2007.111: Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour?

2007.111: C.J. Riley, M.R. Muldoon, J.P. Huke and D.S. Broomhead (2007) Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour?

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Abstract

In biological systems, chemical reactions often take place in complex spatial environments. For example, the translation of m-RNA to produce protein within eukaryotic cells takes place within the extremely crowded cytoplasmic environment and appears to require the spatial coordination of many translation factors. It is important, therefore, to understand the transport processes within such an environment. While there is growing interest in both experimental and computational studies of such environments, it is also important to develop suitable mathematical models. Here, as an example of such a model, we study a reaction-diffusion equation defined on the Sierpinski gasket. Both experimental and computational studies of analogous systems have shown power law behaviour and associated deviations from mass action kinetics. The analysis presented here allows us to distinguish the roles of the fractal domain and of the discreteness of molecular interactions in producing this effect. Indeed, we show that the fractal domain alone is insufficient.

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