Feedback Driven Spt Piezo Particle Tracking Molecular Sub Millisecond
Measurements on single particles can reveal information about dynamic processes that are averaged out in typical ensemble experiments. Single particle tracking (SPT) therefore has been established as an important tool for studying systems with particle dynamics at the nanoscale. 1–3 1. M. J. Saxton and K. Jacobson, Annu. Rev. Biophys. Biomol. Struct. 26, 373 (1997). https://doi.org/10.1146/annurev.biophys.26.1.373 2. H. Cang, C. Shan Xu, and H. Yang, Chem. Phys. Lett. 457, 285 (2008). https://doi.org/10.1016/j.cplett.2008.03.098 3. A. Dupont and D. C. Lamb, Nanoscale 3, 4532, (2011). https://doi.org/10.1039/c1nr10989h Temporal resolution is an important benchmark for the performance of any SPT instrument. Originally, sub-millisecond temporal resolution was achieved only with light-scattering targets. 4 4. T. Fujiwara, K. Ritchie, H. Murakoshi, K. Jacobson, and A. Kusumi, J. Cell Biol. 157, 1071 (2002). https://doi.org/10.1083/jcb.200202050 Especially in biological applications, however, it is often desirable to work with
due to the advantages of highly specific, significantly smaller, and less perturbing labels and imaging in multicolor and inside cells.
Progress in feedback-driven SPT (fdSPT) has enabled sub-millisecond tracking over large three-dimensional (3D) volumes. 5–7 5. H. Cang, C. S. Xu, D. Montiel, and H. Yang, Opt. Lett. 32, 2729 (2007). https://doi.org/10.1364/OL.32.002729 6. 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, Nano Lett. 10, 4732 (2010). https://doi.org/10.1021/nl103247v 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 Pioneered for scattering targets by Peters et al., 8 8. I. M. Peters, B. G. de Grooth, J. M. Schins, C. G. Figdor, and J. Greve, Rev. Sci. Instrum. 69, 2762 (1998). https://doi.org/10.1063/1.1149012 fdSPT maximizes temporal resolution by limiting readout to the immediate vicinity of a single particle of interest. To enable the observation of trajectories exceeding the dimensions of the
volume, 3D stage
driven by a fast feedback loop is used. 8 8. I. M. Peters, B. G. de Grooth, J. M. Schins, C. G. Figdor, and J. Greve, Rev. Sci. Instrum. 69, 2762 (1998). https://doi.org/10.1063/1.1149012 Fluorescence-based variants of fdSPT have either extracted particle positions by modulating the signal using circular scans of a focused laser around the particle 9–12 9. J. Enderlein, Appl. Phys. B: Lasers Opt. 71, 773 (2000). https://doi.org/10.1007/s003400000409 10. V. Levi, Q. Ruan, and E. Gratton, Biophys. J. 88, 2919 (2005). https://doi.org/10.1529/biophysj.104.044230 11. K. McHale, A. J. Berglund, and H. Mabuchi, Nano Lett. 7, 3535 (2007). https://doi.org/10.1021/nl0723376 12. Y. Katayama, O. Burkacky, M. Meyer, C. Bräuchle, E. Gratton, and D. C. Lamb, ChemPhysChem 10, 2458 (2009). https://doi.org/10.1002/cphc.200900436 or using multiple point
5,6,13 5. H. Cang, C. S. Xu, D. Montiel, and H. Yang, Opt. Lett. 32, 2729 (2007). https://doi.org/10.1364/OL.32.002729 6. 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, Nano Lett. 10, 4732 (2010). https://doi.org/10.1021/nl103247v 13. G. A. Lessard, P. M. Goodwin, and J. H. Werner, Appl. Phys. Lett. 91, 224106 (2007). https://doi.org/10.1063/1.2819074
We have previously combined fdSPT with electron-multiplying charge-coupled device (EM-CCD)
by reading out only five lines of the
chip, enabling temporal resolutions down to ∼300μs. 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 3D localization is obtained using a biplane
scheme originally developed for widefield SPT 14,15 14. P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, IEEE Trans. Nanobiosci. 3, 237 (2004). https://doi.org/10.1109/TNB.2004.837899 15. E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, Nano Lett. 7, 2043 (2007). https://doi.org/10.1021/nl0709120 and localization-based nanoscopy. 16 16. M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, Nat. Methods 5, 527 (2008). https://doi.org/10.1038/nmeth.1211
feedback was implemented by steering the excitation laser focus using a tip/tilt
for lateral (x and y)
and an objective piezo for the axial (z) direction. While being able to track free
with
coefficients >2μm2/s, this method featured an inferior axial response of ∼5 ms compared to the lateral response of ∼2 ms. In addition, it could not be ruled out that the observed dynamics are influenced by the objective
via mechanical coupling through the immersion medium.
Here, we describe a beam steering scheme for fdSPT that eliminates mechanical perturbation of the sample and provides a ∼2.5-fold faster axial response (∼2 ms). Instead of moving the stage or objective for axial positioning in the sample, we use remote focusing based on
which does not couple any mechanical
to the sample. While the mechanical response time sets bounds for the observable dynamic regime, it does not limit the temporal resolution, which measures the bandwidth for
direction changes. This is due to the fact that we calculate the position signal as the superposition of the focus position during each
frame and the reconstructed particle position within the focus. This method generates a position measure independent of the delayed instrument response. Temporal resolution is limited to 130μs by the maximum
frame rate.
Fig. 1 presents a schematic of the instrument. The system is based on our previous design 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 with the following major modifications: in addition to our fast tip/tilt piezo
a deformable
(DM; 15 mm 37-ch "OKO Mirror," OKO Flexible Optical) is also conjugate to the objective's back focal plane (BFP). The DM can be programmed at a repetition rate of 1 kHz. After reflecting from the DM, a small fraction of excitation light is focused onto a pinhole and
by a silicon photodiode (SM05PD2A, Thorlabs), whose signal is used to track the focal shift introduced by the DM. For calibration of the DM, a Shack-Hartmann wavefront
(SHWS; WFS150, Thorlabs) can be mounted on the microscope by removing the objective lens and replacing it by a tube-mounted lens system containing the SHWS, which places the
in a plane conjugate to the BFP. Higher
frame rates are enabled by using the isolated crop mode (ICM) of the EM-CCD
(iXon DU-860, 128 × 128 pixels, Andor Technology). In addition to the tracking channel, which is optimized for green fluorescent
(GFP), Alexa 488, and spectrally similar fluorophores, we added a conventional widefield
channel to provide a structural overview in a second color using red-emitting fluorophores (e.g., mCherry and Cy5). See "Supplementary Material" for additional descriptions. 17 17. See supplementary material at http://dx.doi.org/10.1063/1.4803538 for a detailed description of the optical setup and the protocol used for cell culture and fluorescent labeling.
FIG. 1. Schematic of optical setup. Labeled components: acousto-optic tunable filter (AOTF), pinholes (PH1/2), cylindrical lens (CL), dichroic mirrors (D1–D4), deformable mirror (DM), field aperture (FA), photodiode (PD), tube lens (TL), objective lens (Obj.), neutral beamsplitter cube (50:50), bandpass filters (BP1-BP3), electron-multiplying CCD camera (EM-CCD), conventional interline CCD camera (CCD), neutral density filter wheel (ND).
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- High-resolution
DMs are frequently used to correct for image-degrading phase aberrations in microscopy. 18 18. M. J. Booth, Philos. Trans. R. Soc. A 365, 2829 (2007). https://doi.org/10.1098/rsta.2007.0013 The DM employed for this system consists of a circular reflective membrane that is fixed around the edges and is suspended over a hexagonal array of 37 electrodes. Applying a voltage pattern to the electrodes creates a deflection of the
surface, which can be used to imprint a phase profile onto a reflected wavefront.
The suitability of membrane DMs for introducing simple defocus (i.e., adding a spherical deformation to a wavefront) is well known. 19 19. L. Zhu, P.-C. Sun, and Y. Fainman, Appl. Opt. 38, 5350 (1999). https://doi.org/10.1364/AO.38.005350 However, focusing of a purely spherical wavefront with a high-numerical aperture (NA) objective lens leads to an aberrated focus. Botcherby et al. 20 20. E. J. Botcherby, R. Juškaitis, M. J. Booth, and T. Wilson, Opt. Commun. 281, 880 (2008). https://doi.org/10.1016/j.optcom.2007.10.007 showed that, as a consequence of the optical sine condition, the BFP wavefront required to achieve an aberration-free axial focus shift contains an infinite series of spherical aberrations (SA). Ignoring higher order SA, we created a two-dimensional lookup table of DM voltage sets for varying amounts of defocus and primary SA. First, the DM control signal for each defocus-SA combination was found using an iterative procedure developed by Zhu et al. 21 21. L. Zhu, P.-C. Sun, D.-U. Bartsch, W. R. Freeman, and Y. Fainman, Appl. Opt. 38, 6019 (1999). https://doi.org/10.1364/AO.38.006019 In short, the laser profile in the BFP is imaged onto the SHWS and the measured wavefront in each frame is decomposed into Zernike modes. The root mean square (RMS) deviation of the measured wavefront from the desired wavefront is minimized by varying the DM control voltages according to a steepest-descent iteration formula. Using this method, we determined the optimal voltage sets for 117 different DM settings ranging from −3.2μm to +3.2μm (step size 0.53μm) of defocus in the sample and from −0.08μm to +0.08μm RMS (step size 0.02μm) of SA in the BFP.
Second, by measuring a 3D point-spread function (PSF) with a 200 nm fluorescent bead (FluoSpheres Carboxylate-Modified Yellow-Green Microspheres, Life Technologies) for each setting, extracting the peak intensity for each PSF, and dividing by the overall maximum value, we obtained a map of Strehl ratios normalized by the maximum Strehl ratio achieved as shown in Fig. 2(a) . The Strehl ratio S, a common measure for the optical quality of an imaging system, reflects aberrations—including SA—according to the approximation S ≈ exp(−σΦ 2), where σΦ 2 is the aberrated wavefront variance across the BFP. 22 22. V. N. Mahajan, J. Opt. Soc. Am. 73, 860 (1983) https://doi.org/10.1364/JOSA.73.000860. The diagonal ridge in the plot, Fig. 2(a) , demonstrates the SA correction performance of the DM and shows that the amount of SA is approximately proportional to the applied defocus. Fig. 2(b) shows the improvement in PSF quality achieved by correcting for SA at maximum defocus. A DM voltage set lookup table was compiled for the following experiments by choosing the parameters which resulted in the PSF with the highest normalized Strehl ratio for each defocus setting. During fdSPT operation, DM voltages were determined from the lookup table by linear interpolation. The created lookup table assumes that the sample is embedded in water (refractive index n = 1.33). Sample-dependent variations in refractive index can be accounted for by measuring PSFs of immobilized beads through liquid layers of defined thickness and refractive index. 23 23. A. Diaspro, F. Federici, and M. Robello, Appl. Opt. 41, 685 (2002). https://doi.org/10.1364/AO.41.000685
FIG. 2. Characterization of DM performance. (a) Normalized Strehl ratio. A two-dimensional lookup table for varying amounts of defocus (measured as focal displacement in the sample) and primary SA was created for the DM as described in the article. For each of the 117 mirror settings, the PSF of the setup was recorded, using the same bead for all measurements. A low excitation power was chosen to guarantee that no significant photobleaching occurred over the course of the experiment. The plot shows the peak intensity as extracted from the brightest pixel of each PSF. (b) PSFs with "naive" defocus of +3.2μm (top) and after pre-compensation of fourth-order SA (bottom). The color table emphasizes low intensity values. Scale bars: 1μm.
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- High-resolution
To characterize the performance of the DM-based remote focusing mechanism for axial tracking, we mounted a 3-axis piezo stage (P-733.3DD, Physik Instrumente) on the microscope stage. The elementary response of the tracking loop is characterized by performing step displacements of the piezo stage, monitored separately along the three axes. For this purpose, a sample containing fixed 200 nm fluorescent beads was mounted on the piezo stage. The laser intensity was chosen to yield a sufficiently bright signal at 130μs exposure time while avoiding strong photobleaching. Every 50 ms, the stage was shifted in either direction by 200 nm, while the instrument was set to track the position of the bead.
Fig. 3 shows the results of the z direction measurement, which reflects the performance of the DM. The measurement was carried out at the maximum ICM frame rate of 7.6 kHz. For each frame, the position estimator was calculated as described before. 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 For example, the position along the z axis was estimated by taking the logarithmic ratio of the integrated signal in each of the two
planes. The generated feedback signal leads to a response of the beam-steering element which is delayed by ∼2 ms due to mechanical and electronic response times. This ∼2.5-fold shorter time delay, compared to the previously used objective piezo, is similar to the performance of the tip/tilt
used for lateral tracking 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 and allows the system to track faster
even in the z direction. In post-processing, the feedback signal is combined with the position estimator to obtain a precise, non-delayed measure of the particle position. As mentioned above, this approach effectively removes the mechanical instrument response from the obtained trajectory to yield camera-limited sub-millisecond time resolution.
FIG. 3. Axial step response of the system. A fluorescent bead attached to a coverslip is mounted on a piezo stage attached to the microscope. The stage is moved in the z direction by 200 nm steps as shown by the stage-sensor signal in black. The dark gray curve displays the axial offset from the center of the detection volume as determined by the position estimator in live-feedback mode, measured at 7.6 kHz frame rate (130μs temporal resolution). This feedback signal generates a defocus mode of the DM, whose response is represented by the photodiode signal in red (dashed curve). Combining the focus position with the detected offset data removes the observed delay and provides a sub-millisecond measure of the particle position in z as displayed in light blue.
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- High-resolution
Using the approach detailed above, up to ±3.5μm of focal z displacement in the sample can be achieved. Lateral beam steering using the piezo
allows ∼10μm of focal x and y movements in the sample. 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 The instrument's localization precision σ is estimated from the position standard deviation over 150 frames while the stage is stationary in one position and yields σx = 7 nm, σy = 8 nm, and σz = 27 nm. This is consistent with the shape of the PSF, which is about 3-fold larger axially than laterally, and confirms operation of the DM feedback system at the expected limit. As demonstrated previously, 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 the localization precision scaled with the inverse of the square root of the number of
photons, in agreement with the theoretical expectation.
To demonstrate the live-cell tracking capabilities of the instrument, we monitored intracellular trafficking of fluorescently labeled Transferrin (Tf), a
that is used to take up iron into cells. Extracellular Tf binds Tf receptor (TfRc) at the cell surface and is subsequently internalized via clathrin-coated pits. 24 24. K. M. Mayle, A. M. Le, and D. T. Kamei, Biochim. Biophys. Acta 1820, 264 (2012). https://doi.org/10.1016/j.bbagen.2011.09.009 Human endothelial cells were stimulated to internalize Alexa488-tagged Tf (see Supplementary Material). 17 17. See supplementary material at http://dx.doi.org/10.1063/1.4803538 for a detailed description of the optical setup and the protocol used for cell culture and fluorescent labeling. To find regions of high activity, cells expressing mCherry-labeled TfRc were used. Experiments were carried out at 37 °C using a heated stage (TC-202 A, Harvard Apparatus).
Regions of interest (ROIs) in the cells were identified by examining the TfRc-mCherry signal in the widefield overview channel (Fig. 4(a) ). In each ROI, particles were found by systematically scanning the laser focus over a specified volume and automatically switching to tracking mode when an assigned intensity threshold was exceeded. As expected,
containing multiple Tf-Alexa488 molecules were
in regions with a high concentration of the receptor, TfRc-mCherry. Trajectories of 68
in several cells were recorded at a temporal resolution of 1 ms, which was chosen to achieve a sufficient signal in this specific experiment. Continuous trajectories were confirmed in the acquired data files by looking for characteristic photobleaching curves in the recorded photon counts per frame. The lengths of obtained trajectories ranged from 63 to 841 frames. Figs. 4(b) and 4(d) show an example trajectory and the corresponding photon trace (estimated by multiplying the CCD counts by a conversion factor obtained in a calibration experiment), 7 7. M. F. Juette and J. Bewersdorf, Nano Lett. 10, 4657 (2010). https://doi.org/10.1021/nl1028792 respectively.
FIG. 4. fdSPT of Tf-containing vesicles in living cells. (a) Widefield overview of an EA.hy926 cell expressing TfRc-mCherry. The tracking beam was positioned in a receptor-rich area of the perinuclear region (white circle) and a trajectory of a vesicle containing Tf-Alexa488 was recorded. The inset is a magnified view of the area bounded by the white rectangle, overlayed with a projection of the trajectory shown in (b). Scale bars: overview 10μm, inset 200 nm. (b) 3D reconstruction of the vesicle trajectory consisting of 330 frames at 1 ms exposure time (blue), along with projections along the x, y, and z axes (gray). (c) MSD (orange) as a function of lag time τ for the same trajectory. A second order polynomial fit (black) was used to estimate the diffusion coefficient D and velocity v as displayed above the graph. (d) Estimated photon counts per frame for the same data over a 1 s long time window. The trajectory in (b) corresponds to the gray box. (e) Distribution of estimated velocities v and diffusion coefficients D for 68 trajectories with durations ranging from 63 to 841 frames.
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- High-resolution
The mean square displacement (MSD) for each trajectory was computed and the first 20% of each MSD (to discard data of high variance) were fitted with a second order polynomial, describing a superposition of diffusive and directed
(Fig. 4(c) ). 1 1. M. J. Saxton and K. Jacobson, Annu. Rev. Biophys. Biomol. Struct. 26, 373 (1997). https://doi.org/10.1146/annurev.biophys.26.1.373 We observed a heterogeneous distribution of
coefficients, D, and transport velocities, v, as displayed in Fig. 4(e) . About half of the
show very low
coefficients (D < 0.01μm2/s) and velocities (v < 1μm/s) suggesting an immobile fraction of
while the others exhibit significant directed or diffusive
over the course of the measurement.
We have realized an fdSPT microscope which is optimized for maximum temporal resolution, high sensitivity, and an extended 3D tracking range. Reading out only five lines of an EM-CCD
with ICM allows temporal resolutions down to 130μs, similar to the fastest reported fdSPT using point
(100μs), but at higher sensitivity. 5 5. H. Cang, C. S. Xu, D. Montiel, and H. Yang, Opt. Lett. 32, 2729 (2007). https://doi.org/10.1364/OL.32.002729 The two 5 × 5 pixel readout areas of only 750 nm side length inherently optimize the signal-to-noise ratio by acting as confocal pinholes which, in combination with focused laser excitation, results in excellent suppression of out-of-focus
The low readout noise and high quantum efficiency of the EM-CCD
guarantee high sensitivity for weak
signals.
Our feedback mechanism relies on beam steering instead of slower stage scanning and provides a uniformly fast system performance in all three dimensions (∼2 ms mechanical step response time). The concept of using a membrane DM for axial tracking enables SA-corrected focusing over a depth range of ∼7μm without any mechanical sample perturbation.
As exemplified by the tracking of intracellular Tf-Alexa488
this technology can be readily applied to a large range of biomedical problems, including investigations of viruses, nanoparticles, nucleic acids, or
clusters. The high sensitivity and efficient background suppression enable tracking of dim objects in thick samples. Artifacts are minimized by the high temporal resolution and tracking speed combined with decoupling of tracking
from sample movement. Combining our approach with multicolor tracking capabilities and additional readouts such as Förster Resonant Energy Transfer (FRET) will further expand the application range to correlate molecular interactions with sub-millisecond dynamics on the nanoscale.
We thank Joachim Spatz for support, Martin Booth for valuable discussions, Walther Mothes for providing the heated stage, and Edward Allgeyer for comments on the manuscript. M.F.J. was supported by a fellowship from the German Academic Exchange Service (DAAD Doktorandenstipendium). This work was supported by the Wellcome Trust (095927/A/11/Z). J.B. discloses significant financial interest in Vutara, Inc.
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Feedback Driven Spt Piezo Particle Tracking Molecular Sub Millisecond
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