MOTIVATION: The reconstruction of possible histories given a sample of genetic data in the presence of recombination and recurrent mutation is a challenging problem, but can provide key insights into the evolution of a population. We present KwARG, which implements a parsimony-based greedy heuristic algorithm for finding plausible genealogical histories (ancestral recombination graphs) that are minimal or near-minimal in the number of posited recombination and mutation events. RESULTS: Given an input dataset of aligned sequences, KwARG outputs a list of possible candidate solutions, each comprising a list of mutation and recombination events that could have generated the dataset; the relative proportion of recombinations and recurrent mutations in a solution can be controlled via specifying a set of 'cost' parameters. We demonstrate that the algorithm performs well when compared against existing methods. AVAILABILITY AND IMPLEMENTATION: The software is available at https://github.com/a-ignatieva/kwarg. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: A standard procedure in many areas of bioinformatics is to use a single multiple sequence alignment (MSA) as the basis for various types of analysis. However, downstream results may be highly sensitive to the alignment used, and neglecting the uncertainty in the alignment can lead to significant bias in the resulting inference. In recent years, a number of approaches have been developed for probabilistic sampling of alignments, rather than simply generating a single optimum. However, this type of probabilistic information is currently not widely used in the context of downstream inference, since most existing algorithms are set up to make use of a single alignment. RESULTS: In this work we present a framework for representing a set of sampled alignments as a directed acyclic graph (DAG) whose nodes are alignment columns; each path through this DAG then represents a valid alignment. Since the probabilities of individual columns can be estimated from empirical frequencies, this approach enables sample-based estimation of posterior alignment probabilities. Moreover, due to conditional independencies between columns, the graph structure encodes a much larger set of alignments than the original set of sampled MSAs, such that the effective sample size is greatly increased. CONCLUSIONS: The alignment DAG provides a natural way to represent a distribution in the space of MSAs, and allows for existing algorithms to be efficiently scaled up to operate on large sets of alignments. As an example, we show how this can be used to compute marginal probabilities for tree topologies, averaging over a very large number of MSAs. This framework can also be used to generate a statistically meaningful summary alignment; example applications show that this summary alignment is consistently more accurate than the majority of the alignment samples, leading to improvements in downstream tree inference. Implementations of the methods described in this article are available at http://statalign.github.io/WeaveAlign .

Abstract Motivation: Many computational methods for RNA secondary structure prediction, and, in particular, for the prediction of a consensus structure of an alignment of RNA sequences, have been developed. Most methods, however, ignore biophysical factors, such as the kinetics of RNA folding; no current implementation considers both evolutionary information and folding kinetics, thus losing information that, when considered, might lead to better predictions. Results: We present an iterative algorithm, Oxfold, in the framework of stochastic context-free grammars, that emulates the kinetics of RNA folding in a simplified way, in combination with a molecular evolution model. This method improves considerably on existing grammatical models that do not consider folding kinetics. Additionally, the model compares favourably to non-kinetic thermodynamic models. Availability: http://www.stats.ox.ac.uk/∼anderson. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

Over the last five years, graphics cards have become a tempting target for scientific computing, thanks to unrivaled peak performance, often producing a runtime speed-up of x10 to x25 over comparable CPU solutions.

BACKGROUND: Stochastic Context-Free Grammars (SCFGs) were applied successfully to RNA secondary structure prediction in the early 90s, and used in combination with comparative methods in the late 90s. The set of SCFGs potentially useful for RNA secondary structure prediction is very large, but a few intuitively designed grammars have remained dominant. In this paper we investigate two automatic search techniques for effective grammars - exhaustive search for very compact grammars and an evolutionary algorithm to find larger grammars. We also examine whether grammar ambiguity is as problematic to structure prediction as has been previously suggested. RESULTS: These search techniques were applied to predict RNA secondary structure on a maximal data set and revealed new and interesting grammars, though none are dramatically better than classic grammars. In general, results showed that many grammars with quite different structure could have very similar predictive ability. Many ambiguous grammars were found which were at least as effective as the best current unambiguous grammars. CONCLUSIONS: Overall the method of evolving SCFGs for RNA secondary structure prediction proved effective in finding many grammars that had strong predictive accuracy, as good or slightly better than those designed manually. Furthermore, several of the best grammars found were ambiguous, demonstrating that such grammars should not be disregarded.

BACKGROUND: RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. RESULTS: In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. CONCLUSIONS: Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.

BACKGROUND: The dynamic motions of many proteins are central to their function. It therefore follows that the dynamic requirements of a protein are evolutionary constrained. In order to assess and quantify this, one needs to compare the dynamic motions of different proteins. Comparing the dynamics of distinct proteins may also provide insight into how protein motions are modified by variations in sequence and, consequently, by structure. The optimal way of comparing complex molecular motions is, however, far from trivial. The majority of comparative molecular dynamics studies performed to date relied upon prior sequence or structural alignment to define which residues were equivalent in 3-dimensional space. RESULTS: Here we discuss an alternative methodology for comparative molecular dynamics that does not require any prior alignment information. We show it is possible to align proteins based solely on their dynamics and that we can use these dynamics-based alignments to quantify the dynamic similarity of proteins. Our method was tested on 10 representative members of the PDZ domain family. CONCLUSIONS: As a result of creating pair-wise dynamics-based alignments of PDZ domains, we have found evolutionarily conserved patterns in their backbone dynamics. The dynamic similarity of PDZ domains is highly correlated with their structural similarity as calculated with Dali. However, significant differences in their dynamics can be detected indicating that sequence has a more refined role to play in protein dynamics than just dictating the overall fold. We suggest that the method should be generally applicable.

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 user-friendly 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 summarization 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 summarized in several ways, and new postprocessing plugins may also be installed.

Given a set D of input sequences, a genealogy for D can be constructed backward in time using such evolutionary events as mutation, coalescent, and recombination. An ancestral configuration (AC) can be regarded as the multiset of all sequences present at a particular point in time in a possible genealogy for D. The complexity of computing the likelihood of observing D depends heavily on the total number of distinct ACs of D and, therefore, it is of interest to estimate that number. For D consisting of binary sequences of finite length, we consider the problem of enumerating exactly all distinct ACs. We assume that the root sequence type is known and that the mutation process is governed by the infinite-sites model. When there is no recombination, we construct a general method of obtaining closed-form formulas for the total number of ACs. The enumeration problem becomes much more complicated when recombination is involved. In that case, we devise a method of enumeration based on counting contingency tables and construct a dynamic programming algorithm for the approach. Last, we describe a method of counting the number of ACs that can appear in genealogies with less than or equal to a given number R of recombinations. Of particular interest is the case in which R is close to the minimum number of recombinations for D.

MOTIVATION: Searching for non-coding RNA (ncRNA) genes and structural RNA elements (eleRNA) are major challenges in gene finding today as these often are conserved in structure rather than in sequence. Even though the number of available methods is growing, it is still of interest to pairwise detect two genes with low sequence similarity, where the genes are part of a larger genomic region. RESULTS: Here we present such an approach for pairwise local alignment which is based on foldalign and the Sankoff algorithm for simultaneous structural alignment of multiple sequences. We include the ability to conduct mutual scans of two sequences of arbitrary length while searching for common local structural motifs of some maximum length. This drastically reduces the complexity of the algorithm. The scoring scheme includes structural parameters corresponding to those available for free energy as well as for substitution matrices similar to RIBOSUM. The new foldalign implementation is tested on a dataset where the ncRNAs and eleRNAs have sequence similarity <40% and where the ncRNAs and eleRNAs are energetically indistinguishable from the surrounding genomic sequence context. The method is tested in two ways: (1) its ability to find the common structure between the genes only and (2) its ability to locate ncRNAs and eleRNAs in a genomic context. In case (1), it makes sense to compare with methods like Dynalign, and the performances are very similar, but foldalign is substantially faster. The structure prediction performance for a family is typically around 0.7 using Matthews correlation coefficient. In case (2), the algorithm is successful at locating RNA families with an average sensitivity of 0.8 and a positive predictive value of 0.9 using a BLAST-like hit selection scheme. AVAILABILITY: The program is available online at http://foldalign.kvl.dk/

RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g. as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactory in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots introduce modelling and computational problems. In this paper we consider the problem of predicting RNA secondary structure when certain types of pseudoknots are allowed. We first present an algorithm that in time Ο(n5) and space Ο(n3) predicts the secondary structure of an RNA sequence of length n in a model that allows certain kinds of pseudoknots. We then prove that the general problem of predicting RNA secondary structure containing pseudoknots is NP-complete for a large class of reasonable models of pseudoknots.

A pair in a string is the occurrence of the same substring twice. A pair is maximal if the two occurrences of the substring cannot be extended to the left and right without making them different. The gap of a pair is the number of characters between the two occurrences of the substring. In this paper we present methods for finding all maximal pairs under various constraints on the gap. In a string of length n we can find all maximal pairs with gap in an upper and lower bounded interval in time O(n log n + z) where z is the number of reported pairs. If the upper bound is removed the time reduces to O(n+z). Since a tandem repeat is a pair where the gap is zero, our methods can be seen as a generalization of finding tandem repeats. The running time of our methods equals the running time of well known methods for finding tandem repeats.

We present an analysis of currently used free energy functions for internal loop stability in RNA secondary structure. This analysis enables us to present an O(|s|³) algorithm for evaluating internal loops thus improving the overall complexity of RNA secondary structure prediction from O(|s|^4) to O(|s|³). Using an implementation of this algorithm we examine how reasonable a commonly used heuristic of limiting the size of internal loops evaluated has been.

MOTIVATION: Though not as abundant in known biological processes as proteins, RNA molecules serve as more than mere intermediaries between DNA and proteins. Research in the last 15 years demonstrates that RNA molecules serve in many roles, including catalysis. Furthermore, RNA secondary structure prediction based on free energy rules for stacking and loop formation remains one of the few major breakthroughs in the field of structure prediction, as minimum free energy structures and related quantities can be computed with full mathematical rigor. However, with the current energy parameters, the algorithms used hitherto suffer the disadvantage of either employing heuristics that risk (though highly unlikely) missing the optimal structure or becoming prohibitively time consuming for moderate to large sequences. RESULTS: We present a new method to evaluate internal loops utilizing currently used energy rules. This method reduces the time complexity of this part of the structure prediction from O(n4) to O(n3), thus reducing the overall complexity to O(n3). Even when the size of evaluated internal loops is bounded by k (a commonly used heuristic), the method presented has a competitive edge by reducing the time complexity of internal loop evaluation from O(k2n2) to O(kn2). The method also applies to the calculation of the equilibrium partition function. AVAILABILITY: Source code for an RNA secondary structure prediction program implementing this method is available at ftp://www.ibc.wustl.edu/pub/zuker/zuker .tar.Z