Single molecule tracking of heterogeneous diffusion
Abstract
The mean square displacement of heterogeneous diffusion obeys the Einstein relation, thereby showing no sign of heterogeneities in the ensemble measurement of the diffusion constant. The signature of spatial heterogeneities appears in the time evolution of the nonGaussian distribution and in the cross correlation between the square displacements at different times, both available from single molecule diffusional trajectories. As a quantitative measure, the nonGaussian indicator g(t) decays asymptotically to zero according to 1/t for finite time correlation, but saturates at a plateau value for powerlaw correlation. In addition, the joint moment correlation function f(t,τ) provides a direct probe of the memory effect of the fluctuating rate constant. A twostate diffusion model and a stochastic Gaussian model are constructed to evaluate these quantities and are shown to yield the same result within the second cumulant expansion.
 Publication:

Physical Review E
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevE.63.041101
 Bibcode:
 2001PhRvE..63d1101C
 Keywords:

 82.20.Fd;
 05.40.a;
 82.20.Db;
 Collision theories;
 trajectory models;
 Fluctuation phenomena random processes noise and Brownian motion;
 Transition state theory and statistical theories of rate constants