Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary
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We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar
4 pages, 1 figure, REVTeX4, accepted to Phys Rev Lett, some typos corrected
4 pages, 1 figure, REVTeX4, accepted to Phys Rev Lett, some typos corrected