Stochastic motion on the surface of living cells is critical to promote molecular encounters that are necessary for multiple cellular processes. Often the complexity of the cell membranes leads to anomalous diffusion, which under certain conditions it is accompanied by non-ergodic dynamics. Here, we unravel two manifestations of ergodicity breaking in the dynamics of membrane proteins in the somatic surface of hippocampal neurons. Three different tagged molecules are studied on the surface of the soma: the voltage-gated potassium and sodium channels Kv1.4 and Nav1.6 and the glycoprotein CD4. In these three molecules ergodicity breaking is unveiled by the confidence interval of the mean square displacement and by the dynamical functional estimator. Ergodicity breaking is found to take place due to transient confinement effects since the molecules alternate between free diffusion and confined motion.

Diffusion of nanoparticles in the cytoplasm of live cells has frequently been reported to exhibit an anomalous and even heterogeneous character, i.e. particles seem to switch gears during their journey. Here we show by means of a hidden Markov model that individual trajectories of quantum dots in the cytoplasm of living cultured cells feature a dichotomous switching between two distinct mobility states with an overall subdiffusive mode of motion of the fractional Brownian motion (FBM) type. Using the extracted features of experimental trajectories as input for simulations of different variants of a two-state FBM model, we show that the trajectory-intrinsic and the ensemble-wise heterogeneity in the experimental data is mostly due to variations in the (local) transport coefficients, with only minor contributions due to locally varying anomaly exponents. Altogether, our approach shows that diffusion heterogeneities can be faithfully extracted and quantified from fairly short trajectories obtained by single-particle tracking in highly complex media.

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