Random time-scale invariant diffusion and transport coefficients

Phys Rev Lett. 2008 Aug 1;101(5):058101. doi: 10.1103/PhysRevLett.101.058101. Epub 2008 Jul 28.

Abstract

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement delta2[over ] of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that delta2[over ] differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable delta2[over ]. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Diffusion
  • Escherichia coli / chemistry*
  • Escherichia coli / metabolism
  • Lipid Metabolism
  • Lipids / chemistry*
  • Models, Biological
  • Models, Chemical*
  • RNA, Messenger / chemistry*
  • RNA, Messenger / metabolism
  • Yeasts / chemistry*
  • Yeasts / metabolism

Substances

  • Lipids
  • RNA, Messenger