We utilize advanced physical and mathematical methods to understand the biophysics of complex cellular processes. Phenomena under study include the stochastic biogenesis of coated vesicles involved in endocytosis and other intracellular transport processes We have constructed a multi-element model of receptor mediated endocytosis that encompasses cargo recognition, phosphoinositide metabolism, and clathrin coat formation and dissolution. The analysis demonstrates how the inter-related kinetic elements of these processes determine whether an endocytic vesicle will form. Not only does the model explain how vesicle biogenesis is triggered by, e.g., the binding of ligands to receptors at specific sites, but it also can rationalize the observed probabilistic quality of cell response in the presence of a stimulus. During the past year we have developed a mathematical model that is focused on determining the energy needed to create clathrin coated pits (CCPs). The assembly of a CCP during endocytosis is a highly cooperative process that requires the spatial and temporal coordination of several factors, and tracking the growth of individual CCPs shows large heterogeneity in their lifetimes and sizes. The kinetics of CCP assembly is not well understood, but it is clear that the energy of creating a high curvature bud from a plasma membrane of much lower curvature plays a crucial role. We have developed a mathematical model in which we write the energy of a CCP in terms of its size and curvature, and show the growth of a vesicle is a barrier crossing problem in which the pit has to grow to a critical size before it is energetically favorable for its transformation into a closed vesicle. In a different study, we have been investigating how scattering of incident and emitted light affects fluorescence correlation spectroscopy (FCS) measurements, in anticipation of using this technique to discern motions of molecules occurring within dense biopolymer matrices or optically-opaque tissues. Using physical models, we have applied results of this study to an investigate the effects of macromolecular crowding on the motions of small molecules moving within a complex medium containing various densities of nanoscopic particles.