Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary.
We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with a 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 an 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.
Physics Department, University of Ottawa, Pavillon MacDonald, Ottawa, Ontario K1N 6N5, Canada.
Michael A
MA
Lomholt
Irwin M
IM
Zaid
Ralf
R
Metzler