Universal microscopic correlation functions for products of independent Ginibre matrices

We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process as in the case of a single Ginibre matrix, but with a more complicated weight given by a Meijer G-function depending on n. Using the method of orthogonal polynomials we compute all eigenvalue density correlation functions exactly for finite N and fixed n. They are given by the determinant of the corresponding kernel which we construct explicitly. In the large-N limit at fixed n we first determine the microscopic correlation functions in the bulk and at the edge of the spectrum. After unfolding they are identical to that of the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic correlations we find at the origin differ for each n>1 and generalise the known Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde

One-component plasma on a spherical annulus and a random matrix ensemble

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with \beta = 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.Comment: v2, typos and references corrected, 24 pages, 1 figur

Chemical Genetic Analysis and Functional Characterization of Staphylococcal Wall Teichoic Acid 2-Epimerases Reveals Unconventional Antibiotic Drug Targets

Here we describe a chemical biology strategy performed in Staphylococcus aureus and Staphylococcus epidermidis to identify MnaA, a 2-epimerase that we demonstrate interconverts UDP-GlcNAc and UDP-ManNAc to modulate substrate levels of TarO and TarA wall teichoic acid (WTA) biosynthesis enzymes. Genetic inactivation of mnaA results in complete loss of WTA and dramatic in vitro β-lactam hypersensitivity in methicillin-resistant S. aureus (MRSA) and S. epidermidis (MRSE). Likewise, the β-lactam antibiotic imipenem exhibits restored bactericidal activity against mnaA mutants in vitro and concomitant efficacy against 2-epimerase defective strains in a mouse thigh model of MRSA and MRSE infection. Interestingly, whereas MnaA serves as the sole 2-epimerase required for WTA biosynthesis in S. epidermidis, MnaA and Cap5P provide compensatory WTA functional roles in S. aureus. We also demonstrate that MnaA and other enzymes of WTA biosynthesis are required for biofilm formation in MRSA and MRSE. We further determine the 1.9Å crystal structure of S. aureus MnaA and identify critical residues for enzymatic dimerization, stability, and substrate binding. Finally, the natural product antibiotic tunicamycin is shown to physically bind MnaA and Cap5P and inhibit 2-epimerase activity, demonstrating that it inhibits a previously unanticipated step in WTA biosynthesis. In summary, MnaA serves as a new Staphylococcal antibiotic target with cognate inhibitors predicted to possess dual therapeutic benefit: as combination agents to restore β-lactam efficacy against MRSA and MRSE and as non-bioactive prophylactic agents to prevent Staphylococcal biofilm formation.publishe

Analyzing multitarget activity landscapes using protein-ligand interaction fingerprints: interaction cliffs.

This is the original submitted version, before peer review. The final peer-reviewed version is available from ACS at http://pubs.acs.org/doi/abs/10.1021/ci500721x.Activity landscape modeling is mostly a descriptive technique that allows rationalizing continuous and discontinuous SARs. Nevertheless, the interpretation of some landscape features, especially of activity cliffs, is not straightforward. As the nature of activity cliffs depends on the ligand and the target, information regarding both should be included in the analysis. A specific way to include this information is using protein-ligand interaction fingerprints (IFPs). In this paper we report the activity landscape modeling of 507 ligand-kinase complexes (from the KLIFS database) including IFP, which facilitates the analysis and interpretation of activity cliffs. Here we introduce the structure-activity-interaction similarity (SAIS) maps that incorporate information on ligand-target contact similarity. We also introduce the concept of interaction cliffs defined as ligand-target complexes with high structural and interaction similarity but have a large potency difference of the ligands. Moreover, the information retrieved regarding the specific interaction allowed the identification of activity cliff hot spots, which help to rationalize activity cliffs from the target point of view. In general, the information provided by IFPs provides a structure-based understanding of some activity landscape features. This paper shows examples of analyses that can be carried out when IFPs are added to the activity landscape model.M-L is very grateful to CONACyT (No. 217442/312933) and the Cambridge Overseas Trust for funding. AB thanks Unilever for funding and the European Research Council for a Starting Grant (ERC-2013- StG-336159 MIXTURE). J.L.M-F. is grateful to the School of Chemistry, Department of Pharmacy of the National Autonomous University of Mexico (UNAM) for support. This work was supported by a scholarship from the Secretariat of Public Education and the Mexican government

Cobalamin in inflammation III — glutathionylcobalamin and methylcobalamin/adenosylcobalamin coenzymes: the sword in the stone? How cobalamin may directly regulate the nitric oxide synthases

Several mysteries surround the structure and function of the nitric oxide synthases (NOS). The NOS oxygenase domain structure is unusually open with a large area of solvent that could accommodate an unidentified ligand. The exact mechanism of the two-step five-electron monoxygenation of arginine to NG-hydroxy-L-arginine, thence to citrulline and nitric oxide (NO), is not clear, particularly as arginine/NG-hydroxy-L-arginine is bound at a great distance to the supposed catalytic heme Fe [III], as the anti-stereoisomer. The Return of the Scarlet Pimpernel Paper proposed that cobalamin is a primary indirect regulator of the NOS. An additional direct regulatory effect of the ‘base-off’ dimethylbenzimidazole of glutathionylcobalamin (GSCbl), which may act as a sixth ligand to the heme iron, promote Co-oriented, BH4/BH3 radical catalysed oxidation of L-arginine to NO, and possibly regulate the rate of inducible NOS/NO production by the NOS dimers, is further advanced. The absence of homology between the NOS and methionine synthase/methylmalonyl CoA mutase may enable GSCbl to regulate both sets of enzymes simultaneously by completely separate mechanisms. Thus, cobalamin may exert central control over both pro-and anti-inflammatory systems