Ana Casimiro

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.

An analysis of the positional distribution of DNA motifs in promoter regions and its biological relevance.

BackgroundMotif finding algorithms have developed in their ability to use computationally efficient methods to detect patterns in biological sequences. However the posterior classification of the output still suffers from some limitations, which makes it difficult to assess the biological significance of the motifs found. Previous work has highlighted the existence of positional bias of motifs in the DNA sequences, which might indicate not only that the pattern is important, but also provide hints of the positions where these patterns occur preferentially.ResultsWe propose to integrate position uniformity tests and over-representation tests to improve the accuracy of the classification of motifs. Using artificial data, we have compared three different statistical tests (Chi-Square, Kolmogorov-Smirnov and a Chi-Square bootstrap) to assess whether a given motif occurs uniformly in the promoter region of a gene. Using the test that performed better in this dataset, we proceeded to study the positional distribution of several well known cis-regulatory elements, in the promoter sequences of different organisms (S. cerevisiae, H. sapiens, D. melanogaster, E. coli and several Dicotyledons plants). The results show that position conservation is relevant for the transcriptional machinery.ConclusionWe conclude that many biologically relevant motifs appear heterogeneously distributed in the promoter region of genes, and therefore, that non-uniformity is a good indicator of biological relevance and can be used to complement over-representation tests commonly used. In this article we present the results obtained for the S. cerevisiae data sets.

Topology of moduli spaces of free group representations in real reductive groups

Let G be a real reductive algebraic group with maximal compact subgroup K, and let Fr be a rank r free group. We show that the space of closed orbits in Hom(Fr;G)=G admits a strong deformation retraction to the orbit space Hom(Fr;K)=K. In particular, all such spaces have the same homotopy type. We compute the Poincar e polynomials of these spaces for some low rank groups G, such as Sp(4;R) and U(2; 2). We also compare these real moduli spaces to the real points of the corresponding complex moduli spaces, and describe the geometry of many examples.

STABILITY OF AFFINE G-VARIETIES AND IRREDUCIBILITY IN REDUCTIVE GROUPS

Let G be a reductive affine algebraic group and let X be an affine algebraic G-variety. We establish a (poly)stability criterion for points x ∈ X in terms of intrinsically defined closed subgroups Hx of G and relate it with the numerical criterion of Mumford and with Richardson and Bate–Martin–Rohrle criteria, in the case X = GN. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson–Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.

Quotients on the Sato Grassmannian and the moduli of vector bundles

It is shown that there exists a geometric quotient of the subscheme of stable points of Gr(C((z)) ⊕r ) under the action of Sl(r, C). The consequences in terms of vector bundles on an algebraic curve are studied.