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A three-dimensional (3D) single fluorescent particle tracking strategy based on temporal focusing multiphoton excitation microscopy (TFMPEM) combined with astigmatism imaging is proposed for delivering nanoscale-level axial information that reveals 3D trajectories of single fluorospheres in the axially-resolved multiphoton excitation volume without z-axis scanning. Whereas other scanning spatial focusing multiphoton excitation schemes induce optical trapping interference, temporal focusing multiphoton excitation produces widefield illumination with minimum optical trapping force on the fluorospheres. Currently, the lateral and axial positioning resolutions of the dynamic particle tracking approach are about 14 nm and 21 nm in standard deviation, respectively. Furthermore, the motion behavior and diffusion coefficients of fluorospheres in glycerol solutions with different concentrations are dynamically measured at a frame rate up to 100 Hz. This TFMPEM with astigmatism imaging holds great promise for exploring dynamic molecular behavior deep inside biotissues via its superior penetration, reduced trapping effect, fast frame rate, and nanoscale-level positioning.
© 2014 Optical Society of America
1. Introduction
Multiphoton excitation (MPE) microscopy, a common technique in the biomedical and material research fields, provides the advantages of both fluorescence-based microscopy for fluorescent targeting and optical sectioning capability for three-dimensional (3D) imaging. Based on the nonlinear optical mechanism, MPE microscopy causes fluorophores to fluoresce via focal-point excitation with an ultrafast pulse-laser source, the natural mechanism of which enables 3D optical sectioning fluorescence microscopy. In addition, with an integrated near-infrared (NIR) pulse laser source that captures the benefits of optical window at biotissues, MPE microscopy has empowered a significant approach for deeper imaging in thick tissues and living animals with nominal photobleaching and minimum invasiveness [1]. Concurrently, MPE microscopy has also been adapted to many robust platforms, including multicolor imaging, multiphoton fluorescence-lifetime imaging microscopy, fluorescence correlation spectroscopy, and multimodal imaging, among others [1–5]. Other developments have targeted improvements to MPE microscopy, such as enhancing the efficiency of multiphoton fluorescence with wavelength dependent excitation and higher imaging speed [6,7]. One significant achievement has been the increase of the multiphoton imaging frame rate via techniques including a resonant scanner, line scanning system, multifocal scanning, and temporal focusing multiphoton excitation microscopy (TFMPEM) [7–13]. Our previous study presented a TFMPEM that is able to generate widefield and axially-resolved multiphoton excitation on a plane-by-plane basis with a fast frame rate up to 100Hz [14]. Recently, we demonstrated that a compact TFMPEM approach with a digital micromirror device (DMD), in lieu of a conventional blazed grating, can generate arbitrary patterned illumination at equivalent grating diffraction efficiency [15,16]. Consequently, the system offers the potential to investigate molecular behaviors and features in biological systems.
Single particle tracking approaches have been widely employed to extract information of molecular transport trajectories and functionalities in complex biological systems, for example the lipid dynamics of plasma membranes, movement of molecular motors, traffic mechanisms of cellular uptake, and viral infections of live cells [17–22]. With such a system, the trajectory and motion behavior of molecules or particles of interest can provide their locations and indicate pathway and spatial information for other target objects; further, their variations of diffusion characteristics indicate their interactions with other molecules or the surrounding environment. Moreover, the moving velocity, interaction duration, and step distance of molecules or particles in the tracking process can also be estimated quantitatively. There are two kinds of 3D single particle tracking approaches, namely the active feedback-based and passive imaging-based techniques [23–25]. The active feedback-based technique employs a position-sensing configuration to track one particle with a feedback-controlled 3D stage [23,26]. The imaging-based tracking techniques have several different optical configurations, for instance the 3D image stack, off-focus image, biplane, astigmatism, and interferometer methods [21,27–30]. These methods enable the localization of an individual particle’s 3D position, as well as track multiple particles in one image set. Combined with MPE, a 3D single-particle tracking system with lower photobleaching and thick specimen measurements can be realized. Nevertheless, the primary limitation of such an integrated system is the temporal resolution for dynamics analysis. For example, Levi et al. demonstrated 3D tracking via an MPE microscope that had a time resolution of 32 to 64 ms [31]; to overcome the speed limitation, multifocal MPE with fast two-photon imaging was suggested [32,33]. However, these spatial focusing MPE methods induce optical trapping force on the particles, thereby rendering dynamic particle tracking information questionable.
When employing a particle tracking approach to dynamically analyze molecular and particle behaviors, one must ensure a high specimen count for statistical treatment, sufficient temporal resolution, and low photobleaching. Accordingly, Spille et al. combined astigmatism imaging with light sheet microscopy for high contrast single particle imaging of a few hundred microns to determine 3D particle localizations [34]. Unfortunately, the drawback is that the light sheet from this type of microscopy cannot arbitrarily penetrate into thick tissues; as such, special treatment to allow the light sheet to penetrate from the side is required. In response to these aforementioned shortcomings, a 3D single particle tracking strategy based on TFMPEM combined with astigmatism imaging is proposed to overcome the MPE imaging time resolution limitation and provide 3D nanoscale positioning of fluorescent particles. Compared with other conventional spatial focusing MPE approaches, temporal focusing widefield illumination minimizes the optical trapping force that interferes with tracing measurements.
2. Optical setup and theoretical analysis
2.1. Optical system and sample preparation
Figure 1 illustrates the optical system setup. As shown, it consists of an advanced TFMPEM unit with an integrated high-resolution DMD (DPL7000, from Texas Instrument, USA) as the diffraction component and a 4f lens system mounted on an upright optical microscope (Axio imager 2, Carl Zeiss, Germany), for which the excitation source is a Ti:sapphire ultrafast amplifier (Spitfire Pro, Newport, USA) with a Ti:sapphire ultrafast oscillator (Tsunami, Spectra-Physics, USA) as the seed beam. The 12 mm beam size laser source has a peak power of 400 μJ/pulse, a pulse width of 100 fs, and a repetition rate of 10 kHz. The center wavelength can be adjusted from 750 nm to 850 nm, while the laser power can be controlled via a half-wave plate (HWP) and a linear polarization (LP). The DMD was placed on the image-conjugate plane of the objective lens’ focal plane, the mutual image-conjugate planes of which are highlighted by the red dashed lines. A water-immersion objective (60X PlanApo, Olympus, Japan) with a 1.2 numerical aperture (NA) and a high speed electron multiplying charge-coupled device (EMCCD) camera (iXon Ultra 897, Andor, UK) were used to respectively assemble and collect the multiphoton fluorescence images. Further, a removable cylindrical lens (Thorlabs, USA) with a focal length of 300 mm was coupled with the EMCCD camera to induce astigmatism in the light-collection optical path. To achieve a sufficiently effective image pixel size for two-dimensional (2D) elliptical Gaussian fitting, the MPE fluorescence images were magnified 2.5X by a camera adapter (T2-T2 SLR 2.5X, Carl Zeiss, Germany).
In addition communicating with the EMCCD to record images, the custom-made LabVIEW program created for a data acquisition card equipped with a field-programmable gate array (FPGA) module (PCI-7831R, National Instruments, USA) controlled the acquisition timing of the entire image recording process, including a mechanical shutter (VS14S-2-ZM-0-R3, Uniblitz, USA) for the exposing illumination, and a sample positioning stage, comprising a triple-axis motorized stage (H101A ProScan, Prior, UK) and a z-axis piezo stage (NanoScan Z-200, Prior, UK), for adjusting the specimens’ imaging position, as shown in Fig. 1. For TFMPEM excitation, the dispersed beam must propagate through the 4f lens setup, which comprises a collimating lens and an objective lens; then, the beam wavelength is dispersed and conformed to the pattern information by the DMD. Herein, the DMD acts not only as a blazed grating for the diffraction of temporal focusing, but also provides an amplitude transmittance for arbitrary patterned illumination simultaneously [15,16]. In this manner, an arbitrary MPE pattern can be simply and precisely projected onto the objective lens’ focal plane [15]. Then, by filtering the collected signal through a dichroic mirror and a short-pass filter (Semrock, US), only MPE fluorescence signals are collected via the objective lens, the imaging lens, and the cylindrical lens into the EMCCD camera. Through this system, sequential sectioning images at different sample depths can be obtained by controlling the nano-scale piezo stage in the z-axis via the FPGA, and then rendered into a 3D image stack.
To verify the system, carboxylate-modified fluorospheres (FluoSpheres, Life Technologies, USA) as the testing sample, with nominal bead diameters of 0.2 μm and 0.5 μm, were labeled with absorbing and emitting maximum wavelengths at 505 and 515 nm, respectively. Two types of samples were prepared: one was a fluorosphere solution (~3 ml) dropped and dried onto a coverslip for fixed dispersive fluorospheres; the other involved different diffusion coefficient environments created by adding fluorospheres into deionized (DI) water and mixing with glycerol at four different concentrations, namely 0%, 30%, 55%, and 80% for tracking and measuring the motion behavior of free fluorospheres.
2.2. Comparing the trapping effect between spatial focusing and temporal focusing
The optical force distribution of a small particle in a homogenous medium can be expressed as [35,36]
where E is the electric field, ϕ is the light phase and is the electric polarizability of a particle in the medium, which depends on the material, geometric shape, and size of the particle. According to Eq. (1), the first term is a gradient force resulting from the gradient intensity of the incident light to attract particles, while the second term is a scattering force derived from the radiation pressure via the scattering or absorption of light. Herein, we consider the different gradient intensities of light according to different illumination methods but with the same input laser energy and material conditions, namely the polystyrene particles and medium. Then, the trapping force is dominated by the gradient of light intensity in space (). Consequently, the light intensity gradient of the temporal focusing in TFMPEM is sufficiently low so as not to induce an optical trapping force on the fluorospheres. As opposed to the temporal focusing in TFMPEM, conventional scanning MPE microscopy requires an ultrafast laser beam to be spatially focused via a high NA objective lens to induce sufficient MPE. Consequently, the light intensity gradient is dramatically increased in the focal spot, which in turn generates intense optical trapping force that would influence the particle’s movements. To evaluate and compare the trapping effect between the two approaches, the trapping forces were calculated as follows. Assume a Gaussian laser beam is focused and its complex electric field expressed in terms of the wavelength and objective’s NA. The complex electric field of a Gaussian beam can be calculated by [37]where ρ is the radial distance from the center axis, z is the axial distance from the beam waist, is the initial phase, w(z) is the beam waist, R(z) is the radius of curvature, and w0 is the minimum beam waist. When a Gaussian beam passes through an objective, the beam is focused and the minimum beam waist can be expressed aswhere λ is the wavelength of the beam.Based on the equations, the optical force distribution near the focused region can be estimated. Temporal focusing widefield illumination can use an NA as low as 0.01 to approximately evaluate the optical force distribution based on the collimating beam excitation method. In this estimation, the attracted sphere’s diameter was 500 nm with a refractive index of 1.515, such as polystyrene, assuming the laser power was 1 mW with an excitation wavelength of 750 nm. The optical trapping force distributions of the radial and axial (in the z-direction) components for scanning spatial focusing with an NA of 1.2 are shown in Figs. 2(a) and 2(b), respectively. As can be seen, the maximum trap forces are 1.8 pN and 0.9 pN, for Figs. 2(a) and 2(b), respectively, with an intense area of 800 nm × 800 nm, which involves the point spread function (PSF) of the optical system. For widefield temporal focusing based on a collimating beam with an NA = 0.01, the distributions of the optical trapping force within the 100 μm × 12 mm intense area are shown in Figs. 2(c) and 2(d) for the radial and axial components, respectively. As shown, the maximum trapping forces are respectively estimated to be about 1.1 × 10−6 pN and 4.4 × 10−9 pN for the radial and axial components. Hence, the trapping force in the temporal focusing widefield illumination is respectively 6-order and 9-order lower than those of the spatial focusing scanning illumination for the aforementioned components. According to our experience, the laser power in temporal focusing widefield illumination is usually on the order of tens of mW and about 10 times stronger than the laser power used in spatial focusing scanning illumination (i.e. several mW) to acquire image with enough SNR for the both illuminations. Also, the trapping force is linearly proportional to the light intensity and its gradient, as demonstrated in Eq. (1). To consider the laser power of 20 mW in the temporal focusing widefield illumination for high SNR, the tapping force is 2.2 × 10−5 pN and 8.8 × 10−8 pN for the radial and axial components. Therefore, compared to the trapping force in spatial focusing scanning illumination, the trapping force in temporal focusing widefield illumination is almost negligible. This means that the fluorescent particles can be regarded as in free motion without any optical trapping in solution within the excitation volume of the TFMPEM illumination.
Fig. 2 Optical trapping force distributions for a 500 nm-diameter particle (n = 1.515) with 750 nm wavelength excitation and 1 mW: (a) radial component and (b) axial component by spatial focusing illumination (scanning) with NA = 1.2; (c) radial component and (d) axial component by temporal focusing illumination (widefield) regarded as a collimating beam with NA = 0.01.
3. Experimental results and discussions
3.1. Calibration for 3D localization of fluorescent particles with astigmatism imaging
In this 3D single-particle tracking strategy, the variation in the PSF imaging pattern, which was produced by the astigmatism effect, provided the z-axial location information of the single emitter. Herein, we recorded the fluorescence image of a fixed single fluorescent sphere with a roughly 200 nm diameter, as an emitter, at different z-axis positions by driving the piezo stage mounted on the sample stage. The fixed single fluorescent sphere is from the fluorosphere solution dropped and dried onto a coverslip. At the top of Fig. 3(a), the sectioned zoomed-in images show that the imaging patterns were changed from a vertical ellipse to a horizontal ellipse by shifting the z-axis in 600 nm steps, for a total of 2,400 nm. To create a calibration function between the z location and the pattern variation of the single fluorescent sphere, the sphere’s image stack was recorded at every z position with a step-shift of 20 nm. After being fitted with both the 2D elliptical Gaussian and defocusing functions, Fig. 3(a) shows the fitting results of the elliptical width and reconstructed calibration curves in the x and y directions with a total axial shift of 4 μm. The 3D localization of the single particle, extracted via fitting with 2D elliptical Gaussian functions and two calibration curves, is in agreement with the dynamic measurement in the optical section volume according to TFMPEM. Furthermore, system stability was evaluated by using a fixed particle with long term measurement. The 3D displacements in Fig. 3(b) show the position of a fixed particle with a monitoring time of 1 second. Figures 3(c)–3(e) indicate that the positioning resolutions in the x, y, and z directions are 14 nm, 14 nm, and 21 nm in standard deviation (STD), respectively, as determined from Fig. 3(b).
Fig. 3 (a) Image widths of a fixed fluorescent sphere in the x (red squares) and y (blue circles) directions corresponding to different z positions. The top of Fig. 3(a) shows the sectioned images at five positions with four sequential shifts of 600 nm in the z direction. (b) 3D positions of a fixed fluorescent sphere as a function of time. (c)-(e) Position histograms of the x, y, and z components illustrated in Fig. 3(b).
According to Fig. 3(a), the astigmatic PSF of a fluorosphere is an altering elliptical shape projected on the fluorosphere at the z position relative to the focal plane of the objective lens by adding a cylindrical lens to the imaging path. Both the lateral and axial positioning resolutions of the dynamic particle tracking approach are dependent upon the PSF image quality, i.e. the signal-to-noise ratio (SNR) of the image. Currently, the TFMPEM is a widefield detection scheme that renders the SNR sensitive to the scattering and aberration induced by a turbid medium, especially for emission signals of short wavelengths; hence, the positioning resolutions require improvement for deep tissue imaging. Although the aberration of the astigmatic PSF shaping can be compensated by adaptive optics [38,39], the scattering is still a serious concern in widefield imaging. In our particle tracking study, the scattering can be decreased by utilizing a longer emission wavelength, and then the SNR of tracking particles is increased.
3.2. Dynamic measurements of motion behavior of free fluorescent spheres
To dynamically measure the motion behavior of free fluorescent spheres in different diffusion coefficient environments, the mean square displacement (MSD) of the fluorescent spheres was calculated in this study. Based on the 3D position at each time interval, as determined by fitting the measured results, the MSD as a function of lag time for the 3D motion can be obtained as [40,41]
where is the lag time, is time averaging, and is the 3D positions of the tracked particles at time t. n is the integral and is the temporal resolution, i.e. the reciprocal of the frame rate. In this study, fluorospheres were added to DI water mixed with glycerol at four different concentrations, namely 0%, 30%, 55%, and 80% (wt). It should be noted that the diameters of the fluorospheres range from 180 to 220 nm, as per the product information. Further, according to the 2D elliptical Gaussian fitting and the two calibration curves in Fig. 3(a), the 3D location of a fluorosphere can be extracted in each frame without axial sectioning since the TFMPEM provides a frame rate of 100 Hz, i.e. a temporal resolution of 10 ms. The 3D trajectories of the fluorospheres diffused in pure DI water at 21 °C are shown in Fig. 4(a). In addition, Fig. 4(b) plots the calculated MSD of the fluorescent spheres’ 3D trajectories as a function of time for the 0%, 30%, 55%, and 80% glycerol samples. As can be seen, trajectories are almost linearly proportional to the time, which means that these motion behaviors are akin to an isotropic random walk.Fig. 4 (a) 3D trajectory of a fluorescent sphere in DI water. (b) MSDs of fluorescent spheres in DI water with four glycerol concentrations of 0% (black line), 30% (red line), 55% (green line), and 80% (blue line). Orange dashed lines are the fitting curves.
Based on the Stokes-Einstein predicted relationship, the MSD in 3D could also be estimated by [23,40–42]
where D is the diffusion coefficient and is the normal random diffusion. According to our measurements, the diffusion coefficients by fitting Eq. (5) were 1.290, 0.331, 0.145, and 0.022 μm2/s at the glycerol concentrations of 0%, 30%, 55%, and 80% (wt), respectively. Additionally, the traditional Brownian diffusion coefficient, which is a measure of the speed of diffusion, for a spherical particle is expressed by [40]where is the Boltzmann constant, T is the absolute temperature, is the viscosity of the medium, and d is the diameter of the particle. Herein, assuming the particle diameter was 200 nm and the viscosity were 1.002, 2.5, 8.5, and 60.1 cp for the glycerol concentration of 0%, 30%, 55%, and 80% (wt) at 20 °C, respectively. Based on Eq. (6), the diffusion coefficients were 2.137, 0.857, 0.252, and 0.036 μm2/s. To compare the diffusion coefficients in the experimental measurement and the simulation calculation, the numbers in the experimental measurement are decreased by 0.6 to 0.4 folds compared to the numbers in the simulation calculation. The possible reasons are as follows. The parameters utilized may not be accurate, including the particle size, experimental temperature, and the viscosities of the media. Also, the particles have surface charges which may reduce the diffusion speeds; nevertheless, these charges can be ignored at very low particle concentrations. Furthermore, as indicated earlier, very slight trapping force from the TFMPEM illumination may exist. Be that as it may, the linear responses for the four samples verify that the fluorospheres still possessed random motion behavior, as demonstrated by the proposed particle tracking strategy.4. Conclusions
The proposed 3D particle tracking strategy based on fast TFMPEM with astigmatism imaging can successfully extract 3D trajectories of particles. Some primary advantages of the strategy include: 1) provides 3D localizations of particles in an axially-resolved MPE volume with a temporal resolution of 10 ms; 2) reduces the optical trapping force by about 6 and 9 orders compared with the conventional scanning MPE approach; and, 3) offers lateral and axial positioning resolutions with about 14 nm and 21 nm in STD, respectively. Consequently, this system has a unique and superior ability to measure dynamic motion behavior in 3D. Moreover, this TFMPEM system with astigmatism imaging holds great promise to explore dynamic molecular behavior deep inside biotissues by offering deep penetration, fast frame rate, low trapping effect, and nanoscale-level positioning.
Acknowledgments
This work was supported by the National Science Council (NSC) in Taiwan with grant numbers NSC 100-2113-M-008-006-MY3, NSC 101-2221-E-006-212-MY3, NSC 101-2221-E-006-213-MY3, NSC 102-2627-M-008-003, and NSC 103-2627-M-008-003.
References and links
1. P. T. C. So, C. Y. Dong, B. R. Masters, and K. M. Berland, “Two-photon excitation fluorescence microscopy,” Annu. Rev. Biomed. Eng. 2(1), 399–429 (2000). [CrossRef] [PubMed]
2. R. Yasuda, C. D. Harvey, H. Zhong, A. Sobczyk, L. van Aelst, and K. Svoboda, “Supersensitive Ras activation in dendrites and spines revealed by two-photon fluorescence lifetime imaging,” Nat. Neurosci. 9(2), 283–291 (2006). [CrossRef] [PubMed]
3. G. Alexandrakis, E. B. Brown, R. T. Tong, T. D. McKee, R. B. Campbell, Y. Boucher, and R. K. Jain, “Two-photon fluorescence correlation microscopy reveals the two-phase nature of transport in tumors,” Nat. Med. 10(2), 203–207 (2004). [CrossRef] [PubMed]
4. B. R. Masters and P. T. C. So, “Confocal microscopy and multi-photon excitation microscopy of human skin in vivo,” Opt. Express 8(1), 2–10 (2001). [CrossRef] [PubMed]
5. R. Cicchi, D. Massi, S. Sestini, P. Carli, V. De Giorgi, T. Lotti, and F. S. Pavone, “Multidimensional non-linear laser imaging of Basal Cell Carcinoma,” Opt. Express 15(16), 10135–10148 (2007). [CrossRef] [PubMed]
6. N. S. Makarov, M. Drobizhev, and A. Rebane, “Two-photon absorption standards in the 550-1600 nm excitation wavelength range,” Opt. Express 16(6), 4029–4047 (2008). [CrossRef] [PubMed]
7. P. T. C. So, E. Y. S. Yew, and C. Rowlands, “High-throughput nonlinear optical microscopy,” Biophys. J. 105(12), 2641–2654 (2013). [CrossRef] [PubMed]
8. P. A. Kirkby, K. M. Srinivas Nadella, and R. A. Silver, “A compact acousto-optic lens for 2D and 3D femtosecond based 2-photon microscopy,” Opt. Express 18(13), 13720–13745 (2010). [CrossRef] [PubMed]
9. J. Bewersdorf, A. Egner, and S. W. Hell, “Multifocal multi-photon microscopy,” in Handbook of Biological Confocal Microscopy (Springer, 2006).
10. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]
11. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008). [CrossRef] [PubMed]
12. A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express 18(19), 19645–19655 (2010). [CrossRef] [PubMed]
13. E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010). [CrossRef] [PubMed]
14. L.-C. Cheng, C.-Y. Chang, C.-Y. Lin, K.-C. Cho, W.-C. Yen, N.-S. Chang, C. Xu, C. Y. Dong, and S.-J. Chen, “Spatiotemporal focusing-based widefield multiphoton microscopy for fast optical sectioning,” Opt. Express 20(8), 8939–8948 (2012). [CrossRef] [PubMed]
15. J. N. Yih, Y. Y. Hu, Y. D. Sie, L.-C. Cheng, C. H. Lien, and S.-J. Chen, “Temporal focusing-based multiphoton excitation microscopy via digital micromirror device,” Opt. Lett. 39(11), 3134–3137 (2014). [CrossRef] [PubMed]
16. L.-C. Cheng, C.-H. Lien, Y. Da Sie, Y. Y. Hu, C.-Y. Lin, F.-C. Chien, C. Xu, C. Y. Dong, and S.-J. Chen, “Nonlinear structured-illumination enhanced temporal focusing multiphoton excitation microscopy with a digital micromirror device,” Biomed. Opt. Express 5(8), 2526–2536 (2014). [CrossRef] [PubMed]
17. F. Pinaud, S. Clarke, A. Sittner, and M. Dahan, “Probing cellular events, one quantum dot at a time,” Nat. Methods 7(4), 275–285 (2010). [CrossRef] [PubMed]
18. M. Dahan, S. Lévi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, “Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking,” Science 302(5644), 442–445 (2003). [CrossRef] [PubMed]
19. J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometre-scale precision,” Nature 331(6155), 450–453 (1988). [CrossRef] [PubMed]
20. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003). [CrossRef] [PubMed]
21. N. Arhel, A. Genovesio, K.-A. Kim, S. Miko, E. Perret, J.-C. Olivo-Marin, S. Shorte, and P. Charneau, “Quantitative four-dimensional tracking of cytoplasmic and nuclear HIV-1 complexes,” Nat. Methods 3(10), 817–824 (2006). [CrossRef] [PubMed]
22. K. Welsher and H. Yang, “Multi-resolution 3D visualization of the early stages of cellular uptake of peptide-coated nanoparticles,” Nat. Nanotechnol. 9(3), 198–203 (2014). [CrossRef] [PubMed]
23. D. Montiel and H. Yang, “Real-time three-dimensional single-particle tracking spectroscopy for complex systems,” Laser Photon. Rev. 4(3), 374–385 (2010). [CrossRef]
24. M. F. Juette and J. Bewersdorf, “Three-dimensional tracking of single fluorescent particles with submillisecond temporal resolution,” Nano Lett. 10(11), 4657–4663 (2010). [CrossRef] [PubMed]
25. N. P. Wells, G. A. Lessard, P. M. Goodwin, M. E. Phipps, P. J. Cutler, D. S. Lidke, B. S. Wilson, and J. H. Werner, “Time-resolved three-dimensional molecular tracking in live cells,” Nano Lett. 10(11), 4732–4737 (2010). [CrossRef] [PubMed]
26. H. Cang, C. S. Xu, D. Montiel, and H. Yang, “Guiding a confocal microscope by single fluorescent nanoparticles,” Opt. Lett. 32(18), 2729–2731 (2007). [CrossRef] [PubMed]
27. M. Speidel, A. Jonás, and E.-L. Florin, “Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging,” Opt. Lett. 28(2), 69–71 (2003). [CrossRef] [PubMed]
28. E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7(7), 2043–2045 (2007). [CrossRef] [PubMed]
29. H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67(3), 1291–1300 (1994). [CrossRef] [PubMed]
30. G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 3125–3130 (2009). [CrossRef] [PubMed]
31. V. Levi, Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005). [CrossRef] [PubMed]
32. R. Zhang, E. Rothenberg, G. Fruhwirth, P. D. Simonson, F. Ye, I. Golding, T. Ng, W. Lopes, and P. R. Selvin, “Two-photon 3D FIONA of individual quantum dots in an aqueous environment,” Nano Lett. 11(10), 4074–4078 (2011). [CrossRef] [PubMed]
33. B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013). [CrossRef] [PubMed]
34. J.-H. Spille, T. Kaminski, H.-P. Königshoven, and U. Kubitscheck, “Dynamic three-dimensional tracking of single fluorescent nanoparticles deep inside living tissue,” Opt. Express 20(18), 19697–19707 (2012). [CrossRef] [PubMed]
35. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994). [CrossRef] [PubMed]
36. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
37. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
38. R. McGorty, J. Schnitzbauer, W. Zhang, and B. Huang, “Correction of depth-dependent aberrations in 3D single-molecule localization and super-resolution microscopy,” Opt. Lett. 39(2), 275–278 (2014). [CrossRef] [PubMed]
39. I. Izeddin, M. El Beheiry, J. Andilla, D. Ciepielewski, X. Darzacq, and M. Dahan, “PSF shaping using adaptive optics for three-dimensional single-molecule super-resolution imaging and tracking,” Opt. Express 20(5), 4957–4967 (2012). [CrossRef] [PubMed]
40. M. J. Saxton, “Single-particle tracking: the distribution of diffusion coefficients,” Biophys. J. 72(4), 1744–1753 (1997). [CrossRef] [PubMed]
41. V. Levi, Q. Q. Ruan, and E. Gratton, “3-D particle tracking in a two-photon microscope: application to the study of molecular dynamics in cells,” Biophys. J. 88(4), 2919–2928 (2005). [CrossRef] [PubMed]
42. R. M. Mazo, Brownian Motion: Fluctuations, Dynamics, and Applications (Oxford University, 2009).
