Trace as an alternative decategorification functor

Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" functor. Algebras are typically categorified to additive categories with additional structure and decategorification is usually given by the (split) Grothendieck group. In this expository article we study an alternative decategorification functor given by the trace or the zeroth Hochschild--Mitchell homology. We show that this form of decategorification endows any 2-representation of the categorified quantum sl(n) with an action of the current algebra U(sl(n)[t]) on its center.Comment: 47 pages with tikz figures. arXiv admin note: text overlap with arXiv:1405.5920 by other author

IQGAP1 Interacts with Components of the Slit Diaphragm Complex in Podocytes and Is Involved in Podocyte Migration and Permeability In Vitro

IQGAP1 is a scaffold protein that interacts with proteins of the cytoskeleton and the intercellular adhesion complex. In podocytes, IQGAP1 is associated with nephrin in the glomerular slit diaphragm (SD) complex, but its role remains ill-defined. In this work, we investigated the interaction of IQGAP1 with the cytoskeleton and SD proteins in podocytes in culture, and its role in podocyte migration and permeability. Expression, localization, and interactions between IQGAP1 and SD or cytoskeletal proteins were determined in cultured human podocytes by Western blot (WB), immunocytolocalization (IC), immunoprecipitation (IP), and In situ Proximity Ligation assay (IsPL). Involvement of IQGAP1 in migration and permeability was also assessed. IQGAP1 expression in normal kidney biopsies was studied by immunohistochemistry. IQGAP1 expression by podocytes increased during their in vitro differentiation. IC, IP, and IsPL experiments showed colocalizations and/or interactions between IQGAP1 and SD proteins (nephrin, MAGI-1, CD2AP, NCK 1/2, podocin), podocalyxin, and cytoskeletal proteins (α-actinin-4). IQGAP1 silencing decreased podocyte migration and increased the permeability of a podocyte layer. Immunohistochemistry on normal human kidney confirmed IQGAP1 expression in podocytes and distal tubular epithelial cells and also showed an expression in glomerular parietal epithelial cells. In summary, our results suggest that IQGAP1, through its interaction with components of SD and cytoskeletal proteins, is involved in podocyte barrier properties

Phosphatidylinositol 3-Kinase Couples Localised Calcium Influx to Activation of Akt in Central Nerve Terminals

The efficient retrieval of synaptic vesicle membrane and cargo in central nerve terminals is dependent on the efficient recruitment of a series of endocytosis modes by different patterns of neuronal activity. During intense neuronal activity the dominant endocytosis mode is activity-dependent endocytosis (ADBE). Triggering of ADBE is linked to calcineurin-mediated dynamin I dephosphorylation since the same stimulation intensities trigger both. Dynamin I dephosphorylation is maximised by a simultaneous inhibition of its kinase glycogen synthase kinase 3 (GSK3) by the protein kinase Akt, however it is unknown how increased neuronal activity is transduced into Akt activation. To address this question we determined how the activity-dependent increases in intracellular free calcium ([Ca(2+)](i)) control activation of Akt. This was achieved using either trains of high frequency action potentials to evoke localised [Ca(2+)](i) increases at active zones, or a calcium ionophore to raise [Ca(2+)](i) uniformly across the nerve terminal. Through the use of either non-specific calcium channel antagonists or intracellular calcium chelators we found that Akt phosphorylation (and subsequent GSK3 phosphorylation) was dependent on localised [Ca(2+)](i) increases at the active zone. In an attempt to determine mechanism, we antagonised either phosphatidylinositol 3-kinase (PI3K) or calmodulin. Activity-dependent phosphorylation of both Akt and GSK3 was arrested on inhibition of PI3K, but not calmodulin. Thus localised calcium influx in central nerve terminals activates PI3K via an unknown calcium sensor to trigger the activity-dependent phosphorylation of Akt and GSK3