Tsukuba BB: a branch and bound algorithm for local multiple alignment of DNA and protein sequences.

In this paper we present a branch and bound algorithm for local gapless multiple sequence alignment (motif alignment) and its implementation. The algorithm uses both score-based bounding and a novel bounding technique based on the "consistency" of the alignment. A sequence order independent search tree is used in conjunction with a technique for avoiding redundant calculations inherent in the structure of the tree. This is the first program to exploit the fact that the motif alignment problem is easier for short motifs. Indeed, for a short fixed motif width, the running time of the algorithm is asymptotically linear in the size of the input. We tested the performance of the program on a dataset of 300 E. coli promoter sequences and a dataset of 85 lipocalin protein sequences. For a motif width of 4, the optimal alignment of the entire set of sequences can be found. For the more natural motif width of 6, the program can align 21 sequences of length 100, more than twice the number of sequences which can be aligned by the best previous exact algorithm. The algorithm can relax the constraint of requiring each sequence to be aligned, and align 105 of the 300 promoter sequences with a motif width of 6. For the lipocalin dataset, we introduce a technique for reducing the effective alphabet size with a minimal loss of useful information. With this technique, we show that the program can find meaningful motifs in a reasonable amount of time by optimizing the score over three motif positions.     

DNA motif representation with nucleotide dependency

The problem of discovering novel motifs of binding sites is important to the understanding of gene regulatory networks. Motifs are generally represented by matrices (position weight matrix (PWM) or position specific scoring matrix (PSSM) or strings. However, these representations cannot model biological binding sites well because they fail to capture nucleotide interdependence. It has been pointed out by many researchers that the nucleotides of the DNA binding site cannot be treated independently, e.g. the binding sites of zinc finger in proteins. In this paper, a new representation called Scored Position Specific Pattern (SPSP), which is a generalization of the matrix and string representations, is introduced which takes into consideration the dependent occurrences of neighboring nucleotides. Even though the problem of discovering the optimal motif in SPSP representation is proved to be NP-hard, we introduce a heuristic algorithm called SPSP-Finder, which can effectively find optimal motifs in most simulated cases and some real cases for which existing popular motif finding software, such as Weeder, MEME and AlignACE, fail.     

Relation between weight matrix and substitution matrix: motif search by similarity

MOTIVATION: The discovery of patterns shared by several sequences that differ greatly is a basic task in sequence analysis, and still a challenge. Several methods have been developed for detecting patterns. Methods commonly used for motif search include the Gibbs sampler, Expectation-Maximization (EM) algorithm and some intuitive greedy approaches. One cannot guarantee the optimality of the result produced by the Gibbs sampler in a single run. The deterministic EM methods tend to get trapped by local optima. Solutions found by greedy approaches are rarely sufficiently good. RESULTS: A simple model describing a motif or a portion of local multiple sequence alignment is the weight matrix model, in which a motif is characterized with position-specific probabilities. Two substitution matrices are proposed to relate the sequence similarity with the weight matrix. Combining the substitution matrix and weight matrix, we examine three typical sets of protein sequences with increasing complexity. At a low score threshold for pair similarity, sliding windows are compared with a seed window to find the score sum, which provides a measure of statistical significance for multiple sequence comparison. Such a similarity analysis reveals many aspects of motifs. Blocks determined by similarity can be used to deduce a primary weight matrix or an improved substitution matrix. The algorithm successfully obtains the optimal solution for the test sets by just greedy iteration.     

MotifCut: regulatory motifs finding with maximum density subgraphs

MOTIVATION: DNA motif finding is one of the core problems in computational biology, for which several probabilistic and discrete approaches have been developed. Most existing methods formulate motif finding as an intractable optimization problem and rely either on expectation maximization (EM) or on local heuristic searches. Another challenge is the choice of motif model: simpler models such as the position-specific scoring matrix (PSSM) impose biologically unrealistic assumptions such as independence of the motif positions, while more involved models are harder to parametrize and learn. RESULTS: We present MotifCut, a graph-theoretic approach to motif finding leading to a convex optimization problem with a polynomial time solution. We build a graph where the vertices represent all k-mers in the input sequences, and edges represent pairwise k-mer similarity. In this graph, we search for a motif as the maximum density subgraph, which is a set of k-mers that exhibit a large number of pairwise similarities. Our formulation does not make strong assumptions regarding the structure of the motif and in practice both motifs that fit well the PSSM model, and those that exhibit strong dependencies between position pairs are found as dense subgraphs. We benchmark MotifCut on both synthetic and real yeast motifs, and find that it compares favorably to existing popular methods. The ability of MotifCut to detect motifs appears to scale well with increasing input size. Moreover, the motifs we discover are different from those discovered by the other methods. AVAILABILITY: MotifCut server and other materials can be found at motifcut.stanford.edu.     

RankMotif++: a motif-search algorithm that accounts for relative ranks of K-mers in binding transcription factors

MOTIVATION: The sequence specificity of DNA-binding proteins is typically represented as a position weight matrix in which each base position contributes independently to relative affinity. Assessment of the accuracy and broad applicability of this representation has been limited by the lack of extensive DNA-binding data. However, new microarray techniques, in which preferences for all possible K-mers are measured, enable a broad comparison of both motif representation and methods for motif discovery. Here, we consider the problem of accounting for all of the binding data in such experiments, rather than the highest affinity binding data. We introduce the RankMotif++, an algorithm designed for finding motifs whenever sequences are associated with a semi-quantitative measure of protein-DNA-binding affinity. RankMotif++ learns motif models by maximizing the likelihood of a set of binding preferences under a probabilistic model of how sequence binding affinity translates into binding preference observations. Because RankMotif++ makes few assumptions about the relationship between binding affinity and the semi-quantitative readout, it is applicable to a wide variety of experimental assays of DNA-binding preference. RESULTS: By several criteria, RankMotif++ predicts binding affinity better than two widely used motif finding algorithms (MDScan, MatrixREDUCE) or more recently developed algorithms (PREGO, Seed and Wobble), and its performance is comparable to a motif model that separately assigns affinities to 8-mers. Our results validate the PWM model and provide an approximation of the precision and recall that can be expected in a genomic scan. AVAILABILITY: RankMotif++ is available upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Subtle motifs: defining the limits of motif finding algorithms

MOTIVATION: What constitutes a subtle motif? Intuitively, it is a motif that is almost indistinguishable, in the statistical sense, from random motifs. This question has important practical consequences: consider, for example, a biologist that is generating a sample of upstream regulatory sequences with the goal of finding a regulatory pattern that is shared by these sequences. If the sequences are too short then one risks losing some of the regulatory patterns that are located further upstream. Conversely, if the sequences are too long, the motif becomes too subtle and one is then likely to encounter random motifs which are at least as significant statistically as the regulatory pattern itself. In practical terms one would like to recognize the sequence length threshold, or the twilight zone, beyond which the motifs are in some sense too subtle. RESULTS: The paper defines the motif twilight zone where every motif finding algorithm would be exposed to random motifs which are as significant as the one which is sought. We also propose an objective tool for evaluating the performance of subtle motif finding algorithms. Finally we apply these tools to evaluate the success of our MULTIPROFILER algorithm to detect subtle motifs.     

MUSA: a parameter free algorithm for the identification of biologically significant motifs

MOTIVATION: The ability to identify complex motifs, i.e. non-contiguous nucleotide sequences, is a key feature of modern motif finders. Addressing this problem is extremely important, not only because these motifs can accurately model biological phenomena but because its extraction is highly dependent upon the appropriate selection of numerous search parameters. Currently available combinatorial algorithms have proved to be highly efficient in exhaustively enumerating motifs (including complex motifs), which fulfill certain extraction criteria. However, one major problem with these methods is the large number of parameters that need to be specified. RESULTS: We propose a new algorithm, MUSA (Motif finding using an UnSupervised Approach), that can be used either to autonomously find over-represented complex motifs or to estimate search parameters for modern motif finders. This method relies on a biclustering algorithm that operates on a matrix of co-occurrences of small motifs. The performance of this method is independent of the composite structure of the motifs being sought, making few assumptions about their characteristics. The MUSA algorithm was applied to two datasets involving the bacterium Pseudomonas putida KT2440. The first one was composed of 70 sigma(54)-dependent promoter sequences and the second dataset included 54 promoter sequences of up-regulated genes in response to phenol, as suggested by quantitative proteomics. The results obtained indicate that this approach is very effective at identifying complex motifs of biological significance. AVAILABILITY: The MUSA algorithm is available upon request from the authors, and will be made available via a Web based interface.     

RNAProfile: an algorithm for finding conserved secondary structure motifs in unaligned RNA sequences

The recent interest sparked due to the discovery of a variety of functions for non-coding RNA molecules has highlighted the need for suitable tools for the analysis and the comparison of RNA sequences. Many trans-acting non-coding RNA genes and cis-acting RNA regulatory elements present motifs, conserved both in structure and sequence, that can be hardly detected by primary sequence analysis alone. We present an algorithm that takes as input a set of unaligned RNA sequences expected to share a common motif, and outputs the regions that are most conserved throughout the sequences, according to a similarity measure that takes into account both the sequence of the regions and the secondary structure they can form according to base-pairing and thermodynamic rules. Only a single parameter is needed as input, which denotes the number of distinct hairpins the motif has to contain. No further constraints on the size, number and position of the single elements comprising the motif are required. The algorithm can be split into two parts: first, it extracts from each input sequence a set of candidate regions whose predicted optimal secondary structure contains the number of hairpins given as input. Then, the regions selected are compared with each other to find the groups of most similar ones, formed by a region taken from each sequence. To avoid exhaustive enumeration of the search space and to reduce the execution time, a greedy heuristic is introduced for this task. We present different experiments, which show that the algorithm is capable of characterizing and discovering known regulatory motifs in mRNA like the iron responsive element (IRE) and selenocysteine insertion sequence (SECIS) stem–loop structures. We also show how it can be applied to corrupted datasets in which a motif does not appear in all the input sequences, as well as to the discovery of more complex motifs in the non-coding RNA.     

Finding subtle motifs by branching from sample strings

Many motif finding algorithms apply local search techniques to a set of seeds. For example, GibbsDNA (Lawrence et al. 1993, Science, 262, 208-214) applies Gibbs sampling to random seeds, and MEME (Bailey and Elkan, 1994, Proceedings of the Second International Conference on Intelligent Systems for Molecular Biology (ISMB-94), 28-36) applies the EM algorithm to selected sample strings, i.e. substrings of the sample. In the case of subtle motifs, recent benchmarking efforts show that both random seeds and selected sample strings may never get close to the globally optimal motif. We propose a new approach which searches motif space by branching from sample strings, and implement this idea in both pattern-based and profile-based settings. Our PatternBranching and ProfileBranching algorithms achieve favorable results relative to other motif finding algorithms. Availability: http://www-cse.ucsd.edu/groups/bioinformatics/software.html     

CytoKavosh: A Cytoscape Plug-In for Finding Network Motifs in Large Biological Networks

Network motifs are small connected sub-graphs that have recently gathered much attention to discover structural behaviors of large and complex networks. Finding motifs with any size is one of the most important problems in complex and large networks. It needs fast and reliable algorithms and tools for achieving this purpose. CytoKavosh is one of the best choices for finding motifs with any given size in any complex network. It relies on a fast algorithm, Kavosh, which makes it faster than other existing tools. Kavosh algorithm applies some well known algorithmic features and includes tricky aspects, which make it an efficient algorithm in this field. CytoKavosh is a Cytoscape plug-in which supports us in finding motifs of given size in a network that is formerly loaded into the Cytoscape work-space (directed or undirected). High performance of CytoKavosh is achieved by dynamically linking highly optimized functions of Kavosh's C++ to the Cytoscape Java program, which makes this plug-in suitable for analyzing large biological networks. Some significant attributes of CytoKavosh is efficiency in time usage and memory and having no limitation related to the implementation in motif size. CytoKavosh is implemented in a visual environment Cytoscape that is convenient for the users to interact and create visual options to analyze the structural behavior of a network. This plug-in can work on any given network and is very simple to use and generates graphical results of discovered motifs with any required details. There is no specific Cytoscape plug-in, specific for finding the network motifs, based on original concept. So, we have introduced for the first time, CytoKavosh as the first plug-in, and we hope that this plug-in can be improved to cover other options to make it the best motif-analyzing tool.     

MotViz: a tool for sequence motif prediction in parallel to structural visualization and analyses

Linking similar proteins structurally is a challenging task that may help in finding the novel members of a protein family. In this respect, identification of conserved sequence can facilitate understanding and classifying the exact role of proteins. However, the exact role of these conserved elements cannot be elucidated without structural and physiochemical information. In this work, we present a novel desktop application MotViz designed for searching and analyzing the conserved sequence segments within protein structure. With MotViz, the user can extract a complete list of sequence motifs from loaded 3D structures, annotate the motifs structurally and analyze their physiochemical properties. The conservation value calculated for an individual motif can be visualized graphically. To check the efficiency, predicted motifs from the data sets of 9 protein families were analyzed and MotViz algorithm was more efficient in comparison to other online motif prediction tools. Furthermore, a database was also integrated for storing, retrieving and performing the detailed functional annotation studies. In summary, MotViz effectively predicts motifs with high sensitivity and simultaneously visualizes them into 3D strucures. Moreover, MotViz is user-friendly with optimized graphical parameters and better processing speed due to the inclusion of a database at the back end. MotViz is available at http://www.fi-pk.com/motviz.html.     

Finding a common motif of RNA sequences using genetic programming: the GeRNAMo system

We focus on finding a consensus motif of a set of homologous or functionally related RNA molecules. Recent approaches to this problem have been limited to simple motifs, require sequence alignment, and make prior assumptions concerning the data set. We use genetic programming to predict RNA consensus motifs based solely on the data set. Our system -- dubbed GeRNAMo (Genetic programming of RNA Motifs) -- predicts the most common motifs without sequence alignment and is capable of dealing with any motif size. Our program only requires the maximum number of stems in the motif, and if prior knowledge is available the user can specify other attributes of the motif (e.g., the range of the motif's minimum and maximum sizes), thereby increasing both sensitivity and speed. We describe several experiments using either ferritin iron response element (IRE); signal recognition particle (SRP); or microRNA sequences, showing that the most common motif is found repeatedly, and that our system offers substantial advantages over previous methods.     

A greedier approach for finding tag SNPs

MOTIVATION: Recent studies have shown that a small subset of Single Nucleotide Polymorphisms (SNPs) (called tag SNPs) is sufficient to capture the haplotype patterns in a high linkage disequilibrium region. To find the minimum set of tag SNPs, exact algorithms for finding the optimal solution could take exponential time. On the other hand, approximation algorithms are more efficient but may fail to find the optimal solution. RESULTS: We propose a hybrid method that combines the ideas of the branch-and-bound method and the greedy algorithm. This method explores larger solution space to obtain a better solution than a traditional greedy algorithm. It also allows the user to adjust the efficiency of the program and quality of solutions. This algorithm has been implemented and tested on a variety of simulated and biological data. The experimental results indicate that our program can find better solutions than previous methods. This approach is quite general since it can be used to adapt other greedy algorithms to solve their corresponding problems. AVAILABILITY: The program is available upon request.     

An O(N2) algorithm for discovering optimal Boolean pattern pairs

We consider the problem of finding the optimal combination of string patterns, which characterizes a given set of strings that have a numeric attribute value assigned to each string. Pattern combinations are scored based on the correlation between their occurrences in the strings and the numeric attribute values. The aim is to find the combination of patterns which is best with respect to an appropriate scoring function. We present an O(N²) time algorithm for finding the optimal pair of substring patterns combined with Boolean functions, where N is the total length of the sequences. The algorithm looks for all possible Boolean combinations of the patterns, e.g., patterns of the form p nland notq, which indicates that the pattern pair is considered to occur in a given string s, if p occurs in s, and q does not occur in s. An efficient implementation using suffix arrays is presented, and we further show that the algorithm can be adapted to find the best k-pattern Boolean combination in O(N^k) time. The algorithm is applied to mRNA sequence data sets of moderate size combined with their turnover rates for the purpose of finding regulatory elements that cooperate, complement, or compete with each other in enhancing and/or silencing mRNA decay