Figure S4.
MSD-∆t plots ensemble averaged over all trajectories, obtained by ultrahigh-speed single-molecule imaging of Cy3 molecules immobilized on coverslips or diffusing in the apical and basal PMs of T24 cells (using oblique-angle and TIR illuminations, respectively), providing estimates of single-molecule localization errors for diffusing molecules (as well as immobile molecules). All SEMs, including the error bars, are shown in the figure. The purposes of showing these figures are (1) to explain how to determine the single-molecule localization precisions of diffusing molecules in the PM using the MSD-∆t plot (because the method described in the caption to Fig. S2 is only useful for immobilized molecules) and (2) to show the actual localization precisions of diffusing molecules in the apical and basal PMs. First, see the panels in the left column, showing the MSD-∆t plots for molecules immobilized on the glass. Experimental MSD-∆t plots even for immobile molecules are expected to exhibit an offset, due to the position determination error; i.e., the flat MSD-∆t plot with a constant value (against ∆t), which equals 4σxy2 (where σxy = [σx + σy]/2; Dietrich et al., 2002; Martin et al., 2002). The linear fitting indeed showed that the slopes were ≈0; the localization precisions determined here for Cy3 on the glass at 10 and 30 kHz were 22 and 37 nm, respectively (TIR illumination at 79 µW/µm2). These results are consistent with those for immobilized molecules determined by the first method described in Fig. S2 (based on the standard deviations of the x and y position determinations for 15 consecutive frames) and shown in Fig. S3, B and C (20 and 34 nm, respectively; all SEMs for these values are provided in the figure; also see Fig. 1 F and Table 1). Next, see the panels in the middle and right columns, showing the MSD-∆t plots for molecules undergoing diffusion in the PM. As shown in the panels in the left column (immobilized molecules), the MSD values almost reach a plateau (which is the offset value) by the second step (∆t = 0.2 and 0.066 ms for Cy3 at 10 and 30 kHz, respectively). This means that the offset value of the MSD-∆t plot for diffusing molecules in the PM can be estimated as the y-intercept (by extrapolation) of the linear-fit function for the second, third, and fourth steps in the MSD-∆t plot (Fujiwara et al., 2002; middle column; see green keys), which is 4σxy2. Hence, the MSD-∆t plot that represents the diffusion effects can be obtained by plotting MSD − 4σxy2 against ∆t, as shown in Fig. 4 A. The single-molecule localization precisions determined this way (middle column) for Cy3-DOPE in the basal PM at 10 and 30 kHz were 34 and 51 nm, respectively, which were inferior to those found for the same molecules fixed on the glass (22 and 37 nm, respectively; left column). For Cy3-DOPE in the apical PM at 10 kHz, the localization precision was 49 nm, which was much worse than that in the basal PM (34 nm). The single-molecule localization precisions in the basal PM were worse than those determined on the glass, probably due to the higher background caused by cellular autofluorescence and the diffusional blurring of single-molecule spots. (A) The TIR laser illumination results of the ensemble-averaged MSD-∆t plots, for single Cy3 molecules covalently linked to the cover-glass surface coated with 3-aminopropyltriethoxysilane (left column) and for single Cy3-DOPE incorporated in the basal PM (middle and right columns), using the highest laser intensities of TIR illumination available for this instrument at 532 nm (79 µW/µm2). (a–d) This provided the best single-molecule localization precisions for recordings of Cy3 at 10 and 30 kHz, which were 22 and 37 nm on the glass (left column, a and b; n = 40 and 50, respectively), and 34 and 51 nm on the basal PM (middle column, c and d; n = 50 and 50, respectively). In the panels in the right column, the green curves are the best-fit functions describing the MSD-∆t plots for the confined-diffusion model, in which molecules undergo free diffusion while totally confined within a limited area during the observation period (Eqs. 11–13 in Kusumi et al., 1993). Since the observation durations for single molecules (1.5 and 0.75 ms full x-axis scales) were shorter as compared with the dwell time of Cy3-DOPE within a compartment, the confined fitting, rather than the hop-diffusion fitting, was employed. (B) The oblique-angle laser illumination results of the ensemble-averaged MSD-∆t plots, for single Cy3 molecules and 5xCy3-Tf on the coverslip (left column) and for single Cy3-DOPE, Cy3-Tf (with a dye-to-protein molar ratio of 0.2, so that virtually all of the single Tf molecules are labeled with either 0 or 1 Cy3 molecule) bound to TfR, and 5xCy3-Tf bound to TfR in the apical PM (middle and right columns). The oblique-angle laser illumination is widely applicable and useful because it can illuminate molecules located deeper in the cytoplasm as well as those present in the apical PM. Therefore, it is extensively used in the present research (standard conditions using an oblique-angle laser illumination power density of 23 µW/µm2). The numbers of examined spots: a and b, n = 17; d and e, n = 50; c, n = 40; f, n = 150 (a–c and d–f are on glass and on the apical PM, respectively). The illumination laser power densities were selected so that they were just beneath the level where dye saturation is obvious, and the single-molecule localization errors for various Cy3 specimens observed at different frame rates were similar to each other (see Fig. S3, B and C). More specifically, Cy3 and Cy3-DOPE at 10 kHz and 23 µW/µm2 (B a and d), Cy3 and Cy3-Tf at 6 kHz and 14 (23 × [6/10]) µW/µm2 (B b and e; because the frame time is [10/6]-times longer at 6 kHz), and 5xCy3-Tf at 45 kHz at 43 µW/µm2 (B c and f). Panels in the left column (molecules on the glass): The localization precisions determined here for Cy3 at 10 kHz (38 nm at 23 µW/µm2) and for 5xCy3-Tf at 45 kHz (39 nm at 43 µW/µm2) were consistent with those found in Fig. S3 B (37 and 38 nm, respectively). Panels in the middle and right columns (molecules in/on the apical PM): The single-molecule localization precisions determined for Cy3-DOPE (10 kHz, 23 µW/µm2), Cy3-Tf (6 kHz, 14 µW/µm2), and 5xCy3-Tf (45 kHz, 43 µW/µm2) in/on the apical PM were determined to be 49, 50, and 50 nm, respectively, which were inferior to those found for the same molecules fixed on the glass (38, 39, and 39 nm, respectively; left column). The localization errors were greater in the apical PM, probably due to the higher background caused by cellular autofluorescence and the blurring of single-molecule spots due to molecular diffusion within a frame time. In the right column in d and e, the green curves are the best-fit functions describing the MSD-∆t plots for an idealized hop-diffusion model (hop-diffusion fitting; see Supplemental theory 2 in the Supplemental text). In f, since the observation duration for single 5xCy3-Tf molecules employed here (0.5 ms full x-axis scale) was shorter as compared with the dwell time of TfR within a compartment, the confined fitting, rather than hop-diffusion fitting, was employed.

MSD-∆t plots ensemble averaged over all trajectories, obtained by ultrahigh-speed single-molecule imaging of Cy3 molecules immobilized on coverslips or diffusing in the apical and basal PMs of T24 cells (using oblique-angle and TIR illuminations, respectively), providing estimates of single-molecule localization errors for diffusing molecules (as well as immobile molecules). All SEMs, including the error bars, are shown in the figure. The purposes of showing these figures are (1) to explain how to determine the single-molecule localization precisions of diffusing molecules in the PM using the MSD-∆t plot (because the method described in the caption to Fig. S2 is only useful for immobilized molecules) and (2) to show the actual localization precisions of diffusing molecules in the apical and basal PMs. First, see the panels in the left column, showing the MSD-∆t plots for molecules immobilized on the glass. Experimental MSD-∆t plots even for immobile molecules are expected to exhibit an offset, due to the position determination error; i.e., the flat MSD-∆t plot with a constant value (against ∆t), which equals 4σxy2 (where σxy = [σx + σy]/2; Dietrich et al., 2002; Martin et al., 2002). The linear fitting indeed showed that the slopes were ≈0; the localization precisions determined here for Cy3 on the glass at 10 and 30 kHz were 22 and 37 nm, respectively (TIR illumination at 79 µW/µm2). These results are consistent with those for immobilized molecules determined by the first method described in Fig. S2 (based on the standard deviations of the x and y position determinations for 15 consecutive frames) and shown in Fig. S3, B and C (20 and 34 nm, respectively; all SEMs for these values are provided in the figure; also see Fig. 1 F and Table 1). Next, see the panels in the middle and right columns, showing the MSD-∆t plots for molecules undergoing diffusion in the PM. As shown in the panels in the left column (immobilized molecules), the MSD values almost reach a plateau (which is the offset value) by the second step (∆t = 0.2 and 0.066 ms for Cy3 at 10 and 30 kHz, respectively). This means that the offset value of the MSD-∆t plot for diffusing molecules in the PM can be estimated as the y-intercept (by extrapolation) of the linear-fit function for the second, third, and fourth steps in the MSD-∆t plot (Fujiwara et al., 2002; middle column; see green keys), which is 4σxy2. Hence, the MSD-∆t plot that represents the diffusion effects can be obtained by plotting MSD − 4σxy2 against ∆t, as shown in Fig. 4 A. The single-molecule localization precisions determined this way (middle column) for Cy3-DOPE in the basal PM at 10 and 30 kHz were 34 and 51 nm, respectively, which were inferior to those found for the same molecules fixed on the glass (22 and 37 nm, respectively; left column). For Cy3-DOPE in the apical PM at 10 kHz, the localization precision was 49 nm, which was much worse than that in the basal PM (34 nm). The single-molecule localization precisions in the basal PM were worse than those determined on the glass, probably due to the higher background caused by cellular autofluorescence and the diffusional blurring of single-molecule spots. (A) The TIR laser illumination results of the ensemble-averaged MSD-∆t plots, for single Cy3 molecules covalently linked to the cover-glass surface coated with 3-aminopropyltriethoxysilane (left column) and for single Cy3-DOPE incorporated in the basal PM (middle and right columns), using the highest laser intensities of TIR illumination available for this instrument at 532 nm (79 µW/µm2). (a–d) This provided the best single-molecule localization precisions for recordings of Cy3 at 10 and 30 kHz, which were 22 and 37 nm on the glass (left column, a and b; n = 40 and 50, respectively), and 34 and 51 nm on the basal PM (middle column, c and d; n = 50 and 50, respectively). In the panels in the right column, the green curves are the best-fit functions describing the MSD-∆t plots for the confined-diffusion model, in which molecules undergo free diffusion while totally confined within a limited area during the observation period (Eqs. 11–13 in Kusumi et al., 1993). Since the observation durations for single molecules (1.5 and 0.75 ms full x-axis scales) were shorter as compared with the dwell time of Cy3-DOPE within a compartment, the confined fitting, rather than the hop-diffusion fitting, was employed. (B) The oblique-angle laser illumination results of the ensemble-averaged MSD-∆t plots, for single Cy3 molecules and 5xCy3-Tf on the coverslip (left column) and for single Cy3-DOPE, Cy3-Tf (with a dye-to-protein molar ratio of 0.2, so that virtually all of the single Tf molecules are labeled with either 0 or 1 Cy3 molecule) bound to TfR, and 5xCy3-Tf bound to TfR in the apical PM (middle and right columns). The oblique-angle laser illumination is widely applicable and useful because it can illuminate molecules located deeper in the cytoplasm as well as those present in the apical PM. Therefore, it is extensively used in the present research (standard conditions using an oblique-angle laser illumination power density of 23 µW/µm2). The numbers of examined spots: a and b, n = 17; d and e, n = 50; c, n = 40; f, n = 150 (a–c and d–f are on glass and on the apical PM, respectively). The illumination laser power densities were selected so that they were just beneath the level where dye saturation is obvious, and the single-molecule localization errors for various Cy3 specimens observed at different frame rates were similar to each other (see Fig. S3, B and C). More specifically, Cy3 and Cy3-DOPE at 10 kHz and 23 µW/µm2 (B a and d), Cy3 and Cy3-Tf at 6 kHz and 14 (23 × [6/10]) µW/µm2 (B b and e; because the frame time is [10/6]-times longer at 6 kHz), and 5xCy3-Tf at 45 kHz at 43 µW/µm2 (B c and f). Panels in the left column (molecules on the glass): The localization precisions determined here for Cy3 at 10 kHz (38 nm at 23 µW/µm2) and for 5xCy3-Tf at 45 kHz (39 nm at 43 µW/µm2) were consistent with those found in Fig. S3 B (37 and 38 nm, respectively). Panels in the middle and right columns (molecules in/on the apical PM): The single-molecule localization precisions determined for Cy3-DOPE (10 kHz, 23 µW/µm2), Cy3-Tf (6 kHz, 14 µW/µm2), and 5xCy3-Tf (45 kHz, 43 µW/µm2) in/on the apical PM were determined to be 49, 50, and 50 nm, respectively, which were inferior to those found for the same molecules fixed on the glass (38, 39, and 39 nm, respectively; left column). The localization errors were greater in the apical PM, probably due to the higher background caused by cellular autofluorescence and the blurring of single-molecule spots due to molecular diffusion within a frame time. In the right column in d and e, the green curves are the best-fit functions describing the MSD-∆t plots for an idealized hop-diffusion model (hop-diffusion fitting; see Supplemental theory 2 in the Supplemental text). In f, since the observation duration for single 5xCy3-Tf molecules employed here (0.5 ms full x-axis scale) was shorter as compared with the dwell time of TfR within a compartment, the confined fitting, rather than hop-diffusion fitting, was employed.

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