Diffusion governs the rates of many molecular processes of biomedical importance. These processes include the rate of action of enzymes such as acetylcholinesterase, which achieves the high speed necessary for its function in synaptic activity in part by electrostatic guidance of substrate diffusion to its active site. The diffusional encounter of proteins with one another, with lipid bilayers, or with nucleic acids, plays a central role in signal transduction, gene expression, cytoskeletal remodeling, and a host of other processes in cell biology. The broad objectives of this work are to provide new computer simulation tools that will enable the detailed analysis of the role of molecular diffusion in biological processes at the subcellular level, and the application of these tools to selected problems where close contact with experimental work is possible. Specific aims for the next project period include the following. (1) Several improvements will be made in the methods for generating Brownian dynamics trajectories. (2) Methods will be developed to allow for the fluctuation of surface loops on proteins in simulations of protein-protein encounter. (3) Methods will be developed to allow simulations of molecular binding to sites on extended surfaces. (4) Applications will be pursued for several systems for which abundant experimental biophysical data are available. Training of undergraduate, graduate, and postdoctoral students will continue to be a key aspect of this project.