A new Paradigm in Single-Particle Tracking in Live Cells: Onset of Ergodicity Breaking

Abstract

Experimental single-particle tracking (SPT) is extensively used to study the dynamics of membrane proteins and lipids in living cells. Most studies show that molecular motion in the plasma membrane, as well as in the cytoplasm and the nucleus, undergoes anomalous subdiffusion. SPT data is usually analyzed in terms of the temporal mean square displacement because averaging along individual trajectories is more readily available than ensemble averages. However, in some intriguing physical phenomena ergodicity is broken and thus temporal averages do not converge to the ensemble measurements. Here we measured more than 1,000 Kv2.1 potassium channel trajectories in live human embryonic kidney (HEK) cells, analyzed their ergodic and non-ergodic properties and uncovered the physical mechanism underlying their anomalous diffusion pattern. We have labeled Kv2.1 channels with quantum dots (QDs) in HEK cells, imaged the cell basal membrane with total internal fluorescence microscopy and analyzed the individual channel trajectories. We found that the distributions of the two types of averages are clearly different. The temporal average yielded a much broader MSD than the ensemble-average. Nevertheless, the diffusion pattern of these channels follows anomalous subdiffusion in the lag time, i.e. the MSD is sublinear, both for the temporal and the ensemble averages. Our data reveal that two processes simultaneously coexist and only one of them is ergodic. The ergodicity breaking is found to be maintained by a set of anchoring points associated to the actin cytoskeleton. Control experiments indicate these effects are not induced by the quantum dots. These results are accurately modeled by a continuous time random walk on a fractal structure. When the actin cytoskeleton is disrupted, ergodicity is recovered. These experimental observations have direct biological implications in the dynamics of membrane proteins.