Figure 5.
Ultrafast SFMI further supports the concept of hop diffusion of membrane molecules in the apical PM, by enabling two new analyses: the distribution of the residency time of each molecule within each compartment and the diffusion anomalies based on log(MSD/time) vs. log(time) in the time range over five orders of magnitude.(A) The distributions of the residency times within a compartment for Cy3-DOPE and TfR, determined by the TILD analysis, with the best-fit exponential curves (see “Expected distribution of the residency times: development of the hop diffusion theory” in the caption to Fig. S5). (B) An anomaly analysis of single-molecule trajectories based on the plot of log(MSD/time) vs. log(time), supporting the hop-diffusion model in the compartmentalized PM for both Cy3-DOPE and TfR (see the main text). Using the data obtained at time resolutions of 0.022 ms (45 kHz; only for TfR labeled with 5xCy3-Tf), 0.1 ms (10 kHz; for Cy3-DOPE), 0.167 ms (6 kHz; for TfR labeled with Cy3-Tf), and 33 ms (30 Hz; for Cy3-DOPE and TfR labeled with Cy3-Tf), the mean values of log(MSD/time) averaged over all trajectories were obtained and plotted as a function of log(time). The results of TfR using Cy3-Tf and 5xCy3-Tf were different in the time ranges shorter than 1 ms, due to the differences in the observation frame rates (6 and 45 kHz, respectively). During 0.167 ms, which is the frame time in 6-kHz observations, TfR still collides with the compartment boundaries, but this occurs much less often when the frame time is 0.022 ms (frame time in 45-kHz observations). Therefore, in shorter time ranges, the results obtained at 45 kHz (using 5xCy3-Tf) are better (see the simulation results shown by the dashed cyan curve). For the same reason, the 10-kHz data using Cy3-DOPE show that due to the insufficient time resolution, the pure simple-Brownian diffusion within a compartment could not be measured even at this frame rate. Dashed curves represent the results of the Monte Carlo simulations, resembling the experimental data (see Materials and methods for the simulation parameters). Note that the phospholipid probes are located in the PM outer leaflet, and yet they undergo hop diffusion. This is probably because, as proposed previously (Fujiwara et al., 2002), the transmembrane proteins anchored to and aligned along the actin mesh (pickets; see Fig. 3 A) form the diffusion barrier in both the outer and inner leaflets of the PM. The picket effect is due not only to the steric hindrance of the picket proteins, but also to the hydrodynamic-friction-like effect from the surface of the immobilized picket proteins on the surrounding medium (Fujiwara et al., 2002). Monte Carlo simulations showed that 20—30% occupancy of the compartment boundary by the immobile picket proteins (bound to the actin fence) is sufficient to cause confined + hop diffusion of the phospholipids in the PM outer leaflet (Fujiwara et al., 2002).

Ultrafast SFMI further supports the concept of hop diffusion of membrane molecules in the apical PM, by enabling two new analyses: the distribution of the residency time of each molecule within each compartment and the diffusion anomalies based on log(MSD/time) vs. log(time) in the time range over five orders of magnitude. (A) The distributions of the residency times within a compartment for Cy3-DOPE and TfR, determined by the TILD analysis, with the best-fit exponential curves (see “Expected distribution of the residency times: development of the hop diffusion theory” in the caption to Fig. S5). (B) An anomaly analysis of single-molecule trajectories based on the plot of log(MSD/time) vs. log(time), supporting the hop-diffusion model in the compartmentalized PM for both Cy3-DOPE and TfR (see the main text). Using the data obtained at time resolutions of 0.022 ms (45 kHz; only for TfR labeled with 5xCy3-Tf), 0.1 ms (10 kHz; for Cy3-DOPE), 0.167 ms (6 kHz; for TfR labeled with Cy3-Tf), and 33 ms (30 Hz; for Cy3-DOPE and TfR labeled with Cy3-Tf), the mean values of log(MSD/time) averaged over all trajectories were obtained and plotted as a function of log(time). The results of TfR using Cy3-Tf and 5xCy3-Tf were different in the time ranges shorter than 1 ms, due to the differences in the observation frame rates (6 and 45 kHz, respectively). During 0.167 ms, which is the frame time in 6-kHz observations, TfR still collides with the compartment boundaries, but this occurs much less often when the frame time is 0.022 ms (frame time in 45-kHz observations). Therefore, in shorter time ranges, the results obtained at 45 kHz (using 5xCy3-Tf) are better (see the simulation results shown by the dashed cyan curve). For the same reason, the 10-kHz data using Cy3-DOPE show that due to the insufficient time resolution, the pure simple-Brownian diffusion within a compartment could not be measured even at this frame rate. Dashed curves represent the results of the Monte Carlo simulations, resembling the experimental data (see Materials and methods for the simulation parameters). Note that the phospholipid probes are located in the PM outer leaflet, and yet they undergo hop diffusion. This is probably because, as proposed previously (Fujiwara et al., 2002), the transmembrane proteins anchored to and aligned along the actin mesh (pickets; see Fig. 3 A) form the diffusion barrier in both the outer and inner leaflets of the PM. The picket effect is due not only to the steric hindrance of the picket proteins, but also to the hydrodynamic-friction-like effect from the surface of the immobilized picket proteins on the surrounding medium (Fujiwara et al., 2002). Monte Carlo simulations showed that 20—30% occupancy of the compartment boundary by the immobile picket proteins (bound to the actin fence) is sufficient to cause confined + hop diffusion of the phospholipids in the PM outer leaflet (Fujiwara et al., 2002).

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