Development of ultrafast camera-based single fluorescent-molecule imaging for cell biology

Abstract

The spatial resolution of fluorescence microscopy has recently been greatly enhanced. However, improvements in temporal resolution have been limited, despite their importance for examining living cells. Here, we developed an ultrafast camera system that enables the highest time resolutions in single fluorescent-molecule imaging to date, which were photon-limited by fluorophore photophysics: 33 and 100 µs with single-molecule localization precisions of 34 and 20 nm, respectively, for Cy3, the optimal fluorophore we identified. Using theoretical frameworks developed for the analysis of single-molecule trajectories in the plasma membrane (PM), this camera successfully detected fast hop diffusion of membrane molecules in the PM, previously detectable only in the apical PM using less preferable 40-nm gold probes, thus helping to elucidate the principles governing the PM organization and molecular dynamics. Furthermore, as described in the companion paper, this camera allows simultaneous data acquisitions for PALM/dSTORM at as fast as 1 kHz, with 29/19 nm localization precisions in the 640 × 640 pixel view-field.

Figure 1.

Basic design of the ultrahigh-speed intensified CMOS camera system and ultrafast single fluorescent-molecule imaging and tracking (SFMI) of Cy3 molecules immobilized on coverslips, performed to establish suitable conditions for ultrafast SFMI. To obtain the data shown here, total internal reflection (TIR) illumination was employed. The mean ± SEM and/or the median values are provided in the figures throughout this report. (A) Schematic diagram of the camera system. See Materials and methods. (B and C) All of the single Cy3 molecules detected at 60 Hz were also detectable at 10 (B) and 30 (C) kHz (the same field of view). Typical snapshots are shown. (D) Typical snapshots of single Cy3 molecules excited at various laser powers, observed at 10 kHz. (E) The number of detected photons/molecule/frame emitted from single Cy3 molecules during frame times of 0.1 ms (10 kHz) and 0.033 ms (30 kHz; n = 50 Cy3 molecules for each measured point; the same for F, G, and H), plotted against the excitation laser power density. See the caption to Fig. S3 A. (F) The localization errors for single Cy3 molecules imaged at 10 and 30 kHz, plotted against the excitation laser intensity. Orange, cyan, and purple data points are color-matched with the arrowheads in B, C, and D. (G and H) The number of detected photons/molecule/frame (G) and the localization error (H) for single Cy3 molecules imaged at 60 Hz, plotted as a function of the excitation laser power density. See the caption to Fig. S2 D. The green data points are color-matched with the arrowheads in B, C, and I. (I) Virtually all of the single 5xCy3-Tf molecules (3–8 molecules of Cy3 bound to Tf) were detectable at 45 kHz (compare with the 60-Hz image); typical snapshots.

Figure S1.

Establishing the intensifier set up for detecting single photons using the electron amplification of the image intensifier (8,100×). (A) The readout noise of individual pixels of the CMOS chip used here. The map (top) of the means (left) and variances (right) of pixels (256 × 256 pixels) and their histograms (bottom; Huang et al., 2013) for 1,000 frames obtained at 10 kHz. (B) Typical images of single photons obtained as a function of the intensifier gain, using the newly developed camera system. They were obtained by amplifying single electrons emitted from the image-intensifier photocathode by the arrivals of single photons (uniform Köhler illumination by the strongly attenuated halogen lamp of the microscope). The amplifications were 506, 8,100, and 129,600 (increases by a factor of 16 from left to middle and middle to right images). Note that the term “overall electron amplification (of the camera system)” always excludes the 40% quantum efficiency of the image intensifier photocathode throughout this report, because we discuss the amplification of the number of electrons from the photoelectrons emitted by the photocathode. The range of the gray levels of the images shown here (both B and C) was set for 8 bits from 0 to 550 electrons/pixel at the CMOS sensor (from black to white). (C) As an example, we show that an overall electron amplification of 506× by the camera system would not be sufficient for the consistent detection of single photons, due to the readout noise. (C a) A schematic figure showing a 7 × 7 pixelated image for a single detected photon amplified to a total of 517 electrons (without noise and background; computer-generated, assuming an overall amplification of 506× with an SD of 0.28 ± 0.085 pixels as in B left). The number of amplified electrons in each pixel on the CMOS sensor is shown. A full well of 45,000 electrons/pixel of the CMOS sensor (SA1) is scaled to 12 bits (4,095 camera counts, and hence a unit camera count = 10.99 [≈11] electrons per pixel), and thus each number is a multiple of 11 electrons. (C b) Three arbitrarily selected (experimentally obtained) 7 × 7 pixelated images representing the spatial distributions of the readout noise of the CMOS sensor employed in this study (37-root-mean-square electrons/pixel/frame; see “Ultrahigh-speed intensified CMOS camera system: Design and operation” in Materials and methods). To detect a (photon-converted) emitted electron, its image, such as that shown in a, must be detectable in the presence of spatiotemporally varying noise, as shown here. The detectability will be enhanced by an increase of the electron amplification. See D. (D) Stochastic gain variations (fluctuations) of the image intensifier. At the level of detecting single photons, the gain variations are large (at the level of detecting single molecules, relative variations will become smaller due to averaging over all detected photons). In these histograms, the distributions of the number of total electrons stored at the CMOS sensor of the camera system for each single detected photon at the image-intensifier photocathode (i.e., for each discernible spot in images like those in B) are shown for the overall electron amplifications of 506×, 8,100×, and 129,600× (the y axis is normalized by the peak value in each histogram; the full x scale is increased by a factor of 16 from the left figure to the middle figure and from the middle figure to the right figure). The spots in the images (like those in B) were identified and the total number of electrons in each spot was evaluated using the functions of the ThunderSTORM plugin of ImageJ (Ovesný et al., 2014). For the spot detection with localization precisions at the pixel level (the peak pixel), we employed the “Wavelet filtering” (B-Spline order = 3 and B-Spline scale = 2.0) and the “Local maximum method” (Peak intensity threshold = 4.5 and Connectivity = 8-neighborhood). For the determination of the total number of electrons in a spot (and subpixel localization of each spot), we performed the Gaussian fitting of the image (i.e., the number of electrons/pixel in 11 × 11 pixels surrounding the peak pixel) and then integrated the best-fit function, using the Subpixel localization of molecules. These histograms were obtained using six 5,000-frame image sequences recorded at 10 kHz with a frame size of 13.4 × 13.4 µm on the focal plane, detecting 62,066, 459,156, and 510,165 photons (electrons emitted from the photocathode of the image intensifier) for overall amplifications of 506×, 8,100×, and 129,600×, respectively. They represent both the stochastic gain variations and the detectability of a photon image produced by the amplified electrons. See the histogram for 506×. The occurrences of the number of amplified electrons/detected photon sharply decreased when the number of amplified electrons was reduced below ≈650 electrons (the peak in the histogram). This is very likely due to a sharp reduction in the detectability of the spots produced by <650 electrons. Namely, when the signal intensity (the number of electrons) after amplification is small, the chance that the signal becomes less than the readout noise increases, because the readout noise pattern also fluctuates spatiotemporally (see C). (E) The probability of detecting a single photon was increased to 90.0% of the saturation level, at an overall electron amplification of 8,100×. Here, the number of detected photons per frame (mean ± SD); i.e., the number of discernible spots in the images like those in B (detected by the method described in D), is plotted as a function of the overall electron amplification (averaged over six 5,000-frame image sequences). With an increase in the overall electron amplification, the number of discernible spots increases. At an overall electron amplification of 8,100×, the number of discernible spots was 90.0% of the saturated number of spots (i.e., at the maximal overall electron amplification possible with the present instrument, which is 129,600× amplification). At the overall amplifications giving the saturated number of spots, virtually every photoelectron emitted from the photocathode is considered to be detected. Therefore, throughout the present research, we employed 8,100× as the overall electron amplification of the image intensifier (see “Ultrahigh-speed intensified CMOS camera system: Design and operation” in Materials and methods).

Figure S2.

Establishing the photophysics of various fluorescent probe molecules by independently evaluating the number of detected photons (proportional to the emitted photons) from a single fluorescent molecule during a single frame time (N; x-axis) and single-molecule localization precision (${\sigma }_{\mathrm{x}\mathrm{y}}=\left[{\sigma }_{\mathrm{x}}+{\sigma }_{\mathrm{y}}\right]/2$; y-axis), under various excitation laser powers and single-frame durations. These plots can be fitted well with the equation later in this legend, indicating that these measurements were performed with satisfactory accuracies. With an increase of the excitation laser power (at the sample), some dyes emit more photons than others, showing that they are more suitable for ultrafast SFMI. These curves are useful for determining the fluorescent probes to be used in the experiments and for predicting the single-molecule localization precisions that can be obtained under the given excitation laser powers. The results for 30, 10, and 0.06 kHz; i.e., the frame times of 0.033, 0.1 and 16.7 ms, respectively, are shown (45 kHz/0.022 ms for 5xCy3-Tf is also shown). For the method to evaluate N, see the subsection “Determination of the number of detected photons/molecule/frame (N)” in Materials and methods. In high-speed single fluorescent-molecule imaging, one of the crucial problems is whether single fluorescent molecules emit sufficient numbers of photons (during a single frame time) required for obtaining the desired single-molecule localization precisions. The results shown here demonstrate that a 10-kHz frame rate is applicable for various dye molecules, and Cy3 could even be used at 30 kHz. These plots were fitted well by the theoretical equation derived previously (Mortensen et al., 2010), indicating that the developed camera system functions as planned, even at high frequencies. The excess noise factor (F) of the developed camera system was evaluated by this fitting. Throughout this report (except for the measurements in the plasma membrane (PM), as described in Fig. S4), the localization precision (σ_xy) is defined as [σ_x + σ_y]/2, where σ_x and σ_y are the standard deviations of the x and y position determinations, respectively, following the convention of the super-resolution imaging field (Dietrich et al., 2002; Martin et al., 2002). σ_xy was determined in 15 consecutive frames for n = 50 trajectories for each condition. All of the fluorescent dye molecules were covalently bound to coverslips coated with 3-aminopropylethoxysilane, and 5xCy3-Tf was adsorbed on the coverslip coated with poly-D-lysine (Materials and methods). (A and B) Plots for single Cy3 molecules observed at 10 and 30 kHz and single 5xCy3-Tf molecules observed at 45 kHz (A) and those for various fluorescent molecules observed at 10 kHz (B). Five TIR laser illumination intensities were employed for each dye (50 molecules for each laser intensity), as indicated by the different colors of the data points. Various ranges of the laser power densities were used for different dyes, because the dyes are saturated differently (shown in each box). The plots (σ_xy vs. N) shown in A and B could be fitted well (non-linear least-squares fitting by the Levenberg–Marquardt algorithm) using the following equation derived previously (Mortensen et al., 2010). ${\sigma }_{xy}=F{\left\{\frac{16\left(s^2+a^2/12\right)}{9N}+\frac{8\pi b^2{\left(s^2+a^2/12\right)}^2}{a^2{N}^2}\right\}}^{1/2}\text{,}$ where F is the sole fitting parameter, representing the excess noise factor (a coefficient describing the stochastic gain fluctuation in the electron amplification process in the image intensifier; F is shown in each box, but its value is 1.2—1.4 for all cases), s is the standard deviation of the Gaussian spot profile, 123 ± 1.1 nm for Cy3 on the sample plane (determined by the Gaussian fitting of each image for 50 Cy3 molecules immobilized on the glass excited by the TIR illumination at 79 µW/µm²; compared with our standard condition of the oblique illumination at 23 µW/µm², these observation conditions provided ∼3 times more detected photons; see Fig. 1 E, top; note that s depends on the observed fluorescent molecules), a is the pixel size (55.1 nm), and b is the standard deviation of the background noise. (For example, 0.038 ± 0.059 detected photons/pixel/frame [mean ± SD] for the TIR illumination and 0.035 ± 0.058 detected photons/pixel/frame for the oblique illumination at 10 kHz; n = 76,800 pixels = 32 × 32 pixels × 15 frames x 5 different positions.) The estimated excess noise factor F of the image intensifier shows that it is comparable to or slightly smaller (less noisy) than that of the EM-CCD electron multiplier (F = 1.4). Cy3 exhibited the least tendency to saturate, and thus provided better single-molecule localization precisions, consistent with the analysis results shown in Fig. S3, A and C. Note that s and b were determined for each fluorescent probe (with different illumination and excitation wavelengths and optics). 5xCy3-Tf data are considered to represent fluorescent spots generated by various numbers of Cy3 molecules placed within a few nanometers, mostly in the range of 3 to 8 molecules (1 and 2 Cy3 molecules/Tf, representing ≈12% of the 5xCy3-Tf spots, gave low signals, inducing extremely large errors in single-molecule localizations; meanwhile, the probability of 9 or more Cy3 molecules being attached to a Tf molecule will be <7%). Due to the photobleaching of multiple Cy3 molecules bound to a Tf molecule, the numbers detected on a Tf molecule decreased quickly upon laser illumination. (C) Plot for single Cy3 molecules observed at 60 Hz, with TIR illumination laser power densities ≤0.16 µW/µm² (indicated by different colors of the data points; 50 molecules for each laser intensity). The excess noise factor F was estimated to be 1.2, consistent with the results shown in A. (D) Summary plot for single Cy3 molecules observed at 60 Hz, with TIR illumination laser power densities up to 79 µW/µm²: 0.018, 0.029, 0.047, 0.088, 0.16 (employed for the plot in c), 0.48, 1.6, 4.8, 14, 23, 43, and 79 µW/µm² (note that in this plot, in contrast to the others, the x-axis is in the log scale). The single-molecule localization precisions obtained with the laser power densities equal to and >14 µW/µm² were calculated using the equation above with F = 1.2, as found in C. This method for obtaining the single-molecule localization precisions employed here is different from that used for evaluating the precisions shown in Fig. 1 F and Fig. S2, A–C; and Fig. S3, B and C. Since most Cy3 molecules were photobleached within a single 16.7 ms frame, the more-prevalent method could not be employed. The x-axis of this figure covers the entire practical scale for the number of detected photons/molecule/frame (N) for a single Cy3 molecule, from 25.0 ± 1.4 at a laser power density of 0.018 µW/µm² up to 11,400 ± 700 at 79 µW/µm² (mean ± SEM). This upper limit was given by the photobleaching and excitation power saturation of Cy3, and provided the best single-molecule localization precision of 2.6 ± 0.099 nm (mean ± SEM) for Cy3 (no further improvements could be obtain even by employing higher laser intensities; Fig. 1, G and H).

Figure S3.

The numbers of detected photons/frame from single molecules (N, proportional to the emitted photons during a frame time) are saturated under stronger excitation laser intensities, and thus the improvement of single-molecule localization precision (σ_xy) with an increase of the laser intensity is limited. For experimental details, see the caption to Fig. S2. (A) For various commonly used fluorescent probes, the numbers of detected photons/molecule/frame are plotted against the laser power density at the focal plane (TIR illumination; the additional examinations using oblique illuminations were only performed for Cy3 and 5xCy3-Tf), showing that Cy3 and Alexa555 are less prone to laser-power saturation. With an increase in the excitation laser intensity, the number of detected photons from single dye molecules initially increased proportionally, and then leveled off (saturation occurred), probably due to “triplet bottleneck saturation” (see “Estimation of the number of photons that can be emitted by a single Cy3 molecule during 0.1 ms: Triplet bottleneck saturation” in Materials and methods). This occurred from around 23 µW/µm² for Cy3 (the results of Cy3 at 10 and 30 kHz shown here are the same as those shown in Fig. 1 E, and are reproduced here for ease of comparison with the results of other dyes). Cy3 and Alexa555 are less prone to saturation, as compared with the other dyes tested here. In the present study, we primarily used Cy3. (B) Distributions of the localization precisions of single molecules of eight fluorophores observed at 10 kHz (an integration time of 0.1 ms), single Cy3 molecules at 30 kHz (0.033 ms), and 5xCy3-Tf at 45 kHz (0.022 ms), evaluated at various laser illumination intensities (provided on the right). Arrowheads indicate the median values. (C) For various commonly used fluorescent probes, single-molecule localization precisions (mean ± SEM) are plotted against the laser intensity (the results for Cy3 at 10 and 30 kHz shown here are the same as those shown in Fig. 1 F, and are reproduced here for ease of comparison with the results of other dyes). These results show that Cy3 and Alexa555 provide better single-molecule localization precisions at higher laser intensities, due to their lower tendency to saturate. Since Cy3 provided slightly better single-molecule localization precision at 10 kHz at saturation than Alexa555, we primarily used Cy3 throughout the remaining part of this report. Based on the results described in A and C, and also due to the versatility of the oblique-angle illumination to enable the observations of single molecules in both the basal and apical PMs, as well as in endomembranes and the cytoplasm in general (see the subsection “TIR and oblique illuminations for ultrafast SFMI” in the main text), we comprehensively tested and performed ultrafast single-molecule imaging-tracking under the oblique-angle illumination conditions, with a laser power density of 23 µW/µm² at the specimen plane. These are the “standard test conditions,” using Cy3 molecules on the coverslip as the standard sample.

Figure 2.

Trackable durations of single Cy3 molecules under two typical laser illumination conditions and minimal photo-induced damage to cells during ultrafast SFMI. (A–C) Single Cy3 molecules immobilized on a coverslip were observed. The trackable durations are limited by photoblinking/photobleaching, stochastic fluctuations of the signal, and photon shot noise. (A a–c) Typical time-dependent fluorescence signal intensities (number of detected photons/0.1-ms-frame) of three single Cy3 molecules (a, b, and c) excited by oblique-angle illumination at 23 µW/µm², and observed at 10 kHz (background signal in gray). See Materials and methods for details. (B a–c) The signal-to-noise ratios (SNRs) for the images of the three molecules (a, b, and c) shown in A fall in the range between 2.4 and 3.2. See Materials and methods. (C) The distributions of the durations of the on-periods and those after neglecting the off-periods (non-emission periods) lasting for 1, 2, or 3 frames (gap closing; see Materials and methods) of single Cy3 molecules immobilized on a coverslip and excited by oblique-angle illumination at 23 µW/µm² (standard conditions; left) or by TIR illumination at 79 µW/µm² (right), observed at 10 kHz (totals of 264 and 593 molecules, respectively). The three-frame gap closing was employed in single-molecule tracking under the standard test conditions (thick orange curve; left). (D and E) Photo-induced damage to the cells during ultrahigh-speed SFMI is very limited under our standard experimental conditions. Cell viability was examined by staining with 1 µM TOTO-3 iodide, which selectively stains dead cells, at 37°C for 5 min, and then observing the stained cells using epi-illumination with a 594-nm laser. (D) Representative images of the nuclei stained with TOTO-3 iodide. Control, a reference image of a living cell (n = 24 images). H₂O₂, a reference image of a dead cell after the treatment with 100 µM H₂O₂ at 37°C for 1 h (n = 48 images). (E) Histograms showing the fluorescence intensity of TOTO-3 in the 5.5 × 5.5-µm area inside the nucleus (see the square box in D; n = the number of examined cells). Top: Live cells without laser illumination (negative control). Second: Dead cells after the H₂O₂ treatment (positive control). Based on the results of the negative and positive controls (top and second boxes, respectively), a threshold fluorescence intensity of 4.0 × 10⁵ (arbitrary unit = AU) was selected to categorize the live and dead cells (96% [90%] of the negative [positive] control cells were categorized as alive [dead]). Third and Fourth: Cells were subjected to illumination under our typical 10-kHz single Cy3 molecule imaging conditions (oblique-angle 532-nm laser illumination at 23 µW/µm²) for 1 and 10 min, respectively, which are longer by factors of 12 and 120 than our longest illumination duration of 5 s/cell (10 500-ms image sequences = 5 × 10⁴ frames). We concluded that the light-induced damage to the cells is insignificant under our standard experimental conditions.

Figure 3.

Ultrafast SFMI of Cy3-labeled DOPE and TfR in the apical PM. (A) Schematic drawing showing that membrane molecules undergo hop diffusion in the PM, which is compartmentalized by the actin-based membrane-skeleton (MSK) meshes (fences; brown mesh) and rows of transmembrane-protein pickets anchored to and aligned along the actin fence (gray molecules). (B) A typical snapshot of single Cy3-DOPE molecules in the apical PM observed under our standard conditions, with an integration time of 0.1 ms. (C) A representative image sequence of a single Cy3-DOPE molecule diffusing in the apical PM, recorded every 0.1 ms (shown every 100 image frames = every 10 ms). The colors in the trajectory indicate the diffusion in different plausible compartments (order of appearance: purple, blue, green, orange, red, and then back to purple; the same color order is used throughout this report), detected by the TILD analysis software (Fig. S5). (D) Typical single-molecule trajectories of Cy3-DOPE and Cy3-Tf-TfR in intact and actin-depleted blebbed apical PMs, recorded at normal video rate and enhanced rates. The order of the compartments that the molecule visited (parenthesized integers) and the residency times there, as determined by the TILD analysis, are indicated (intact PMs).

Figure 4.

Ultrafast SFMI can detect hop diffusion of Cy3-DOPE and TfR in the apical PM, previously found by ultrafast single gold-particle tracking. (A a–c) Typical MSD-∆t plot for a single molecule (a), and the ensemble-averaged MSD-∆t plots with two different y-axis scales (b and c: 20× of b) in the intact apical PM (black) and the blebbed apical PM (purple). The MSD-∆t plots of the top and middle boxes in (b) are those after subtracting 4σ_xy², shown in Fig. S4 (σ_xy = single-molecule localization precision). Only in the typical MSD-∆t plot for a single 5xCy3-Tf molecule bound to TfR obtained at 45 kHz (a, bottom), 4σ_xy² was not subtracted due to large errors in its estimation. Green curves are the best-fit functions for the hop-diffusion fitting (top and middle rows) and confined-diffusion fitting (bottom row for 45 kHz observations of 5xCy3-Tf). (B) Approximately 80% of Cy3-DOPE and TfR undergo suppressed diffusion in the intact apical PM, whereas >90% of them undergo simple-Brownian diffusion in the actin-depleted blebbed PM (shaded histograms in b), as revealed by the method for the statistical classification of each single-molecule trajectory into a suppressed-, simple-Brownian-, or directed-diffusion mode. (B a) The basic idea for the classification of trajectories into suppressed, simple-Brownian, and directed diffusion: the parameter RD (relative deviation) describes the extent to which the observed diffusion deviates from simple-Brownian diffusion at a time sufficiently later from time 0; i.e., the actual MSD divided by the calculated MSD from the short-term diffusion coefficient (D_2-4) assuming simple-Brownian diffusion. See Materials and methods. The RD value is <<, ≈, or >> 1, when the molecules are undergoing suppressed, simple-Brownian, or directed diffusion, respectively (Fujiwara et al., 2002; Kusumi et al., 1993; Murase et al., 2004; Suzuki et al., 2005). The suppressed-diffusion mode includes both the confined-diffusion and hop-diffusion modes. (B b) Classification of individual trajectories based on the RD histograms for simulated simple-Brownian particles (open bars; n = 5,000). The RD values giving the 2.5 percentiles of the particles from both ends of the distribution, referred to as RD_min and RD_MAX, were obtained (red and blue vertical lines, respectively). Each experimental single-molecule trajectory was classified into suppressed (confined and hop), simple-Brownian, or directed diffusion when its RD value was smaller than RD_min, between RD_min and RD_MAX, and greater than RD_MAX (no trajectory fell in this category), respectively. The distributions of RDs for the Cy3-DOPE and TfR trajectories are shown by shaded histograms (n = 50 and 20 for the intact and actin-depleted blebbed PM, respectively). (C a and b) In the blebbed apical PM, Cy3-DOPE (a) and Cy3-Tf bound to TfR (b) exhibited single diffusion coefficients that are ≈20× greater than D_MACRO in the intact apical PM. The distributions of D_micro (=D_2–4) are underestimated due to the insufficient time resolution for measuring D_micro within a compartment, even at a 0.1-ms resolution. Arrowheads indicate the median values (summarized in Table 2). These diffusion coefficients in the blebbed PM are slightly smaller than those obtained with gold probes (Fujiwara et al., 2002; Fujiwara et al., 2016). This is probably due to the residual actin filaments in the T24 cells employed here, since the membrane-bound actin filament meshes are much denser in T24 cells than the NRK cells used previously. (D) Cy3-DOPE and TfR exhibited similar compartment size distributions, suggesting that the underlying mechanism for the compartmentalization would be the same for the phospholipid and the transmembrane protein. Arrowheads indicate the median values. The statistical test methods, parameters (number of experiments), and P values are summarized in Table 2.

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 4σ_xy² (where σ_xy = [σ_x + σ_y]/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 4σ_xy². Hence, the MSD-∆t plot that represents the diffusion effects can be obtained by plotting MSD − 4σ_xy² 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.

Figure S5.

The TILD method for detecting the moment (instance) when a diffusing molecule in the PM undergoes the hop movement from a compartment to an adjacent one in the PM. We developed an improved method for detecting the hop moment (instance). This method detects the Transient Increase of the effective Local Diffusion (TILD) in a single-molecule trajectory. TILDs are likely to occur when a molecule hops between two membrane compartments, but our analysis itself remains model-independent of any particular model. During an intercompartmental hop, a molecule experiences two compartments instead of one within the time window that includes the hop instance, thus leading to an increase in the effective local diffusion coefficient. To identify TILDs in a given trajectory, consider a window with a size of n frames (n steps), starting from a frame m (m ∼ m + n). Within this window, the center of the n recorded coordinates (n points) is defined, the radial displacements for all of these n points from this center are calculated, and then their maximal value R_MAX(m,n) is determined. Next, the relative diffusion coefficient for this window is defined as $D_{rel}\left(m,n\right)\equiv \frac{\frac{R_{\mathit{MAX}}^2\left(m,n\right)}{4n\delta t}}{D_{2-4}},$ where δt is the time step in the trajectory (inverse of the frame rate), and D₂₋₄ is the average short-term diffusion coefficient determined for the time interval between 2δt and 4δt (averaged over the whole trajectory; Kusumi et al., 1993), which is included for normalization. For free Brownian diffusion, D_rel(m,n) is ≈ 1 (allowing for statistical variations), independent of m or n. If a molecule is temporarily trapped in a finite domain, then as the window size n increases, D_rel(m,n) decreases due to entrapment. When the window size has increased sufficiently to include the release of the diffusing particle from the finite domain, there will be a sharp increase in D_rel(m,n), due to the extended range of diffusion. To flag releases, the function $H\left(m,n\right)=\left|1/D_{rel}\left(m+1,n\right)-1/D_{rel}\left(m,n\right)\right|$ was employed, and by scanning all possible m and n pairs in the full trajectory, a map of H(m,n) was produced. Releases from the trapped domain are flagged by sharp peaks in H(m,n) for both the special starting position (e.g., if position m is before a hop and position m+1 is after a hop, then for all window sizes n, D_rel(m,n) will be greater than D_rel(m+1,n)) and for the combination of a starting position and a window size (e.g., if the trajectory, starting from position m with a window size n, and ending at point p = m + n, is wholly within an entrapped domain, and if extending the window size by 1 includes release from the entrapped domain, then D_rel(m,n+1) will be greater than D_rel(m,n) for all m and n values, such that m + n = p). The minimum number of points within an entrapped domain required to allow the detection of the moments of TILDs is determined by the stochastic nature of diffusion (+ the diffusion coefficient within the domain and the domain size) and the noise present in the position determination. As such, due caution was exercised to avoid choosing a plethora of small compartments erroneously. Typically, the total length of each trajectory analyzed here was 1,000 steps. The n value was varied from 21 to N−m, where N is the total number of steps in a trajectory (= 1,000). In addition to this anterograde direction of analysis over a single trajectory, the same trajectory was analyzed in the retrograde direction in the same way as for the anterograde direction, in order to determine whether the sudden increase in H(m,n) can also be observed for the same m in the anterograde analysis. Therefore, for a single m value, H(m,n) was calculated for [N−40] windows ([N−m−20] + [m−20]). Here, we first describe the results of testing the TILD method using Monte-Carlo simulated hop and simple-Brownian trajectories with a single-molecule localization precision of 50 nm (error for Cy3 in the apical PM, which is the worst precision in the present report; A). Second, we describe the application of the TILD method to detect the hop moments in single-molecule trajectories of Cy3-DOPE, observed in the intact apical PM as well as in the actin-depleted blebbed PM (B). (A) Testing the TILD detection method using computer-generated hop and simple-Brownian diffusion trajectories, and examination of the exponential distributions of the residency times within a compartment. (A a) Typical hop-diffusion (left) and simple-Brownian (right) trajectories generated by Monte Carlo simulation (every 0.1 ms; the initial 400-steps of the 1,000-step-long trajectories are shown here, whereas the TILD analysis was performed for the full 1,000 steps for all of the trajectories). The moments of TILDs determined by the developed protocol are shown by the thick, short red subtrajectories (three-frame trajectories defined by the TILD moment ±1 frame; note their tilde-like shapes). This particular hop-diffusion trajectory (400-frames long) on the left contained three TILDs. The simple-Brownian trajectory (400-frames long) on the right exhibits no TILD. Hop-diffusion trajectories were generated as described previously (Ritchie et al., 2005), except that the unit time step was 0.1 µs. Using a two-dimensional square array of partially permeable barriers separated by 100 nm (L), with a probability of transmission per attempt of 0.0005, the experimental D_MACRO for Cy3-DOPE in the intact apical PM (0.30 µm²/s; Table 2) was reproduced (D_micro was set at 9 µm²/s, as shown in Fujiwara et al., 2002). A single-molecule localization error of 0, 25, or 50 nm was added as the Gaussian noise to each x- and y-coordinate in the hop trajectories (here, the trajectories including a 50-nm localization error are shown). Among 100 trajectories generated by the simulation (1,000 frames per trajectory), 97, 94, and 80 trajectories were statistically classified into the suppressed diffusion mode in the presence of single-molecule localization errors of 0, 25, and 50 nm, respectively. Test trajectories of simple-Brownian particles were generated by Monte Carlo simulations, using a diffusion coefficient of 6 µm²/s, as experimentally obtained in blebbed PMs (Table 2; employing 9 µm²/s made virtually no difference), and Gaussian localization errors were added. (A b) Typical plots of H(m,n) vs. m (only the results with window sizes of n = 100, 200, and 300 for the trajectories shown in A a. The sharp changes (peaks) in H(m,n) are likely to represent the hop movements (transient increase of local diffusion coefficient), and spurious peaks from statistical variations and noise can mostly be distinguished because they only appear in the displays for limited numbers of windows. Briefly, for the same frame number m, H(m,n) was calculated for all possible n’s (N−40 windows), and when the percentage of windows in which H(m,n) ≥ 1 was >20% among a total of [N−40] windows, the molecule was regarded as undergoing the process of intercompartmental hopping. In this figure, the peaks that satisfied these thresholds are highlighted by vertical pink bars, indicating the occurrences of TILDs, i.e., hop events. Other peaks in this display did not satisfy the threshold conditions explained here, and do not represent TILDs. In the application of the TILD detection method to individual trajectories, a three-frame running average (replacing the position of the kth frame with the position averaged for the k−1, k, and k+1 frames) was first applied to each trajectory, to minimize the effect of apparently large displacements that stochastically occurred due to the 50-nm single-molecule localization error. The detectability percentages of hop events (given by the simulation program) for simulated trajectories classified into suppressed diffusion were 82, 76, and 66%; and the accuracies of the predicted hop events were 75, 66, and 60% at localization errors of 0, 25, and 50 nm, respectively. In our standard conditions for long-term single-molecule tracking experiments (1,000 steps; 0.1-ms resolution; a 532-nm laser excitation laser power of 23 µW/µm² at the sample), the single-molecule localization error was 49 nm in the apical PM. (A c) Distributions of the residency lifetimes within a compartment for Monte-Carlo simulated test particles undergoing hop diffusion. The residency time of a particle within a compartment was obtained as the duration between two consecutive TILDs. Top (Ground Truth Distribution Given by the Simulation): The correct distribution of the residency times determined from the hop events (given by the simulation program), which occurred in 100 simulated 1,000-frame long hop trajectories. The residency times shorter than 40 frames (4 ms) were neglected, due to various uncertainties in the short time ranges. The distribution could be fitted with a single exponential function with a decay time constant of 9.0 ± 0.088 ms (mean ± SEM; SEM is provided as the fitting error of the 68.3% confidence interval). The exponential distribution of the residency times found for simulated hop-diffusion trajectories can actually be predicted theoretically, as summarized in Supplemental theory 1 in the Supplemental text. The theory also predicts that its decay time constant can be described by L²/4D_MACRO. In the present simulation, the average dwell time calculated using this equation was 8.3 ms (L = 100 nm, the average D_MACRO obtained from the simulation was 0.3 µm²/s). This value agrees quite well with the dwell lifetimes obtained by simulated hop-diffusion trajectories (9.0 ± 0.088 ms). Bottom (TILD Detection Test): The residency time distribution, determined by the TILD-detection method from 100 simulated 1,000-frame long hop trajectories that included a single-molecule localization precision of 50 nm (residencies in 763 compartments with durations longer than 4 ms). The decay time constant was 9.0 ± 0.17 ms. This agrees well with the correct distribution, suggesting that the developed protocol is useful for evaluating the residency lifetime, although at the level of individual hops, our software misses hops (66% detectability) and incorrectly detects hops (60% accuracy). The number of detected TILDs per 1,000-frame simulated simple-Brownian trajectories, using a diffusion coefficient of 6 µm²/s and a localization precision of 50 nm, was only 0.35/trajectory (n = 100 trajectories; 0.33 when a diffusion coefficient of 9 µm²/s was assumed). (B) Detecting TILDs in Cy3-DOPE and TfR trajectories obtained in intact and actin-depleted blebbed PMs. (B a) Typical Cy3-DOPE trajectories (0.1-ms resolution) in the intact apical PM (left, the 40-ms-long initial part of the trajectory shown in Fig. 3 C) and in the actin-depleted blebbed apical PM (right; typical among 50 and 20 trajectories, respectively). The moments of TILDs, detected as shown in B b, are shown by the thick, red three-step subtrajectories. The trajectory obtained in the intact apical PM contained three TILDs, whereas that in the actin-depleted blebbed apical PM exhibited no TILDs. In the trajectory obtained in the intact apical PM (left), the colors of the trajectories are changed across the short red TILD trajectory, and this convention was used throughout this report. (B b) The plots of H(m,n) vs. m for the trajectories shown in B a. TILDs were detected in all of the experimental trajectories of Cy3-DOPE and TfR obtained in the intact apical PM (see Fig. 3 D; 50 trajectories with a length of 1,000 frames for Cy3-DOPE at a frame rate of 10 kHz and for TfR at a frame rate of 6 kHz). The average numbers of detected TILDs (with intervals longer than 2 ms) per 1,000-frame long trajectory classified into the suppressed-diffusion mode were 7.8 (= 297 events/38 trajectories) for Cy3-DOPE and 4.4 (= 175 events/40 trajectories) for TfR. Meanwhile, in the actin-depleted blebbed PM, where more than 90% of the trajectories were statistically classified into the simple-Brownian diffusion mode (20 trajectories were examined for both Cy3-DOPE and TfR; Table 2), the numbers of detected TILDs per 1,000-frame long trajectory classified into the simple-Brownian diffusion mode were only 0.22 (= 4 events/18 trajectories) for Cy3-DOPE and 0.68 (= 13 events/19 trajectories) for TfR. (B c) Distributions of the dwell times within a compartment for Cy3-DOPE (50 trajectories; 337 residencies) in the intact apical PM, with the best-fit exponential curves and dwell lifetimes of 9.2 ± 0.34 ms. The exponential shape of this distribution is consistent with the hop-diffusion model (under strong-type confinements; see Supplemental theory 1). Furthermore, the exponential residency lifetime found for Cy3-DOPE (9.2 ms) agrees well with that found for the simulated hop-diffusion trajectories, using parameters similar to the experimentally determined values for Cy3-DOPE (9.0 ms; A c, top).

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).

Figure 6.

Ultrafast SFMI of TfR and Cy3-DOPE revealed that the basal PM outside the FAs (bulk basal PM) is compartmentalized like the apical PM and that the dwell lifetimes of TfR and Cy3-DOPE within a compartment in the bulk basal PM are the same as those in the apical PM. The data about the apical PM are reproduced in figures B–E here from Fig. 4, B and D; and Fig. 5 A for the ready comparison. (A) Typical ultrafast single fluorescent-molecule trajectories of TfR (6 kHz) and Cy3-DOPE (10 kHz), diffusing in the bulk basal PM and in the apical PM. The order of the compartments visited by the molecules (parenthesized integers) and their respective dwell lifetimes there, as determined by the TILD analysis (Fig. S5), are shown in the figure. TMR was used to label the Halo-tag protein fused to the cytoplasmic domain of TfR (N-terminus). Since Cy3 (and Alexa555), which exhibited superior throughput among all the dyes tested (Figs. S2 and S3), is membrane impermeable, the availability of a membrane-permeable dye, TMR, for ultrafast observations is very useful. (B) Motional mode classification based on RD, performed as described in Fig. 4 B. Shaded and open bars show the RD distributions, obtained by experiments and simulation for simple-Brownian particles, respectively. The percentages of molecules categorized into the suppressed and simple-Brownian diffusion modes are indicated. (C) Distributions of the compartment sizes determined from the hop-diffusion fitting of the MSD-∆t plot for each TfR and Cy3-DOPE molecule. The MSD-∆t plot data that could not be fit (due to large noise and the closeness of D_micro and D_MACRO) were not included. Arrowheads indicate the median values. (D) Distributions of the TfR and Cy3-DOPE residency times within a compartment determined by the TILD analysis, with the best-fit single exponential functions. The decay time constants of these curves provide the dwell lifetimes (see the caption to Fig. 5 A). (E) Distribution of D_MACRO determined by the hop-diffusion fitting of the MSD-∆t plot for each TfR and Cy3-DOPE molecule (shaded histogram, bulk basal PM; open histogram, apical PM). Arrowheads indicate the median values. The statistical test methods, parameters (number of experiments), and P values are summarized in Table 3.

Figure 7.

EGFR and ligand-engaged EGFR in the basal PM detected virtually the same compartment sizes as those found with TfR and Cy3-DOPE, supporting the PM compartmentalization, and the dwell lifetime of the engaged EGFR was longer than that of non-engaged EGFR (same compartment sizes). Following the stimulation with 10 nM EGF, microscope observations were performed between 2.5 and 5 min after the EGF addition. (A) Typical ultrafast (6 kHz) single fluorescent-molecule trajectories of EGFR, before and after EGF stimulation (n = 41 and 39 trajectories, respectively). (B) Distributions of the compartment sizes detected by the single-molecule diffusion of EGFR in the basal PM, before (top) and after (bottom) EGF stimulation. Arrowheads indicate the median values of 106 nm for both before and after stimulation. (C) Distributions of the EGFR residency times within a compartment determined by the TILD analysis, with the best-fit exponential curves, providing the dwell lifetimes (τ). Before (top) and after (bottom) EGF stimulation. Statistically significant difference between before and after stimulation with P = 0.044, using the log-rank test. (D) Distributions of D_MACRO for EGFR in the basal PM determined by the hop-diffusion fitting of the MSD-∆t plot for each EGFR molecule (shaded histogram, before stimulation; green open histogram, after stimulation). Arrowheads indicate the median values. D_MACRO was reduced by a factor of 1.7 after stimulation.The statistical test methods, parameters (number of experiments), and P values are summarized in Table 3.