The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

Pseudomonas aeruginosa mutants defective in glucose uptake have pleiotropic phenotype and altered virulence in non-mammal infection models

Pseudomonas spp. are endowed with a complex pathway for glucose uptake that relies on multiple transporters. In this work we report the construction and characterization of Pseudomonas aeruginosa single and multiple mutants with unmarked deletions of genes encoding outer membrane (OM) and inner membrane (IM) proteins involved in glucose uptake. We found that a triple \u394gltKGF \u394gntP \u394kguT mutant lacking all known IM transporters (named GUN for Glucose Uptake Null) is unable to grow on glucose as unique carbon source. More than 500 genes controlling both metabolic functions and virulence traits show differential expression in GUN relative to the parental strain. Consistent with transcriptomic data, the GUN mutant displays a pleiotropic phenotype. Notably, the genome-wide transcriptional profile and most phenotypic traits differ between the GUN mutant and the wild type strain irrespective of the presence of glucose, suggesting that the investigated genes may have additional roles besides glucose transport. Finally, mutants carrying single or multiple deletions in the glucose uptake genes showed attenuated virulence relative to the wild type strain in Galleria mellonella, but not in Caenorhabditis elegans infection model, supporting the notion that metabolic functions may deeply impact P. aeruginosa adaptation to specific environments found inside the host