Abstract
In normal lateral diffusion, the mean-square displacement of the diffusing species is proportional to time. But in disordered systems anomalous diffusion may occur, in which the mean-square displacement is proportional to some other power of time. In the presence of moderate concentrations of obstacles, diffusion is anomalous over short distances and normal over long distances. Monte Carlo calculations are used to characterize anomalous diffusion for obstacle concentrations between zero and the percolation threshold. As the obstacle concentration approaches the percolation threshold, diffusion becomes more anomalous over longer distances; the anomalous diffusion exponent and the crossover length both increase. The crossover length and time show whether anomalous diffusion can be observed in a given experiment.
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Abney J. R., Scalettar B. A., Owicki J. C. Self diffusion of interacting membrane proteins. Biophys J. 1989 May;55(5):817–833. doi: 10.1016/S0006-3495(89)82882-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Almeida P. F., Vaz W. L., Thompson T. E. Lateral diffusion and percolation in two-phase, two-component lipid bilayers. Topology of the solid-phase domains in-plane and across the lipid bilayer. Biochemistry. 1992 Aug 11;31(31):7198–7210. doi: 10.1021/bi00146a024. [DOI] [PubMed] [Google Scholar]
- Kopelman R. Fractal reaction kinetics. Science. 1988 Sep 23;241(4873):1620–1626. doi: 10.1126/science.241.4873.1620. [DOI] [PubMed] [Google Scholar]
- Nagle J. F. Long tail kinetics in biophysics? Biophys J. 1992 Aug;63(2):366–370. doi: 10.1016/S0006-3495(92)81602-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Nieuwenhuizen TM, van Velthoven PF, Ernst MH. Diffusion and long-time tails in a two-dimensional site-percolation model. Phys Rev Lett. 1986 Nov 17;57(20):2477–2480. doi: 10.1103/PhysRevLett.57.2477. [DOI] [PubMed] [Google Scholar]
- Qian H., Sheetz M. P., Elson E. L. Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. Biophys J. 1991 Oct;60(4):910–921. doi: 10.1016/S0006-3495(91)82125-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saffman P. G., Delbrück M. Brownian motion in biological membranes. Proc Natl Acad Sci U S A. 1975 Aug;72(8):3111–3113. doi: 10.1073/pnas.72.8.3111. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saxton M. J. Lateral diffusion and aggregation. A Monte Carlo study. Biophys J. 1992 Jan;61(1):119–128. doi: 10.1016/S0006-3495(92)81821-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saxton M. J. Lateral diffusion in a mixture of mobile and immobile particles. A Monte Carlo study. Biophys J. 1990 Nov;58(5):1303–1306. doi: 10.1016/S0006-3495(90)82470-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saxton M. J. Lateral diffusion in an archipelago. Dependence on tracer size. Biophys J. 1993 Apr;64(4):1053–1062. doi: 10.1016/S0006-3495(93)81471-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saxton M. J. Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient. Biophys J. 1989 Sep;56(3):615–622. doi: 10.1016/S0006-3495(89)82708-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saxton M. J. Lateral diffusion in an archipelago. Single-particle diffusion. Biophys J. 1993 Jun;64(6):1766–1780. doi: 10.1016/S0006-3495(93)81548-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Saxton M. J. Lateral diffusion in an archipelago. The effect of mobile obstacles. Biophys J. 1987 Dec;52(6):989–997. doi: 10.1016/S0006-3495(87)83291-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Zhang F., Lee G. M., Jacobson K. Protein lateral mobility as a reflection of membrane microstructure. Bioessays. 1993 Sep;15(9):579–588. doi: 10.1002/bies.950150903. [DOI] [PubMed] [Google Scholar]