  The stochastic motions of a diffusing particle contain information concerning
the particle's interactions with binding partners and with its local
environment. However, accurate determination of the underlying diffusive
properties, beyond normal diffusion, has remained challenging when analyzing
particle trajectories on an individual basis. Here, we introduce the maximum
likelihood estimator (MLE) for confined diffusion and fractional Brownian
motion. We demonstrate that this MLE yields improved estimation over
traditional mean square displacement analyses. We also introduce a model
selection scheme (that we call mleBIC) that classifies individual trajectories
to a given diffusion mode. We demonstrate the statistical limitations of
classification via mleBIC using simulated data. To overcome these limitations,
we introduce a new version of perturbation expectation-maximization (pEMv2),
which simultaneously analyzes a collection of particle trajectories to uncover
the system of interactions which give rise to unique normal and/or non-normal
diffusive states within the population. We test and evaluate the performance of
pEMv2 on various sets of simulated particle trajectories, which transition
among several modes of normal and non-normal diffusion, highlighting the key
considerations for employing this analysis methodology.
