Hard and easy instances of L-Tromino tilings

In this work we study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either remains NP-complete or has a polynomial time algorithm. First, we characterize the possibility of when an Aztec rectangle has an L-tromino tiling, and hence also an Aztec diamond; if an Aztec rectangle has an unknown number of defects or holes, however, the problem of deciding a tiling is NP-complete. Then, we study tilings of arbitrary regions where only 180∘ rotations of L-trominoes are available. For this particular case we show that deciding the existence of a tiling remains NP-complete; yet, if a region does not contain so-called “forbidden polyominoes” as subregions, then there exists a polynomial time algorithm for deciding a tiling

Multidrug efflux pumps:structure, function and regulation

Infections arising from multidrug-resistant pathogenic bacteria are spreading rapidly throughout the world and threaten to become untreatable. The origins of resistance are numerous and complex, but one underlying factor is the capacity of bacteria to rapidly export drugs through the intrinsic activity of efflux pumps. In this Review, we describe recent advances that have increased our understanding of the structures and molecular mechanisms of multidrug efflux pumps in bacteria. Clinical and laboratory data indicate that efflux pumps function not only in the drug extrusion process but also in virulence and the adaptive responses that contribute to antimicrobial resistance during infection. The emerging picture of the structure, function and regulation of efflux pumps suggests opportunities for countering their activities

The multidrug efflux pump MdtEF protects against nitrosative damage during the anaerobic respiration in Escherichia coli

Drug efflux represents an important protection mechanism in bacteria to withstand antibiotics and environmental toxic substances. Efflux genes constitute 6-18% of all transporters in bacterial genomes, yet the expression and functions of only a handful of them have been studied. Among the 20 efflux genes encoded in the Escherichia coli K-12 genome, only the AcrAB-TolC system is constitutively expressed. The expression, activities, and physiological functions of the remaining efflux genes are poorly understood. In this study we identified a dramatic up-regulation of an additional efflux pump, MdtEF, under the anaerobic growth condition of E. coli, which is independent of antibiotic exposure. We found that expression of MdtEF is upregulated more than 20-fold under anaerobic conditions by the global transcription factor ArcA, resulting in increased efflux activity and enhanced drug tolerance in anaerobically grown E. coli. Cells lacking mdtEF display a significantly decreased survival rate under the condition of anaerobic respiration of nitrate. Deletion of the genes responsible for the biosynthesis of indole, tnaAB, or replacing nitrate with fumarate as the terminal electron acceptor during the anaerobic respiration restores the decreased survival of ΔmdtEF cells. Moreover, ΔmdtEF cells are susceptible to indole nitrosative derivatives, a class of toxic byproducts formed and accumulated within E. coli when the bacterium respires nitrate under anaerobic conditions. Taken together, we conclude that the multidrug efflux pump MdtEF is up-regulated during the anaerobic physiology of E. coli to protect the bacterium from nitrosative damage through expelling the nitrosyl indole derivatives out of the cells. © 2011 by The American Society for Biochemistry and Molecular Biology, Inc.link_to_OA_fulltex