On the spectral radius and energy of signless Laplacian matrix of digraphs.

Let D be a digraph of order n and with a arcs. The signless Laplacian matrix Q ( D ) of D is defined as Q ( D ) = D e g ( D ) + A ( D ) , where A ( D ) is the adjacency matrix and D e g ( D ) is the diagonal matrix of vertex out-degrees of D. Among the eigenvalues of Q ( D ) the eigenvalue with largest modulus is the signless Laplacian spectral radius or the Q-spectral radius of D. The main contribution of this paper is a series of new lower bounds for the Q-spectral radius in terms of the number of vertices n, the number of arcs, the vertex out-degrees, the number of closed walks of length 2 of the digraph D. We characterize the extremal digraphs attaining these bounds. Further, as applications we obtain some bounds for the signless Laplacian energy of a digraph D and characterize the extremal digraphs for these bounds.

Structure, regulation, and host interaction of outer membrane protein U (OmpU) of Vibrio species.

OmpU is a multimeric, cation selective outer membrane protein of Vibrio and related species that non-covalently interact with peptidoglycan layer. Interaction of OmpU with human host cells triggers signaling pathways to promote cytokine secretion, reactive oxygen species production, and caspase independent death in immune and epithelial cells. Non-choleric OmpU imparts resistance to antimicrobial peptides and induces actin cytoskeletal reorganization in the host cells. Further, OmpU isolated from Vibrio species elicits an immune response in several aquaculture hosts. Importantly, in-vivo studies using recombinant OmpU or OmpU derived mimotopes reveal a short-lasting immunity, and protection against Vibrio in the aquaculture sector. In conclusion, OmpU is a key adhesion protein and an important virulence factor for successful colonization of Vibrio species into hosts. This review article provides a broad overview of structural, regulatory, and functional mechanisms of OmpU in normal and disease states.