Reactive clusters on a membrane

We investigate the reaction dynamics of diffusive molecules with immobile binding partners. The fixed reactants build clusters that comprise just a few tens of molecules, which leads to small cluster sizes. These molecules participate in the reaction only if they are activated. The dynamics of activation is mapped to a time-dependent size of an active region within the cluster. We focus on the deterministic description of the dynamics of a single cluster. The spatial setup accounts for one of the most important determinants of the dynamics of a cluster, i.e. diffusional transport of reaction partners toward or away from the active region of the cluster. We provide numerical and analytical evidence that diffusion influences decisively the dynamic regimes of the reactions. The application of our methods to intracellular Ca²⁺ dynamics shows that large local concentrations saturate the Ca²⁺ feedback to the channel state control. That eliminates oscillations depending on this feedback.