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Lomholt MA, Zaid IM, Metzler R. Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary. Phys Rev Lett. 2007;98(20):200603doi: 10.1103/PhysRevLett.98.200603.
Lomholt, M. A., Zaid, I. M., & Metzler, R. (2007). Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary. Physical review letters, 98(20), 200603. https://doi.org/10.1103/PhysRevLett.98.200603
Lomholt, Michael A, et al. "Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary." Physical review letters vol. 98,20 (2007): 200603. doi: https://doi.org/10.1103/PhysRevLett.98.200603
Lomholt MA, Zaid IM, Metzler R. Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary. Phys Rev Lett. 2007 May 18;98(20):200603. doi: 10.1103/PhysRevLett.98.200603. Epub 2007 May 16. PMID: 17677681.
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Phys Rev Lett. 2007 May 18;98(20):200603. doi: 10.1103/PhysRevLett.98.200603. Epub 2007 May 16.

Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary.

Physical review letters

Michael A Lomholt, Irwin M Zaid, Ralf Metzler

Affiliations

  1. Physics Department, University of Ottawa, Pavillon MacDonald, Ottawa, Ontario K1N 6N5, Canada.

PMID: 17677681 DOI: 10.1103/PhysRevLett.98.200603

Abstract

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.

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