the operation to be performed, making the design modular. The IDL interfaces presented here are not specific to Clustal and can be implemented on top of different sequence alignment algorithm implementations.     

Picking alignments from (Steiner) trees.

The application of Needleman-Wunsch alignment techniques to biological sequences is complicated by two serious problems when the sequences are long: the running time, which scales as the product of the lengths of sequences, and the difficulty in obtaining suitable parameters that produce meaningful alignments. The running time problem is often corrected by reducing the search space, using techniques such as banding, or chaining of high-scoring pairs. The parameter problem is more difficult to fix, partly because the probabilistic model, which Needleman-Wunsch is equivalent to, does not capture a key feature of biological sequence alignments, namely the alternation of conserved blocks and seemingly unrelated nonconserved segments. We present a solution to the problem of designing efficient search spaces for pair hidden Markov models that align biological sequences by taking advantage of their associated features. Our approach leads to an optimization problem, for which we obtain a 2-approximation algorithm, and that is based on the construction of Manhattan networks, which are close relatives of Steiner trees. We describe the underlying theory and show how our methods can be applied to alignment of DNA sequences in practice, successfully reducing the Viterbi algorithm search space of alignment PHMMs by three orders of magnitude.     

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.     

A generalized affine gap model significantly improves protein sequence alignment accuracy

Sequence alignment underpins common tasks in molecular biology, including genome annotation, molecular phylogenetics, and homology modeling. Fundamental to sequence alignment is the placement of gaps, which represent character insertions or deletions. We assessed the ability of a generalized affine gap cost model to reliably detect remote protein homology and to produce high-quality alignments. Generalized affine gap alignment with optimal gap parameters performed as well as the traditional affine gap model in remote homology detection. Evaluation of alignment quality showed that the generalized affine model aligns fewer residue pairs than the traditional affine model but achieves significantly higher per-residue accuracy. We conclude that generalized affine gap costs should be used when alignment accuracy carries more importance than aligned sequence length.     

2D fast rotational matching for image processing of biophysical data

In 3D single particle reconstruction, which involves the translational and rotational matching of a large number of electron microscopy (EM) images, the algorithmic performance is largely dependent on the efficiency and accuracy of the underlying 2D image alignment kernel. We present a novel fast rotational matching kernel for 2D images (FRM2D) that significantly reduces the cost of this alignment. The alignment problem is formulated using one translational and two rotational degrees of freedom. This allows us to take advantage of fast Fourier transforms (FFTs) in rotational space to accelerate the search of the two angular parameters, while the remaining translational parameter is explored, within a limited range, by exhaustive search. Since there are no boundary effects in FFTs of cyclic angular variables, we avoid the expensive zero padding associated with Fourier transforms in linear space. To verify the robustness of our method, efficiency and accuracy tests were carried out over a range of noise levels in realistic simulations of EM images. Performance tests against two standard alignment methods, resampling to polar coordinates and self-correlation, demonstrate that FRM2D compares very favorably to the traditional methods. FRM2D exhibits a comparable or higher robustness against noise and a significant gain in efficiency that depends on the fineness of the angular sampling and linear search range.     

Hierarchical clustering based upon contextual alignment of proteins: a different way to approach phylogeny

We perform a computational study using a new approach to the analysis of protein sequences. The contextual alignment model, proposed recently by Gambin et al. (2002), is based on the assumption that, while constructing an alignment, the score of a substitution of one residue by another depends on the surrounding residues. The contextual alignment scores calculated in this model were used to hierarchical clustering of several protein families from the database of Clusters of Orthologous Groups (COG). The clustering has been also constructed based on the standard approach. The comparative analysis shows that the contextual model results in more consistent clustering trees. The difference, although small, is with no exception in favour of the contextual model. The consistency of the family of trees is measured by several consensus and agreement methods, as well as by the inter-tree distance approach.     

Mathematical modelling of extracellular matrix dynamics using discrete cells: fiber orientation and tissue regeneration.

Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the factors involved in orientation and alignment. Within this framework, cells are considered as discrete objects, while the matrix is modelled as a continuum. Using numerical simulations, we investigate the effect on alignment of changing cell properties and of varying cell interactions with collagen and fibrin.     

Evolutionary Triplet Models of Structured RNA

The reconstruction and synthesis of ancestral RNAs is a feasible goal for paleogenetics. This will require new bioinformatics methods, including a robust statistical framework for reconstructing histories of substitutions, indels and structural changes. We describe a “transducer composition” algorithm for extending pairwise probabilistic models of RNA structural evolution to models of multiple sequences related by a phylogenetic tree. This algorithm draws on formal models of computational linguistics as well as the 1985 protosequence algorithm of David Sankoff. The output of the composition algorithm is a multiple-sequence stochastic context-free grammar. We describe dynamic programming algorithms, which are robust to null cycles and empty bifurcations, for parsing this grammar. Example applications include structural alignment of non-coding RNAs, propagation of structural information from an experimentally-characterized sequence to its homologs, and inference of the ancestral structure of a set of diverged RNAs. We implemented the above algorithms for a simple model of pairwise RNA structural evolution; in particular, the algorithms for maximum likelihood (ML) alignment of three known RNA structures and a known phylogeny and inference of the common ancestral structure. We compared this ML algorithm to a variety of related, but simpler, techniques, including ML alignment algorithms for simpler models that omitted various aspects of the full model and also a posterior-decoding alignment algorithm for one of the simpler models. In our tests, incorporation of basepair structure was the most important factor for accurate alignment inference; appropriate use of posterior-decoding was next; and fine details of the model were least important. Posterior-decoding heuristics can be substantially faster than exact phylogenetic inference, so this motivates the use of sum-over-pairs heuristics where possible (and approximate sum-over-pairs). For more exact probabilistic inference, we discuss the use of transducer composition for ML (or MCMC) inference on phylogenies, including possible ways to make the core operations tractable.     

Parametric genome rearrangement

Algorithms inspired by comparative genomics calculate an edit distance between two linear orders based on elementary edit operations such as inversion, transposition and reciprocal translocation. All operations are generally assigned the same weight, simply by default, because no systematic empirical studies exist verifying whether algorithmic outputs involve realistic proportion of each. Nor de we have data on how weights should vary with the length of the inverted or transposed segment of the chromosome. In this paper, we present a rapid algorithm that allows each operation to take on a range of weights, producing an relatively tight bound on the distance between single-chromosome genomes, by means of a greedy search with look-ahead. The efficiency of this algorithm allows us to test random genomes for each parameter setting, to detect gene order similarity and to infer the parameter values most appropriate to the phylogenetic domain under study. We apply this method to genome segments in which the sa me gene order is conserved in Escherichia coli and Bacillus subtilis, as well as to the gene order in human versus Drosophila mitochondrial genomes. In both cases, we conclude that it is most appropriate to assign somewhat more than twice the weight to transpositions and inverted transpositions than to inversions. We also explore segment-length weighting for fungal mitochondrial gene orders.     

Mathematical modelling of anisotropy in fibrous connective tissue

We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial differential equations operating on a macroscopic scale. We show that a model consisting of a single extracellular matrix material aligned by fibroblasts via flux and stress exhibits behaviour that is incompatible with experimental observations. We extend the model to two matrix types and show that the results of this extended model are robust and consistent with experiment. The second model represents cells as discrete objects in a continuum of ECM. We show that this model predicts patterns of alignment on macroscopic length scales that are lost in a continuum model of the cell population.     

Complexity and non-commutativity of learning operations on graphs

We present results from numerical studies of supervised learning operations in small recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors, which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the sequence of inputs, this structure is generally non-commutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated.     

A Fast and Scalable Kymograph Alignment Algorithm for Nanochannel-Based Optical DNA Mappings

Optical mapping by direct visualization of individual DNA molecules, stretched in nanochannels with sequence-specific fluorescent labeling, represents a promising tool for disease diagnostics and genomics. An important challenge for this technique is thermal motion of the DNA as it undergoes imaging; this blurs fluorescent patterns along the DNA and results in information loss. Correcting for this effect (a process referred to as kymograph alignment) is a common preprocessing step in nanochannel-based optical mapping workflows, and we present here a highly efficient algorithm to accomplish this via pattern recognition. We compare our method with the one previous approach, and we find that our method is orders of magnitude faster while producing data of similar quality. We demonstrate proof of principle of our approach on experimental data consisting of melt mapped bacteriophage DNA.     

A probabilistic model for sequence alignment with context-sensitive indels

Probabilistic approaches for sequence alignment are usually based on pair Hidden Markov Models (HMMs) or Stochastic Context Free Grammars (SCFGs). Recent studies have shown a significant correlation between the content of short indels and their flanking regions, which by definition cannot be modelled by the above two approaches. In this work, we present a context-sensitive indel model based on a pair Tree-Adjoining Grammar (TAG), along with accompanying algorithms for efficient alignment and parameter estimation. The increased precision and statistical power of this model is shown on simulated and real genomic data. As the cost of sequencing plummets, the usefulness of comparative analysis is becoming limited by alignment accuracy rather than data availability. Our results will therefore have an impact on any type of downstream comparative genomics analyses that rely on alignments. Fine-grained studies of small functional regions or disease markers, for example, could be significantly improved by our method. The implementation is available at www.mcb.mcgill.ca/~blanchem/software.html.     

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.     

Genome rearrangement based on reversals that preserve conserved intervals

The order of genes in the genomes of species can change during evolution and can provide information about their phylogenetic relationship. An interesting method to infer the phylogenetic relationship from the gene orders is to use different types of rearrangement operations and to find possible rearrangement scenarios using these operations. One of the most common rearrangement operations is reversals, which reverse the order of a subset of neighbored genes. In this paper, we study the problem to find the ancestral gene order for three species represented by their gene orders. The rearrangement scenario should use a minimal number of reversals and no other rearrangement operations. This problem is called the Median problem and is known to be NP--complete. In this paper, we describe a heuristic algorithm for finding solutions to the Median problem that searches for rearrangement scenarios with the additional property that gene groups should not be destroyed by reversal operations. The concept of conserved intervals for signed permutations is used to describe such gene groups. We show experimentally, for different types of test problems, that the proposed algorithm produces very good results compared to other algorithms for the Median problem. We also integrate our reversal selection procedure into the well-known MGR and GRAPPA algorithms and show that they achieve a significant speedup while obtaining solutions of the same quality as the original algorithms on the test problems.     

Understanding disease control: influence of epidemiological and economic factors

We present a model of disease transmission on a regular and small world network and compare different control options. Comparison is based on a total cost of epidemic, including cost of palliative treatment of ill individuals and preventive cost aimed at vaccination or culling of susceptible individuals. Disease is characterized by pre-symptomatic phase, which makes detection and control difficult. Three general strategies emerge: global preventive treatment, local treatment within a neighborhood of certain size and only palliative treatment with no prevention. While the choice between the strategies depends on a relative cost of palliative and preventive treatment, the details of the local strategy and, in particular, the size of the optimal treatment neighborhood depend on the epidemiological factors. The required extent of prevention is proportional to the size of the infection neighborhood, but depends on time till detection and time till treatment in a non-nonlinear (power) law. The optimal size of control neighborhood is also highly sensitive to the relative cost, particularly for inefficient detection and control application. These results have important consequences for design of prevention strategies aiming at emerging diseases for which parameters are not nessecerly known in advance.     

Estimating divergence time and ancestral effective population size of Bornean and Sumatran orangutan subspecies using a coalescent hidden Markov model

Due to genetic variation in the ancestor of two populations or two species, the divergence time for DNA sequences from two populations is variable along the genome. Within genomic segments all bases will share the same divergence-because they share a most recent common ancestor-when no recombination event has occurred to split them apart. The size of these segments of constant divergence depends on the recombination rate, but also on the speciation time, the effective population size of the ancestral population, as well as demographic effects and selection. Thus, inference of these parameters may be possible if we can decode the divergence times along a genomic alignment. Here, we present a new hidden Markov model that infers the changing divergence (coalescence) times along the genome alignment using a coalescent framework, in order to estimate the speciation time, the recombination rate, and the ancestral effective population size. The model is efficient enough to allow inference on whole-genome data sets. We first investigate the power and consistency of the model with coalescent simulations and then apply it to the whole-genome sequences of the two orangutan sub-species, Bornean (P. p. pygmaeus) and Sumatran (P. p. abelii) orangutans from the Orangutan Genome Project. We estimate the speciation time between the two sub-species to be thousand years ago and the effective population size of the ancestral orangutan species to be , consistent with recent results based on smaller data sets. We also report a negative correlation between chromosome size and ancestral effective population size, which we interpret as a signature of recombination increasing the efficacy of selection.