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 a cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. This disparity poses analytical and numerical difficulties in extracting properties from experimental data, from biophysical models, and from Brownian dynamics simulation of diffusion in multi-scale structures. Some of these difficulties are resolved by the methods described in Chaps. 7 and 8, which are applied here to the analysis and simulations of subcellular processes and to the quantification of their biological functions.