Abstract
The spatial resolution of fluorescence microscopy has recently been greatly improved. However, its temporal resolution has not been improved much, despite its importance for examining living cells. Here, by developing an ultrafast camera system, we achieved the world’s highest time resolutions for single fluorescent-molecule imaging of 33 (100) µs (multiple single molecules simultaneously) with a single-molecule localization precision of 34 (20) nm for Cy3 (best dye found), and for PALM data acquisition of a view-field of 640×640 pixels at 1 kHz with a single-molecule localization precision of 29 nm for mEos3.2. Both are considered the ultimate rates with available probes. This camera system (1) successfully detected fast hop diffusion of membrane molecules in the plasma membrane, detectable previously only by using less preferable 40-nm gold probes and bright-field microscopy, and (2) enabled PALM imaging of the entire live cell, while revealing meso-scale dynamics and structures, caveolae and paxillin islands in the focal adhesion, proving its usefulness for cell biology research.
Summary An ultrafast camera developed by Fujiwara et al. allows single fluorescent-molecule imaging every 33 μs with a localization precision of 34 nm (every 100 μs; 20 nm), and enables ultrafast PALM imaging of whole live cells.
Introduction
Extensive attention has recently focused on improving the spatial resolution of fluorescence microscopy, leading to the development of various types of super-resolution methods (Shcherbakova et al., 2014; Liu et al., 2015; Nicovich et al., 2017; Sahl et al., 2017; von Diezmann et al., 2017; Baddeley and Bewersdorf, 2018; Sigal et al., 2018; Sezgin et al., 2019; Lelek et al., 2021). Meanwhile, efforts toward enhancing the temporal resolution of fluorescence microscopy, particularly in single fluorescent-molecule imaging and single-molecule localization microscopy (SMLM), have been quite limited (Wieser et al., 2007; Jones et al., 2011; Huang et al., 2013; Hiramoto-Yamaki et al., 2014; Kinoshita et al., 2017). However, for observing living cells, and particularly for investigating the dynamic movements and interactions of molecules at the single molecule level (Baboolal et al., 2016), improving the temporal resolution is critically important (Koyama-Honda et al., 2020). This was exemplified by our detection of hop diffusion of membrane molecules in the plasma membrane (PM) by improving the time resolution of single-particle tracking down to 25 µs (Fujiwara et al., 2002, 2016; Murase et al., 2004). However, this method required the use of large (40-nm diameter) gold particles as probes. Since fluorescent probes are much smaller (<1 nm) and used far more broadly than gold probes, in the present study, we tried to improve the temporal resolution of imaging single fluorescent molecules (many molecules at the same time) to levels similar to those of gold-particle tracking.
For tracking just one molecule at a time, a method called MINFLUX has recently been developed. For molecules adsorbed on glass, it provides 2.4-nm and <20 nm localization precisions with 400- and 117-µs temporal resolutions, respectively; in live E. coli, it provides 48-nm precision with 125-µs time resolution (Balzarotti et al., 2017; Eilers et al., 2018; Schmidt et al., 2021). However, MINFLUX does not allow observations of more than one molecule at a time, and thus it cannot be used to study molecular interactions and simultaneous events occurring in various parts of the cell. Consequently, its applications would be quite limited.
Here, we developed a camera-based method that allows the observations of several tens to hundreds of molecules simultaneously in a field of view (like in a cell). This method would be useful for investigating the interactions and assemblies of molecules in live cells and simultaneously studying the different behaviors of molecules in various parts of the cell. This ultrafast camera system enables the simultaneous tracking of many single fluorescent molecules in the view-field at 10 kHz or every 100 µs, with a localization precision down to 20 nm with a frame size of 14 x 14 µm2 (256 x 256 pixels), and in the case of 30 kHz or every 33 µs, to a localization precision of 34 nm with a frame size of 7.1 x 6.2 µm2 (128 x 112 pixels) (for previous results using other cameras, see the summary in Table 1).
These frame rates are 333x and 1,000x faster than video rate, respectively, and comparable to the rate at which MINFLUX tracks just one molecule. For camera-based technology, this rate is likely to represent the ultimate attainable with the currently available fluorescent dyes: the camera system itself could be operated faster, and thus the instrument is no longer the limitation for faster observations. With the future development of fluorescent dyes with faster fluorescent photon emission, we should be able to observe single molecules at 45 kHz (every 22 µs; with a frame size of 7 x 3.5 µm2) or even faster rates.
We examined the applicability of this camera system to live cells by testing whether it can detect the hop diffusions of (Cy3-labeled) single molecules, a phospholipid and a transmembrane protein, transferrin receptor (TfR), which were previously detectable only by tracking 40-nm gold particles bound to these molecules in the apical (dorsal) plasma membrane (PM; since 40-nm-diameter gold particles cannot enter the space between the basal PM and the coverslip, the hop diffusion in the basal PM could not be investigated previously; this will be described in the companion paper [Fujiwara et al., 2021]). The single fluorescent-molecule imaging system based on the ultrafast camera developed here successfully reproduced the gold particle data, without affecting cell viability. Furthermore, coupled with improved analysis methods, it allowed the determination of the residency time of each single molecule in each membrane compartment.
At the same time, the developed camera system has greatly improved the time resolution and the obtainable image size of SMLM (in the present report, we focus on PALM, but it would also improve the time resolutions of fPALM, iPALM, STORM, and dSTORM). With the developed ultrafast camera system, the PALM instrument should be able to operate at 10 kHz or faster, but just like the case of ultrafast single-molecule imaging, we found that one of the best photoconvertible fluorescent proteins available for PALM today, mEos3.2 (Zhang et al., 2012), only allowed us to operate the instrument at 1 kHz. However, even under these conditions, the PALM data acquisition of a view-field of 640 x 640-pixels (35.3 x 35.3 µm2) for 10,000 (or 300) frames was shortened to 10 (0.33) s, with a single-molecule localization precision for mEos3.2 of 29 ± 0.22 (SEM) nm. The spatial resolution of the PALM image was ∼75 nm, as determined by a parameter-free decorrelation analysis (Descloux et al., 2019), which is somewhat worse than the conventional live-cell PALM images (generally ∼60 nm; Shroff et al., 2008; Huang et al., 2013) due to the ∼2x lower quantum efficiency of the photosensor of this camera system, as compared with those of generally employed cameras (for comparisons with previously used cameras, see Table 1). Namely, this camera system now allows observations of almost the entire live cell at ∼75-nm resolutions every 0.33 – 10 s. With the future development of photoconvertible molecules with faster photon emission and photobleaching, we would be able to obtain PALM images >10 times faster; i.e., at video rate or faster.
In the companion paper, we describe further applications of this ultrafast camera system (Fujiwara et al., 2021). We report the compartmentalization of the basal PM as well as the apical PM, the hop diffusion of phospholipids and transmembrane proteins, TfR and EGF receptor (EGFR), in the basal PM, and the compartmentalization of the focal adhesion region for the diffusion of membrane molecules.
Results
Basic design of the ultrafast camera system
Our camera system consists of a microchannel-plate image intensifier (Fig. 1 A-a), a high-speed complementary metal-oxide semiconductor (CMOS) sensor (Fig. 1 A-b), and an optical-fiber bundle, which couples the phosphor screen of the image intensifier to the CMOS sensor chip (Fig. 1 A-c; Materials and methods). The image intensifier (Hamamatsu, V8070U-74) comprises a third-generation GaAsP photocathode with a quantum efficiency of 40% at 570 nm (Fig. 1 A-a-α), a three-stage microchannel plate allowing maximal gain over 106, in which a non-linear noise increase was virtually undetectable (Fig. 1 A-a-β), and a P46 phosphor screen with a decay time of approximately 0.3 µs from 90% to 10% (Fig. 1 A-a-γ). A CMOS sensor (the sensor developed for a Photron 1024PCI camera), with a global shutter exposure was used (Table 1).
A straight (1:1) optical-fiber bundle (Fig. 1 A-c) was directly adhered to the phosphor screen of the image intensifier on one side (Fig. 1 A-a-γ, input side) and to the CMOS sensor on the other side (Fig. 1 A-b, output side). This enhanced the signal reaching the CMOS sensor by a factor of 5-10, as compared with the lens coupling used for our standard camera system employed for single fluorescent-molecule imaging (Suzuki et al., 2012; Kinoshita et al., 2017). The electrons generated at the CMOS sensor were transferred, amplified (Fig. 1 A-d), and digitized (Fig. 1 A-e) in 64 and 8 parallel paths, respectively, and then transferred to the host PC.
Basic conceptual strategy to address the large readout noise of the CMOS sensor
We used the CMOS sensor instead of the sCMOS sensor, which is prevalently used in biomedical research. This is because the frame rates of the sCMOS sensor cannot reach 10∼100 kHz (10,000∼100,000 frames per second), the speed that we hoped to achieve, in contrast to the CMOS sensor. However, the readout noise of the CMOS sensor is generally greater than that of the sCMOS sensor by factors of several 10s (this is why CMOS sensors are rarely used in fluorescence microscopy). Therefore, to employ the CMOS sensor for single-molecule imaging, the problem of high levels of readout noise had to be solved.
Our basic conceptual strategy to address this problem was the following: we should place an amplifier before the noisy detector, so that both the input signal and noise can be amplified (they will be amplified in the same way by the amplifier) at least to the level that the amplified noise (be mindful that this must be the noise and not the signal) becomes comparable to the noise that the detector generates. In the case of the CMOS camera (noisy detector), we placed an image intensifier (more specifically the microchannel plate; a-β in Fig. 1 A), before the CMOS sensor (b in Fig. 1 A), so that the noise (including the background) generated by the photocathode of the image intensifier (the first step of light detection; a-α in Fig. 1 A) is amplified at least to the level comparable to the readout noise of the CMOS sensor (signal at the photocathode is amplified by the same factor as the noise, but in the present argument, the amplification of the noise is the critical issue). Here, we explain why this basic strategy would work.
We refer to the average intensities of the signal and noise + background at the photocathode of the image intensifier as Sp and Np, respectively, that of the readout noise as Nr, and the image intensifier amplification gain as G. Note that when using the CMOS sensor for single-molecule observations, generally Np << Nr.
The signal-to-noise (including the background intensity) ratio (S /N) of the output from the CMOS sensor can be written as a function of G, because both the signal and noise at the photocathode stage are amplified by a factor of G (neglecting the noise generated by the amplifier). Note that when there is no gain; i.e., G =1, because Np << Nr. Namely, the S /Nratio of the CMOS sensor output is dominated by the large readout noise of the CMOS sensor Nr, and we will not be able to detect the single-molecule signal, Sp, due to the large Nr (i.e., Sp /N (G=1) < 1).
With an increase of the gain G, Nr/G becomes much smaller than Np (or Nr << Np xG; namely, when the noise at the photocathode is amplified so that the amplified noise becomes greater than the readout noise of the CMOS sensor Nr) and Eq. 1 can be written as where ε represents the very small value of Nr/G. Eq. 3 shows that with an increase of the amplifier gain G, the S/N of the output signal from the CMOS sensor is no longer dominated by Nr, and thus increased close to that at the photocathode (Sp/Np). Eq. 3 is consistent with the general truth that amplifier placement cannot increase the output S/N to more than the input S/N. Note that, in this argument, the key is not to compare Sp with Nr, but to compare Np (or Np xG) with Nr.
Namely, when the detector itself is a large noise generator and the limiting factor for the S/N of the entire system, this problem can be minimized by placing an amplifier before the noisy detector. Eqs. 1 and 3 indicate that larger gains are preferrable. However, since the amplifier itself can also generate noise and since the full-well capacity of each pixel of the CMOS sensor is limited, there is an upper limit for the amplifier gain.
When we set the gain G so that Np xG = Nr (the noise at the photocathode Np is amplified to become comparable to the readout noise Nr); i.e., if we set G = Nr /Np, Namely, under these conditions, the output S/N of the CMOS sensor is half the S/N at the photocathode output. This provides a rule of thumb that the noise at the photocathode (Np) should be amplified at least to a level comparable to the readout noise of the CMOS sensor (Nr). For the actual values of Nr and Np, see Materials and methods, “Ultrahigh-speed intensified CMOS camera system: design and operation-Basic design concept of the camera system (B) The use of an image intensifier”.
Apart from the basic concept, for determining the useful amplifier gain for experiments, we obtained actual image readout noise, images of single photons obtained as a function of the intensifier gain, stochastic gain variations (fluctuations) of the image intensifier, and the probability of detecting single photons (Fig. S1; Materials and methods, “Ultrahigh-speed intensified CMOS camera system: design and operation-Basic design concept of the camera system (B) The use of an image intensifier”). We decided to generally employ the overall electron amplification gain of 8,100x, because it enables the detection of a photon-converted electron emitted at the photocathode of the image intensifier with a probability as high as 90.0% (Fig. S1; Materials and methods).
The developed camera system is typically operated at 10 and 30 kHz (100- and 33-µs resolutions) with frame sizes of 256 x 256 and 128 x 112 pixels, respectively, but can be operated faster with reduced image sizes (for example at 45 kHz or every 22 µs, with a frame size of 7 x 3.5 µm2). Virtually all of the single Cy3 molecules immobilized on coverslips that were observed at 60 Hz were also detectable at frame rates of 10 and 30 kHz (Fig. 1, B-D).
Ultrafast imaging of many single molecules at 10 and 30 kHz
The single-molecule localization precision is fundamentally determined by the number of detected photons/molecule during the single frame time of the camera, as described by the Mortensen equation (Mortensen et al., 2010; see the caption to Fig. S2). We thus evaluated whether a sufficient number of photons can be emitted from single fluorescent molecules of various fluorophores during the 33 and 100 µs frame times of the developed camera system (30 and 10 kHz, respectively; neglecting a readout time of 812 ns). The plots of single-molecule localization precision vs. the number of detected photons/molecule during a single-frame time (using fluorescent molecules bound to the coverslip) were consistent with the Mortensen equation for all dye molecules investigated here (Fig. S2). These plots demonstrated that the number of detected photons/molecule/frame and the single-molecule localization precision were enhanced with an increase of the excitation laser intensity, but to a limited degree (Fig. 1, E and F; Fig. S3). This occurs because the number of photons emitted from a single fluorescent molecule during a frame time under higher excitation light intensities is limited by the triplet bottleneck saturation (Materials and methods, “Estimation of the number of photons that can be emitted by a single Cy3 molecule during 0.1 ms: triplet bottleneck saturation”). The saturation became apparent from around 23 µW/µm2 for Cy3 (Fig. 1, E and F; Fig. S3). Among the eight dyes we tested, Cy3 exhibited the lowest tendency to saturate (Figs. S2 B and S3 A). Therefore, we employed Cy3 most often, but also used tetramethylrhodamine (TMR) as a membrane-permeable probe.
The best single-molecule localization precision for Cy3 at a frame integration time of 0.1 ms (10-kHz frame rate) was 20 ± 0.71 nm, using total internal reflection (TIR) laser illumination at a density of 79 µW/µm2 at the sample plane (n = 50 molecules; mean ± standard error of means [SEM] are given throughout this report; Fig. 1 F; Figs. S2, A and B and S3, B and C). At 30 kHz, since fewer photons were emitted from a Cy3 molecule during a frame time of 33 µs, the localization precision was worse (34 ± 1.0 nm; n = 50 molecules; Fig. 1 F; Figs. S2 A and S3, B and C; Table 1). The best single-molecule localization precision achieved with this camera system was 2.6 ± 0.099 nm, with a maximum number of detected photons/molecule/frame of 11,400 ± 700, at a frame integration time of 16.7 ms (60-Hz frame rate) in which most of the Cy3 molecules were photobleached (within a single frame; n = 50 molecules; Fig. 1, G and H; Fig. S2, C and D) (summarized in Table 1).
Taken together, we conclude that the observation frame rates of 10 – 30 kHz (with localization precisions of 20 – 34 nm, using the view-fields of 256 x 256 – 128 x 112 pixels [14.1 x 14.1 µm2 – 7.1 x 6.2 µm2]), represent the ultimate fastest frame rates employable for single-molecule tracking in living cells, using the currently available fluorescent molecules. Meanwhile, the camera itself could be operated much faster. The Photron 1024PCI CMOS sensor, which was used most extensively here, can be operated at 10 kHz (256 x 256 pixels), 45 kHz (128 x 64 pixels; or 256 x 256 pixels using the newer SA1 sensor), and 110 kHz (128 x 16 pixels) (summarized and compared with the results with other cameras in Table 1; Materials and methods, “Ultrahigh-speed intensified CMOS camera system: design and operation”). Therefore, the camera is no longer the limitation for the faster frame rates, and with the future development of fluorescent dyes with higher throughputs, we should be able to perform single-molecule tracking at even better time resolutions. In fact, single transferrin (Tf) molecules bound by an average of 5.0 Cy3 molecules (5xCy3-Tf) adsorbed on the coverslip could be imaged and tracked at 45 kHz, with localization precisions of 30 (38) and 29 (34) nm, using TIR (oblique-angle) illuminations of 43 and 79 µW/µm2, respectively (Figs. S2 A and S3, B and C; Table 1).
TIR and oblique illuminations for ultrafast single-molecule imaging
In this study, we employed both TIR and oblique-angle laser illuminations. TIR illumination is useful for observing single molecules in the basal (ventral, bottom) PM by suppressing the signals from the cytoplasm and the enhanced evanescent electric field for the same laser intensity. The TIR illumination provides better localization precisions than the oblique-angle illumination at the same laser intensities (27 vs. 38 nm; Fig. 1 F).
On the other hand, the oblique-angle illumination is more versatile: it can be used to illuminate the apical PM, endomembranes, and cytoplasm, which cannot be accomplished using the TIR illumination. Particularly, in this research, since we hoped to compare the present single fluorescent-molecule tracking results of the phospholipid diffusion with our previous 40-kHz single gold-probe tracking data obtained in the apical PM (Fujiwara et al., 2002, 2016; Murase et al., 2004), we had to use the oblique-angle illumination. Therefore, as our “standard test conditions” in the present research (the end of the caption to Fig. S3), we employed the oblique-angle illumination with a laser intensity of 23 µW/µm2 at the sample plane (the dye saturation starts around this laser intensity; Fig. 1, E and F; Fig. S3), despite its worse localization precisions as compared with the TIR illumination.
Trajectory length and cell viability under the standard conditions
Under the standard test conditions (oblique-angle illumination at 23 µW/µm2), single Cy3 molecules immobilized on the coverslip could be observed at 10 kHz with an average signal-to-noise ratio (SNR) of 2.5 ± 0.11 (Fig. 2, A and B; Video 1), and the fractions of the trajectories with durations (uninterrupted length of the trajectories) longer than 100, 300, and 1,000 frames (after the 3-frame gap-closing, which neglects the non-detectable periods lasting for 3 frames or less) were 14, 2.9, and 0.31% among all obtained trajectories (Fig. 2 C). Therefore, performing single-molecule tracking for 100 – 300 frames (10 – 30 ms at 10 kHz) is quite practical. Meanwhile, under the conditions for the best localization precision with TIR illumination of 79 µW/µm2 (20 ± 0.71 nm), the fractions were 1.6, 0.13, and 0.0%, respectively (Fig. 2 C), making it difficult to obtain trajectories longer than 100 frames (for the summary and comparison with results using other cameras, see Table 1).
These results indicate that, for successful single-molecule tracking, a proper compromise between the localization precision and the trajectory length is necessary. This is one of the major differences between single-molecule tracking and SMLM. SMLM basically requires only one localization for a single molecule (observations lasting only for a single frame) before photobleaching, while single-molecule tracking needs many localizations to obtain long trajectories (essentially, longer is better) before photobleaching/photoblinking.
Under the standard test conditions, the laser illumination (oblique-angle at 23 µW/µm2 of the 532-nm line) for 1 min hardly affected the cell viability, although half of the T24 cells did not survive after 10-min irradiation (Fig. 2, D and E). Because all our ultrafast measurements were finished within 5 s, we conclude that the toxic effect of the illumination laser is minimal for our observations. In the previous report (Wäldchen et al., 2014), the light toxicity was found strongly dependent on the cell type, and our result using T24 cells is close to their result using HeLa cells. However, the direct comparison with the present result with the previous result is difficult due to the differences in the viability test method, laser wavelength (532 vs. 514 nm), and illumination durations (1 and 10 min vs. 4 min; our result suggests non-linear dependence of the viability on the illumination duration).
Testing the ultrafast camera system using PM molecules undergoing hop diffusion 1: qualitative observations
As stated in the Introduction, we previously detected non-Brownian diffusion (hop diffusion) of phospholipid and transmembrane protein molecules in the PM, using large (40-nm diameter) gold particles as a probe (Fujiwara et al., 2002, 2016; Murase et al., 2004; Kusumi et al., 2005, 2012a, b; also see Sheetz, 1983). This was made possible by improving the time resolution of single-particle imaging using bright-field microscopy down to 25 µs (Fujiwara et al., 2002, 2016; Murase et al., 2004). The hop diffusion is influenced by modulating the actin-based membrane-skeleton meshes (Fig. 3 A). Therefore, we concluded that the entire apical PM is compartmentalized, by the steric hindrance of actin-based membrane-skeleton meshes (fences) and the steric hindrance + hydrodynamic friction-like effects from rows of transmembrane-protein pickets anchored to and aligned along the actin fence (Fig. 3 A). In the compartmentalized PM, both transmembrane proteins and lipids undergo short-term confined diffusion within a compartment plus occasional hop movements to an adjacent compartment, which was termed hop diffusion (Kusumi et al., 2005; Kusumi et al., 2012a; Jacobson et al., 2019).
Each gold-tagged molecule in the PM exhibited two diffusion coefficients: the microscopic diffusion coefficient (Dmicro), which describes the unhindered diffusion within a compartment, and the macroscopic diffusion coefficient (DMACRO), which is largely determined by the compartment size and the hop frequency across intercompartmental boundaries composed of the picket-fence. DMACRO is significantly smaller than Dmicro.
The compartment sizes were in the range of 40 - 230 nm depending on the cell type (∼110 nm in human epithelial T24 cell line used here), and the dwell lifetimes of membrane molecules within a compartment are in the range of several to a few 10s of milliseconds (Murase et al., 2004; Fujiwara et al., 2016). Therefore, the hop diffusion of membrane molecules in the apical PM appeared to be quite suitable for testing single fluorescent-molecule imaging using the developed ultrafast camera system. Indeed, this project was originally undertaken to develop a fast single fluorescent-molecule imaging method to observe the hop diffusion of membrane molecules in the PM. We examined whether we could detect the hop diffusion of L-α-dioleoylphosphatidylethanolamine (DOPE) conjugated with Cy3, Cy3-DOPE, at a time resolution of 0.1 ms (10 kHz, 333 times faster than normal video rate) and transferrin receptor (TfR) tagged with Cy3-conjugated transferrin (average dye to protein molar ratio of 0.2) at a frame rate of 6 kHz (0.167-ms resolution; 200 times faster than normal video rate; slowed from 10 kHz because the hop rate of TfR was expected to be slower than that of Cy3-DOPE). The observations were made in the apical PM using the oblique-angle illumination (Fig. 3, B-D; Videos 2-4), for making the direct comparisons with the previous single gold-particle tracking data. All of the cell experiments reported here were performed at 37°C, using human epithelial T24 cells (previously called ECV304 cells).
Virtually all of the single-molecule images and trajectories (Fig. 3, B-D; Videos 2-4) gave the impression that the Cy3-DOPE and TfR molecules underwent rapid diffusion within a confined domain of ∼100 nm and occasionally moved out of this domain, became confined again at the place where it moved to, and repeated such behaviors. These typical behaviors appear to reproduce the movement of gold-tagged DOPE and TfR quite well.
Testing the ultrafast camera system using PM molecules undergoing hop diffusion 2: quantitative and statistical analyses
Apart from the subjective impression, the trajectories of single fluorescent molecules were examined quantitatively and statistically, using the plot of mean-square displacement (MSD) vs. time interval (Δt) (Qian et al., 1991) (called the MSD-Δt plot, which also provides single-molecule localization precisions; Fig. 4 A; Fig. S4). The results were compared with those obtained by single gold-particle imaging.
Based on the MSD-Δt plot (Fig. 4 A-a), each trajectory could be classified into a suppressed-, simple-Brownian-, or directed-diffusion mode (Kusumi et al., 1993; see the caption to Fig. 4 B-a). More than three-quarters of the Cy3-DOPE and TfR trajectories obtained in the intact apical PM at 10 and 6 kHz (0.1-ms and 0.167-ms resolutions, respectively) were categorized into the suppressed-diffusion mode (top boxes in Fig. 4 B-b; also see Table 2), reproducing the results obtained by single gold-particle tracking at 40 kHz (Table 2, in which all of the statistical parameters and the statistical test results for the diffusion parameters are also summarized).
Meanwhile, in the f-actin-depleted blebbed PM, almost all of the Cy3-DOPE and TfR trajectories, obtained at 10 and 6 kHz, respectively, were classified into the simple-Brownian-diffusion mode (Fig. 4 A-c; Fig. 4 B-b; Table 2), again consistent with the data obtained by single gold-particle tracking in the blebbed PMs of NRK cells (Fujiwara et al., 2002, 2016). As concluded previously, these results indicate that the actin-based membrane skeleton is involved in inducing the suppressed diffusion of both phospholipids and transmembrane proteins (Fujiwara et al., 2002, 2016; Murase et al., 2004; Hiramoto-Yamaki et al., 2014).
The MSD-Δt plot obtained for each trajectory was then fitted, using an equation based on the hop-diffusion theory (Kenkre et al., 2008) (called “hop-diffusion fitting”; Fig. 4 A; see the subsection “Hop-diffusion fitting: the function describing the MSD-Δt plot for particles undergoing hop diffusion” in the caption to Fig. S5). The hop-diffusion fitting provided two diffusion coefficients for each trajectory observed in the PM: Dmicro and DMACRO. The presence of two diffusion coefficients for a single trajectory observed in the PM and only one diffusion coefficient in the actin-depleted blebbed PM (Fig. 4 C) again reproduced the observations obtained by using single gold-particle imaging (Fujiwara et al., 2002, 2016).
The hop-diffusion fitting of each trajectory obtained in the intact PM also provided the average compartment size L for each trajectory (Fig. 4 D; Table 2). Importantly, the L’s for Cy3-DOPE and TfR were quite similar, with median values of 101 and 103 nm, respectively (non-significant difference; in the following discussions and calculations, we will use a compartment size of 100 nm). This result suggests that the underlying mechanisms for confining phospholipids and transmembrane proteins are based on the same cellular structures, perhaps by the actin-based membrane-skeleton meshes (fences) and the transmembrane picket proteins bound to and aligned along the actin-fence (Fig. 3 A). The compartment sizes L found here (median sizes of 101 and 103 nm for Cy3-DOPE and TfR, respectively) are quite comparable to those previously detected by using gold-conjugated molecules in the same T24 cells (110 and 100 nm for gold-tagged DOPE and TfR, respectively; Table 2).
Taken together, our ultrafast single fluorescent-molecule imaging based on the ultrafast camera system developed here could successfully detect the hop diffusion of membrane molecules, which was previously detectable only by using gold probes and high-speed bright-field microscopy. Therefore, the ultrafast single fluorescent-molecule imaging developed here is likely to be suitable to observe the fast molecular dynamics occurring in living cells.
Here, we add a remark on the Dmicros for Cy3- and gold-labeled molecules in the PM. The model of hop diffusion in the compartmentalized PM suggests that Dmicro is about the same as the diffusion coefficient of unhindered diffusion in the actin-depleted PM, but in all the molecules and cells examined thus far, the Dmicros in the intact PM were smaller than those for the unhindered diffusion coefficients in the actin-depleted PM (Table 2; Fujiwara et al., 2002, 2016; Murase et al., 2004; Suzuki et al., 2005). This is probably because the time resolutions of 25 - 100 µs achieved thus far (10 - 40 kHz) are not sufficient to observe trajectories near the compartment boundaries, thus effectively reducing the step sizes in the trajectory, which will reduce the diffusion coefficient within the compartment, Dmicro (Ritchie et al., 2005).
We examined the possibility that the hop diffusion might simply be an apparent phenomenon due to the photo response non-uniformity (PRNU) of the developed camera system. The PRNU induced by the effects of pixel-to-pixel variations on the sensitivity of the developed camera system might have made the simple-Brownian diffusion of membrane molecules appear like hop diffusion. The result is shown in Fig. S1 of the companion paper, and indicates that the PRNU of the developed camera system is not more than that of the conventional EM-CCD camera, and thus is unlikely to induce hop diffusion-like movies.
Direct determination of the dwell lifetime of each membrane molecule within each compartment using ultrafast single fluorescent-molecule imaging
We directly evaluated the dwell lifetime of each molecule in each compartment by using ultrafast single fluorescent-molecule imaging and developing an improved method for detecting the moment (instance) at which the observed molecule undergoes the hop movement across the compartment boundary. The moments of hops of the observed molecule can be found in its single-molecule trajectory by the method of detecting a Transient Increase of the effective Local Diffusion (TILD) in the trajectory (Fig. S5). TILDs are likely to occur when a molecule hops between two membrane compartments, but the analysis itself remains model-independent. TILDs were detected in all of the experimental trajectories obtained at 0.1- and 0.167-ms resolutions (for Cy3-DOPE and TfR, respectively) in the intact PM (see Fig. 3, C and D); however, in the blebbed PM, where all of the trajectories were statistically classified into the simple-Brownian diffusion mode, TILDs were detected in only 4% [9%] of the trajectories (one TILD per 750-step trajectory) for Cy3-DOPE [TfR]. These results support the occurrences of hop diffusion in the intact PM and simple-Brownian diffusion in the blebbed PM.
The duration between two consecutive TILD events represents the dwell lifetime within a compartment. The distributions of the dwell lifetimes are shown in Fig. 5 A. They could be fitted with single exponential decay functions, with lifetimes of 9.2 ± 0.34 ms for Cy3-DOPE and 23 ± 1.5 ms for TfR. The exponential shape of this distribution is consistent with the prediction by hop diffusion theory developed here (in the subsection “Expected distribution of the dwell lifetimes: development of the hop diffusion theory” in the caption to Fig. S5). The dwell lifetime for TfR is longer than that for Cy3-DOPE by a factor of 2.5, probably because the fence and picket effects both act on TfR, whereas only the picket effect works on Cy3-DOPE.
The average dwell lifetime within a compartment could be obtained from the median values of L and DMACRO determined by the hop fitting of the MSD-Δt plot, using the equation τ = L2/4DMACRO (Fig. 4, C and D; Table 2; theory in Fig. S5). This provided dwell lifetimes of 8.5 ms for Cy3-DOPE and 24 ms for TfR, which are in good agreement with the values obtained based on the dwell lifetime distributions determined by the TILD method (Table 2).
Previously, with gold probes, we obtained L from ultrafast single-gold-particle tracking, but needed to separately obtain DMACRO using fluorescently-tagged molecules (by observing them at video rate) to obtain the average dwell lifetime within a compartment (Fujiwara et al., 2002, 2016; Murase et al., 2004). This is because gold probes induced crosslinking of the target molecules, elongating the dwell lifetime, and thus provided reduced DMACRO values. Using the ultrafast single fluorescent-molecule imaging, we can directly determine the dwell lifetime of each molecule in each compartment (not just the averaged lifetime).
An anomaly analysis provided further proof of the hop diffusion of Cy3-DOPE and TfR in the compartmentalized PM
Generally, the MSD can be expressed as a function of the time interval Δt, where 0 ≤ α ≤ 2 (α = 1 for simple-Brownian diffusion, 0 ≤ α < 1 for suppressed anomalous diffusion, 1 < α < 2 for super diffusion, and α = 2 for ballistic motion) (Saxton, 1994, 1996; Feder et al., 1996; Simson et al., 1998; Fujiwara et al., 2002). This equation can be rewritten as, This relationship is plotted in Fig. 5 B. A very broad time range of ∼5 orders of magnitude (from 0.044 ms to 2 s) was covered, which was made possible by the development of the ultrafast single fluorescent-molecule imaging.
In this display, simple-Brownian type diffusion is represented by a flat line (since α = 1 in simple-Brownian cases, the slope α - 1 ∼ 0; i.e., no time dependence) and suppressed diffusion is characterized by negative slopes ([α - 1] < 0; i.e., α < 1). Namely, the level of the diffusion anomaly can be parameterized by the parameter α (Feder et al., 1996; Simson et al., 1998). In the actin-depleted blebbed PM, both Cy3-DOPE and TfR exhibited flat lines in the entire time range of 0.3 – 30 ms, unequivocally showing that they both undergo simple-Brownian diffusion in the blebbed PM.
On the contrary, in the intact apical PM, the plots for Cy3-DOPE and TfR (Cy3-Tf and 5xCy3-Tf) exhibited suppressed diffusion (negative slopes) in the time ranges of 0.5 – 30 and 0.13 – 70 ms, respectively, indicating that the suppressed diffusion of Cy3-DOPE and TfR was detectable in these time ranges. Meanwhile, in longer and shorter time ranges, the plots asymptotically approached flattened plots, consistent with simple-Brownian diffusion in these time regimes.
These results can readily be explained by the hop diffusion model in the compartmentalized PM for both Cy3-DOPE and TfR. In the shorter time regime (<0.5 and 0.13 ms, respectively), Cy3-DOPE and TfR collide with the compartment boundaries less frequently, approaching simple-Brownian diffusion and thus providing the diffusion coefficient of Dmicro within a compartment (although this is still underestimated due to the collisions with the compartment boundaries. However, in this time regime, translocation across the compartment boundaries hardly occurs). In the longer time regime (>30 and 70 ms, respectively), the diffusion of Cy3-DOPE and TfR represents that among compartments, because the detailed shorter-term behaviors are averaged out, and their movements thus resemble simple-Brownian diffusion again, with a diffusion coefficient of DMACRO. In the time ranges of 0.5 – 30 and 0.13 – 70 ms for Cy3-DOPE and TfR (Cy3-Tf and 5xCy3-Tf), respectively, since the effect of confinement within a compartment becomes increasingly evident with a lengthening of the observed time window until occasional hops across the compartment boundaries start alleviating this confinement, the MSD/(4t), which is the y-axis in this plot, is expected to decrease from Dmicro until it reaches DMACRO.
The dashed curves in Fig. 5 B represent the results of the Monte Carlo simulations that resemble the experimental data. The cyan curve would be the best for representing the diffusion of TfR in the apical PM. In the longer time regime (>70 ms), it approached the experimental result for Cy3-Tf at 30 Hz, while in the shorter time regime (<0.8 ms), it approached the experimental data for 5xCy3-Tf at 45 kHz, and at its shorter limit, it approached the flat line of the Cy3-Tf observed in the blebbed PM.
Ultrafast PALM, making PALM practical for live-cell observations
PALM imaging (and all other single-molecule localization microscopy methods) of live cells requires a good balance between the reasonable view-field size and the time resolution (Jones et al., 2011; Huang et al., 2013; see the bottom six rows in Table 1). The newly developed camera system greatly improved these parameters. Using one of the best photoconvertible fluorescent proteins available for PALM, mEos3.2 (Zhang et al., 2012), the developed camera system allowed us to employ a PALM data acquisition view-field of 640 x 640 pixels (35.3 x 35.3 µm2), with PALM time resolutions quite useful for observing morphological changes of subcellular structures of 0.33 - 10 s (1-kHz data acquisition for 330 - 10,000 frames), with a single-molecule localization precision of 29 nm. Therefore, the time-dependent changes of meso-scale (on the order of several tens to several hundreds nm) structures could be observed in the view-field of a whole live cell in the time scale of 0.33 - 10 s, as explained in the following.
The data acquisition frame rate, and thus the PALM time resolution, could not be increased to 10 kHz, as done for single Cy3 molecule tracking. This is due to the low throughput of the available fluorescent probes. Even mEos3.2 (fused to the C-terminus of mouse caveolin-1 and expressed in T24 cells) cannot be photobleached faster than 1.2 ms (cannot be excited at higher rates) at 561-nm excitation laser intensities up to 100 µW/µm2 (Fig. 6 A-a). Therefore, a frame rate of 1 kHz is about the fastest useful frame rate, as long as mEos3.2 is used as the PALM probe. However, even this is 33 times faster than video rate, and thus shortened the PALM data acquisition time by a factor of ∼33 (as compared with the video-rate acquisition method) to 0.33 – 10 s (1 ms/frame x 333 – 10,000 frames).
A single mEos3.2 molecule emits the largest number of photons during its on-time at a laser intensity of 30 µW/µm2 at the sample plane (Fig. 6 A-b and c; Alexa647 exhibits similar power dependence as reported by Lin et al. [2015]), providing the best single-molecule localization precision of 29 nm (Fig. 6 A-d). Therefore, we employed the laser intensity of 30 µW/µm2 and a camera frame rate of 1 kHz throughout this study (Fig. 6 B). With the future advent of photoconvertible molecules that can emit photons faster and photobleach faster, we could use 10 (or 30) kHz, rather than 1 kHz, for the data acquisition, which will allow us to obtain PALM images at least 10 times faster than the rate achieved here using the developed camera system.
The single-molecule localization precision using the more prevalent sCMOS was 22 nm (256 x 256 pixels with a data acquisition time of 0.5 s; 0.6 kHz for 300 frames) (Huang et al., 2013), which is better by a factor of 1.3 compared with the developed camera system (29 nm; Table 1). This is due to the lower quantum efficiency of the photosensor of the image intensifier used here (∼40%), as compared with that of sCMOS sensors (70–80%) ([70/40]1/2 ≈1.3).
Typical time-series of expanded PALM images of caveolin-1-mEos3.2 in a live T24 cell, generated in a reconstruction time window of 1 s (data acquisition at 1 kHz x 1,000 frames; 10 x 10 µm2 in 181 x 181 pixels), are shown in Fig. 7 A. Considering the localization precision of 29 nm, the obtained caveolin PALM images were consistent with the size of a caveola (60 ∼ 80 nm in diameter; Parton and del Pozo, 2013). The whole caveola sometimes moves together on the PM (compare Fig. 7 A with Fig. 7 B), and when the caveola migration occurs, it can suddenly move for ∼100 nm or so in <0.33 s, suggesting the movement from one actin-induced compartment to an adjacent one.
The cost of the increased image acquisition rates is the spatial resolution of the PALM images. The spatial resolutions of the PALM images shown in Fig. 7 A-a and B-a were 75 and 77 nm, as evaluated by a parameter-free decorrelation analysis (Descloux et al., 2019), whereas the conventional sCMOS would provide a spatial resolution of >58 [75/1.3] nm (from quantum efficiencies) (Lelek et al., 2021).
Ultrafast PALM for the entire live cell at a 75-nm spatial resolution
Although the PALM data acquisition rate was limited to 1 kHz using mEos3.2, this camera system allows us to use the data acquisition frame size of 640 x 640 pixels (35.3 x 35.3 µm2 with the pixel size of 55.1 nm) at 1 kHz. The PALM image of mEos3.2 fused to human paxillin, a focal adhesion structural protein, expressed on the basal PM, with the acquisition of the images of 640 x 640 pixels at 1 kHz for 10,000 frames (10 s) is shown in Fig. 8. Almost the entire live cell is seen in the view-field with a spatial resolution of 75 nm (Descloux et al., 2019), exhibiting the distributions of focal adhesions in the cell, and at the same time, the nano-scale fine structures including paxillin within each focal adhesion could be visualized. This image size was the largest ever for any PALM data obtained in the time scale of 0.33 – 10 s (1 ms/frame x 333 – 10,000 frames), the time range useful for observing live cells (for the comparison with previous results, see Table 1). The presence of paxillin islands is consistent with previous reports (Shroff et al., 2008; Patla et al., 2010; Rossier et al., 2012; Levet et al., 2015; Changede and Sheetz, 2017; Spiess et al., 2018; Orré et al., 2021). For our further analysis of the focal adhesion simultaneously using single-molecule imaging and PALM, please see the companion paper (Fujiwara et al., 2021).
We emphasize here that, with the present camera development, the instrument is no longer the limitation for the speed of PALM imaging. Instead, the probe is now the limitation. With the future development of photoconvertible molecules that could emit photons faster and photobleach faster, we would be able to obtain PALM images 10 times more quickly than we can now using the developed instrument (by employing the data acquisition rate of 10 kHz rather than 1 kHz for 640 x 640 pixels), enabling PALM imaging at video rate (for the acquisition of 300 frames).
Discussion
The ultrahigh-speed camera system developed here has enabled the fastest single fluorescent-molecule imaging ever performed. This would also be the ultimate rate possible with the currently available fluorescent molecules; e.g., 0.1-ms resolution with a 20-nm localization precision for single Cy3 molecules, using a saturating TIR (standard oblique-angle) illumination laser intensity of 79 µW/µm2, for a frame size of 256 x 256 pixels (14 x 14 µm2). Under these conditions, approximately 1.6% of the single Cy3 molecules could be tracked for periods longer than 100 frames (10 ms; corresponding to 3.3 s at video rate) (for 39-nm precision, the laser intensity is 23 µW/µm2, and 14% of single Cy3 molecules could be tracked for the same period). When better fluorophores (faster emission and slower photobleaching) are developed, the time resolution for single-molecule imaging could be enhanced to 22 µs or more (for a frame size of 7.5 x 3 µm2 in 128 x 64 pixels), without affecting other parameters (Fig. 1, Table 1).
For tracking just one molecule at a time, MINFLUX has recently been developed, and its performance on the glass is superb (Balzarotti et al., 2017; Eilers et al., 2018; Schmidt et al., 2021). It has achieved single-molecule localization precisions of 2.4-nm and <20 nm with 400- and 117-µs temporal resolutions, respectively. However, it can track only one molecule at a time (but could be expanded to track a few isolated molecules at a time). In contrast, the camera-based single molecule imaging allows the observations of several tens to hundreds of molecules simultaneously in a field of view (like an entire cell). The camera-based method can thus be used to investigate the interactions and assemblies of molecules in live cells and study the different behaviors of molecules simultaneously in various parts of the cell, which is impossible with one molecule/cell technologies.
In live E. coli, MINFLUX provided a single-molecule localization precision of 48 nm with a 125-µs time resolution, under the conditions of observing the same molecule 742 times (Balzarotti et al., 2017). This is quite comparable to the results we obtained using the camera-based method, which allows us to simultaneously observe many single molecules at single-molecule localization precisions of 20 and 34 nm (27 and 55 nm) at time resolutions of 100 and 33 µs using TIR (oblique-angle) illumination (Table 1). However, practically speaking, the same single molecules could be observed for 100 – 300 frames (10 – 30 ms at 10 kHz; localizing them 100 − 300 times), as compared with localizing one molecule 742 times with MINFLUX. Therefore, the ultrafast camera-based single-molecule imaging and MINFLUX provide complementary methods for examining the very fast dynamics of membrane molecules in living cells: MINFLUX is useful for tracking a single molecule for longer periods, whereas the ultrafast camera-based single-molecule imaging provides a method for observing many molecules at once to investigate their interactions and the location-dependent behaviors of single molecules in a cell. Single molecules labeled with two or three different colors could also be investigated readily using the two or three cameras, respectively.
The ultrafast camera system developed here was tested by examining whether it can detect the hop diffusion of Cy3-tagged DOPE and TfR in the PM of live cells, as expected from the previous observations using gold-tagged molecules (Fujiwara et al., 2002, 2016; Murase et al., 2004). We found that it can indeed detect the hop diffusion of Cy3-tagged molecules (Figs. 3 - 5; Table 2) and the same compartment size as found by ultrafast gold-tracking (∼100 nm in the PM of T24 cells; Fig. 4 D; Table 2).
Ultrafast single fluorescent-molecule tracking has brought forth new knowledge about the hop diffusion of membrane molecules. First, the distribution of the dwell lifetimes in each compartment (not the overall average lifetime) was obtained. By the theory developed here, we found that the distribution of the dwell lifetimes indeed follows single exponential functions (Fig. 5 A). Second, ultrafast single fluorescent-molecule tracking allowed an anomaly analysis of a very broad time range of ∼5 orders of magnitude (from 0.044 ms to 2 s) for determining the diffusion properties of Cy3-tagged molecules. The anomaly analysis confirmed the hop diffusion of Cy3-DOPE and TfR in the PM and their simple-Brownian diffusion in the actin-depleted blebbed PM (Fig. 5 B).
Meanwhile, the simple-Brownian diffusion of both Cy3-DOPE and TfR in the actin-depleted blebbed PM indicates that actin filaments (and their associated transmembrane picket proteins) are responsible for compartmentalizing the PM (Fig. 3 A). This conclusion is consistent with previous observations, including the changes of the compartment sizes after the treatments with actin-modulating chemicals, latrunculin, cytochalasin D, and jasplakinolide (Fujiwara et al., 2002; Fujiwara et al., 2016; Murase et al., 2004), the equality of the compartment sizes determined by the lipid diffusion data and the actin mesh sizes on the apical PM cytoplasmic surface determined by electron tomography (Morone et al., 2006) and super-resolution microscopy (Xia et al., 2019), and the results of single-molecule optical trapping (Sako and Kusumi, 1995; Sako et al., 1998). New data about the hop diffusion of membrane molecules in the basal PM and even in the focal adhesions in the basal PM are reported in the companion paper.
We believe that the PM compartmentalization is fundamentally important for understanding the PM function. It would allow the cells to locally enhance phosphorylation at particular places on the PM, by confining the kinases in the compartment (due to higher local concentrations of kinases than phosphatases, which are more prevalent in the cytoplasm) (Kalay et al., 2012; Kusumi et al., 2012a), to localize stimulation-induced stabilized raft domains (Kusumi et al., 2004; Kusumi et al., 2011, 2012a, b; Suzuki et al., 2012; Kusumi et al., 2020), and to suppress the diffusion of engaged receptor oligomers (oligomerization-induced trapping) (Iino et al., 2001). However, due to the difficulties in using large gold probes and visualizing them at high frame rates, very few scientists have directly investigated and detected hop diffusion in the PM. With the developed ultrafast camera system with single fluorescent-molecule sensitivities, PM compartmentalization and hop/confined diffusion of membrane molecules could be studied quite readily by many more scientists, and thus their investigations could progress much faster.
This camera system now allows us to perform the fastest PALM, with a data acquisition rate of 1 kHz in the largest view-field (640 x 640 pixels; 35.3 x 35.3 µm2 with the pixel size of 55.1 nm) (Figs. 7 and 8). The data acquisition of 333 – 10,000 frames takes only 0.33 – 10 s, enabling live-cell PALM for certain structures such as caveolae and FA (Figs. 7 and 8). Although a single-molecule localization precision of 29 nm (for mEos3.2 at 1 kHz) is worse as compared with 2 – 25 nm (Betzig et al., 2006), 12 – 29 nm (Shroff et al., 2007), and 12 nm (Zhang et al., 2012) using EM-CCD and sCMOS sensors, the gain in time resolution and the applicability to observations of live-cell events could compensate for the spatial resolution deterioration. The ultrafast PALM also affords the possibility of performing PALM imaging of live cells at video rate, when new fluorescent dyes and proteins that can be photoconverted or photoactivated more efficiently become available.
Meanwhile, ultrafast PALM and ultrafast single fluorescent-molecule imaging could be performed simultaneously, as described in the companion paper (Fujiwara et al., 2021). Namely, the developed ultrafast camera system now allows us to observe subcellular structures in/on the PM with nano-scale precisions, and at the same time, to detect how individual single molecules interact with or behave in these structures. Therefore, we conclude that the ultrafast camera system developed in the present work will become an especially powerful tool for cell biology.
Materials and methods
Ultrahigh-speed intensified CMOS camera system: design and operation
Detailed description of the camera system (Fig. 1; Figs. S1-S3; Table 1) See the schematic diagram of the developed camera system shown in Fig. 1 A. The new ultrahigh-speed camera system consists of the following three major components.
(a) A Hamamatsu image intensifier (V8070U-74), comprising a third-generation GaAsP photocathode with a quantum efficiency of 40% at 570 nm (Fig. 1 A-a-α), a three-stage microchannel plate allowing maximal gain over 106, in which a non-linear noise increase was virtually undetectable (Fig. 1 A-a-β), and a P46 phosphor screen with a decay time of approximately 0.3 µs from 90% to 10% (Fig. 1 A-a-γ).
(b) A CMOS sensor (unless otherwise specified, we report the results obtained with the sensor developed for a Photron 1024PCI camera, but for some tests, we additionally report the results obtained with the newer sensor developed for a Photron SA1 camera), with a global shutter exposure was used (Table 1). The 1024PCI (SA1) sensor is composed of 1,024 x 1,024 pixels with a 17 x 17-µm (20 x 20-µm) unit pixel size, and operates up to 1 kHz or every 1 ms (5.4 kHz or every 0.19 ms) for the full-frame readout. The 1024PCI sensor can be operated at 10 kHz (0.1-ms resolution) with a frame size of 256 x 256 pixels, at 45 kHz (0.022-ms resolution) with a frame size of 128 x 64 pixels, and at 110 kHz (0.009-ms resolution) with a frame size of 128 x 16 pixels. The SA1 sensor can also be operated at 16 kHz (0.063-ms resolution) with a frame size of 512 x 512 pixels, and at 45 kHz (0.022-ms resolution) with a frame size of 256 x 256 pixels (Table 1).
However, the actual observation frame rates for single-molecule tracking with reasonable single-molecule localization precisions (say ≤50 nm) were limited to 10 - 30 kHz. This is because the number of fluorescent photons that can be emitted from a single fluorophore during < 0.033 - 0.1 ms (the integration time of a camera frame); i.e., the frequency that a single fluorophore can be excited, is limited, as quantitatively described in “Estimation of the number of photons that can be emitted by a single Cy3 molecule during 0.1 ms: triplet bottleneck saturation” in the Materials and methods (also see Fig. 1, E and F; Fig. S3). Namely, with the development of our ultrafast camera system, the instrument is no longer the limitation for achieving higher time resolutions (faster than 10 - 30 kHz) for single fluorescent-molecule imaging, and now the availability of fluorescent dyes has become the limitation. With the future development of new dyes with faster excitation and emission, without making a transition to the triplet state, observations even at 110 kHz would be possible. Indeed, we showed that when an average (mean) of five Cy3 molecules were attached to a single Tf protein (5xCy3-Tf), it can be observed at a rate of 45 kHz (Fig. 1 I; Figs. S2 A and S3; Table 1).
The readout noise, including the dark noise, of the 1024PCI and SA1 sensors at the full-speed readout at 21°C was 37 root-mean-square electrons/pixel, as measured by the manufacturer (Photron), and provided dynamic ranges of ∼800 and ∼1,200, respectively. The quantum efficiency of the CMOS sensor employed here was 40% (for both sensors), but since the CMOS sensor is placed after the image intensifier, the lower quantum efficiency of the CMOS sensor is not a critical issue in the developed camera system (the quantum efficiency of the image intensifier photocathode matters).
(c) A straight (1:1) optical-fiber bundle directly adhered to the phosphor screen of the image intensifier on one side (Fig. 1 A-a-γ, input side) and to the CMOS sensor on the other side (Fig. 1 A-b, output side). This enhanced the signal reaching the CMOS sensor by a factor of 5-10, as compared with the lens coupling used for our standard camera system employed for single fluorescent-molecule imaging (Suzuki et al., 2012; Kinoshita et al., 2017).
The electrons generated at the CMOS sensor were transferred, amplified (Fig. 1 A-d), and digitized (Fig. 1 A-e) in 64 and 8 parallel paths, respectively, and then transferred to the host PC.
Basic design concept of the camera system
(A) The use of a CMOS sensor rather than an sCMOS sensor or an EM-CCD sensor
To achieve ultrahigh-speed single fluorescent-molecule imaging, we used a CMOS sensor rather than an sCMOS sensor or an EM-CCD sensor, which are broadly employed in fluorescence microscopy. This is because the maximum frame rates attainable with the sCMOS sensors and EM-CCD sensors (typically 1.2 – 4 ms/frame for a 256 x 256-pixel image) are at least 10 times slower than those of the CMOS sensors employed here (0.1 and 0.015 ms/frame for a 256 x 256-pixel image, using the Photron 1024PCI sensor and SA1 sensor, respectively; no binning). To avoid image distortions and achieve higher rates, we employed CMOS sensors with a global shutter (most sCMOS cameras employ rolling shutters; although some newer sCMOS cameras are equipped with global shutters, their frame rates are slower than those when rolling shutters are employed).
(B) The use of an image intensifier (also see the beginning of Results in the main text)
An obvious problem when using the CMOS camera is its high readout noise (30∼40 vs. <5 root-mean-square electrons/pixel/frame for CMOS vs. sCMOS; the term “readout noise” used in this report always includes the dark noise of the sensor). As described in the previous section, the readout noise of the 1024PCI and SA1 sensors employed in this study was 37 root-mean-square electrons/pixel/frame (at the full-speed readout at 21°C). Meanwhile, the background noise signal (b in the equation in the caption to Fig. S2) was 0.035 ± 0.058 detected photons/pixel/frame on the glass using the oblique illumination (mean ± SD; in the case of TIR illumination, b = 0.038 ± 0.059 detected photons/pixel/frame) and 0.068 ± 0.17 detected photons/pixel/frame on the cellular apical PM (oblique illumination). Therefore, the background noise signal is much smaller than the readout noise, as expected (i.e., Np << Nr as described in the subsection “Basic conceptual strategy to address the large readout noise of the CMOS sensor” in the main text). As shown in Eq. 3 there, G should be much greater than Nr/Np, i.e., G>>Nr/Np. Therefore, G>>37/0.035 (or 0.068) or G>>1,100 (or 540) for single fluorescent molecules on the glass (apical PM). As described in the following paragraphs, by also considering Sp, we found a total amplification gain G of 8,100 useful for single fluorescent-molecule imaging.
Next, we address the signals from the fluorophores. Consider our standard test conditions for observing a single Cy3 molecule, using a frame rate of 10 kHz and oblique illumination for excitation at 23 µW/µm2 (i.e., instrumentally less optimal as compared with the TIR illumination, but necessary for observing molecules in the apical PM as well as in the basal PM). Under these conditions, we obtained 34 ± 2.4 detected photons/molecule/frame (Fig. 1 E top; including a quantum efficiency of the image intensifier photocathode of 0.4 at 570 nm; i.e., the number of photons that arrived at the photocathode of the intensifier was 85 ± 6.0 photons/molecule/frame), which realized a single Cy3-molecule localization precision of 38 ± 1.7 nm on the coverslip (Fig. 1 F top). Namely, an average (total number of) of 34 ± 2.4 photons is detected on the CMOS sensor in the two-dimensional Gaussian image of a standard deviation (SD; radius) of 123 ± 1.1 nm (2.2 ± 0.020 pixels x 55.1 nm/pixel) on the sample plane. (This image size was determined by the Gaussian fitting of each image for 50 Cy3 molecules immobilized on the glass under the TIR illumination at 79 µW/µm2; this higher illumination was employed to determine the Gaussian image size more precisely than that obtainable under the oblique illumination at 23 µW/µm2, by generating approximately 3 times more detected photons; see Fig. 1 E top; image magnification by a factor of 300 [150 x 2]).
Consider how the 34 photons are distributed in the pixelized Gaussian image; i.e., the 2-dimensional intensity profile (point-spread function) of a single-molecule emitter pixelized by the CMOS sensor. The expected number of photons in the pixel located at the integer position (m, n), I(m, n), is given as (Huang et al., 2011), Here Itotal is the total number of detected photons in the image; i.e., 34 photons, and Em and En are where erfrepresents a Gaussian error function, (mo, no) is the sub-pixel emitter position, and s is the SD of the Gaussian spot profile; i.e., 2.2 ± 0.020 pixels. Using these equations, the peak pixel intensity I(0,0) (the number of detected photons at (m, n) = (0,0)) when a single-molecule emitter is located exactly at the center of the pixel (0,0) is estimated to be only 1.1 photons.
Under such low signal conditions, in which the pixel intensities within the Gaussian spot profile fluctuate frame by frame at the level of single photons, the photoelectrons emitted at the photocathode of the image intensifier should be amplified until the readout noise of 37 root-mean-square electrons/pixel/frame, which also fluctuates spatiotemporarily, becomes negligible. To satisfy this condition, the photon amplification gain of the image intensifier of 33,200 (the ratio of the number of photons emitted from the phosphor screen of the image intensifier vs. the number of detected photons) was used throughout this study (see the following estimates for details). The image intensifier was coupled to the CMOS sensor by an optical fiber bundle. Therefore, due to the 39% loss (61% coupling efficiency) by the optical fiber bundle and the quantum efficiency of the CMOS sensor of 40%, the overall electron amplification (after photon detection) was a factor of 8,100 (33,200 x 0.61 x 0.4). Since the quantum yield of the photocathode of the image intensifier was 0.4, the total amplification of the incident photon of this camera system was 3,240 (one photon that arrived on the photocathode of the image intensifier generated an average of 3,240 electrons in the CMOS chip).
The overall electron amplification of 8,100x (after photon detection) was selected based on the following two considerations. First, the probability that the electron signal at the CMOS sensor amplified from a single detected photon (at the photocathode of the image intensifier) becomes greater than the readout noise should be sufficiently high. As shown in Fig. S1 E, the probability of detecting a single photon (as normalized by the number of detected photons/frame at the saturating levels of electron amplification) was increased to 90.0% at an overall electron amplification of 8,100x.
Second, the upper limit of the overall electron amplification is given by the full-well capacity of 30,000 electrons for the individual pixel (for the 1024PCI sensor employed for most experiments in this study). Considering the stochastic fluctuation of the signal, we set the electron amplification of the image intensifier so that the average signal in the peak pixel of 1.1 electrons/pixel/frame was amplified to less than 1/3 of the full well capacity (<10,000 electrons); i.e., amplification by a factor of <9,090 (= 10,000/1.1). Combining these two considerations, we employed an overall electron amplification by a factor of 8,100 (33,200 at the image intensifier), 10% less than the factor 9,090, to further reduce the possibility of pixel intensity saturation. (For detecting dimers and larger oligomers, the image intensifier gain should be reduced, although the probability of missing monomers would increase slightly.)
(C) The design and conditions for visualizing and tracking single molecules for many frames (Fig. 2 C)
Note that these illumination and amplification conditions were selected so that we could track single molecules for many frames in the apical PM (e.g., for longer than 99 frames for 14% of the Cy3 molecules immobilized on the glass, under the conditions of 3-frame gap closing, as shown in Fig. 2 C). When only much shorter tracking is required (such as a single frame or in the case of PALM), much higher excitation laser power density could be employed for better single-molecule localization precisions. The best single-molecule localization precision we achieved with this camera system was 2.6 ± 0.099 nm (mean ± SEM), with a maximum number of detected photons/molecule/frame of 11,400 ± 700 (mean ± SEM; n = 50 Cy3 molecules; Fig. 1 G and H and Fig. S2 D), using a TIR illumination power density at 79 µW/µm2 and a signal integration time of 16.7 ms. This is because, under these conditions, most Cy3 molecules become photobleached within a single frame (16.7 ms; i.e., virtually all of the photons possibly obtained from single molecules are concentrated in a single frame) due to the use of a TIR illumination density of 79 µW/µm2, by which the photon emission rate from a single Cy3 molecule is saturated (Fig. 1 E).
Estimation of the number of photons that can be emitted by a single Cy3 molecule during 0.1 ms: triplet bottleneck saturation (Fig. 1 E and F; Figs. S2 − S3)
In ultrahigh-speed single fluorescent-molecule imaging, the number of photons emitted from a single molecule during the duration of a single camera frame is the key limiting factor. This critically depends on how fast a molecule returns to the ground state from the excited state. In a conventional three-state model (ground, singlet-excited, and triplet-excited states), the maximum photon emission rate, kem (photons/s), can be described as (Schmidt et al., 1995) where τs and τT represent the lifetimes of the singlet- and triplet-excited states, respectively, kisc (= ΦT⁄τs) is the intersystem crossing rate, Φ is the fluorescence quantum yield, and ΦT is the quantum yield for triplet formation. Namely, the maximum photon emission rate, kem, critically depends on the triplet yield and lifetime, and hence this phenomenon is known as “triplet bottleneck saturation”.
For Cy3, τs ≈ 1 ns, τT ≈ 1 µs (in a specimen equilibrated with atmospheric molecular oxygen, the triplet lifetime is dominated by the collision rate of molecular oxygen with the fluorophore, which is about 106/s) (Kusumi et al., 1982), Φ = 0.15, and ΦT = 0.003 were employed (Sanborn et al., 2007; Dempsey et al., 2011). These values provide a kem of 3.8 x 107 photons/s. Therefore, the maximum number of photons available to form an image of a single Cy3 molecule, during the integration duration of 0.1 ms for each frame, is approximately 3,800. Although this number would vary, depending on the spectroscopic parameters in the given environment, it provides a baseline for understanding such fast imaging. Assuming that 5-10% of the emitted photons will reach the intensifier photocathode (Rasnik et al., 2007; Gould et al., 2009), 190 - 380 photons will reach the photocathode of the image intensifier and be detected with a ∼40% quantum efficiency of the GaAsP photocathode at the Cy3 peak emission wavelength of 570 nm, providing the maximum number of photons detected during a 0.1-ms camera frame time of 80 - 150.
This estimate agrees well with the experimental results for evaluating the maximal photon emission rate of Cy3 by TIR illumination (here, since we are discussing saturation conditions, we focus on the results obtained by the TIR illumination rather than the oblique illumination) shown in Fig. 1 E top and Fig. S2 A left (the data displayed in Fig. S2 A left show the relationship of the single-molecule localization error with the number of detected photons/spot/frame obtained at a frame rate of 10 kHz, which was found to be consistent with the theory developed previously; Mortensen et al., 2010). In Fig. 1 E and F (top), with an increase of the illumination intensity, both the number of detected photons/molecule/frame and the single-molecule localization precision were enhanced. However, the extents of the enhancement were saturated, because the number of photons that a single molecule can emit during the 0.1-ms frame time was limited. Under the near-saturation conditions at a laser power density of 79 µW/µm2 at the sample plane, the number of detected photons was ∼100 photons/frame (Fig. 1 E top). This confirmed that the experimental result is consistent with the estimate of the maximum photon emission rate based on the three-state model (ground, singlet-excited, and triplet-excited states; 80 – 150 photons during 0.1 ms) as described in the previous paragraph, indicating that the saturation of Cy3 photoemission can be explained by the “triplet bottleneck saturation”. Under the Cy3 saturation conditions, the improvement of the single-molecule localization precisions with an increase of the laser excitation intensity was limited to (saturated at) ∼20 nm for recordings at 10 kHz (Fig. 1 F top and Fig. S2 A left).
Among the eight dyes examined here, JF549, TMR, JF646, Atto647N, SeTau647, and Cy5 exhibited saturation more readily than Cy3 and Alexa555 (Fig. S2 B). Furthermore, the average numbers of detected photons from single molecules during the 0.1-ms frame time obtainable at saturation were smaller than those of Cy3 and Alexa555, and thus their single-molecule localization precisions at 10 kHz at saturation were worse than those of Cy3 and Alexa555 (Fig. S3). At saturation, Cy3 provided slightly better single-molecule localization precision at 10 kHz than Alexa555 (Fig. S3 B). Therefore, we primarily employed Cy3 throughout the remaining part of this report. Note that this result depended not only on the photophysical properties of individual dyes, but also on the wavelength dependence of the photocathode quantum yield of the image intensifier. The quantum yield is lower (∼0.2) for the near-IR dyes, JF646, Atto647N, SeTau647, and Cy5, as compared with that (∼0.4) for the Cy3, Alexa555, JF549, and TMR dyes.
Determination of the number of detected photons/molecule/frame (N) (Fig. 1, E and G; Fig. 2, A and B; Fig. 6, A-b and c; Figs. S2−S3)
All of the fluorescent dye molecules used for determining the number of detected photons/molecule/frame were covalently bound to the coverslip coated with 3-APS, and 5xCy3-Tf was adsorbed on the coverslip coated with poly-D-lysine (see the previous subsection). The number of detected photons/molecule/frame was evaluated by multiplying the pixel intensity and the gain conversion factor of the developed camera system. This factor was determined by detecting the same number of photons on both the developed camera system and an Andor iXon DU-897 back-illuminated EM-CCD camera, with the known gain conversion factor of 0.03622 photons/pixel count at an EM gain of 50 and an imaging depth of 16 bits (measured by Zeiss for an ELYRA P.1 PALM system). Briefly, the images of fluorescent beads immobilized on a coverslip were split by a 50/50 beam splitter, and each image was projected onto the new camera system and the EM-CCD camera at the same time. The number of detected photons from each fluorescent bead/frame was obtained by multiplying the gain conversion factor of the EM-CCD camera and the entire pixel intensities of the spot on the EM-CCD camera. The number of photons that reached the EM-CCD camera was then obtained by dividing it by the quantum efficiency of the EM-CCD camera (0.95). The same number of photons must have reached the photoelectric cathode of the developed camera, and therefore, by multiplying with the quantum efficiency of the developed camera (0.4), the number of detected photons/frame/spot was obtained. By comparing this number with the entire pixel count of the fluorescent spot, the conversion factor of the developed camera system was evaluated. At the typical overall electron amplification of 8,100x employed for the observations at a frame rate of 10 kHz (0.1-ms frame time) in the present research, the gain conversion factor of the developed camera system was estimated to be 0.00363 (0.00136) photons/pixel count in an imaging depth of 10 (12) bits for the 1024PCI (SA1) sensor.
Detecting single-molecule fluorescence spots and determining their positions in the image
Each and every fluorescent spot in an image was detected and its position was determined, by using an in-house computer program based on a spatial cross-correlation matrix (Gelles et al., 1988; Fujiwara et al., 2002, 2016). The image (signal intensity profile) was correlated with a symmetric 2-dimensional Gaussian point spread function (PSF) with a standard deviation of 123 nm (kernel; 123 nm was used for Cy3 and the value was individually determined for each fluorescent probe; see the caption to Fig. S2) (Mashanov and Molloy, 2007). The “maximum entropy” thresholding (Sahoo et al., 1988) was applied to the cross-correlation matrix. The spot representing a single molecule was detected as that containing an area with a size greater than or equal to 5 pixels, which was defined as the size of the area where the values of the cross-correlation matrix were greater than or equal to the threshold value (a constant value for the whole image). The spot position (x, y coordinates) was determined in the following way. First, the centroid of the cross-correlation matrix was calculated, and then an 830-nm-diameter circular region (55.1 nm/pixel x 15 pixels) with its center placed at the centroid was determined as the region that includes the intensity profile of the fluorescent spot. Second, the spot position was determined by fitting the intensity profile in the circular region to a symmetric 2-dimensional Gaussian PSF, using the following formula: where the fitting parameters were A (amplitude), (xo, yo) (the sub-pixel center position of the spot), and sxy (standard deviation of the symmetric Gaussian PSF), and the value for B (background intensity offset) was measured (background signal intensity divided by the number of pixels).
Observing the time series of the number of detected photons/0.1-ms-frame from single Cy3 molecules, determining the signal-to-noise ratios (SNRs) of single Cy3 molecule images, and evaluating the durations in which single Cy3 molecules could be consecutively observed (the bright/dark periods [on/off-periods] in the images of single Cy3 molecules and the gap closing for short off-periods) (Fig. 2)
Time-dependent changes in the number of detected photons/0.1-ms-frame from single Cy3 molecules immobilized on a coverslip were observed at 10 kHz, under our standard oblique-angle laser illumination conditions of 23 µW/µm2 (Fig. 2 A). The molecules that were observable in the first frame of the image sequence were selected. The number of detected photons during a single image frame in an 830 nm diameter (55.1 nm/pixel x 15 pixels) circular region including a fluorescent spot, called the “spot intensity”, was measured and plotted against the frame number at 10 kHz. To evaluate the signal intensity in the background, the number of detected photons during a single image frame in an adjacent region with the same shape and size, called the “BG signal intensity” was measured. On- and off-periods were determined based on the thresholding employed for the spot detection.
The signal-to-noise ratio (SNR) for the image of a single molecule was determined in the following way (Fig. 2 B). From the time-dependent fluorescence signal intensities, the histograms of the numbers of detected photons/0.1-ms for the images of single molecules; i.e., the histograms for the “spot signal intensities” and the “background [BG] signal intensities” during the on-periods, were obtained, and their mean signal intensities (ISpot and IBG, respectively) and standard deviations (σSpot and σBG, respectively) were calculated. The SNR was evaluated using the following equation, The mean SNR of single Cy3 molecules immobilized on the coverslip was 2.5 ± 0.11 for 50 Cy3 molecules with on-periods of 15 - 150 frames at 10 kHz, whereas the mean SNR on the apical PM was 1.8 ± 0.056 for 50 Cy3-DOPE molecules with on-periods of 1,000 frames at 10 kHz, as obtained under our standard oblique-angle laser illumination conditions of 23 µW/µm2.
The distributions of the durations of the on-periods and those after neglecting the off-periods lasting for 1, 2, or 3 frames (called “gap closing”) are shown in Fig. 2 C. The off-periods are induced by the occurrences of non-emission periods of a single dye molecule (which could induce no or dim images in a frame, depending on the duration of the non-emitting period; the off-periods tend to occur more often during the observations of living cells, probably due to the existence of various chemicals in the cell and the culture medium). The off-periods also occur when the signal from a single molecule is missed for short periods, due to the fluctuations of the fluorophore signal intensity (ISpot) as well as the higher background (IBG) and its fluctuation (σBG). Therefore, gap closing for 1-3 frames is often employed in single-molecule tracking studies. For describing the results obtained in living cells in the present report, we used 3-frame gap closing.
Cell culture
Human T24 epithelial cells (the same as the ECV304 cell line used in the previous research [Murase et al., 2004], which turned out to be a sub-clone of T24; Dirks et al., 1999) were grown in Ham’s F12 medium (Sigma-Aldrich) supplemented with 10% fetal bovine serum (Sigma-Aldrich). Cells were cultured on 12-mm diameter glass-bottom dishes (IWAKI), and single-molecule observations were performed two days after inoculation. For culturing cells expressing mGFP-paxillin or mEos3.2-paxillin, the glass surface was coated with fibronectin by an incubation with 5 µg/ml fibronectin (Sigma-Aldrich) in phosphate-buffered saline (PBS) (pH 7.4) at 37°C for 3 h.
To form PM blebs (up to 20 µm in diameter) depleted of the actin-based membrane-skeleton, the cells were incubated with 1 mM menadione for 5 h at 37°C (Fujiwara et al., 2002), and then treated with 100 nM latrunculin A (a gift from G. Marriott, University of California, Berkeley) on the microscope stage for 5 min at 37°C. All measurements were performed within 5-15 min after the addition of latrunculin A (Suzuki et al., 2005; Fujiwara et al., 2016).
Examination of the photo-induced damage to the cell during ultrahigh-speed single fluorescent-molecule imaging (Fig. 2, D and E)
The viability of the cells was examined by staining with 1 µM TOTO-3 iodide (Molecular Probes), which only stains dead cells (Zuliani et al., 2003), at 37°C for 5 min and then observing the stained cells using epi-illumination with a 594-nm laser. To obtain reference images of dead cells, the cells were treated with 100 µM H2O2 at 37°C for 1 h. The fluorescence intensity of TOTO-3 in the 5.5 x 5.5-µm area inside the nucleus was measured, and the histograms of signal intensities were obtained. Based on the negative and positive controls (Fig. 2, D and E), a threshold fluorescence intensity of 4.0 x 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]).
Note the following. Once the desired single-molecule localization precision is chosen for each experiment, the required total number of photons emitted from the molecule during a frame to achieve the precision will be the same, irrespective of the frame rate (inverse of the frame time). Therefore, the total number of photons elicited by laser excitation during a frame time will be the same, regardless of whether the observations are made at video rate (33-ms frame time) or at 10 kHz (0.1-ms frame time, if photon emission saturation does not occur). Namely, the direct photo-damage to the cell per frame due to the excitation laser illumination is expected to remain constant even when the laser illumination intensity and the frame rate are increased, as long as the single-molecule localization precision required for the experiment and the number of observed frames (not the total observation duration) are the same (in the absence of photon emission saturation).
However, direct experiments are required to test the phototoxicity to cells, as shown here. This is partly because slight photon-emission saturation occurred under our standard illumination conditions of 23 µW/µm2 (Fig. 1 E), and also because higher illumination photon densities could induce two-photon events and enhance the secondary reactions of the photo-induced molecules produced at high densities in the cell, which could generate cytotoxic substances.
Preparation of Cy3-DOPE and Cy3-Tf, and cell surface labeling
Cy3-DOPE was prepared and incorporated in the PM as described previously (Fujiwara et al., 2002; Murase et al., 2004), except that the final concentration of Cy3-DOPE added to the cells was 10 nM. Cy3-Tf used for the measurements at 6 kHz (0.167-ms resolution) was generated by incubating 6.5 µM monofunctional sulfo-Cy3 (GE Healthcare) with 6.3 µM human holo Tf (Sigma-Aldrich) in 0.1 M carbonate buffer (1 ml, pH 9.0) at 25°C for 60 min, followed by desalting column chromatography (PD-10, GE Healthcare, equilibrated and eluted with PBS) to remove the unreacted dye. The dye/protein molar ratio of the Cy3-Tf was 0.2. At this ratio, more than 90% of the fluorescent spots in the image are expected to represent single Cy3 molecules, based on the Poisson distribution, which was confirmed by single-step photobleaching of the fluorescent spots of Cy3-Tf (as well as Cy3-DOPE). Tf conjugated with multiple Cy3 molecules, used for the measurement at 45 kHz (0.022-ms resolution), was generated by incubating 1.25 mM monofunctional sulfo-Cy3 with 6.3 µM human holo Tf (mixed at a molar ratio of ∼200:1), which provided Cy3-Tf with the dye/protein molar ratio of ∼5 (called 5xCy3-Tf).
To label TfR in the PM with Cy3-Tf, first the Tf (originated from FBS) already bound to TfR on the cell surface was partially removed by incubating the cells in 1 ml Hanks’ balanced salt solution buffered with 2 mM TES (Dojindo), at pH 7.4 (HT medium) and 37°C for 10 min, and then after washing, the HT medium containing 10 nM Cy3-Tf (or 5xCy3-Tf) was added to the cells at a final concentration of 0.5 nM. At this concentration, single molecules of Cy3-Tf bound to the apical PM could be observed without replacing the medium with the Cy3-Tf-free medium. The observations were completed within 10 min after the Cy3-Tf addition.
Ultrahigh-speed imaging of single fluorescent molecules and its application to fluorescent probes bound to coverslips
Each individual fluorescently-labeled molecule on the apical and basal PMs was observed at 37 ± 1°C, using the oblique-angle and TIR illumination modes, respectively, of a home-built objective lens-type TIRF microscope (based on an Olympus IX70 inverted microscope), which was modified and optimized for the camera system developed here. The beam was attenuated with neutral density filters, circularly polarized, and then steered into the edge of a high numerical aperture (NA) oil immersion objective lens (UAPON 150XOTIRF, NA = 1.45, Olympus), focused on the back focal plane of the objective lens. Both TIR and oblique-angle illuminations were used for Cy3 at 10 kHz and 30 kHz, and 5xCy3-Tf at 45 kHz. For other molecules and conditions, only the TIR illumination was used. For exciting Cy3, Alexa555 (Invitrogen), JF549 (Janelia Fluor 549; Tocris Bioscience), and TMR (Molecular Probes and Promega), a 532-nm laser (Millennia Pro D2S-W, 2W, Spectra-Physics; 1.8 to 16 mW for the ∼14-µm diameter observation area) was employed. For exciting JF646 (Janelia Fluor 646; Tocris Bioscience), Atto647N (ATTO-TEC), SeTau647, and Cy5 (sulfo-Cy5; GE Healthcare), a 660-nm laser (Ventus, 750 mW, Laser Quantum; 0.41 to 4.5 mW for the ∼12-µm diameter observation area) was used.
The illumination laser power density was determined as follows. When the field stop was fully open, the excitation laser illuminated a circular (2-dimensional Gaussian) area with a 12.5-µm radius (standard deviation) on the sample plane. By adjusting the field-stop size, the central part of the excitation laser beam was selected to form a circular area with a radius of 7 µm on the sample plane, approximating the largest view-field of 14 x 14 µm2 employed in this research, and the laser power after the objective lens was measured. Since the dimmest intensity in the 7-µm Gaussian area was ∼85% of the peak intensity, the laser power density was calculated assuming a uniform laser intensity in the circular area with a 7-µm radius; i.e., the measured power was simply divided by the area size of 154 µm2 (π x 72).
To observe single fluorescent molecules immobilized on coverslips, dye molecules were covalently linked to 3-aminopropyltriethoxysilane (APS)-coated coverslips (custom-ordered from Matsunami). Briefly, 0.2 – 1 nM succinimidyl ester-modified dye molecules in HT medium were placed on the 3-APS-coated coverslip at 25°C (10-min incubation), and then the coverslip was washed five times with 1 ml HT medium. To immobilize 5xCy3-Tf molecules on the glass surface, the 12-mm diameter glass-bottom dishes were coated with poly-D-lysine, and then incubated in HT medium containing 0.1 nM 5xCy3-Tf at 25°C for 10 min.
The method for evaluating the position determination precisions of Cy3-labeled molecules bound on the coverslips is described in the caption to Fig. S2. The position determination precisions for the molecules in the apical PM were estimated using the ensemble-averaged MSD-Δt plots for single-molecule trajectories of Cy3-DOPE and Cy3-Tf (5xCy3-Tf) bound to TfR, as shown in Fig. S4.
Quantitative analysis of single-molecule trajectories based on the MSD-Δt plots (Fig. 4, A-a and B)
For each single-molecule trajectory, the one-dimensional MSD(x or y) for the x- or y-direction for every time interval was calculated according to the following formula: where δt is the frame time, (x(jδt + nδt) and y(jδt + nδt)) describe the position of the molecule following a time interval nδt after starting at position (x(jδt), y(jδt)), N is the total number of frames in the sequence, n and j are positive integers, and n determines the time increment. In the quantitative analysis of the trajectories, 1-dimensional MSD-Δt plots were employed.
Each single-molecule trajectory was classified into a suppressed-, simple-Brownian-, or directed-diffusion mode using the 2-dimensional MSD-Δt plot, which is the sum of the MSD-Δt plots for the x- and y-directions (Fig. 4 A-a). The basic idea for the classification is shown in Fig. 4 B-a (Kusumi et al. 1993). The classification was based on the relative deviation (RD), which describes the long-term deviation of the actual mean-square displacement, MSD(N, n) at the time nδt, from the expected MSD based on the initial slope of the MSD-Δt plot for molecules undergoing ideal simple-Brownian diffusion, 4D2-4 · nδt; i.e., RD(N, n) = MSD(N, n)/[4D2-4 · nδt] (N = the number of frames in a full trajectory, n = the increment number of frames used for the analysis with the MSD-Δt plot, 1 ≤ n ≤ N, and δt = duration of each frame. Therefore, Δt = nδt, which is the x-axis of the MSD(N, n)-Δt plot; and D2-4 is the short-time diffusion coefficient determined from the slope of the second, third, and fourth points in the MSD-Δt plot). The RD value is ≪, ≈, or ≫ 1, when the molecules are undergoing suppressed, simple-Brownian, or directed diffusion, respectively.
In Fig. 4 B-b, the distributions of RD(N, n)s for the Cy3-DOPE (RD(1,000, 100), δt = 0.1 ms) and TfR trajectories (RD(1,000, 200), δt = 0.167 ms) (shaded bars; n = 50 and 20 for the intact and actin-depleted blebbed PM), as well as for simple-Brownian particles generated by a Monte Carlo simulation (open bars; n = 5,000), are shown. Based on the distribution of the RD(N, n) values determined for simulated simple-Brownian particles (open bars), the RD(N, n) values giving the 2.5 percentiles of the particles from both ends of the distribution, referred to as RDmin and RDMAX, were obtained (red and blue vertical lines in Fig. 4 B-b, respectively; they depend on both N and n). Each experimental single-molecule trajectory was classified into the suppressed (confined and hop)-diffusion mode if its RD(N, n) value (shaded bar) was smaller than RDmin (and into the directed-diffusion mode if its RD(N, n) value was larger than RDMAX).
Monte Carlo simulations for the hop diffusion in the intact PM and simple-Brownian diffusion in the actin-depleted blebbed PM (Fig. 5 B)
Monte Carlo simulations for the hop diffusion were performed as described previously (Ritchie et al., 2005). The hop diffusion simulation parameters are the following (prepresents the probability that a hop movement to an adjacent compartment takes place when the diffusing molecule enters the boundary).
Simulation parameters for simple-Brownian diffusion in the actin-depleted blebbed PM are the following. Gaussian localization error of 50 nm was added (see Fig. S4 B). The MSD-Δt plot ensemble-averaged over 1,000 trajectories was obtained, and the offset due to the localization error was estimated and subtracted based on the y-intercept (by extrapolation) of the linear-fit function for the second, third, and fourth steps in the MSD-Δt plot, as performed for experimental trajectories.
Ultrafast live-cell PALM of caveolin-1-mEos3.2 and mEos3.2-paxillin (Figs. 6-8)
The plasmid encoding mouse caveolin-1 (GenBank: U07645.1) fused to mEos3.2 (caveolin-1-mEos3.2) was generated by replacing the cDNA encoding the EGFP protein, in the caveolin-1-EGFP plasmid (a gift from T. Fujimoto, Nagoya University, Japan; Kogo and Fujimoto, 2000), with that of mEos3.2 (Zhang et al., 2012) (generated by making 3 point mutations, I102N, H158E, and Y189A in the Addgene mEos2 plasmid #20341 [http://n2t.net/addgene:20341; RRID:Addgene_20341], a gift from L. Looger, Janelia Research Campus; McKinney et al., 2009). The plasmid encoding mEos3.2-paxillin was generated from the mGFP-paxillin plasmid, used in the companion paper (Fujiwara et al., 2021). First, the cDNA encoding human paxillin isoform alpha (NCBI reference sequence: NM_002859.3; cloned from the human WI-38 cell line) fused to mGFP at the N-terminus was subcloned into the EBV-based episomal vector, pOsTet15T3 (gift from Y. Miwa, University of Tsukuba, Japan), which bears the tetracycline-regulated expression units, the transactivator (rtTA2-M2), and the TetO sequence (a Tet-on vector) (Shibata et al., 2012, 2013). The mEos3.2-paxillin plasmid was then generated by replacing the cDNA encoding mGFP in the mGFP-paxillin plasmid with that encoding mEos3.2. T24 cells were transfected with the cDNAs encoding caveolin-1-mEos3.2 and mEos3.2-paxillin, using Nucleofector 2b (Lonza) according to the manufacturer’s recommendations.
Data acquisitions of ultrafast live-cell PALM were performed on the basal PM at 37 ± 1°C. We used the TIR illumination mode of our home-built TIRF microscope (based on a Nikon Ti-E inverted microscope) equipped with two ultrafast camera systems developed here and a high NA oil immersion objective lens (CFI Apo TIRF 100x, NA = 1.49, Nikon). Photoconversion of mEos3.2 was induced by a 405-nm diode laser (PhoxX, 120 mW, Omicron) with its laser intensity exponentially increased from 0.014 to 0.036 µW/µm2 during the PALM data recording period of 10 s with an e-folding time τ of 10.6 s (i.e., the photoconversion laser intensity at time t = 0.014 µW/µm2 x exp[t/10.6], and thus that at the end of the 10-s data accumulation time = 0.036 µW/µm2 as t = 10 s), to keep the number densities of mEos3.2 spots in the FA region similar during the e-folding period.
The photoconverted mEos3.2-paxillin was excited using a 561-nm laser (Jive, 500 mW, Cobolt) at 30 µW/µm2, and single-molecule spots were recorded at a frame rate of 1 kHz (with an integration time of 1 ms). The fluorescence image isolated by a bandpass filter of 572-642 nm (FF01-607/70, Semrock) was projected onto the photocathode of the developed ultrafast camera system (more specifically, the photocathode of the image intensifier). The reconstructions of a PALM image with a pixel size of 10 nm were performed using the ThunderSTORM plugin for ImageJ (Ovesny et al., 2014) installed in the Fiji package (Schindelin et al., 2012) and Gaussian rendering with a localization precision of 29 nm (Fig. 6 A-d).
Detection and characterization of FA-protein islands using Voronoï-based segmentation of the PALM images (Fig. 8)
The SR-Tesseler software based on Voronoï polygons (Levet et al., 2015) was applied to the locations of mEos3.2-paxillin to automatically segment the PALM data. Since the blinking correction function of the SR-Tesseler software evaluated that the average number of blinks was 1.1 (the 1-frame gap closing was applied to sequences of captured images using the “Merging” post-processing function in ThunderSTORM, with the maximum off frame of 1 and the maximum search distance of twice the mean localization precision of mEos3.2 in the basal PM of 29 nm; Fig. 6 A-d), further blinking correction was not performed with the SR-Tesseler software. FA contour detection was performed by using a Voronoï polygon density factor of 1.2 (within the ROI), with a minimum area of 2 pixels. The contour of the islands of FA proteins was determined basically in the same way, by using a Voronoï polygon density factor of 1.2 (within the FA contour), with a minimum area of 0.05 pixels.
Data availability
Data supporting the findings of this study are available from the corresponding author upon reasonable request.
Code availability
The code is available from the corresponding author upon reasonable request.
Online supplemental material
Fig. S1 shows how we determined the electron amplification gain of the image intensifier. Fig. S2 shows the relationship of the single-molecule localization precision with the number of detected photons/molecule/frame for various fluorescent dye molecules. Fig. S3 shows that the numbers of detected photons/molecule/frame from single molecules are saturated under stronger excitation laser intensities, and thus the improvement of single-molecule localization precision with an increase of the laser intensity is limited. Fig. S4 shows the MSD-Δt plots ensemble averaged over all trajectories obtained for Cy3 molecules immobilized on coverslips or diffusing in the apical and basal PM of T24 cells, providing estimates of single-molecule localization errors. Fig. S5 shows the TILD method, the expected distribution of the dwell lifetimes (theoretical derivation), and the derivation of the equation used for hop diffusion fitting. Video 1 shows single Cy3 molecules covalently linked to the glass surface observed at 10 kHz. Video 2 shows single Cy3-DOPE molecules diffusing in the intact apical PM in a view-field of 256 x 256 pixels, observed at 10 kHz. Video 3 shows enlarged views of single Cy3-DOPE molecules diffusing in the intact apical PM and the actin-depleted blebbed PM, observed at 10 kHz. Video 4 shows enlarged views of single TfR molecules, bound by Cy3-Tf, diffusing in the intact apical PM and the actin-depleted blebbed PM, observed at 6 kHz.
Author contributions
T.K.F. and A.K. conceived and formulated the project. T.K.F., S.T., Y.N., K.I., and A.K. developed the ultrahigh-speed camera system, T.K.F., K.I., T.A.T., and A.K. developed an ultrafast single-molecule tracking station based on the newly developed camera system, and T.K.F., T.K., T.A.T., and A.K. tested the camera system on the developed station. T.K.F., T.A.T., K.G.N.S., and A.K. designed the biological experiments and participated in discussions. T.K.F. performed virtually all of the ultrahigh-speed single-molecule imaging-tracking experiments, the ultrafast PALM experiments, and the data analysis. T.K.F. and K.P.R. developed the compartment detection algorithm. Z.K., based on discussions with T.K.F., derived the equation describing the MSD-Δt plot for particles undergoing hop diffusion and developed the theory for the distribution of the dwell lifetimes within a compartment for particles undergoing hop diffusion. T.K.F., K.P.R., Z.K., and A.K. evaluated the data. T.K.F., Z.K., and A.K. wrote the manuscript, and all authors discussed the results and participated in revising the manuscript.
Competing interests
S.T. and Y.N. are employees of Photron Limited, a manufacturer of high-speed digital cameras for industrial and scientific applications. T.K. is an employee of Carl Zeiss Microscopy GmbH, a manufacturer of microscope systems for life sciences and materials research. Authors T.K.F., Z.K., T.A.T., K.I., K.P.R., K.G.N.S., and A.K. declare that they have no competing interests.
Supplementary Figures
Expected distribution of the residency times: development of the hop diffusion theory
In the hop-diffusion literature, the average residency time within a compartment has been intuitively approximated as L2⁄4DMACRO. However, this expression has never been proven rigorously. In addition, the distribution of the residency times has remained unknown even for an idealized hop diffusion model, in which molecules undergo free diffusion (in viscous media) in the presence of equally spaced, equi-potential semi-permeable diffusion barriers. Here, we demonstrate that the residency time distribution is given by the sum of exponential distributions, which can be approximated well by a single exponential function with a decay constant of L2⁄4DMACRO, if the confinement effect is strong.
Consider a Brownian particle in a square region with semi-permeable boundaries, and calculate the distribution of first exit times. The residency time distribution is analogous to the distribution of the first time a particle exits a certain region. We assume that diffusion along the x and y directions is independent, which allows us to solve the problem for a one-dimensional (1D) system, and then generalize the results to the two-dimensional (2D) case.
Consider a Brownian particle in 1D, initially placed at x = xo between two boundaries located at x = 0 and x = L, that can diffuse freely in this bounded region. When the particle attempts to leave this region, it faces resistance, and thus the boundaries can be considered as partially permeable barriers. Once the particle crosses the boundary, it can never go back. Therefore, the time when it leaves the region is always the first exit time. The probability distribution of such a particle is governed by the diffusion equation, with the boundary conditions, where D is the microscopic diffusion coefficient within a domain, and p is a constant related to the permeability of the boundaries, such that p → 0 and p → ∞ correspond to impenetrable and completely permeable boundaries, respectively. The solution can easily be obtained by using separation of variables (Carslaw and Jaeger, 1986), and is given in the following form where βn(xo)’s are determined by the initial conditions, α = D⁄pL, and λn’s, n = 1, 2, 3, …, are the positive solutions of If the particle is initially at x = xo such that ρ(x, t) = δ(x - xo), then the coefficient βn becomes so that The cumulative probability distribution can be expressed as Finally, the distribution of exit times fex(t), and its cumulative Fex(t), can be calculated from the cumulative probability distribution above (Redner, 2001) Now we need to generalize this result to two dimensions, and obtain the distribution of exit times from a square compartment of area L2. This was readily achieved by realizing that the time of the first exit is the minimum of the first exit time in the x and y directions. Using the well-known result for the distribution of the minimum of two independent random variables (Gumbel, 2004), we obtain the cumulative probability distribution for the exit time distribution as where Fex,w(t) stands for the probability that the particle exits through one of the boundaries along the w direction until time t, and is explicitly given by where wo is the initial position along the w axis. Usually, the initial conditions are not accessible, so it is reasonable to average all of the different initial states. By averaging Fex,w(t) over all initial positions wo between 0 and L with equal weight, we obtain Using Eq. 13, Eq. 11 further simplifies to as there is no difference in the statistics of the position between the x and y directions after averaging over the initial position. The probability distribution for the exit times, or the residency time distribution, is given by the first derivative of Eq. 14 with respect to time Where .
The contributions of the higher order terms in Eq. 15 are quickly minimized, due to the exponential term. In many cases of practical interest, the first term with n = 1, m= 1 alone could be a good approximation of the result. To assess the validity of this argument, let us consider the ratio of the exponential factors in the first two terms of the double summation in Eq. 15. This ratio is equal to Inspecting the equation for λn’s, Eq. 6, we notice that λn+1 ≈ λn + π, such that Therefore, the higher order terms decay with almost the 10th or greater powers of e-Dt/L2, which are always less than 1 for t > 0. Similarly, it can be shown that the coefficient of the exponential, ξnξmηm, also decreases as n and m increase.
When the confinement effect is strong, the Brownian particle spends a sufficient amount of time in each compartment to cover it uniformly before escaping.
Mathematically, this corresponds to the limit in which ξn is approximately equal to 1. Thus, the residency time distribution given in Eq. 15 can be approximated by a single exponential
As the confinement effect becomes stronger, we would expect the average residency time to diverge. Therefore, in the strong confinement limit, λ1 would be close to 0 such that tan λ1 ≈ λ1, and Eq. 6 can be replaced by an approximate form which gives Therefore, the average residency time is equal to We now need to express α in terms of a quantity that can be experimentally measured. In the strong confinement limit that we are interested in, the Brownian particle behaves much like a random walker in a 2D lattice with lattice spacing L, for durations longer than the average residency time. In this picture, each lattice site corresponds to a square compartment of area L2, and the random walker takes steps between adjacent lattice sites at a rate . As the random walker can move in 4 directions in 2D, the rate of escape is 4F, such that the average residency time is τ̅. This description is appropriate as long as the random walker explores most of each compartment before it leaves. This ensures that the probability distribution within each compartment quickly becomes uniform and that the escape time distribution can be well approximated by a single exponential. The probability of finding the random walker at a lattice site (m, n) is governed by a Master equation (Hughes, 1995) With a straightforward calculation, the mean square displacement of a random walker that is initially at the origin is given by As this description is appropriate for times longer than τ̅, the diffusion coefficient associated with this random walk is the macroscopic diffusion coefficient, Combining Eqs. 23, 25 and 26, we obtain From many published reports (see the Table 1 summary in Kusumi et al., 2005), generally By solving Eq. 27 using this value, which satisfies the condition for strong confinement (Eq. 18, i.e. ≫ 1). Accordingly, under the strong confinement conditions, the second order term proportional to α-2 in Eq. 31 can be neglected, and Eq. 23 can simply be expressed as Therefore, the decay time constant of the exponential distribution of the residency time within a compartment, given by Eq. 23, can be simplified to the expression given by Eq. 30.
We obtained the distribution of the dwell lifetimes in a compartment by directly measuring the dwell time using the TILD analysis (A-c and B-c). In the real PM, the dwell time of diffusing molecules within a compartment would be affected by the variations in the compartment sizes and shapes and in the properties of the compartment boundaries, due to the differences in actin binding proteins and TM picket proteins. However, as shown in B-c and Fig. 5 A, the residency time distribution in the PM is well approximated by an exponential function, probably because these variations both lengthen and shorten the dwell lifetimes quite randomly.
Hop-diffusion fitting: the function describing the MSD-Δt plot for particles undergoing hop diffusion
We developed an equation for the MSD-Δt plot for particles undergoing idealized hop diffusion; i.e., free diffusion in the presence of equally spaced, equi-potential semi-permeable diffusion barriers. Such hop diffusion can be characterized by the following three parameters: the compartment size (the distance between barriers), L, the microscopic diffusion coefficient within a compartment (true diffusion coefficient in the absence of the compartments), Dmicro, and the long-term diffusion coefficient over many compartments, DMACRO. One of the key parameters for hop diffusion, the residency time within a compartment, can be calculated from these parameters as L2⁄4DMACRO, as shown in the previous subsection.
By employing the notations γ = DMACRO⁄(Dmicro - DMACRO) and τ = 4Dmicrot⁄L2, the 1-dimensional MSD in the real time domain, which is the inverse Laplace transform of Eq. 18 in (Kenkre et al., 2008) for a 1-dimensional MSD averaged over all initial locations, can be obtained as where the terms reso(τ) and res(τ) are the sum of the residues that arise from the inverse Laplace transform. The zeroth residue, reso(τ), is expressed as whereas the term res(τ), representing half the sum of all other residues, is expressed as where r(k) (k = 2, 3, 4, . ..) is the kth root of . As performed in (Kenkre et al., 2008), we employed the bisection method to find the roots numerically with high precisions and obtained the accurate result for a sufficiently large N. Namely, by rearranging terms in Eq. 33, we obtain the following equation. We used this equation for fitting the experimental MSD values. As for the physical meaning, the first term characterizes the long term behavior of MSD, which is approximately equal to 2DMACROt for strong confinement (γ ∼ 0) and 2Dmicrot for weak confinement (γ → ∞). The second and third terms describe the transient behavior of the MSD. At around τ ∼ 0, the second and third terms cancel each other out. In the longer time limit, the third term becomes negligible, and the second term becomes equal to the intercept of the linear MSD.
Captions for Videos 1 to 4
Video 1
Single Cy3 molecules covalently linked to the glass surface, observed at 10 kHz (every 0.1 ms) (observation period of 1,500 frames = 150 ms; Replay, 167x-slowed from real time) using oblique-angle illumination at 23 µW/µm2. a, b, and c represent the fluorescent spots corresponding to those in Fig. 2, A and B. The on-periods including short off-periods of up to 3 frames are highlighted by the orange circle, and the off-periods are highlighted by the cyan circle.
Video 2
Single Cy3-DOPE molecules diffusing in the intact apical PM, observed at 10 kHz (every 0.1 ms) (observation period of 750 frames = 75 ms; Replay, 167x-slowed from real time) using oblique-angle illumination at 23 µW/µm2. Most fluorescent spots were photobleached within 100 frames after starting the illumination, but a small percentage of the spots lasted longer than 300 frames. The long-lasting spot enclosed within the yellow square in the movie on the left is enlarged and highlighted by the circle in the movie on the right.
Video 3
Single Cy3-DOPE molecules diffusing in the intact apical PM and the actin-depleted blebbed PM (left and right respectively), observed at 10 kHz (every 0.1 ms) (see Fig. 3, C and D) (observation periods of 750 and 300 frames = 75 and 30 ms, respectively; Replay, 167x-slowed from real time). The statistical analysis method developed in this study classified the trajectories into the suppressed-diffusion and simple-Brownian diffusion modes, respectively. The flickering signals seen in the movies, in addition to the long-lasting spots (indicated by the trajectories), are probably due to the fluctuation of the autofluorescence signal from the cytoplasm, because they are also found in the movies of Cy3-Tf (Video 4).
Video 4
Single TfR molecules, bound by Cy3-Tf, diffusing in the intact apical PM or the actin-depleted blebbed PM (left and right respectively), observed at 6 kHz (every 0.167 ms) (observation periods of 600 and 180 frames = 100 and 30 ms, respectively; Replay, 167x-slowed from real time) (see Fig. 3 D). The statistical analysis method developed in this study classified the trajectories into the suppressed-diffusion and simple-Brownian diffusion modes, respectively.
Acknowledgements
We thank Profs. G. Marriott of the University of California, Berkeley, Y. Miwa of the University of Tsukuba, T. Fujimoto of Nagoya University School of Medicine, and L. Looger of the Janelia Research Campus, for their kind gifts of latrunculin A, the pOsTet15T3 vector, the cDNA encoding caveolin-1-EGFP, and the mEos2 plasmid, respectively. We also thank Mr. K. Hanaka for his enthusiastic encouragement of this research, Ms. M. Yahara and Ms. A. Chadda for constructing various cDNAs, Ms. J. Kondo-Fujiwara and Mr. K. Kanemasa for preparing the figures, and the members of the Kusumi laboratory for helpful discussions. We are grateful to Prof. Ken Jacobson of the University of North Carolina and Prof. Kathalina Gaus of the University of New South Wales Sydney for critical reading of the manuscript and constructive comments. This work was supported in part by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) (Kiban B to T.K.F. [16H04775, 20H02585], Kiban B to K.G.N.S. [18H02401], and Kiban S and A to A.K. [16H06386 and 21H04772, respectively]), a Grant-in-Aid for Challenging Research (Exploratory) from JSPS to T.K.F. (18K19001), a Grant-in-Aid for Innovative Areas from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) to K.G.N.S. (18H04671), Japan Science and Technology Agency (JST) grants in the Core Research for Evolutional Science and Technology (CREST) program in the field of “Biodynamics” to A.K. and in the field of “Extracellular Fine Particles” to K.G.N.S. (JPMJCR18H2), and a JST grant in the program of the Development of Advanced Measurements and Analysis Systems to A.K. and T.K.F. WPI-iCeMS of Kyoto University is supported by the World Premiere Research Center Initiative (WPI) of MEXT.
Footnotes
Some sentences were revised for clarification.