TABLE OF CONTENTS Physical proximity is an essential requirement for molecular interaction to occur, whether it is between an enzyme and its substrate and modulators or between a receptor and its ligand. Cells have developed many mechanisms to bring molecules together, including structural ones [e.g., calcium-activated ionic channels often cluster with calcium channels in the plasma membrane (Gola and Crest 1993, Issa and Hudspeth 1994] or specific processes like active transport (Nixon 1998). In many situations, however, concentration gradients exist that will affect the local rate of chemical reactions. Such gradients can be static at the time scale of interest [e.g., the polarity of cells (Kasai and Petersen 1994)], or very dynamic [e.g., the intra- and intercellular signaling by traveling calcium waves (Berridge 1997)].
Diffusion is the process by which random Brownian movement of molecules or ions causes an average movement toward regions of lower concentration, which may result in the collapse of a concentration gradient. In the context of cellular models, one distinguishes experimentally and functionally between free diffusion and diffusion across or inside cell membranes (Hille 1992). We will only consider the first case explicitly, but methods similar to those described here can be applied to the latter.
Historically, diffusion has often been neglected in molecular simulations, which are then assumed to operate in a "well-mixed pool." This assumption may be valid when modeling small volumes, for example, inside a spine (Koch and Zador 1993), but should be...
