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Spatial multiscale chemical reaction networks

The dynamics of concentrations of chemical species are governed by chemical reaction equations and their rate constants. Usually, it is assumed that the rate of a reaction is proportional to the number of possible reaction partners, which requires a fast spatial mixing of molecules. If all species change their bundance on the same time scale, this is a one-scale system, and fast spatial mixing leads to mass action kinetics. However, in a multi-scale system some species change their abundance slower and some faster, maybe even faster than the spatial mixing of molecules occurs. In this case, different scaling limits are possible. In my talk I give the example of the Michaelis-Menten dynamics, which is one of the simplest multi-scale reaction networks. This is joint work with Lea Popovic (Montreal).