1. Since the hallmark of glucose metabolism is insulin-stimulated delivery of glucose transporter-4 (GLUT4) to the plasma membrane (PM) and the hallmark of membrane protein organization is its domain structure, we continue to examine insulin's effect on GLUT4 organization in PM of adipose cells. The fruit fly Drosophila melanogaster is an excellent model system for studies of genes controlling development and disease. However, its applicability to physiological systems is less clear because of metabolic differences between insects and mammals. Insulin signaling has been studied in mammals because of relevance to diabetes and other diseases but there are many parallels between mammalian and insect pathways. For example, deletion of Drosophila Insulin-Like Peptides resulted in 'diabetic'flies with elevated circulating sugar levels. Whether this situation reflects failure of sugar uptake into peripheral tissues as seen in mammals is unclear and depends upon whether flies harbor the machinery to mount mammalian-like insulin-dependent sugar uptake responses. Here we asked whether Drosophila fat cells are competent to respond to insulin with mammalian-like regulated trafficking of sugar transporters. Transgenic Drosophila expressing human glucose transporter-4 (GLUT4), the sugar transporter expressed primarily in insulin-responsive tissues, were generated. After expression in fat bodies, GLUT4 intracellular trafficking and localization were monitored by confocal and total internal reflection fluorescence microscopy (TIRFM). We found that fat body cells responded to insulin with increased GLUT4 trafficking and translocation to the plasma membrane. While the amplitude of these responses was relatively weak in animals reared on a standard diet, it was greatly enhanced in animals reared on sugar-restricted diets, suggesting that flies fed standard diets are insulin resistant. Our findings demonstrate that flies are competent to mobilize translocation of sugar transporters to the cell surface in response to insulin. They suggest that Drosophila fat cells are primed for a response to insulin and that these pathways are down-regulated when animals are exposed to constant, high levels of sugar. Finally, these studies are the first to use TIRFM to monitor insulin-signaling pathways in Drosophila, demonstrating the utility of TIRFM of tagged sugar transporters to monitor signaling pathways in insects. 2. Various membrane functional units such as receptors, transporters, and channels, whose action necessarily involves capturing diffusing molecules, are often organized into multimeric complexes forming clusters on the cell and organelle membranes. These functional units themselves are usually oligomers of several integral proteins, which have their own symmetry. Depending on the symmetry, they form clusters on different packing lattices. Moreover, local membrane inhomogeneities, e.g., the so-called membrane domains, rafts, stalks, etc., lead to different patterns even within the structures on the same packing lattice. Units in the cluster compete for diffusing molecules and screen each other. Here we propose a general approach that allows one to quantify the screening effects. The approach is used to derive simple approximate formulas giving the trapping rates of diffusing molecules by clusters of absorbers on lattices of different packing symmetries. The obtained results describe smooth variation of the trapping rate from the sum of the rates of individual absorbers forming the cluster to the effective collective rate. The latter shows how the trapping efficiency of an individual absorber decreases as the number of absorbers in the cluster increases and/or the inter-absorber distance decreases. Numerical tests demonstrate good agreement between the rates predicted by the theory and obtained from Brownian dynamics simulations for clusters of different shapes and sizes. 3. A simple approximate formula is derived for the rate constant that describes steady-state flux of diffusing particles through a cluster of perfectly absorbing disks on the otherwise reflecting flat wall, assuming that the disk centers occupy neighboring sites of a square lattice. A distinctive feature of trapping by a disk cluster is that disks located at the cluster periphery shield the disks in the center of the cluster. This competition of the disks for diffusing particles makes it impossible to find an exact analytical solution for the rate constant in the general case. To derive the approximate formula, we use a recently suggested approach A. M. Berezhkovskii, L. Dagdug, V. A. Lizunov, J. Zimmerberg, and S. M. Bezrukov, J. Chem. Phys. 136, 211102 (2012), which is based on the replacement of the disk cluster by an effective uniform partially absorbing spot. The formula shows how the rate constant depends on the size and shape of the cluster. To check the accuracy of the formula, we compare its predictions with the values of the rate constant obtained from Brownian dynamics simulations. The comparison made for 18 clusters of various shapes and sizes shows good agreement between the theoretical predictions and numerical results.
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