  The Mean Square Displacement is a central tool in the analysis of Single
Particle Tracking experiments, shedding light on various biophysical phenomena.
Frequently, parameters are extracted by performing time-averages on single
particle trajectories followed by ensemble averaging. This procedure however,
suffers from two systematic errors when applied to particles that perform
anomalous diffusion. The first is significant at short time lags and is induced
by measurement errors. The second arises from the natural heterogeneity in
biophysical systems. We show how to estimate and correct these two errors and
improve the estimation of the anomalous parameters for the whole particle
distribution. As a consequence we manage to characterize ensembles of
heterogeneous particles even for rather short and noisy measurements where
regular time averaged mean square displacement analysis fails. We apply this
method to both simulations and in vivo measurements of telomere diffusion in
3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be
subdiffusive with an average exponent constant in time. Individual telomere
exponents are normally distributed around the average exponent. The proposed
methodology has the potential to improve experimental accuracy while
maintaining lower experimental costs and complexity.
