Localization via Quasi-Periodic Bulk-Bulk Correspondence

We report on a direct connection between quasi-periodic topology and the Almost Mathieu (Andre-Aubry) metal insulator transition (MIT). By constructing quasi-periodic transfer matrix equations from the limit of rational approximate projected Green's functions, we relate results from $\text{SL}(2,\mathbb{R})$ co-cycle theory (transfer matrix eigenvalue scaling) to consequences of rational band theory. This reduction links the eigenfunction localization of the MIT to the chiral edge modes of the Hofstadter Hamiltonian, implying the localized phase roots in a topological "bulk-bulk" correspondence, a bulk-boundary correspondence between the 1D AAH system (boundary) and its 2D parent Hamiltonian (bulk). This differentiates quasi-periodic localization from Anderson localization in disordered systems. Our results are widely applicable to systems beyond this paradigmatic model.Comment: 6+12 pages, 2+2 figures, 1 table. Companion paper to arXiv:2109.13933 concerning different themes and new results. Supplementary materials shared with arXiv:2109.13933, but kept for readability and completeness. arXiv admin note: substantial text overlap with arXiv:2109.1393

Characterization of Leishmania donovani Aquaporins Shows Presence of Subcellular Aquaporins Similar to Tonoplast Intrinsic Proteins of Plants

Leishmania donovani, a protozoan parasite, resides in the macrophages of the mammalian host. The aquaporin family of proteins form important components of the parasite-host interface. The parasite-host interface could be a potential target for chemotherapy. Analysis of L. major and L. infantum genomes showed the presence of five aquaporins (AQPs) annotated as AQP9 (230aa), AQP putative (294aa), AQP-like protein (279aa), AQP1 (314aa) and AQP-like protein (596aa). We report here the structural modeling, localization and functional characterization of the AQPs from L. donovani. LdAQP1, LdAQP9, LdAQP2860 and LdAQP2870 have the canonical NPA-NPA motifs, whereas LdAQP putative has a non-canonical NPM-NPA motif. In the carboxyl terminal to the second NPA box of all AQPs except AQP1, a valine/alanine residue was found instead of the arginine. In that respect these four AQPs are similar to tonoplast intrinsic proteins in plants, which are localized to intracellular organelles. Confocal microscopy of L. donovani expressing GFP-tagged AQPs showed an intracellular localization of LdAQP9 and LdAQP2870. Real-time PCR assays showed expression of all aquaporins except LdAQP2860, whose level was undetectable. Three-dimensional homology modeling of the AQPs showed that LdAQP1 structure bears greater topological similarity to the aquaglyceroporin than to aquaporin of E. coli. The pore of LdAQP1 was very different from the rest in shape and size. The cavity of LdAQP2860 was highly irregular and undefined in geometry. For functional characterization, four AQP proteins were heterologously expressed in yeast. In the fps1Δ yeast cells, which lacked the key aquaglyceroporin, LdAQP1 alone displayed an osmosensitive phenotype indicating glycerol transport activity. However, expression of LdAQP1 and LdAQP putative in a yeast gpd1Δ strain, deleted for glycerol production, conferred osmosensitive phenotype indicating water transport activity or aquaporin function. Our analysis for the first time shows the presence of subcellular aquaporins and provides structural and functional characterization of aquaporins in Leishmania donovani