This project is directed at developing and using physical and mathematical methodologies to understand integrative aspects of complex cellular processes. Emphasis has been on studying the propoerties of multicomponent, supramolecular entities such as biological membranes and cytoskeletal networks, particularly their involvement in cellular organization, intracellular transport, and cell shape. These investigations oftentimes require the development and application of new measurement techniques. We study biomimetric models in additional to biological materials. For example, we have used fluorescence correlation spectroscopy (FCS) to obtain quantitative measures of the diffusion time of fluorescent TAMRA molecules in poly(vinyl alcohol) (PVA) samples --solutions and gels -- prepared at various polymer concentrations and crosslink densities. The measurements indicate that the diffusion rate is affected, not only by the polymer concentration, but also by the crosslink density of the gel. For both solutions and gels, the diffusion rate, normalized to the rate in pure water, appears to decrease linearly with the polymer concentration. Below the gelation threshold (approximately 3% PVA w/v), the diffusion rates remain unchanged when one adds cross-linkers, but above the threshold the movement of the probe through the gels is slower than in the corresponding polymer solutions. Interestingly, we find that diffusion of the probe particles in these gels is strongly correlated with network elasticity. We also have been using FCS and dynamic light scattering (DLS) to measure the hydrodynamic diameters of nanoscopic biological structures. In this way, we have been able to monitor the stability of tubulin rings that form in the presence of certain small antimitotic peptides and, by combining FCS and analytical ultracentrifugation of the rings, we have corroborated theories and computational code that provide values of hydrodynamic coefficients of particles of complex geometry. Insights gained from these investigations have been used to guide studies of the shapes of clathrin triskelions in solutions of differing pH and salt concentrations. We also have been studying membrane transformations underlying cell function, most notably the production of small tubulovesicular entities involved in protein trafficking in eucaryotic cells. In particular, receptor mediated endocytosis occurs through the formation of vesicles that are surrounded by polyhedral, cage-like structures assembled from a three-legged heteropolymer known as a clathrin triskelion. We have been investigating how the biogenesis of such clathrin-coated vesicles occurs. To this end we have used a variety of physical methods to infer how coat mechanics influences vesicle formation and to understand how environmental factors and the binding of ancillary proteins (e.g., AP2 complexes) might mediate clathrin lattice assembly. Work previously carried out by our group indicated that coats containing only clathrin and APs are unlikely to bend portions of a typical plasma membrane into small vesicles having a size similar to that of clathrin coated vesicles. To extend this work, we recently developed a new method, based on atomic force microscopy (AFM), to determine the mechanical rigidity of intact clathrin-coated vesicles (CCVs). This direct measurement of the mechanical properties of CCVs allows us to infer the mechanical nature of the protein layer that links the outer clathrin cage to the inner lipid shell of a typical CCV. We find that this protein layer is relatively flexible, implying that changes in coat rigidity can modulate vesicle biogenesis. In a related study, we used static and dynamic light scattering, combined with computer-based structural modeling, to examine the conformations of triskelions in solution. The triskelions were found to have a geometrical form close to that discerned elsewhere by cryoelectron microscopy of reconstituted clathrin cages. Hence, clathrin triskelia, when inserted into cages and coats, probably adjust to the geometry of the coat at the cost of only relatively small strain energy. Also, it is clear that the binding of clathrin-associated proteins to phosphoinositides (PIs) plays an important role in vesicle formation, perhaps by inducing curvature changes in the lipid membrane. Increasing evidence suggests that signaling by membrane lipids, in particular 3? phosphoinositides (3?PIs), is involved in this and other membrane transformations underlying cell function. The best studied of these phenomena is gradient sensing in immune and amoeboid cells, in which information about external chemical stimuli induces cytoskeletal changes giving rise to directed cell locomotion. We have employed mathematical and computational methods to construct and examine a biochemical network for PI signaling that includes actions of PI kinases and phosphatases, small g-proteins, and phosphatidic acid production. The network interactions include coupled feedback and feed-forward loops that can lead to regulated responses that act as switches. By allowing for translocation of molecules from cytosol to membrane that couple responses at distant points on the cell surface, we have shown how different magnitudes of system parameters can result in characteristically different cellular behaviors that mirror environmental changes. Finally, we have been studying aspects of the way polymer ensembles organize in the presence of external stimuli or constraints. For example, we recently have investigated how polyelectrolyte gels respond to strong pH gradients. When unbuffered, finite-sized, agarose gels are subject to electric fields that induce electrolysis, we find that strong pH gradients are established across the gels that migrate in accordance with mathematical predictions of a continuum electrodiffusion model. By using small angle light scattering, we have established that, as the fronts meet, gel domains arise and are oriented perpendicularly to the field. We also have investigated how physical boundaries affect spatial patterns set up by concentrated ensembles of rod-shaped objects, finding that, when confined to containers whose dimensions are of the same order of magnitude as the lengths of the objects, the rods self organize and show a density dependent isotropic-nematic structural transition. A continuum theory of elastic energy explains the complex patterns that emerge as a result of competition between steric rod-rod interactions in the bulk, and interactions of the rods with the walls of the container.