Lightweight comparison of RNAs based on exact sequence–structure matches

Motivation: Specific functions of ribonucleic acid (RNA) molecules are often associated with different motifs in the RNA structure. The key feature that forms such an RNA motif is the combination of sequence and structure properties. In this article, we introduce a new RNA sequence–structure comparison method which maintains exact matching substructures. Existing common substructures are treated as whole unit while variability is allowed between such structural motifs

Bounded Coordinate-Descent for Biological Sequence Classification in High Dimensional Predictor Space

We present a framework for discriminative sequence classification where the learner works directly in the high dimensional predictor space of all subsequences in the training set. This is possible by employing a new coordinate-descent algorithm coupled with bounding the magnitude of the gradient for selecting discriminative subsequences fast. We characterize the loss functions for which our generic learning algorithm can be applied and present concrete implementations for logistic regression (binomial log-likelihood loss) and support vector machines (squared hinge loss). Application of our algorithm to protein remote homology detection and remote fold recognition results in performance comparable to that of state-of-the-art methods (e.g., kernel support vector machines). Unlike state-of-the-art classifiers, the resulting classification models are simply lists of weighted discriminative subsequences and can thus be interpreted and related to the biological problem

Chromosome Descrambling Order Analysis in ciliates

Ciliates are a type of unicellular eukaryotic organism that has two types of nuclei within each cell; one is called the macronucleus (MAC) and the other is known as the micronucleus (MIC). During mating, ciliates exchange their MIC, destroy their own MAC, and create a new MAC from the genetic material of their new MIC. The process of developing a new MAC from the exchanged new MIC is known as gene assembly in ciliates, and it consists of a massive amount of DNA excision from the micronucleus, and the rearrangement of the rest of the DNA sequences. During the gene assembly process, the DNA segments that get eliminated are known as internal eliminated segments (IESs), and the remaining DNA segments that are rearranged in an order that is correct for creating proteins, are called macronuclear destined segments (MDSs). A topic of interest is to predict the correct order to descramble a gene or chromosomal segment. A prediction can be made based on the principle of parsimony, whereby the smallest sequence of operations is likely close to the actual number of operations that occurred. Interestingly, the order of MDSs in the newly assembled 22,354 Oxytricha trifallax MIC chromosome fragments provides evidence that multiple parallel recombinations occur, where the structure of the chromosomes allows for interleaving between two sections of the developing macronuclear chromosome in a manner that can be captured with a common string operation called the shuffle operation (the shuffle operation on two strings results in a new string by weaving together the first two, while preserving the order within each string). Thus, we studied four similar systems involving applications of shuffle to see how the minimum number of operations needed to assemble differs between the types. Two algorithms for each of the first two systems have been implemented that are both shown to be optimal. And, for the third and fourth systems, four and two heuristic algorithms, respectively, have been implemented. The results from these algorithms revealed that, in most cases, the third system gives the minimum number of applications of shuffle to descramble, but whether the best implemented algorithm for the third system is optimal or not remains an open question. The best implemented algorithm for the third system showed that 96.63% of the scrambled micronuclear chromosome fragments of Oxytricha trifallax can be descrambled by only 1 or 2 applications of shuffle. This small number of steps lends theoretical evidence that some structural component is enforcing an alignment of segments in a shuffle-like fashion, and then parallel recombination is taking place to enable MDS rearrangement and IES elimination. Another problem of interest is to classify segments of the MIC into MDSs and IESs; this is the second topic of the thesis, and is a matter of determining the right "class label", i.e. MDS or IES, on each nucleotide. Thus, training data of labelled input sequences was used with hidden Markov models (HMMs), which is a well-known supervised machine learning classification algorithm. HMMs of first-, second-, third-, fourth-, and fifth-order have been implemented. The accuracy of the classification was verified through 10-fold cross validation. Results from this work show that an HMM is more likely to fail to accurately classify micronuclear chromosomes without having some additional knowledge

Fast Pairwise Structural RNA Alignments by Pruning of the Dynamical Programming Matrix

It has become clear that noncoding RNAs (ncRNA) play important roles in cells, and emerging studies indicate that there might be a large number of unknown ncRNAs in mammalian genomes. There exist computational methods that can be used to search for ncRNAs by comparing sequences from different genomes. One main problem with these methods is their computational complexity, and heuristics are therefore employed. Two heuristics are currently very popular: pre-folding and pre-aligning. However, these heuristics are not ideal, as pre-aligning is dependent on sequence similarity that may not be present and pre-folding ignores the comparative information. Here, pruning of the dynamical programming matrix is presented as an alternative novel heuristic constraint. All subalignments that do not exceed a length-dependent minimum score are discarded as the matrix is filled out, thus giving the advantage of providing the constraints dynamically. This has been included in a new implementation of the FOLDALIGN algorithm for pairwise local or global structural alignment of RNA sequences. It is shown that time and memory requirements are dramatically lowered while overall performance is maintained. Furthermore, a new divide and conquer method is introduced to limit the memory requirement during global alignment and backtrack of local alignment. All branch points in the computed RNA structure are found and used to divide the structure into smaller unbranched segments. Each segment is then realigned and backtracked in a normal fashion. Finally, the FOLDALIGN algorithm has also been updated with a better memory implementation and an improved energy model. With these improvements in the algorithm, the FOLDALIGN software package provides the molecular biologist with an efficient and user-friendly tool for searching for new ncRNAs. The software package is available for download at http://foldalign.ku.dk

RNA structure analysis : algorithms and applications

In this doctoral thesis, efficient algorithms for aligning RNA secondary structures and mining unknown RNA motifs are presented. As the major contribution, a structure alignment algorithm, which combines both primary and secondary structure information, can find the optimal alignment between two given structures where one of them could be either a pattern structure of a known motif or a real query structure and the other be a subject structure. Motivated by widely used algorithms for RNA folding, the proposed algorithm decomposes an RNA secondary structure into a set of atomic structural components that can be further organized in a tree model to capture the structural particularities. The novel structure alignment algorithm is implemented using dynamic programming techniques coupled by position-independent scoring matrices. The algorithm can find the optimal global and local alignments between two RNA secondary structures at quadratic time complexity. When applied to searching a structure database, the algorithm can find similar RNA substructures and therefore can be used to identify functional RNA motifs. Extension of the algorithm has also been accomplished to deal with position-dependent scoring matrix in the purpose of aligning multiple structures. All algorithms have been implemented in a package under the name RSmatch and applied to searching mRNA UTR structure database and mining RNA motifs. The experimental results showed high efficiency and effectiveness of the proposed techniques

An exact mathematical programming approach to multiple RNA sequence-structure alignment

One of the main tasks in computational biology is the computation of alignments of genomic sequences to reveal their commonalities. In case of DNA or protein sequences, sequence information alone is usually sufficient to compute reliable alignments. RNA molecules, however, build spatial conformations—the secondary structure—that are more conserved than the actual sequence. Hence, computing reliable alignments of RNA molecules has to take into account the secondary structure. We present a novel framework for the computation of exact multiple sequence-structure alignments: We give a graph- theoretic representation of the sequence-structure alignment problem and phrase it as an integer linear program. We identify a class of constraints that make the problem easier to solve and relax the original integer linear program in a Lagrangian manner. Experiments on a recently published benchmark show that our algorithms has a comparable performance than more costly dynamic programming algorithms, and outperforms all other approaches in terms of solution quality with an increasing number of input sequences

Fast Arc-Annotated Subsequence Matching in Linear Space

An arc-annotated string is a string of characters, called bases, augmented with a set of pairs, called arcs, each connecting two bases. Given arc-annotated strings $P$ and $Q$ the arc-preserving subsequence problem is to determine if $P$ can be obtained from $Q$ by deleting bases from $Q$. Whenever a base is deleted any arc with an endpoint in that base is also deleted. Arc-annotated strings where the arcs are ``nested'' are a natural model of RNA molecules that captures both the primary and secondary structure of these. The arc-preserving subsequence problem for nested arc-annotated strings is basic primitive for investigating the function of RNA molecules. Gramm et al. [ACM Trans. Algorithms 2006] gave an algorithm for this problem using $O(nm)$ time and space, where $m$ and $n$ are the lengths of $P$ and $Q$, respectively. In this paper we present a new algorithm using $O(nm)$ time and $O(n + m)$ space, thereby matching the previous time bound while significantly reducing the space from a quadratic term to linear. This is essential to process large RNA molecules where the space is likely to be a bottleneck. To obtain our result we introduce several novel ideas which may be of independent interest for related problems on arc-annotated strings.Comment: To appear in Algoritmic