Obstructed diffusion propagator analysis for single-particle tracking

Abstract

We describe a method for the analysis of the distribution of displacements, i.e., the propagators, of single-particle tracking measurements for the case of obstructed subdiffusion in two-dimensional membranes. The propagator for the percolation cluster is compared with a two-component mobility model against Monte Carlo simulations. To account for diffusion in the presence of obstacle concentrations below the percolation threshold, a propagator that includes the transient motion in finite percolation clusters and hopping between obstacle-induced compartments is derived. Finally, these models are shown to be effective in the analysis of Kv2.1 channel diffusive measurements in the membrane of living mammalian cells.

Mechanisms Underlying Anomalous Diffusion in the Plasma Membrane

“…In this case, we expect a scale-free distribution of compartment sizes and in turn a distribution of escapes without a characteristic time. Some experiments agree with predictions of this type of anomalous diffusion where a linear MSD regime is not attained (Smith et al, 1999;Weigel, Ragi, et al, 2011;Weigel, Simon, et al, 2011). A different view of diffusion within a scale-free meshwork is that of nested compartmentalization.…”

“…When the obstacle concentration is much smaller than criticality, the cluster sizes are small and transient anomalous diffusion is observed only over small length scales. Thus the MSD is sublinear over short times and linear at longer times (Figure 2(A)) (Saxton, 1996;Weigel, Ragi, et al, 2011). The subdiffusive regime grows as concentration increases and when criticality is reached subdiffusion is observed at all length scales.…”

“…Similarly, while subdiffusion in a percolation cluster at a concentration below criticality is transient, the convergence to normal diffusion can be slow, i.e., subdiffusion may be observed over several orders of magnitude. One clear distinction between fBM and obstructed diffusion is that while the propagator of fBM is Gaussian (Eqn (6)), the propagator for diffusion in a percolation cluster is not (see Eqn (4) in Weigel, Ragi, et al (2011)). …”

“…Several simulations are presented for each obstacle concentration in order to show the small scatter of the mean square displacement (MSD). Simulations are performed in square lattices using a Monte Carlo blind ant algorithm (simulation details can be found inWeigel, Ragi, et al, 2011) so that 41% obstacles is right above the percolation threshold. The simulations with 41% obstacles show anomalous diffusion over the whole simulated time, but all other concentrations exhibit transient subdiffusion with a time upon which the process exhibits normal diffusion, i.e., MSD/D becomes flat, as expected from MSD w D. (B) Example of a trajectory of 10 6 steps in a square lattice with 33% of sites obstructed.…”

Quantifying the dynamic interactions between a clathrin-coated pit and cargo molecules

“…When the power law is truncated, convergence to ergodicity is expected to be remarkably slow compared with the case when the dwell time is characterized by an exponential decay (27). These intrinsic properties should also give rise to anomalous diffusion in the plasma membrane as observed broadly over the last decade (28)(29)(30)(31) and to aging effects as seen recently (23,32). However, this work does not imply this is the main mechanism for anomalous subdiffusion in the plasma membrane, but that this mechanism certainly contributes to the observed anomalies.…”