Subdiffusion and Weak Ergodicity Breaking in the Presence of a Reactive Boundary

2007/04/30 by Michael A. Lomholt, Irwin M. Zaid, Ralf Metzler · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #cond-mat.soft #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physrevlett.98.200603

published as Phys. Rev. Lett. 98, 200603 (2007) · 4 pages, 1 figure, REVTeX4, accepted to Phys Rev Lett, some typos corrected

arxiv created 2007/05/10 · openalex publication_date 2007/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Anomalous transit-time dispersion in amorphous solids
• Anomalous Subdiffusion Is a Measure for Cytoplasmic Crowding in Living Cells
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Kinetics of Protein-DNA Interaction: Facilitated Target Location in Sequence-Dependent Potential

Cited by

• In vivo facilitated diffusion model
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Probing microscopic origins of confined subdiffusion by first-passage observables