The DNA motif discovery problem abstracts the task of discovering short, conserved sites in genomic DNA. Pevzner and Sze recently described a precise combinatorial formulation of motif discovery that motivates the following algorithmic challenge: find twenty planted occurrences of a motif of length fifteen in roughly twelve kilobases of genomic sequence, where each occurrence of the motif differs from its consensus in four randomly chosen positions. Such "subtle" motifs, though statistically highly significant, expose a weakness in existing motif-finding algorithms, which typically fail to discover them. Pevzner and Sze introduced new algorithms to solve their (15,4)-motif challenge, but these methods do not scale efficiently to more difficult problems in the same family, such as the (14,4)-, (16,5)-, and (18,6)-motif problems. We introduce a novel motif-discovery algorithm, PROJECTION, designed to enhance the performance of existing motif finders using random projections of the input's substrings. Experiments on synthetic data demonstrate that PROJECTION remedies the weakness observed in existing algorithms, typically solving the difficult (14,4)-, (16,5)-, and (18,6)-motif problems. Our algorithm is robust to nonuniform background sequence distributions and scales to larger amounts of sequence than that specified in the original challenge. A probabilistic estimate suggests that related motif-finding problems that PROJECTION fails to solve are in all likelihood inherently intractable. We also test the performance of our algorithm on realistic biological examples, including transcription factor binding sites in eukaryotes and ribosome binding sites in prokaryotes.

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Finding motifs using random projections.

One of the greatest challenges that modern molecular biology is facing is the understanding of the complex mechanisms regulating gene expression. A fundamental step in this process requires the characterization of regulatory motifs playing key roles in the regulation of gene expression at transcriptional and post-transcriptional levels. In particular, transcription is modulated by the interaction of transcription factors with their corresponding binding sites. Weeder Web is a web interface to Weeder, an algorithm for the automatic discovery of conserved motifs in a set of related regulatory DNA sequences. The motifs found are in turn likely to be instances of binding sites for some transcription factor. Other than providing access to the program, the interface has been designed so to make usage of the program itself as simple as possible, and to require very little prior knowledge about the length and the conservation of the motifs to be found. In fact, the interface automatically starts different runs of the program, each one with different parameters, and provides the user with an overall summary of the results as well as some 'advice' on which motifs look more interesting according to their statistical significance and some simple considerations. The web interface is available at the address www.pesolelab.it by following the 'Tools' link.

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Weeder Web: discovery of transcription factor binding sites in a set of sequences from co-regulated genes

Pevzner and Sze [23] considered a precise version of the motif discovery problem and simultaneously issued an algorithmic challenge: find a motif M of length 15, where each planted instance differs from M in 4 positions. Whereas previous algorithms all failed to solve this (15,4)-motif problem. Pevzner and Sze introduced algorithms that succeeded. However, their algorithms failed to solve the considerably more difficult (14,4)-, (16,5)-, and (18,6)-motif problems.We introduce a novel motif discovery algorithm based on the use of random projections of the input's substrings. Experiments on simulated data demonstrate that this algorithm performs better than existing algorithms and, in particular, typically solves the difficult (14,4)-, (16,5)-, and (18,6)-motif problems quite efficiently. A probabilistic estimate shows that the small values of d for which the algorithm fails to recover the planted (l, d)-motif are in all likelihood inherently impossible to solve. We also present experimental results on realistic biological data by identifying ribosome binding sites in prokaryotes as well as a number of known transcriptional regulatory motifs in eukaryotes.

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Finding motifs using random projections

On-line construction of suffix trees

Background: Unraveling the mechanisms that regulate gene expression is a major challenge in biology. An important task in this challenge is to identify regulatory elements, especially the binding sites in deoxyribonucleic acid (DNA) for transcription factors. These binding sites are short DNA segments that are called motifs. Recent advances in genome sequence availability and in highthroughput gene expression analysis technologies have allowed for the development of computational methods for motif finding. As a result, a large number of motif finding algorithms have been implemented and applied to various motif models over the past decade. This survey reviews the latest developments in DNA motif finding algorithms. Results: Earlier algorithms use promoter sequences of coregulated genes from single genome and search for statistically overrepresented motifs. Recent algorithms are designed to use phylogenetic footprinting or orthologous sequences and also an integrated approach where promoter sequences of coregulated genes and phylogenetic footprinting are used. All the algorithms studied have been reported to correctly detect the motifs that have been previously detected by laboratory experimental approaches, and some algorithms were able to find novel motifs. However, most of these motif finding algorithms have been shown to work successfully in yeast and other lower organisms, but perform significantly worse in higher organisms. Conclusion: Despite considerable efforts to date, DNA motif finding remains a complex challenge for biologists and computer scientists. Researchers have taken many different approaches in developing motif discovery tools and the progress made in this area of research is very encouraging. Performance comparison of different motif finding tools and identification of the best tools have proven to be a difficult task because tools are designed based on algorithms and motif models that are diverse and complex and our incomplete understanding of the biology of regulatory mechanism does not always provide adequate evaluation of underlying algorithms over motif models.

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A survey of DNA motif finding algorithms.

This paper introduces two exact algorithms for extracting conserved structured motifs from a set of DNA sequences. Structured motifs may be described as an ordered collection of p ≥ 1 "boxes" (each box corresponding to one part of the structured motif), p substitution rates (one for each box) and p - 1 intervals of distance (one for each pair of successive boxes in the collection). The contents of the boxes - that is, the motifs themselves - are unknown at the start of the algorithm. This is precisely what the algorithms are meant to find. A suffix tree is used for finding such motifs. The algorithms are efficient enough to be able to infer site consensi, such as, for instance, promoter sequences or regulatory sites, from a set of unaligned sequences corresponding to the noncoding regions upstream from all genes of a genome. In particular, both algorithms time complexity scales linearly with N2n where n is the average length of the sequences and N their number. An application to the identification of prom...

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

We present in this paper an exact algorithm for motif extraction. Efficiency is achieved by means of an improvement in the algorithm and data structures that applies to the whole class of motif inference algorithms based on suffix trees. An average case complexity analysis shows a gain over the best known exact algorithm for motif extraction. A full implementation was developed and made available online. Experimental results show that the proposed algorithm is more than two times faster than the best known exact algorithm for motif extraction.

RISOTTO: fast extraction of motifs with mismatches

This paper introduces two exact algorithms for extracting conserved structured motifs from a set of DNA sequences. Structured motifs are composed of p g 2 parts separated by constrained spacers These algorithms use a suffix tree for fulfilling this task. They are efficient enough to be able to extract site consensus, such as promoter sequences, from a whole collection of non coding sequences extracted from a genome. In particular, their time complexity scales linearly with N2n where n is the average length of the sequences and N their number. An application with interesting results to the identification of promoter consensus sequences in bacterial genomes is shown.

Extracting structured motifs using a suffix tree—algorithms and application to promoter consensus identification

The subset X0={AAC,AAT,ACC,ATC,ATT,CAG,CTC,CTG,GAA,GAC,GAG,GAT,GCC,GGC,GGT,GTA,GTC,GTT,TAC,TTC} of 20 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. This subset X0 is a complementary maximal circular code with two permutated maximal circular codes X1 and X2 in the frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5′–3′ direction). X0 is called a C3 code (Arques and Michel, 1997, J. Biosyst 44, 107–134). A quantitative study of these three subsets X0, X1 and X2 in the three frames 0, 1 and 2 of eukaryotic protein genes shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of X0, X1 and X2 in the frame 0 of eukaryotic protein genes are 48.5%, 29% and 22.5% respectively. These properties are not observed in the 5′ and 3′ regions of eukaryotes where X0, X1 and X2 occur with variable frequencies around the random value (1/3). Several frequency asymmetries unexpectedly observed, e.g. the frequency difference between X1 and X2 in the frame 0, are related to a new property of the C3 code X0 involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 20 codons (trinucleotides in the frame 0) of X0 with equiprobability (1/20) followed by t≈4 substitutions per codon according to the proportions p≈0.1, q≈0.1 and r=1−p−q≈0.8 in the three codon sites respectively, retrieves the frequencies of X0, X1 and X2 observed in the three frames of protein genes and explains these asymmetries. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine. Finally, the evolutionary analytical method developed could be applied to the phylogenetic tree reconstruction and the DNA sequence alignment.

Laurent Marsan

Papers

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

RISOTTO: fast extraction of motifs with mismatches

Extracting structured motifs using a suffix tree—algorithms and application to promoter consensus identification

An evolutionary analytical model of a complementary circular code.

RISOTTO : Fast extraction of motifs with mismatches