Non-additivity in protein-DNA binding.

MOTIVATION: Localizing protein binding sites within genomic DNA is of considerable importance, but remains difficult for protein families, such as transcription factors, which have loosely defined target sequences. It is generally assumed that protein affinity for DNA involves additive contributions from successive nucleotide pairs within the target sequence. This is not necessarily true, and non-additive effects have already been experimentally demonstrated in a small number of cases. The principal origin of non-additivity involves the so-called indirect component of protein-DNA recognition which is related to the sequence dependence of DNA deformation induced during complex formation. Non-additive effects are difficult to study because they require the identification of many more binding sequences than are normally necessary for describing additive specificity (typically via the construction of weight matrices). RESULTS: In the present work we will use theoretically estimated binding energies as a basis for overcoming this problem. Our approach enables us to study the full combinatorial set of sequences for a variety of DNA-binding proteins, make a detailed analysis of non-additive effects and exploit this information to improve binding site predictions using either weight matrices or support vector machines. The results underline the fact that, even in the presence of significant deformation, non-additive effects may involve only a limited number of dinucleotide steps. This information helps to reduce the number of binding sites which need to be identified for successful predictions and to avoid problems of over-fitting. AVAILABILITY: The SVM software is available upon request from the authors.

Distributions of singular values for some random matrices.

The singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of singular values of low-rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic and saddle point integration techniques, we extend these results to heterogeneous and correlated noise sources. We also provide perturbative estimates of error bars on the reconstructed low-rank matrix obtained by truncating a singular value decomposition.