1. Introduction

Measuring the motion of individual small particles on small length scales and short timescales by optical means is a powerful approach to characterize the mechanisms in many systems including biological cells [1–4]. Nanoparticles that possess optical properties (e.g. fluorescence and scattering) can be detected because of their capability of creating contrast from the background environment. The position of the particle can be determined by localizing the center of its point spread function. This technique, known as single-particle tracking (SPT), has greatly enhanced our understanding of the underlying principles of cell biology [5–7]. The use of optical linear scattering from nanoparticles as signal for studying cell biology can be traced back to 1980s [8], and this approach has been optimized and proved to be promising for high-speed SPT in recent years [5,9,10]. In contrary to fluorescence, linear scattering is stable without photobleaching or blinking effects. In addition, the scattering power can be linearly increased by raising the illumination intensity, providing sufficient optical signal within short exposure time for high-speed SPT. Gold nanoparticles (GNPs) are commonly used as labels because of their enhanced optical cross-sections at plasmon resonance wavelengths [11]. The scattering-based high-speed SPT has offered the opportunity to investigate rapid dynamics taking place at molecular scale within sub-milliseconds. Nan et al. used 150 nm GNP to monitor the motion of kinesin and dynein at 1.5 nm spatial precision at 40 kHz [9]. Kusumi et al. found the cell plasma membrane is compartmentalized into zones of hundreds of nanometers by tracking 40 nm GNPs attaching to lipids and protein molecules diffusing in cell membranes with 16 nm spatial precision at 40 kHz [5]. Ueno et al. observed stepwise nanometer-scale movement of motor proteins on microsecond timescales by labeling the protein molecule with 40 nm GNP and tracking its motion with < 2 nm spatial precision at 110 kHz [10]. In the above studies, high temporal resolution is absolutely necessary for revealing rapid motions of the target molecules. These movements would be smeared out if the acquisition rate is not sufficient (< 10 kHz).

In SPT, close attention has to be paid to the possible influence of the labeled particle to the target molecule [12]. Reduction of particle size is generally desirable for minimizing the effect of heavy mass loading and the spatial hindrance [13]. Decreasing the size of particle, however, puts a severe challenge in scattering-based SPT because scattering intensity is proportional to the power of sixth of the particle radius: scattering signal drops dramatically as the particle size decreases. Such weak signal can be readily overwhelmed in the readout noise of high-speed electronics, which has set a limit of detection sensitivity [10]. As a result, GNPs smaller than 40 nm in diameter are rarely used in high-speed SPT (acquisition rate > 1 kHz).

Interferometric detection is a promising approach to circumvent the limit of sensitivity set by electronic noise [14]. Instead of detecting the weak scattering intensity directly, a strong coherent reference beam is superimposed to the scattering signal and their interference is detected. Such homodyne detection brings the system to shot-noise limited regime even in the presence of considerable electronic noise of the detector. It has been demonstrated that interferometric detection of scattering signal (iSCAT) makes it possible to visualize and thus to track nano-objects, such as virus particles, lipid vesicles and very small gold nanoparticles [15–20]. Using iSCAT microscopy, lipid diffusion that exhibits multi-mobilities and nanoscopic confinements has been detected in supported bilayer membranes by tracking 20 nm GNP at an acquisition rate of 1 kHz [20]. Extension of the acquisition rate to MHz will ultimately allow us to monitor lipid diffusion in membranes without blurring effects and therefore to investigate the fundamental diffusion characteristics at single-particle level. The main challenge of realizing such a system has been the integration of a high-speed CMOS camera, which is not optimized for sensitive detection, into an optical microscope system for high-precision measurements. In this work, we successfully extend the temporal resolution of iSCAT microscopy to 1.64 μs by using one of the fastest commercial high-speed CMOS cameras and rigorously examine its shot-noise limited sensitivity in iSCAT detection. With this microsecond iSCAT (μs-iSCAT) microscopy, we achieve localization of 20 nm GNP with 2 nm spatial precision at an acquisition rate up to 500 kHz. The localization precision realized in our system agrees well with the theoretical calculation considering the ideal situation where the dominant noise is the shot noise of photons. We further demonstrate a high-speed measurement of lipid diffusion in a supported membrane by tracking single 20 nm GNPs labeled to lipid molecules. Our μs-iSCAT microscopy sets a new standard of spatiotemporal resolution for SPT using 20 nm nanoparticles. The precise and high-speed SPT provides the opportunity to investigate diffusion of molecules in a membrane on molecular scale with unprecedented temporal resolution.

2. Methods

2.1 Experimental setup: μs-iSCAT microscopy

A home-built inverted iSCAT microscope is constructed for high-speed tracking of GNPs (see Fig. 1). The light source is a continuous wave diode-pump solid-state (DPSS) laser at 532 nm (Finesse Pure, Laser Quantum). The laser light is focused at the back focal plane of an oil-immersion microscope objective (UPLSAPO 100XO, NA1.4 Olympus), creating a wide-field illumination on the sample with an area of ~9 μm in diameter (FWHM). When the acquisition rate is less than 5 kHz, the illumination is rapidly scanned at ~100 kHz by two-axis acousto-optic deflectors (DTSXY-400, AA Opto-Electronic), and thereby creating a uniform illumination over a larger field of view [17]. When imaging at higher frame rate, even the scanning by deflectors is too slow for providing homogeneous illumination. In such high-speed imaging, a stationary wide-field illumination without beam scanning is employed. The illumination is partially reflected at the interface of the supporting coverslip and the aqueous solution of the sample due to the mismatch in refractive index, and this reflected beam readily serves as the reference beam for interferometric detection (see inset of Fig. 1). The transmitted illumination is scattered by the GNPs. Both the backscattered signal and the reference beam are collected by the objective, picked up by a 50:50 non-polarizing cube beamsplitter, and finally imaged on a high-speed CMOS camera (Phantom v711, Vision Research) where the interference of the scattered signal and reflected reference beam is recorded.

 

Fig. 1 Schematics of the experimental setup. AOD1 and AOD2: acoustic optical deflectors for beam scanning in two directions; L1: wide-field lens (f₁ = 20 cm) focusing laser beam at the back focal plane of the objective lens; BS: 50:50 non-polarizing beamsplitter; OBJ: 100x oil-immersion objective (NA 1.4); L2: camera lens (f₂ = 75 cm), placed at a position such that its front focal plane coincides with the back focal plane of the OBJ; M1 and M2: mirrors. The CMOS camera records the iSCAT image formed via interference between the backscattered light from GNPs and the reflection from the glass-water interface (see inset and text for details).

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The microscope system is carefully aligned such that the unwanted reflections from the optical components do not arrive on the camera. We emphasize that this alignment is critical in order to achieve maximal interference signal because the reflections with optical path differences longer than the coherence length of the laser (6 mm in our case) do not interfere with the signal but only contribute an intensity offset. The optical magnification is chosen such that each pixel of the camera corresponds to an imaging area of 48 × 48 nm² on the sample. As will become clear later, such high magnification is necessary for achieving nanometer localization precision. The temporal resolution is limited by the acquisition rate of the CMOS camera which depends on the resolution of the image (thus the field of view). In our present scheme, acquisition rate of 215,600 frames per second (fps) can be achieved with resolution of 128 × 128 pixels (field of view of ~6 × 6 μm²). Such field of view is reasonable for observing motion of lipid molecules in bilayer membranes at diffusion rate of 1 μm²/s for 1 second. For scenarios where a reduced field of view of 1.5 × 1.5 μm² is allowed, one can even achieve acquisition rate of > 680,000 fps (exposure time of 1.09 μs). The mechanical vibration of the microscope is measured to be less than 1 nm by localizing single 60 nm GNPs fixed on a coverslip (data not shown).

2.2 Sample preparation for imaging single 20 nm GNPs

20 nm GNPs (BBI Solutions) are randomly deposited on a clean coverslip by spin-coating. The sample of GNPs is then embedded in water to mimic the condition of SPT in cellular environment. Figure 2(a) shows the iSCAT image of individual 20 nm GNPs at the glass-water interface, imaged at 5 kHz. The dark spots are the results of destructive interference between the scattered fields from individual GNPs and the reference beam [15]. Figure 2(b) plots the normalized intensity profile along the line shown in Fig. 2(a) together with a Gaussian fit. The normalized intensity is defined as $\left(I-I_r\right)/I_r$ where $I$ and $I_r$ are the measured intensity and the intensity of the reflected reference beam without GNP respectively [16]. The standard deviation of the fitted Gaussian function in Fig. 2(b) is 95 ± 9 nm. The uniform optical contrast of individual diffraction-limited spots implies that the signal is from single GNPs of similar size. Notice that the interference contrast is proportional to the strength of scattered field, and therefore proportional to the volume of the GNP. The histogram of the normalized intensity measured from 115 diffraction-limited spots is plotted in Fig. 2(c). The narrow distribution of the normalized intensity of −0.13 ± 0.04 suggests the size of GNPs under analysis is uniform with a diameter of 20 ± 2 nm. This estimated size distribution agrees well with the information provided by the supplier of the GNP and is further verified by a transmission electron microscope measurement (data not shown).

 

Fig. 2 (a) iSCAT image of 20 nm GNPs randomly deposited on a coverslip embedded in water. (b) Normalized intensity line profile of a selected particle shown in (a). Squares are the measured data, and the red curve is the corresponding Gaussian fit. (c) Histogram of the amplitude of the normalized intensity measured from 115 particles. The mean amplitude of the normalized intensity is 0.13, and the standard deviation is 0.04.

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The distribution of single 20 nm GNPs on the coverslip without aggregates is also confirmed by imaging the sample separately with a scanning electron microscopy (data not shown). The normalized intensity of 20 nm GNP measured in our system is larger than the value reported previously [16]. We believe the larger interference signal is achieved in our system by avoiding non-interfering reflections arriving on the detector. In addition, we point out that nonlinear (saturated) pixel response with respect to light intensity under strong illumination can lead to smaller amplitude of the measured normalized intensity.

3. Results and discussion

3.1 Shot-noise limited sensitivity of μs-iSCAT microscopy

To examine the shot-noise limited sensitivity of our μs-iSCAT microscopy, we measure the intensity fluctuation of each pixel under different levels of illumination intensity at acquisition rate of 500 kHz. The linearity of the pixel response with respect to illumination intensity is carefully measured and compensated. The average and the standard deviation of detected number of photons, written as $N_{\det }$ and ${\sigma }_{\det }$ respectively, are calculated for each pixel assuming the full well capacity is 23,200 photoelectrons (according to the manufacturer). The measured ${\sigma }_{\det }$ is contributed by many sources of noise, including the camera noise ${\sigma }_{camera}$ (dark noise and readout noise), the laser noise ${\sigma }_{laser}$, and also the fundamental shot noise of photon ${\sigma }_{photon}=\sqrt{N_{\det }}$. The detected fluctuation can be written as

 

Fig. 3 Noise amplitude (${\sigma }_{\det }$) measured at different illumination intensities. The experimental data are shown as dots. The red solid curve shows the theoretical noise amplitude considering the camera noise and the photon noise. The cyan dashed line shows the noise fluctuation only due to the photon noise. It is clear that the measured noise is dominated by the shot noise of photon at high intensities.

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Interferometric detection circumvents the limit on sensitivity set by the electronic readout noise of the detector by introducing a strong reference beam as a local oscillator. The total number of detected photons $N_{\det }$ by a pixel can be written as

3.2 Localization of single 20 nm GNP at 500 kHz

The shot-noise limited sensitivity and thus optimal localization precision can be realized at any speed available with the camera. One would only need to adjust the power of illumination according to the acquisition rate such that sufficient number of photons arrives at the detector within each exposure. Figure 4(a) shows an optical image of a GNP immobilized on a coverslip embedded in water, captured by μs-iSCAT microscopy at 500 kHz. Background correction is essential in order to remove the stationary inhomogeneous pixel response and the non-uniform illumination (details of background correction are described in Appendix). Notice that the bright ring around the dark spot is the result of interferometric detection which shows the distribution of optical field, not intensity. The normalized intensity of this particular GNP is found to be −0.16. The slightly stronger normalized intensity than the average value (−0.13, see Fig. 2(c)) is believed to be due to a slightly larger particle size (a 21.4 nm GNP can give the normalized intensity of −0.16 assuming a 20 nm GNP gives the normalized intensity of −0.13). The GNP shown in Fig. 4(a) is imaged for 1000 frames at 500 kHz and its position is determined in every image. The histogram of localization precision in two lateral directions is plotted together in Fig. 4(b). Here, the localization precision is calculated as the accuracy of the nonlinear least-squares fitting of the measured point spread function with a 2D Gaussian function [22]. The histogram shows a narrow distribution peaked at 2.01 ± 0.24 nm.

 

Fig. 4 (a) iSCAT image of a 20 nm GNP deposited on a coverslip embedded in water acquired at 500 kHz. (b) Histogram of localization precision of the GNP displayed in (a). The average localization precision is 2.01 nm, and the standard deviation is 0.24 nm.

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We compare the measured localization precision with its theoretical limit by calculating number of detected signal photons in each image. The excitation intensity for tracking at 500 kHz (exposure time of 1.64 μs) is measured to be 3.7 mW/μm². Consider the scattering cross section of a 20 nm GNP at the wavelength of 532 nm is ~3.3 × 10⁻¹⁴ cm² [11], the total number of scattered photons within the exposure time of 1.64 μs is ~53,000. The overall collection efficiency of our microscope is estimated to be 0.0365 (considering the collection efficiency of the objective for a dipole radiation, transmission of optical components, and quantum efficiency of the camera). Therefore, the total number of scattered photons detected in each frame $N_{s,total}$ is ~1,932. Provided with this number of signal photons, one can calculate the optimal achievable localization precision $\sqrt{〈{\left(\Delta x\right)}^2〉}$, assuming that the only sources of noise are the inevitable photon noise and pixelation noise [23]:

3.3 Localization of 20 nm GNP with nanometer spatial precision at various imaging speeds

In order to confirm that the shot-noise limited localization can be truly realized at various acquisition rates, a series of measurements are performed on the same GNP shown in Fig. 4(a) at various acquisition rates from 10 kHz to 500 kHz. The excitation intensity is adjusted corresponding to the exposure time such that the number of detected photons from the reference beam in each frame remains identical. Figure 5 shows the measured localization precisions and the normalized intensities of the GNP at different acquisition rates. We measure the same normalized intensity and the same localization precision at all acquisition rates, confirming that shot-noise limited sensitivity is indeed achieved at all speeds.

 

Fig. 5 (a) Localization precision and (b) normalized intensity of a 20 nm GNP measured at various acquisition rates. In (a) and (b), squares are the average values and error bars are the standard deviations of the measurements of 1,000 images. The localization precision and the normalized intensity show no dependency on the acquisition rate. The small variation in the values measured at different acquisition rates is thought to be due to the slight difference in the axial position of the sample, leading to small changes in the spot size and the contrast of the point-spread functions.

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The results shown in Fig. 5 also imply that no difference in scattering mechanism of 20 nm GNP is detected at these excitation intensities. It has been reported that the heat generated by GNP via absorption of optical energy can induce a change in refractive index around the particle and thus induce scattering [25]. In our measurement at the highest acquisition rate of 500 kHz, the excitation intensity is 3.7 mW/μm², and the temperature raise at the surface of a 20 nm GNP is estimated to be ~10 K [26]. The similar normalized intensities measured at various speeds (at various illumination intensities) suggest that the contribution of induced scattering via absorption is negligible in our experiment. We remark that a local temperature raise of 10 K via particle heating seems not to be harmful to viability of living cells [27]. Nevertheless, in the application of biological imaging, care may have to be taken for the effect of local heating near the particle surface.

3.4 Tracking 20 nm GNP labeled to lipid molecules in supported bilayer membranes

We demonstrate our μs-iSCAT microscopy for a study of lipid diffusion on supported bilayer membranes. Compared to our previous studies of anomalous lipid diffusion using iSCAT microscopy [20], here the temporal resolution is improved by two orders of magnitude. We emphasize that diffusion characteristics generally depend on the length scale and the timescale of observation, and thus high spatial and temporal resolutions are essential for investigating the rapid motion of molecules in membranes. The nanometer localization precision of 20 nm GNP within microseconds allows us to monitor lipid diffusion at unprecedented spatiotemporal resolution with minimal perturbation.

Lipid bilayers were prepared on a coverslip by vesicle fusion [28]. The membrane consists of 1 mol% of 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(cap biotinyl) (biotin-cap-DPPE, Avanti) in host lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC, Avanti). 20nm GNP conjugated with streptavidin (purchased from BBI) is used to label biotin-cap-DPPE diffusing in the membrane (see Fig. 6(a)). Unbound GNPs are removed from the solution by gentle buffer exchange.

 

Fig. 6 (a) Schematics of a GNP labeled to biotinylated lipid molecules in a supported bilayer membrane. (b) Snapshot of iSCAT image of a 20 nm GNP diffusing on the membrane. (c) Diffusion trajectory of a GNP labeled to biotin-cap-DPPE in DOPC membrane, recorded at 100,000 fps for 1 second. Inset: close-up view revealing details of the diffusion trajectory. (d) Measured MSD data of the trajectory displayed in (c) (shown as squares) and the corresponding fit with a model of anomalous diffusion (red curve). The blue line connects the first two MSD data points and extrapolates for longer time delays, which illustrates the nonlinear dependency of the measured MSD data with respect to time delays. (e) Measured diffusion rate as a function of time delay. The diffusion rate of the GNP remains constant at long timescale (> 150 μs) and starts to show a gradual increase at short timescale (< 150 μs), which is a typical diffusion characteristic of anomalous diffusion.

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Images are taken at 100 kHz with an exposure time of 9.65 μs for 1 second under an illumination intensity of 0.6 mW/μm². A snapshot of a GNP diffusing on the membrane is shown in Fig. 6(b).The lateral position of the GNP is determined in each image and then connected sequentially into a trajectory. A typical diffusion trajectory of the GNP is shown in Fig. 6(c). Such precise and long trajectory provides great amount of statistical information of diffusion. We calculate the mean square displacement (MSD) from the measured trajectory for time delays $\Delta \text{t}$ ranging from 10 μs to 300 μs (see Fig. 6(d)) [3]. The clear nonlinear dependency of the MSD with respect to $\Delta \text{t}$ implies that the diffusion is not free. The measured MSD can be described with a model of anomalous diffusion [3]

In order to better visualize the time-dependent diffusion characteristics, one can alternatively consider the MSD as

4. Conclusion

We demonstrated a μs-iSCAT microscope that allowed us to track single 20 nm GNP with 2 nm localization precision up to 500,000 fps. The scattering signal from small GNP was detected by interference and shot-noise limited sensitivity was achieved even in the presence of considerable electronic noise of a high-speed CMOS camera. Using μs-iSCAT microscope, membrane diffusion was investigated by tracking single GNPs attached to lipid molecules with unprecedented spatiotemporal resolution. Anomalous diffusion was observed in the timescale from 10 μs to 150 μs possibly due to the effect of multivalent binding and substrate-membrane interaction. It is worth noting that the sensitivity of iSCAT microscope is determined by the number of photoelectrons each pixel can hold before saturation (i.e., the full well capacity). One could choose to gain sensitivity for detecting even smaller nano-objects by increasing the virtual full well capacity via integrating a number of frames into one image where the temporal resolution is compromised [33,34]. We also remark that the phase sensitive interferometric detection readily makes the localization in all three dimensions as the axial information is encoded in the contrast of the point spread function [35]. Our methodology of high-speed imaging of weak scattering signal from nano-objects via interference is general, and it can be extended to other scattering-based detection schemes, e.g., determination of orientation and rotation of nanorods on cell membranes [36]. Finally, with the combination of nanometer spatial precision and microsecond temporal resolution, we foresee new membrane physics to be revealed by μs-iSCAT microscope, such as the dynamics in coexisting liquid-disordered and liquid-ordered phases (i.e., lipid rafts) [37].

Appendix: Background correction

In SPT, high spatial localization precision relies on high SNR of the point spread function of the probe. In order to achieve nanometer localization precision, the systematic artifacts caused by the inhomogeneous pixel response of the camera and the inevitable non-uniform illumination have to be corrected. Since the effects mentioned above are relatively stationary within our observation timescale of seconds, they can be measured as a stationary background and thus their effects can be digitally removed. In the case of localizing GNP immobilized on a coverslip, we intentionally modulate the sample position in one lateral direction when recording images and the stationary background can be conveniently obtained by calculating the temporal median value of each pixel of the stack of recorded images. In the case of tracking a diffusing GNP on the membrane, the GNP moves across many pixels during recording, so the background can be again found by directly calculating the temporal median value of each pixel of the stack of images. Figures 7(a) and 7(c) show the images of a 20 nm GNP immobilized on a coverslip before and after background correction (the background used for correction is shown in Fig. 7(b)). It can be seen that the quality of the image is dramatically improved after the correction.

 

Fig. 7 (a) Raw iSCAT image of a 20 nm GNP. (b) Background image (see text for details). (c) Background corrected image from (a).

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Acknowledgments

This work is supported by Academia Sinica and the National Science Council, Taiwan (grants no. 102-2112-M-001-002-MY3). The authors thank the Core Facility for Nanoscience and Nanotechnology at Academia Sinica for helping the measurement with electron microscopes. The authors thank Dr. Juen-Kai Wang for fruitful discussions.

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