Control of flux by narrow passages and hidden targets in cellular biology.

Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. We report here recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, from biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures. This progress is achieved by developing an analytical approximation methodology for solving the model equations. The reported results are applied to analysis and simulations of subcellular processes and to the quantification of their biological functions.