A Bregman-proximal point algorithm for robust non-negative matrix factorization with possible missing values and outliers - application to gene expression analysis.

BACKGROUND: Non-Negative Matrix factorization has become an essential tool for feature extraction in a wide spectrum of applications. In the present work, our objective is to extend the applicability of the method to the case of missing and/or corrupted data due to outliers. RESULTS: An essential property for missing data imputation and detection of outliers is that the uncorrupted data matrix is low rank, i.e. has only a small number of degrees of freedom. We devise a new version of the Bregman proximal idea which preserves nonnegativity and mix it with the Augmented Lagrangian approach for simultaneous reconstruction of the features of interest and detection of the outliers using a sparsity promoting ℓ 1 penality. CONCLUSIONS: An application to the analysis of gene expression data of patients with bladder cancer is finally proposed.

Incidence of partial charges on ion selectivity in potassium channels.

Potassium channels are membrane proteins known to select potassium over sodium ions at a high diffusion rate. We conducted ab initio calculations on a filter model of KcsA of about 300 atoms at the Hartree-Fock level of theory. Partial charges were derived from the quantum mechanically determined electrostatic potential either with Merz-Kollman or Hinsen-Roux schemes. Large polarization and/or charge transfer occur on potassium ions located in the filter, while the charges on sodium ions remain closer to unity. As a result, a weaker binding is obtained for K(+) ions. Using a simplified version of a permeation model based on the concerted-motion mechanism for ion translocation within the single-file ion channel [P. H. Nelson, J. Chem. Phys. 117, 11396 (2002)], we discuss how differences in polarization effects in the adducts with K(+) and Na(+) can play a role as for ionic selectivity and conductance.

Reaction between ellagic acid and an ultimate carcinogen.

The reaction coordinate between a typical ultimate carcinogen benzo[a]pyrene-7,8-diol-9,10-epoxide (BPDE) and ellagic acid, a proven chemopreventive agent active against cancers caused by polycyclic aromatic hydrocarbons (PAHs), was examined by density functional theory (DFT) and semiempirical MO calculations, and activation energy was calculated. The effect of a polar environment was included using Tomasi and the Langevin dipoles methods. The calculated BPDE/ellagic acid reaction free energy of activation is found to be in decent agreement with experimental data [Sayer, J. M. et al. J. Am. Chem. Soc. 1982, 104, 5562-5564]. This work sheds light on the mechanism of action of ellagic acid. Quantum chemical calculations of this kind are valuable for the design of ellagic acid derivatives with even lower activation energy and increased reactivity toward ultimate carcinogens as well as controlled reactivity toward DNA.