FIGURE 6.

Parameters characterizing hop diffusion are severely affected by time-averaging over the frame time, the number of observations made during the residency period within a compartment, and the total observation time, which, if inappropriately chosen, may lead to an erroneous conclusion that the diffusion is simple Brownian. (A) MSDs for single trajectories of hop diffusion (those shown in Fig. 5) observed at frame times of 25 μs (left) and 33 ms (right). Note that both x and y axes are expanded 1000-fold in the figure on the right (for 33 ms). At a frame time of 33 ms (right), the plot can be fitted with a linear line, showing (apparent) simple Brownian character. However at a frame time of 25 μs, typical hop diffusion characteristics are apparent: fast rise in the short-time regime and slower linear growth of MSD with time in the long-time regime, with a slope comparable to that found in the 33-ms MSD-t plot. (B) Apparent microscopic diffusion coefficient D_2–4 plotted against the frame time (at least 100 simulations for each frame time). The set diffusion coefficient in the simulation was 9 μm²/s. At short frame times, the diffusion coefficient within a compartment can be detected with reasonable levels of fidelity. See the trajectories in Fig. 5. It is clear that at shorter frame times, the diffusion coefficient within a compartment dominates. At much longer frame times, the apparent diffusion coefficient levels off. In this time regime, the diffusion coefficient within a compartment (set at 9 μm²/s) becomes negligible, and the apparent diffusion coefficient is determined by the hop diffusion between the compartments, i.e., the compartment size and the residency time within a compartment (see trajectories in Fig. 5). (C) The plot of log(MSD/time) against log(time), covering six orders of magnitude in time. Note that the time here is not frame time, but the actual time interval of the observation of simulated particles. The individual solid curves are those obtained for each frame time. The vertical broken lines show the time taken to first sense the barriers (at 0.1 ms) and the median residency time within a compartment (at 23 ms). Very clear anomalous diffusion (the best fit for the α-value ∼0.23, i.e., a slope of −0.77) is observed in between these lines, whereas simple Brownian diffusion is observed at time-windows below and above these crossover timescales (the slope ∼0).