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Diffusion. In Computational Modeling of Genetic and Biochemical Networks.

G. Bormann, F. Brosens, E. De Schutter

TNB

MIT Press, Boston -:189-224 (2001)

Abstract - 1. Introduction 1.1 Why model diffusion in cells? 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 which will affect the local rate of chemical reactions. Such gradients can be static at the timescale of interest, e.g. the polarity of cells (Kasai and Petersen, 1994), or very dynamic like for example the intra- and intercellular signaling by traveling calcium waves (Berridge, 1997). Diffusion is the process by which random Brownian movement of molecules or ions cause an average movement towards regions of lower concentration, which may result in the collapse of the 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 similar methods as described here can be applied to the latter. Historically, diffusion has often been neglected in molecular simulations which are then assumed to operate in the well-mixed pool . This assumption may be valid when modeling small volumes, e.g. inside a spine (Koch and Zador, 1993), but should be carefully evaluated in all other contexts. As we will see in this chapter, the introduction of diffusion into a model raises many issues which otherwise do not apply: spatial scale, dimensionality, geometry and which individual molecules or ions can be considered to be immobile or not. The need for modeling diffusion should be evaluated for each substance separately. In general, if concentration gradients exist within the spatial scale of interest it is highly likely that diffusion will have an impact on the modeling results, unless the gradients change so slowly that they can be considered stationary compared to the timescale of interest. Simulating diffusion is in general a computationally expensive decision which is a more practical explanation of why it is often not implemented. This may very well change in the near future. A growing number of modeling studies (Markram et al., 1998, Naraghi and Neher, 1997) have recently emphasised the important effects diffusion can have on molecular interactions.