  We analyse mobile-immobile transport of particles that switch between the
mobile and immobile phases with finite rates. Despite this seemingly simple
assumption of Poissonian switching we unveil a rich transport dynamics
including significant transient anomalous diffusion and non-Gaussian
displacement distributions. Our discussion is based on experimental parameters
for tau proteins in neuronal cells, but the results obtained here are expected
to be of relevance for a broad class of processes in complex systems.
Concretely, we obtain that when the mean binding time is significantly longer
than the mean mobile time, transient anomalous diffusion is observed at short
and intermediate time scales, with a strong dependence on the fraction of
initially mobile and immobile particles. We unveil a Laplace distribution of
particle displacements at relevant intermediate time scales. For any initial
fraction of mobile particles, the respective mean squared displacement displays
a plateau. Moreover, we demonstrate a short-time cubic time dependence of the
mean squared displacement for immobile tracers when initially all particles are
immobile.
