A mathematically rigorous definition of a global supermanifold is given. This forms an appropriate model for a global version of superspace, and a class of functions is defined which corresponds to superfields. This new construction is compared with several pre-existing definitions of supermanifold and graded manifold; it is shown to include all these definitions and to go beyond them, particularly in admitting the possibility of nontrivial topology in the anticommuting sector. Local differential geometry and potential applications to supergravity are considered.
The adaptor protein-2 sigma subunit (AP2σ2) is pivotal for clathrin-mediated endocytosis of plasma membrane constituents such as the calcium-sensing receptor (CaSR). Mutations of the AP2σ2 Arg15 residue result in familial hypocalciuric hypercalcaemia type 3 (FHH3), a disorder of extracellular calcium (Ca2+o) homeostasis. To elucidate the role of AP2σ2 in Ca2+o regulation, we investigated 65 FHH probands, without other FHH-associated mutations, for AP2σ2 mutations, characterized their functional consequences and investigated the genetic mechanisms leading to FHH3. AP2σ2 mutations were identified in 17 probands, comprising 5 Arg15Cys, 4 Arg15His and 8 Arg15Leu mutations. A genotype–phenotype correlation was observed with the Arg15Leu mutation leading to marked hypercalcaemia. FHH3 probands harboured additional phenotypes such as cognitive dysfunction. All three FHH3-causing AP2σ2 mutations impaired CaSR signal transduction in a dominant-negative manner. Mutational bias was observed at the AP2σ2 Arg15 residue as other predicted missense substitutions (Arg15Gly, Arg15Pro and Arg15Ser), which also caused CaSR loss-of-function, were not detected in FHH probands, and these mutations were found to reduce the numbers of CaSR-expressing cells. FHH3 probands had significantly greater serum calcium (sCa) and magnesium (sMg) concentrations with reduced urinary calcium to creatinine clearance ratios (CCCR) in comparison with FHH1 probands with CaSR mutations, and a calculated index of sCa × sMg/100 × CCCR, which was ≥ 5.0, had a diagnostic sensitivity and specificity of 83 and 86%, respectively, for FHH3. Thus, our studies demonstrate AP2σ2 mutations to result in a more severe FHH phenotype with genotype–phenotype correlations, and a dominant-negative mechanism of action with mutational bias at the Arg15 residue.
SummarySpatial control of G-protein-coupled receptor (GPCR) signaling, which is used by cells to translate complex information into distinct downstream responses, is achieved by using plasma membrane (PM) and endocytic-derived signaling pathways. The roles of the endomembrane in regulating such pleiotropic signaling via multiple G-protein pathways remain unknown. Here, we investigated the effects of disease-causing mutations of the adaptor protein-2 σ subunit (AP2σ) on signaling by the class C GPCR calcium-sensing receptor (CaSR). These AP2σ mutations increase CaSR PM expression yet paradoxically reduce CaSR signaling. Hypercalcemia-associated AP2σ mutations reduced CaSR signaling via Gαq/11 and Gαi/o pathways. The mutations also delayed CaSR internalization due to prolonged residency time of CaSR in clathrin structures that impaired or abolished endosomal signaling, which was predominantly mediated by Gαq/11. Thus, compartmental bias for CaSR-mediated Gαq/11 endomembrane signaling provides a mechanistic basis for multidimensional GPCR signaling.
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