Random time-scale invariant diffusion and transport coefficients.
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.
He
Y
Y
Department of Physics, Bar Ilan University, Ramat-Gan, Israel.
Burov
S
S
Metzler
R
R
Barkai
E
E