Fast algorithms for computing sequence distances by exhaustive substring composition

The increasing throughput of sequencing raises growing needs for methods of sequence analysis and comparison on a genomic scale, notably, in connection with phylogenetic tree reconstruction. Such needs are hardly fulfilled by the more traditional measures of sequence similarity and distance, like string edit and gene rearrangement, due to a mixture of epistemological and computational problems. Alternative measures, based on the subword composition of sequences, have emerged in recent years and proved to be both fast and effective in a variety of tested cases. The common denominator of such measures is an underlying information theoretic notion of relative compressibility. Their viability depends critically on computational cost. The present paper describes as a paradigm the extension and efficient implementation of one of the methods in this class. The method is based on the comparison of the frequencies of all subwords in the two input sequences, where frequencies are suitably adjusted to take into account the statistical background.     

VARUN: discovering extensible motifs under saturation constraints

The discovery of motifs in biosequences is frequently torn between the rigidity of the model on one hand and the abundance of candidates on the other hand. In particular, motifs that include wild cards or "don't cares" escalate exponentially with their number, and this gets only worse if a don't care is allowed to stretch up to some prescribed maximum length. In this paper, a notion of extensible motif in a sequence is introduced and studied, which tightly combines the structure of the motif pattern, as described by its syntactic specification, with the statistical measure of its occurrence count. It is shown that a combination of appropriate saturation conditions and the monotonicity of probabilistic scores over regions of constant frequency afford us significant parsimony in the generation and testing of candidate overrepresented motifs. A suite of software programs called Varun is described, implementing the discovery of extensible motifs of the type considered. The merits of the method are then documented by results obtained in a variety of experiments primarily targeting protein sequence families. Of equal importance seems the fact that the sets of all surprising motifs returned in each experiment are extracted faster and come in much more manageable sizes than would be obtained in the absence of saturation constraints.     

Efficient algorithms for the discovery of gapped factors

Background

With an increasing number of plant genome sequences, it has become important to develop a robust computational method for detecting plant promoters. Although a wide variety of programs are currently available, prediction accuracy of these still requires further improvement. The limitations of these methods can be addressed by selecting appropriate features for distinguishing promoters and non-promoters.

Methods

In this study, we proposed two feature selection approaches based on hexamer sequences: the Frequency Distribution Analyzed Feature Selection Algorithm (FDAFSA) and the Random Triplet Pair Feature Selecting Genetic Algorithm (RTPFSGA). In FDAFSA, adjacent triplet-pairs (hexamer sequences) were selected based on the difference in the frequency of hexamers between promoters and non-promoters. In RTPFSGA, random triplet-pairs (RTPs) were selected by exploiting a genetic algorithm that distinguishes frequencies of non-adjacent triplet pairs between promoters and non-promoters. Then, a support vector machine (SVM), a nonlinear machine-learning algorithm, was used to classify promoters and non-promoters by combining these two feature selection approaches. We referred to this novel algorithm as PromoBot.

Results

Promoter sequences were collected from the PlantProm database. Non-promoter sequences were collected from plant mRNA, rRNA, and tRNA of PlantGDB and plant miRNA of miRBase. Then, in order to validate the proposed algorithm, we applied a 5-fold cross validation test. Training data sets were used to select features based on FDAFSA and RTPFSGA, and these features were used to train the SVM. We achieved 89% sensitivity and 86% specificity.

Conclusions

We compared our PromoBot algorithm to five other algorithms. It was found that the sensitivity and specificity of PromoBot performed well (or even better) with the algorithms tested. These results show that the two proposed feature selection methods based on hexamer frequencies and random triplet-pair could be successfully incorporated into a supervised machine learning method in promoter classification problem. As such, we expect that PromoBot can be used to help identify new plant promoters. Source codes and analysis results of this work could be provided upon request.     

Efficient algorithms for the discovery of gapped factors

Background  

The discovery of surprisingly frequent patterns is of paramount interest in bioinformatics and computational biology. Among the patterns considered, those consisting of pairs of solid words that co-occur within a prescribed maximum distance -or gapped factors- emerge in a variety of contexts of DNA and protein sequence analysis. A few algorithms and tools have been developed in connection with specific formulations of the problem, however, none can handle comprehensively each of the multiple ways in which the distance between the two terms in a pair may be defined.     

Incremental paradigms of motif discovery.

We examine the problem of extracting maximal irredundant motifs from a string. A combinatorial argument poses a linear bound on the total number of such motifs, thereby opening the way to the quest for the fastest and most efficient methods of extraction. The basic paradigm explored here is that of iterated updates of the set of irredundant motifs in a string under consecutive unit symbol extensions of the string itself. This approach exposes novel characterizations for the base set of motifs in a string, hinged on notions of partial order. Such properties support the design of ad hoc data structures and constructs, and lead to develop an O(n(3)) time incremental discovery algorithm.     

Optimal amnesic probabilistic automata or how to learn and classify proteins in linear time and space.

Statistical modeling of sequences is a central paradigm of machine learning that finds multiple uses in computational molecular biology and many other domains. The probabilistic automata typically built in these contexts are subtended by uniform, fixed-memory Markov models. In practice, such automata tend to be unnecessarily bulky and computationally imposing both during their synthesis and use. Recently, D. Ron, Y. Singer, and N. Tishby built much more compact, tree-shaped variants of probabilistic automata under the assumption of an underlying Markov process of variable memory length. These variants, called Probabilistic Suffix Trees (PSTs) were subsequently adapted by G. Bejerano and G. Yona and applied successfully to learning and prediction of protein families. The process of learning the automaton from a given training set S of sequences requires theta(Ln2) worst-case time, where n is the total length of the sequences in S and L is the length of a longest substring of S to be considered for a candidate state in the automaton. Once the automaton is built, predicting the likelihood of a query sequence of m characters may cost time theta(m2) in the worst case. The main contribution of this paper is to introduce automata equivalent to PSTs but having the following properties: Learning the automaton, for any L, takes O (n) time. Prediction of a string of m symbols by the automaton takes O (m) time. Along the way, the paper presents an evolving learning scheme and addresses notions of empirical probability and related efficient computation, which is a by-product possibly of more general interest.     

Mining, compressing and classifying with extensible motifs

Background  

Motif patterns of maximal saturation emerged originally in contexts of pattern discovery in biomolecular sequences and have recently proven a valuable notion also in the design of data compression schemes. Informally, a motif is a string of intermittently solid and wild characters that recurs more or less frequently in an input sequence or family of sequences. Motif discovery techniques and tools tend to be computationally imposing, however, special classes of "rigid" motifs have been identified of which the discovery is affordable in low polynomial time.