Anomalous Diffusion in Living Cells

by D. S. Grebenkov

Laboratory of Condensed Matter Physics,
CNRS - Ecole Polytechnique, F-91128 Palaiseau France

Anomalous diffusion, for which the mean-square displacement (MSD)
exhibits a power-law dependence on time, is a generic situation
for tracers moving in complex or viscoelastic media, notably in 
living cells. After a brief overview of main theoretical models 
for anomalous diffusion, we present our recent results for the 
mean, variance and probability distribution of the time-averaged 
MSD for dynamics governed by generalized Langevin equation. We 
also suggest an alternative quadratic functional of the trajectory, 
the so-called time-averaged squared root mean-square displacement
(sRMS). The challenging problem of characterization of a stochastic 
process from its single random realization is discussed, with a
focus on single-particle tracking techniques such as optical 
tweezers.