The lysosome is the final destination for degradation of endocytic cargo, plasma membrane constituents, and intracellular components sequestered by macroautophagy. Fusion of endosomes and autophagosomes with the lysosome depends on the GTPase Rab7 and the homotypic fusion and protein sorting (HOPS) complex, but adaptor proteins that link endocytic and autophagy pathways with lysosomes are poorly characterized. Herein, we show that Pleckstrin homology domain containing protein family member 1 (PLEKHM1) directly interacts with HOPS complex and contains a LC3-interacting region (LIR) that mediates its binding to autophagosomal membranes. Depletion of PLEKHM1 blocks lysosomal degradation of endocytic (EGFR) cargo and enhances presentation of MHC class I molecules. Moreover, genetic loss of PLEKHM1 impedes autophagy flux upon mTOR inhibition and PLEKHM1 regulates clearance of protein aggregates in an autophagy- and LIR-dependent manner. PLEKHM1 is thus a multivalent endocytic adaptor involved in the lysosome fusion events controlling selective and nonselective autophagy pathways.
Analytic solutions of the Teukolsky equation in Kerr geometries are presented in the form of series of hypergeometric functions and Coulomb wave functions. Relations between these solutions are established. The solutions provide a very powerful method not only for examining the general properties of solutions and physical quantities when they are applied to, but also for numerical computations. The solutions are given in the expansion of a small parameter ǫ ≡ 2Mω, M being the mass of black hole, which corresponds to Post-Minkowski expansion by G and to post-Newtonian expansion when they are applied to the gravitational radiation from a particle in circular orbit around a black hole. It is expected that these solutions will become a powerful weapon to construct the theoretical template towards LIGO and VIRGO projects.
It is well known that the perturbation equations of massless fields for the Kerr-de Sitter geometry can be written in the form of separable equations. The equations have five definite singularities, so it has been thought that their analysis would be difficult. We show that these equations can be transformed into Heun's equations, for which we are able to use a known technique to analyze solutions. We reproduce known results for the Kerr geometry and de Sitter geometry in the confluent limits of Heun's functions. Our analysis can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and ~. §1. IntroductionOne of the most non-trivial aspects of the perturbation equations for Kerr geometry is the separability of the radial and the angular parts. Carter 1) first found that the scalar wave function is separable in the Kerr-Newman-de Sitter geometries. Later, this observation was extended for spin 1/2, electromagnetic fields, gravitational perturbations and gravitinos for the Kerr geometries and even for the Kerr-de Sitter class of geometries. These perturbation equations are called Teukolsky equations. 2 ) Except for electromagnetic and gravitational perturbations, the separability persists even for the Kerr-Newman-de Sitter solutions. An important application of this fact is the proof of the stability of the Kerr black hole. 3) Though the Teukolsky equations for Kerr geometries are separable, both spheroidal and radial equations have two regular singularities and one irregular singularity, so that the solutions cannot be written in a single form of any special functions, but they can be expressed as a series of special functions whose coefficients satisfy three term recurrence relations. 4) -7) The solution of the angular equation is expressed in the form of a series of Jacobi functions. 4 ) The solution of the radial equation is rather complicated, because we need a solution which is valid in the entire region extending from the outer horizon to infinity. The solutions are written in the form of a series of confluent hypergeometric functions 5) which are convergent around infinity and hypergeometric functions 6), 7) which are convergent around the outer horizon. By matching these solutions in the region where both solutions are convergent, we can obtain a solution which is valid from the outer horizon to infinity. 6)-8) The great benefit of this kind of solution is that the coefficients of the series are obtained through the post Minkowskian expansion. 6), 7) This technique has been *)
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