Single molecule tracking of heterogeneous diffusion - art. no. 041101

The mean square displacement of heterogeneous diffusion obeys the Einstein relation, thereby showing no sign of heterogeneities in the ensemble measur ement of the diffusion constant. The signature of spatial heterogeneities a ppears in the time evolution of the non-Gaussian distribution and in the cr oss correlation between the square displacements at different times, both a vailable from single molecule diffusional trajectories. As a quantitative m easure, the non-Gaussian indicator g(t) decays asymptotically to zero accor ding to l/t for finite time correlation, but saturates at a plateau value f or power-law correlation. In addition, the joint moment correlation functio n f(t, tau) provides a direct probe of the memory effect of the fluctuating rate constant. A two-state diffusion model and a stochastic Gaussian model are constructed to evaluate these quantities and are shown to yield the sa me result within the second cumulant expansion.