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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014
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Three-dimensional tracking of a single fluorescent nanoparticle using four-focus excitation in a confocal microscope

James A. Germann and Lloyd M. Davis  »View Author Affiliations


Optics Express, Vol. 22, Issue 5, pp. 5641-5650 (2014)
http://dx.doi.org/10.1364/OE.22.005641


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Abstract

We report high sensitivity detection and tracking of a single fluorescent nanoparticle in solution by use of four alternately pulsed laser diodes for fluorescence excitation in a confocal microscope. Slight offsets between the centers of the overlapping laser foci together with time-resolved photon counting enable sub-micron precision position measurements. Real-time correction for diffusional motion with a xyz-piezo stage then enables tracking of a nanoparticle with diffusivity up to ~12 μm2 s−1. Fluorescence correlation spectroscopy and calibration measurements indicate a net fluorescence photon detection efficiency of ~6–9%, comparable to that of an optimized single-molecule microscope.

© 2014 Optical Society of America

1. Introduction

Ultrasensitive fluorescence detection of single molecules provides an effective methodology for the study of complex behavior unobscured by ensemble averaging in a host of nanoscale systems [1

1. W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12596–12602 (2007). [CrossRef] [PubMed]

]. New and improved schemes for position determination of a point-like emitter may be useful for super-resolution fluorescence imaging, which presents a static view of subcellular structure, and also single-molecule or single-nanoparticle tracking and trapping, which reveal the dynamics and pathways of unsynchronized individuals, while extending their observation by postponing escape from view by diffusion [1

1. W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12596–12602 (2007). [CrossRef] [PubMed]

]. While early developments for fluorescent nanoparticle tracking initially focused on motion confined to two dimensions, extension of methods to three dimensions and subsequent progress in single-molecule tracking spectroscopy [2

2. H. Cang, C. S. Xu, and H. Yang, “Progress in single-molecule tracking spectroscopy,” Chem. Phys. Lett. 457(4-6), 285–291 (2008). [CrossRef]

] has been spurred on by significant applications in cellular and molecular biology [3

3. A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011). [CrossRef] [PubMed]

5

5. A. Dupont, M. Gorelashvili, V. Schuller, F. Wehnekamp, D. Arcizet, Y. Katayama, D. C. Lamb, and D. Heinrich, “Three-dimensional single-particle tracking in live cells: News from the third dimension,” New J. Phys. 15(075008), 1–17 (2013).

]. Although the three-dimensional (3D) position of a single fluorescent particle can be determined by use of a CCD camera by wide-field imaging with multiple focal planes [6

6. S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012). [CrossRef] [PubMed]

], or by fitting the shape of the image acquired with an astigmatic [7

7. J. K. King, B. K. Canfield, and L. M. Davis, “Three-dimensional anti-Brownian electrokinetic trapping of a single nanoparticle in solution,” Appl. Phys. Lett. 103(043102), 1–5 (2013), doi:. [CrossRef]

] or double-helical [8

8. M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010), doi:. [CrossRef] [PubMed]

] point spread function, the image frame rate typically limits the temporal resolution to tens of milliseconds, unless tracking is confined to just a single particle at any time and the CCD readout is restricted to just a small number of pixels, in which case sub-millisecond timing is achievable [9

9. 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]

]. Confocal fluorescence detection with a point detector such as a single-photon avalanche diode (SPAD) similarly offers sub-millisecond time resolution, essentially limited only by the photon count rate [10

10. A. J. Berglund, K. McHale, and H. Mabuchi, “Feedback localization of freely diffusing fluorescent particles near the optical shot-noise limit,” Opt. Lett. 32(2), 145–147 (2007). [CrossRef] [PubMed]

], while also enabling microsecond latency for feedback-driven trapping [11

11. L. M. Davis, B. K. Canfield, X. Li, W. H. Hofmeister, G. Shen, I. P. Lescano-Mendoza, B. W. Bomar, J. P. Wikswo, D. A. Markov, P. C. Samson, C. Daniel, Z. Sikorski, and W. N. Robinson, “Electrokinetic delivery of single fluorescent biomolecules in fluidic nanochannels,” Proc. SPIE 7035(70350A), 1–12 (2008). [CrossRef]

], spatial filtering for discrimination of background from nearby structures, and sub-nanosecond photon timing for fluorescence lifetime measurements [12

12. C. Hellriegel and E. Gratton, “Real-time multi-parameter spectroscopy and localization in three-dimensional single-particle tracking,” J. R. Soc. Interface 6(Suppl 1), S3–S14 (2009). [CrossRef] [PubMed]

,13

13. 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]

].

Feedback-driven tracking, which relies on rapid 3D-position determination followed by low latency application of motion to counteract Brownian diffusion, has been demonstrated by a number of techniques, each with their advantages, complexities, and shortcomings. The counter motion to diffusion may be applied in various ways, including translating the sample with xyz-piezo stages [13

13. 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]

17

17. K. McHale, A. J. Berglund, and H. Mabuchi, “Quantum dot photon statistics measured by three-dimensional particle tracking,” Nano Lett. 7(11), 3535–3539 (2007). [CrossRef] [PubMed]

], moving the focused laser excitation spot in the xy-focal plane by use of galvanometer [12

12. C. Hellriegel and E. Gratton, “Real-time multi-parameter spectroscopy and localization in three-dimensional single-particle tracking,” J. R. Soc. Interface 6(Suppl 1), S3–S14 (2009). [CrossRef] [PubMed]

,18

18. V. Levi, Q. Ruan, K. Kis-Petikova, and E. Gratton, “Scanning FCS, a novel method for three-dimensional particle tracking,” Biochem. Soc. Trans. 31(5), 997–1000 (2003). [CrossRef] [PubMed]

,19

19. 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]

] or piezo-driven [9

9. 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]

,20

20. Y. Katayama, O. Burkacky, M. Meyer, C. Bräuchle, E. Gratton, and D. C. Lamb, “Real-time nanomicroscopy via three-dimensional single-particle tracking,” ChemPhysChem 10(14), 2458–2464 (2009). [CrossRef] [PubMed]

] scanning mirrors (which may also be used for de-scanned collection) or acousto-optic beam deflectors [17

17. K. McHale, A. J. Berglund, and H. Mabuchi, “Quantum dot photon statistics measured by three-dimensional particle tracking,” Nano Lett. 7(11), 3535–3539 (2007). [CrossRef] [PubMed]

] while translating the microscope objective in the axial z-direction with a piezo stage, or using a piezo-driven deformable mirror to move the focused laser spot in the z-direction [21

21. M. F. Juette, F. E. Rivera-Molina, D. K. Toomre, and J. Bewersdorf, “Adaptive optics enables three-dimensional single particle tracking at the sub-millisecond scale,” Appl. Phys. Lett. 102(173702), 1–4 (2013), doi:. [CrossRef]

]. Although piezo stages with resonance frequencies of ~2.5 kHz are available, the programming update rate, which is at best ~1 kHz for current piezo systems, including the deformable mirror, is usually the overriding limitation for the bandwidth of the control [3

3. A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011). [CrossRef] [PubMed]

]. Much faster positional response has been achieved by adjusting the voltages across the electrodes of a microfluidic device to regulate electro-kinetic motion for feedback-driven trapping in two dimensions [1

1. W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12596–12602 (2007). [CrossRef] [PubMed]

]. Electrokinetic trapping has also been demonstrated in a 3D-device [7

7. J. K. King, B. K. Canfield, and L. M. Davis, “Three-dimensional anti-Brownian electrokinetic trapping of a single nanoparticle in solution,” Appl. Phys. Lett. 103(043102), 1–5 (2013), doi:. [CrossRef]

], but it is not usable for experiments within live cells.

Feedback-driven tracking experiments have similarly employed a number of different techniques for measuring the nanoparticle position. Overall these entail scanning one or two focused laser spots around the particle to temporally modulate the fluorescence signal, or using multiple single-point detectors [16

16. 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]

], or using a combination of both methods. In cases where position measurements are made with a single detector by scanning a single focused excitation spot in a 3D-orbit around the particle [12

12. C. Hellriegel and E. Gratton, “Real-time multi-parameter spectroscopy and localization in three-dimensional single-particle tracking,” J. R. Soc. Interface 6(Suppl 1), S3–S14 (2009). [CrossRef] [PubMed]

,18

18. V. Levi, Q. Ruan, K. Kis-Petikova, and E. Gratton, “Scanning FCS, a novel method for three-dimensional particle tracking,” Biochem. Soc. Trans. 31(5), 997–1000 (2003). [CrossRef] [PubMed]

,19

19. 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]

], the speed of the piezo system limits the rate at which position measurements can be made, at least for the z-axis, for which acousto-optic scanning is not possible. Faster z-axis position measurements can be made by using two alternately modulated laser excitation foci scanning in circles at different depths [17

17. K. McHale, A. J. Berglund, and H. Mabuchi, “Quantum dot photon statistics measured by three-dimensional particle tracking,” Nano Lett. 7(11), 3535–3539 (2007). [CrossRef] [PubMed]

], or by at using a beam splitter to divide the collected fluorescence onto two detectors, which image different focal depths [20

20. Y. Katayama, O. Burkacky, M. Meyer, C. Bräuchle, E. Gratton, and D. C. Lamb, “Real-time nanomicroscopy via three-dimensional single-particle tracking,” ChemPhysChem 10(14), 2458–2464 (2009). [CrossRef] [PubMed]

,22

22. N. F. Reuel, A. Dupont, O. Thouvenin, D. C. Lamb, and M. S. Strano, “Three-dimensional tracking of carbon nanotubes within living cells,” ACS Nano 6(6), 5420–5428 (2012). [CrossRef] [PubMed]

]. Rather than use circular scanning with two detectors, 3D position can be measured by further splitting the collected fluorescence onto four single-point detectors, which image transversely and axially offset locations spaced in a tetrahedral pattern [13

13. 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]

15

15. N. P. Wells, G. A. Lessard, and J. H. Werner, “Confocal, three-dimensional tracking of individual quantum dots in high-background environments,” Anal. Chem. 80(24), 9830–9834 (2008). [CrossRef] [PubMed]

]. In this case, just a single laser focus can be used without scanning its position. However, when the nanoparticle z-position is determined by splitting the collected light amongst detectors that image different depths, one expects some loss of signal, as the z-sensitivity is achieved by spatial filtering or decreasing the collection efficiency of light from outside the focal plane of each detector. A further loss of signal is expected if the transverse position is determined by imaging onto separated collection zones, such as closely placed fiber cores separated by their claddings [13

13. 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]

15

15. N. P. Wells, G. A. Lessard, and J. H. Werner, “Confocal, three-dimensional tracking of individual quantum dots in high-background environments,” Anal. Chem. 80(24), 9830–9834 (2008). [CrossRef] [PubMed]

], as fluorescence signal from the center of the laser focus, where the nanoparticle is most likely to be found, is imaged to a region centered on the claddings and so is rejected, at least partially.

Below we describe an alternate method for single-nanoparticle tracking, which uses four laser foci spaced in a tetrahedral pattern and which achieves high efficiency collection of light into a single detection channel. In principle, just one single-point detector is needed, but in our implementation, a polarizing beam splitter and two SPADs are used to provide future polarization-resolving capabilities. The experiment uses temporally modulated laser diodes together with time-gated single-photon counting for 3D nanoparticle position estimation. The modulation of the lasers can in principle be faster than the photon count rate so as to not limit the rate at which position measurements can be made. However, the bandwidth of the tracking is limited by our 3D-piezo stage, which can be updated at only 0.54 kHz. A notable difference between this method and the use of four tetrahedrally spaced collection zones is that the four excitation focal volumes are substantially overlapping. The offsets between their centers are ideally such that the total laser irradiance is approximately constant in the region between their centers [23

23. L. M. Davis, B. K. Canfield, J. A. Germann, J. K. King, W. N. Robinson, A. D. Dukes III, S. J. Rosenthal, P. C. Samson, and J. P. Wikswo, “Four-focus single-particle position determination in a confocal microscope,” Proc. SPIE 7571(757112), 1–10 (2010).

]. Fluorescence is collected from the entire excitation volume, including from this central region. In separate experiments, fluorescence correlation spectroscopy and calibration measurements are used to determine the net fluorescence photon detection efficiency, which is found to be ~6–9%, which is at the upper end of the typical 1−8% range of modern single-molecule microscopes [24

24. W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]

].

2. Experimental setup

2.1 Optical configuration

The fluorescence excitation is provided by four 635-nm laser diodes (Lasermate, T63E-PFC1-21-S4) each pigtailed to a 4/125 μm single-mode fiber, which spatially filters the beam to enable close to diffraction-limited focusability. Each diode is soldered to a driver board that provides regulated adjustable power up to 1 mW and TTL-driven modulation at up to 100 kHz (Lasermate, APCT-42X). As shown schematically in Fig. 1
Fig. 1 Schematic of the beam combining optics. Each of the four laser diode beams passes through a single-mode fiber (SMF) with fiber coupler (FC) screwed to a collimator (Col) separated by distance F1 or F2, with ~500 µm additional spacing for F2 provided by five washers between couplers and collimators, as shown in the inset. The four beams are overlapped using 3 beamsplitters (BS) and mirrors (M) and pass through a linear polarizer (Pol) to the microscope.
, the exit of each fiber has an FC connector that attaches to a beam collimator (Thorlabs, discontinued model, similar to F280APC-A), which produces a beam focused ~3.12 m from the collimator. However, five 100 µm thick washers are inserted between the FC connector and collimator for two of the fibers to produce beams focused ~0.85 m from the collimators. Three 50% beamsplitters (Thorlabs BSW10) are used to overlap the beams so that they are almost collinear. The beams pass through a polarizer (Oriel PHLL-10) to ensure all have the same linear polarization.

At a distance of 1.33 m from the collimators, the four beams have the same size, with two converging and two diverging. This point is imaged with 3 × magnification to the entrance pupil of the microscope objective (Olympus UPLSAPO 60 × , numerical aperture NA = 1.2, water immersion n = 1.33) using two lenses with 100 mm and 300 mm focal lengths separated by ~400 mm (Thorlabs AC254-100-A and LA1509-A), shown as L1 and L2 in Fig. 2
Fig. 2 Schematic of four-focus microscope. Components are: L1: 100 mm lens, L2: 300 mm lens, BS: beam sampler, BD: beam dump, O: objective, S: sample, PS: piezoelectric stage, F: filter, M: mirrors, L3: 250 mm lens, P: pinhole, L4: 150 mm lens, PBS: polarizing beam splitter, SPAD, single-photon avalanche diode. The system uses a National Instruments LabVIEW RealTime (RT) Desktop with PCI 6602 card to control the modulation of the laser diodes and count TTL pulses from the SPADs and PCI DIO-96 card to communicate with the piezoelectric stage. Data is streamed from the RT desktop to another computer (Host PC).
. Each of the beams almost fills the objective pupil to enable tight focusing. The microscope is custom built in an inverted confocal epi-illumination configuration. The laser beams enter the microscope by reflecting from the uncoated surface of a fused silica beam sampler (Newport 10Q40NC.1) with a reflection efficiency of 6.84%, as measured using a power meter (Coherent LM-2 VIS). Collected fluorescence passes through the beam sampler (~4.5% Fresnel reflection loss for unpolarized light), through a bandpass interference filter to reject scattered laser light (Omega 3RD660-740) and is imaged by a 250 mm lens (Thorlabs LA1461-A) through a pinhole (Newport UNH-150, diameter d = 150 µm). The objective would give 60 × magnification if it were used with the design 180 mm focal length tube lens, hence with the 250 mm lens the magnification is M = 83.3 × (250/180 × 60 × ). Thus the pinhole acts as a spatial filter with efficient collection of light from a sample region with ~1.8 μm diameter (d/M), which is relatively large compared to the four focused laser beams. Light that passes the pinhole is collimated by a 150 mm lens (Thorlabs LA1433-A), split with a polarizing splitter (Thorlabs PBS121) and focused by 8 mm asphere lenses (Thorlabs C240TME-B) onto two SPADs (Perkin-Elmer SPCM-AQR-15, with Micro Photonic Devices custom quenching circuit).

2.2 Position determination and particle repositioning

As shown in Fig. 2, the TTL pulses required for modulating the four laser diode drivers are provided by a counter timer card (National Instruments, PCI 6602), which also counts TTL pulses from the two SPADs into four channels in synchrony with the pulsing of the four lasers. The counter timer card is in a desktop computer configured to run real-time software (National Instruments, LabVIEW Real-Time 12.0.1), which provides a software timing precision of 1 μs. The control program has three loops that execute in parallel, one that pulses the lasers and counts photons, a synchronous loop that estimates the nanoparticle position from the photon counts and sets a digital input/output card (National Instruments, PCI-DIO-96) to update the piezo system (Physik Intrumente, E-710.P3D digital controller with programmed input/output interface and P-733.3DD xyz-stage), and a third low priority loop that streams photon count and piezo movement data to another computer (Host PC) and receives commands for parameter updates.

Tracking experiments are performed using 40 nm fluorescently labeled polystyrene beads (Life Technologies, 660/680 fluoSpheres®, F-8789). The nanoparticle position with respect to the center of the excitation volume, (x', y', z'), is estimated from the numbers of photon counts Ni, i = 0, 1, 2, 3, collected from both SPADs during the interval for which the corresponding laser is turned on and from the displacements of the four excitation foci from the center, (Δx, Δy, Δz)i, i = 0, 1, 2, 3, which are determined in calibration measurements. A maximum-likelihood method has been developed for optimal estimation of the position and its error [23

23. L. M. Davis, B. K. Canfield, J. A. Germann, J. K. King, W. N. Robinson, A. D. Dukes III, S. J. Rosenthal, P. C. Samson, and J. P. Wikswo, “Four-focus single-particle position determination in a confocal microscope,” Proc. SPIE 7571(757112), 1–10 (2010).

], but in this work, a computationally faster linear approximation estimate is used, given by

(x,y,z)=i=03Ni(Δx,Δy,Δz)i/i=03Ni.
(1)

The displacements of the four excitation foci from the center are determined by using the piezo stage to raster scan a single fluorescent nanoparticle embedded in polyvinyl alcohol through the foci and are listed in Table 1

Table 1. Displacement from the center of the confocal volume to the center of each focusa

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. Note that the Δx and Δy displacements are easily set during the initial alignment of the optics by adjusting the tilts of the beamsplitters and mirrors in Fig. 1 while using a camera to image the reflection of the beams from the surface of the coverslip (see Fig. 4 of [23

23. L. M. Davis, B. K. Canfield, J. A. Germann, J. K. King, W. N. Robinson, A. D. Dukes III, S. J. Rosenthal, P. C. Samson, and J. P. Wikswo, “Four-focus single-particle position determination in a confocal microscope,” Proc. SPIE 7571(757112), 1–10 (2010).

]). However, the Δz displacements depend on the initial differences from exact collimation of each beam, which are set by the distances F1 or F2 in Fig. 1, and these distances are not continuously adjustable or easily set for the fiber-coupler components used in this work.

For the given foci displacements, the precision of each position measurement is ~60 nm on plane and ~300 nm on axis (standard deviation) for a nanoparticle at the center of the tetrahedral region with 10 photon counts in total, as computed from the effects of photon shot noise in Eq. (1). As is usually the case, the z-precision is poorer, due to axial elongation of the focus of each beam.

2.3 Net fluorescence detection efficiency

Separate measurements are performed to estimate the net fluorescence detection efficiency of the instrument averaged over the spatial profile of the probe volume to enable future comparison with that of other single-molecule tracking techniques. In a confocal fluorescence microscope, the efficiency varies through the probe region due to the variation of transmission of the spatial filter (pinhole). Fluorescence correlation spectroscopy (FCS) provides a means to characterize the profile of the confocal volume and determine the efficiency of photon detection averaged over the profile. When the experimental autocorrelation function is fit to the standard model, which accounts for diffusion of fluorescent molecules through an ellipsoidal, 3D-Gaussian confocal volume, if the background rate is negligible compared to the fluorescence rate, the peak of the normalized autocorrelation has an amplitude of
g(0)=1+(γ/N),
(3)
where γ = 2−3/2 and N is mean number of effective molecules within the confocal volume [26

26. D. A. Ball, G. Q. Shen, and L. M. Davis, “Single-molecule detection with axial flow into a micrometer-sized capillary,” Appl. Opt. 46(7), 1157–1164 (2007). [CrossRef] [PubMed]

]. An effective molecule is one at the center of the confocal volume, where the fluorescence rate is highest. The mean photon count rate per effective molecule averaged over the 3D profile is then R/N, where R is the time averaged fluorescence photon detection rate during the acquisition of the autocorrelation function.

To measure R/N for a particular fluorophore, an aqueous solution of ~5 nM streptavidin conjugated Alexa 647 (Life Technologies, S32357 Lot 42304A) is placed on a coverslip on top of the objective. While the laser diodes are alternately pulsed by the system described in section 2.1 (but with the piezo stage stationary), another counter timer card (National Instruments, PCI 6602) and computer are used to record the photon times of arrival, from which the normalized autocorrelation functions are calculated [26

26. D. A. Ball, G. Q. Shen, and L. M. Davis, “Single-molecule detection with axial flow into a micrometer-sized capillary,” Appl. Opt. 46(7), 1157–1164 (2007). [CrossRef] [PubMed]

]. Fluorescence counts are collected from both SPADs for three 30 s runs. The average of the six correlation functions is plotted in Fig. 3
Fig. 3 Experimental autocorrelation function of Alexa 647-streptavidin in water collected using the four-focus confocal microscope and curve fit to the standard model with inclusion of an exponential decay factor to account for triplet crossing. (Small peaks near the tail are artifacts arising from the laser diode modulation.)
together with a fit to the standard 3-D Gaussian model (Eq. (3) of [26

26. D. A. Ball, G. Q. Shen, and L. M. Davis, “Single-molecule detection with axial flow into a micrometer-sized capillary,” Appl. Opt. 46(7), 1157–1164 (2007). [CrossRef] [PubMed]

]) with inclusion of an extra factor (1 − ξ + ξ exp(−τ/τT)) to account for triplet crossing (Eq. (4) of [27

27. L. M. Davis and G. Q. Shen, “Accounting for triplet and saturation effects in FCS measurements,” Curr. Pharm. Biotechnol. 7(4), 287–301 (2006). [CrossRef] [PubMed]

]). The fitted triplet component amplitude is ξ = 0.0047 and the autocorrelation amplitude is g(0) = 1.66, which gives N = 0.54. As discussed in [27

27. L. M. Davis and G. Q. Shen, “Accounting for triplet and saturation effects in FCS measurements,” Curr. Pharm. Biotechnol. 7(4), 287–301 (2006). [CrossRef] [PubMed]

], triplet crossing leads to saturation, but the effect here is insignificant, leading to a value for N higher by a factor of up to 1.0047. The average fluorescence signal during acquisition of the data in Fig. 3 is R = 50,700 ± 100 s−1 with a background rate of 186 ± 2 s−1, which gives an experimental value of R/N = 95,000 s−1 molecule−1.

The net fluorescence detection efficiency E is the ratio of R/N to Rf, where Rf is the total rate of fluorescence emission from a single particle at the center of the probe region. As each streptavidin particle is labeled with three Alexa 647 fluorophores (as specified on the certificate of analysis), the emission rate for a single particle at the center of the Gaussian focus of beam i is
Ri=3×2Piπω02×σΦfEγ,
(4)
where Pi is the laser power at the sample, ωo is the waist of each beam (0.45 μm), as measured from separate single-beam FCS experiments, with D = 130 μm2s−1 for Alexa 647-streptavidin in water, σ is the absorption cross section of a single Alexa 647 at the excitation wavelength of λ = 635 nm (4.71´10−16 cm2), Φf is the fluorescence quantum efficiency of Alexa 647 (0.33), and Eγ is the energy per photon at 635 nm (3.12´10−19 J). As each of the four foci is displaced by Δx or Δy ( ± 0.25 μm) and Δz ( ± 0.97 μm) from the center of the confocal volume,
Rf=exp(2Δx2/ω02(1+(λΔz/πω02)2))/(1+(λΔz/πω02)2)×Ri0.38×Ri.
(5)
The total power P = ΣPi from the four beams entering the sample is determined by measuring the power just before the objective (9.58 μW) and measuring the transmission T of the objective and coverglass in a separate experiment (0.61). T is determined from the ratio of the power of the four beams before the objective to that after transmission through the objective, reflection from a mirror (Thorlabs PF10-03-P01) positioned in water within the sample volume, and transmission back through the objective and through the beam sampler, with the mirror position adjusted so as to reform a collimated beam at the power meter, where the ratio is taken to be 1/(T 2TBS), and where TBS = 0.955 is the transmission of the beam sampler. The measured objective and coverglass transmission (0.61) is lower than that reported by the manufacturer (0.87) [28], possibly in part due to coverglass reflection losses at high angles when the objective is used near its full numerical aperture. With Rf given by Eqs. (5) and (4) and with the transmission of the objective and coverglass taken to be in the range of 0.87–0.61, the net fluorescence detection efficiency is estimated to be E ~6.4–9.2%. As discussed in the introduction, the optical throughput is expected to be higher for the four-focus microscope than for techniques that rely on spatial filtering for the position measurement, although efficiencies have not been given in these prior works [13

13. 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]

15

15. N. P. Wells, G. A. Lessard, and J. H. Werner, “Confocal, three-dimensional tracking of individual quantum dots in high-background environments,” Anal. Chem. 80(24), 9830–9834 (2008). [CrossRef] [PubMed]

,20

20. Y. Katayama, O. Burkacky, M. Meyer, C. Bräuchle, E. Gratton, and D. C. Lamb, “Real-time nanomicroscopy via three-dimensional single-particle tracking,” ChemPhysChem 10(14), 2458–2464 (2009). [CrossRef] [PubMed]

,22

22. N. F. Reuel, A. Dupont, O. Thouvenin, D. C. Lamb, and M. S. Strano, “Three-dimensional tracking of carbon nanotubes within living cells,” ACS Nano 6(6), 5420–5428 (2012). [CrossRef] [PubMed]

].

3. Tracking results

Tracking experiments reported in this section are performed with solutions of 40 nm diameter fluorescent beads (660/680 fluoSpheres®, Life Technologies, F-8789) made with varying concentrations of glycerol to produce a range of diffusivities, as derived by [29

29. N. S. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47(9), 3285–3288 (2008). [CrossRef]

] and noted in Table 2

Table 2. Solutions of 40 nm fluorescent beads used in experimentsa

table-icon
View This Table
| View All Tables
. Each solution has a nominal 360 fM concentration of beads. Also listed in Table 2 are conservative (upper) estimates for the mean diffusional escape time τe of a particle of the given diffusivity D from the confocal volume, calculated as τe < r2/(4D), where r is taken as the sum of the waist of each beam (0.45 μm) and its offset from the center of the volume (0.25 μm).

An example of the trajectory a single nanoparticle undergoing diffusion is shown in Fig. 5
Fig. 5 A single instance of nanoparticle tracking in 50% glycerol by mass. The trajectory (from blue to red) is displayed in a) and photon counts per 1.86 ms cycle are shown in b).
(a). The count rates during tracking, shown in Fig. 5(b), are mostly stable, although Focus 1 exhibits fluctuations that are possibly due to the nanoparticle moving in and out of this focus because the tracking is not working optimally due to the non-ideal axial position of this focus, as listed in Table 1. Improved hardware for beam alignment may improve performance.

3. Conclusions

This paper demonstrates a new method for rapidly measuring the displacement in three dimensions of a point-like emitter from the center of the probe region of a confocal fluorescence microscope and the application of this method to feedback-driven tracking of a single nanoparticle freely diffusing in solution. The displacement estimation, which yields submicron precision with tens of fluorescence photons, is achieved by exciting the confocal volume with four laser foci that are partially overlapping but with centers that are spatially offset in a tetrahedral pattern, sequentially pulsing the four lasers, and using time-gated photon counting to determine the numbers of photons from each laser beam. In this work, successive displacement measurements were made each 1.86 ms, which is faster than that reported by scanning a single laser focus in a 3-dimensional pattern (32 ms [12

12. C. Hellriegel and E. Gratton, “Real-time multi-parameter spectroscopy and localization in three-dimensional single-particle tracking,” J. R. Soc. Interface 6(Suppl 1), S3–S14 (2009). [CrossRef] [PubMed]

,18

18. V. Levi, Q. Ruan, K. Kis-Petikova, and E. Gratton, “Scanning FCS, a novel method for three-dimensional particle tracking,” Biochem. Soc. Trans. 31(5), 997–1000 (2003). [CrossRef] [PubMed]

,19

19. 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]

]). Even faster measurements could be achieved simply by pulsing the lasers more rapidly. While sensitive and fast 3D-position measurements in a confocal microscope have also been performed by splitting the fluorescence onto spatial filters that reject light from outside of four regions spatially offset in a tetrahedral pattern [13

13. 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]

15

15. N. P. Wells, G. A. Lessard, and J. H. Werner, “Confocal, three-dimensional tracking of individual quantum dots in high-background environments,” Anal. Chem. 80(24), 9830–9834 (2008). [CrossRef] [PubMed]

], the four-focus method requires only a single detection channel and all fluorescence is collected, including that from the center of the confocal volume. Experimental measurements indicate that the net efficiency of fluorescence photon detection is ~6–9%, which is at the upper end of the typical 1−8% range of modern confocal single-molecule microscopes [24

24. W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]

]. The requirement for just a single detection channel will facilitate extension of the method to applications requiring polarization- or wavelength-resolved detection. In demonstrating its use for feedback-driven trapping, the bandwidth of control was limited by the 1.86 ms update time for the xyz-stage. Nevertheless, tracking of single fluorescent nanoparticles with diffusivities up to ~12 μm2 s−1 is achieved, albeit for intervals of only ~100 ms. Much longer tracking times are possible for single particles with lowered diffusivities, for example, tracking the motion of a single biomolecule within the viscous confines of the cytoplasm over many seconds has been accomplished in prior works (e.g., [13

13. 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]

]) and should also be possible with the four-focus method with high efficiency of fluorescence detection. For prolonged in vitro observations of a single biomolecule with faster diffusion, the xyz-stage would need to be replaced by a means of faster 3D position control. Feedback trapping of a single nanoparticle in three dimensions has recently been demonstrated by use of a simple four-electrode electrokinetic device [7

7. J. K. King, B. K. Canfield, and L. M. Davis, “Three-dimensional anti-Brownian electrokinetic trapping of a single nanoparticle in solution,” Appl. Phys. Lett. 103(043102), 1–5 (2013), doi:. [CrossRef]

], but the trapping was limited by the 30 Hz astigmatic imaging used for 3D-position determination. Combining fast, high sensitivity four-focus position measurements with the four-electrode electrokinetic position control should enable significant advancements in single-molecule 3D-trapping capabilities [1

1. W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12596–12602 (2007). [CrossRef] [PubMed]

].

Acknowledgments

This work was supported in part through National Science Foundation grant 1004083. We thank Dr. Brian Canfield of the Center for Laser Applications (CLA) for interfacing the piezo controller and CLA for partial support.

References and links

1.

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12596–12602 (2007). [CrossRef] [PubMed]

2.

H. Cang, C. S. Xu, and H. Yang, “Progress in single-molecule tracking spectroscopy,” Chem. Phys. Lett. 457(4-6), 285–291 (2008). [CrossRef]

3.

A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011). [CrossRef] [PubMed]

4.

K. Baba and K. Nishida, “Single-molecule tracking in living cells using single quantum dot applications,” Theranostics 2(7), 655–667 (2012). [CrossRef] [PubMed]

5.

A. Dupont, M. Gorelashvili, V. Schuller, F. Wehnekamp, D. Arcizet, Y. Katayama, D. C. Lamb, and D. Heinrich, “Three-dimensional single-particle tracking in live cells: News from the third dimension,” New J. Phys. 15(075008), 1–17 (2013).

6.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012). [CrossRef] [PubMed]

7.

J. K. King, B. K. Canfield, and L. M. Davis, “Three-dimensional anti-Brownian electrokinetic trapping of a single nanoparticle in solution,” Appl. Phys. Lett. 103(043102), 1–5 (2013), doi:. [CrossRef]

8.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010), doi:. [CrossRef] [PubMed]

9.

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]

10.

A. J. Berglund, K. McHale, and H. Mabuchi, “Feedback localization of freely diffusing fluorescent particles near the optical shot-noise limit,” Opt. Lett. 32(2), 145–147 (2007). [CrossRef] [PubMed]

11.

L. M. Davis, B. K. Canfield, X. Li, W. H. Hofmeister, G. Shen, I. P. Lescano-Mendoza, B. W. Bomar, J. P. Wikswo, D. A. Markov, P. C. Samson, C. Daniel, Z. Sikorski, and W. N. Robinson, “Electrokinetic delivery of single fluorescent biomolecules in fluidic nanochannels,” Proc. SPIE 7035(70350A), 1–12 (2008). [CrossRef]

12.

C. Hellriegel and E. Gratton, “Real-time multi-parameter spectroscopy and localization in three-dimensional single-particle tracking,” J. R. Soc. Interface 6(Suppl 1), S3–S14 (2009). [CrossRef] [PubMed]

13.

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]

14.

G. A. Lessard, P. M. Goodwin, and J. H. Werner, “Three-dimensional tracking of individual quantum dots,” Appl. Phys. Lett. 91(224106), 1–3 (2007), doi:. [CrossRef]

15.

N. P. Wells, G. A. Lessard, and J. H. Werner, “Confocal, three-dimensional tracking of individual quantum dots in high-background environments,” Anal. Chem. 80(24), 9830–9834 (2008). [CrossRef] [PubMed]

16.

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]

17.

K. McHale, A. J. Berglund, and H. Mabuchi, “Quantum dot photon statistics measured by three-dimensional particle tracking,” Nano Lett. 7(11), 3535–3539 (2007). [CrossRef] [PubMed]

18.

V. Levi, Q. Ruan, K. Kis-Petikova, and E. Gratton, “Scanning FCS, a novel method for three-dimensional particle tracking,” Biochem. Soc. Trans. 31(5), 997–1000 (2003). [CrossRef] [PubMed]

19.

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]

20.

Y. Katayama, O. Burkacky, M. Meyer, C. Bräuchle, E. Gratton, and D. C. Lamb, “Real-time nanomicroscopy via three-dimensional single-particle tracking,” ChemPhysChem 10(14), 2458–2464 (2009). [CrossRef] [PubMed]

21.

M. F. Juette, F. E. Rivera-Molina, D. K. Toomre, and J. Bewersdorf, “Adaptive optics enables three-dimensional single particle tracking at the sub-millisecond scale,” Appl. Phys. Lett. 102(173702), 1–4 (2013), doi:. [CrossRef]

22.

N. F. Reuel, A. Dupont, O. Thouvenin, D. C. Lamb, and M. S. Strano, “Three-dimensional tracking of carbon nanotubes within living cells,” ACS Nano 6(6), 5420–5428 (2012). [CrossRef] [PubMed]

23.

L. M. Davis, B. K. Canfield, J. A. Germann, J. K. King, W. N. Robinson, A. D. Dukes III, S. J. Rosenthal, P. C. Samson, and J. P. Wikswo, “Four-focus single-particle position determination in a confocal microscope,” Proc. SPIE 7571(757112), 1–10 (2010).

24.

W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]

25.

J. Bechhoefer, “Feedback for physicists: A tutorial essay on control,” Rev. Mod. Phys. 77(3), 783–836 (2005). [CrossRef]

26.

D. A. Ball, G. Q. Shen, and L. M. Davis, “Single-molecule detection with axial flow into a micrometer-sized capillary,” Appl. Opt. 46(7), 1157–1164 (2007). [CrossRef] [PubMed]

27.

L. M. Davis and G. Q. Shen, “Accounting for triplet and saturation effects in FCS measurements,” Curr. Pharm. Biotechnol. 7(4), 287–301 (2006). [CrossRef] [PubMed]

28.

http://microscope.olympus-global.com/uis2/en/uplsapo60xw/

29.

N. S. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47(9), 3285–3288 (2008). [CrossRef]

OCIS Codes
(180.1790) Microscopy : Confocal microscopy
(180.6900) Microscopy : Three-dimensional microscopy

ToC Category:
Microscopy

History
Original Manuscript: January 30, 2014
Revised Manuscript: February 24, 2014
Manuscript Accepted: February 24, 2014
Published: March 4, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
James A. Germann and Lloyd M. Davis, "Three-dimensional tracking of a single fluorescent nanoparticle using four-focus excitation in a confocal microscope," Opt. Express 22, 5641-5650 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-5-5641


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References

  1. W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12596–12602 (2007). [CrossRef] [PubMed]
  2. H. Cang, C. S. Xu, H. Yang, “Progress in single-molecule tracking spectroscopy,” Chem. Phys. Lett. 457(4-6), 285–291 (2008). [CrossRef]
  3. A. Dupont, D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011). [CrossRef] [PubMed]
  4. K. Baba, K. Nishida, “Single-molecule tracking in living cells using single quantum dot applications,” Theranostics 2(7), 655–667 (2012). [CrossRef] [PubMed]
  5. A. Dupont, M. Gorelashvili, V. Schuller, F. Wehnekamp, D. Arcizet, Y. Katayama, D. C. Lamb, D. Heinrich, “Three-dimensional single-particle tracking in live cells: News from the third dimension,” New J. Phys. 15(075008), 1–17 (2013).
  6. S. Ram, D. Kim, R. J. Ober, E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103(7), 1594–1603 (2012). [CrossRef] [PubMed]
  7. J. K. King, B. K. Canfield, L. M. Davis, “Three-dimensional anti-Brownian electrokinetic trapping of a single nanoparticle in solution,” Appl. Phys. Lett. 103(043102), 1–5 (2013), doi:. [CrossRef]
  8. M. Badieirostami, M. D. Lew, M. A. Thompson, W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010), doi:. [CrossRef] [PubMed]
  9. M. F. Juette, J. Bewersdorf, “Three-dimensional tracking of single fluorescent particles with submillisecond temporal resolution,” Nano Lett. 10(11), 4657–4663 (2010). [CrossRef] [PubMed]
  10. A. J. Berglund, K. McHale, H. Mabuchi, “Feedback localization of freely diffusing fluorescent particles near the optical shot-noise limit,” Opt. Lett. 32(2), 145–147 (2007). [CrossRef] [PubMed]
  11. L. M. Davis, B. K. Canfield, X. Li, W. H. Hofmeister, G. Shen, I. P. Lescano-Mendoza, B. W. Bomar, J. P. Wikswo, D. A. Markov, P. C. Samson, C. Daniel, Z. Sikorski, W. N. Robinson, “Electrokinetic delivery of single fluorescent biomolecules in fluidic nanochannels,” Proc. SPIE 7035(70350A), 1–12 (2008). [CrossRef]
  12. C. Hellriegel, E. Gratton, “Real-time multi-parameter spectroscopy and localization in three-dimensional single-particle tracking,” J. R. Soc. Interface 6(Suppl 1), S3–S14 (2009). [CrossRef] [PubMed]
  13. N. P. Wells, G. A. Lessard, P. M. Goodwin, M. E. Phipps, P. J. Cutler, D. S. Lidke, B. S. Wilson, J. H. Werner, “Time-resolved three-dimensional molecular tracking in live cells,” Nano Lett. 10(11), 4732–4737 (2010). [CrossRef] [PubMed]
  14. G. A. Lessard, P. M. Goodwin, J. H. Werner, “Three-dimensional tracking of individual quantum dots,” Appl. Phys. Lett. 91(224106), 1–3 (2007), doi:. [CrossRef]
  15. N. P. Wells, G. A. Lessard, J. H. Werner, “Confocal, three-dimensional tracking of individual quantum dots in high-background environments,” Anal. Chem. 80(24), 9830–9834 (2008). [CrossRef] [PubMed]
  16. H. Cang, C. S. Xu, D. Montiel, H. Yang, “Guiding a confocal microscope by single fluorescent nanoparticles,” Opt. Lett. 32(18), 2729–2731 (2007). [CrossRef] [PubMed]
  17. K. McHale, A. J. Berglund, H. Mabuchi, “Quantum dot photon statistics measured by three-dimensional particle tracking,” Nano Lett. 7(11), 3535–3539 (2007). [CrossRef] [PubMed]
  18. V. Levi, Q. Ruan, K. Kis-Petikova, E. Gratton, “Scanning FCS, a novel method for three-dimensional particle tracking,” Biochem. Soc. Trans. 31(5), 997–1000 (2003). [CrossRef] [PubMed]
  19. V. Levi, Q. Q. Ruan, 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]
  20. Y. Katayama, O. Burkacky, M. Meyer, C. Bräuchle, E. Gratton, D. C. Lamb, “Real-time nanomicroscopy via three-dimensional single-particle tracking,” ChemPhysChem 10(14), 2458–2464 (2009). [CrossRef] [PubMed]
  21. M. F. Juette, F. E. Rivera-Molina, D. K. Toomre, J. Bewersdorf, “Adaptive optics enables three-dimensional single particle tracking at the sub-millisecond scale,” Appl. Phys. Lett. 102(173702), 1–4 (2013), doi:. [CrossRef]
  22. N. F. Reuel, A. Dupont, O. Thouvenin, D. C. Lamb, M. S. Strano, “Three-dimensional tracking of carbon nanotubes within living cells,” ACS Nano 6(6), 5420–5428 (2012). [CrossRef] [PubMed]
  23. L. M. Davis, B. K. Canfield, J. A. Germann, J. K. King, W. N. Robinson, A. D. Dukes, S. J. Rosenthal, P. C. Samson, J. P. Wikswo, “Four-focus single-particle position determination in a confocal microscope,” Proc. SPIE 7571(757112), 1–10 (2010).
  24. W. E. Moerner, D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]
  25. J. Bechhoefer, “Feedback for physicists: A tutorial essay on control,” Rev. Mod. Phys. 77(3), 783–836 (2005). [CrossRef]
  26. D. A. Ball, G. Q. Shen, L. M. Davis, “Single-molecule detection with axial flow into a micrometer-sized capillary,” Appl. Opt. 46(7), 1157–1164 (2007). [CrossRef] [PubMed]
  27. L. M. Davis, G. Q. Shen, “Accounting for triplet and saturation effects in FCS measurements,” Curr. Pharm. Biotechnol. 7(4), 287–301 (2006). [CrossRef] [PubMed]
  28. http://microscope.olympus-global.com/uis2/en/uplsapo60xw/
  29. N. S. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47(9), 3285–3288 (2008). [CrossRef]

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