Abstract

Advanced optical traps can probe single molecules with Ångstrom-scale precision, but drift limits the utility of these instruments. To achieve Å-scale stability, a differential measurement scheme between a pair of laser foci was introduced that substantially exceeds the inherent mechanical stability of various types of microscopes at room temperature. By using lock-in detection to measure both lasers with a single quadrant photodiode, we enhanced the differential stability of this optical reference frame and thereby stabilized an optical-trapping microscope to 0.2 Å laterally over 100 s based on the Allan deviation. In three dimensions, we achieved stabilities of 1 Å over 1,000 s and 1 nm over 15 h. This stability was complemented by high measurement bandwidth (100 kHz). Overall, our compact back-scattered detection enables an ultrastable measurement platform compatible with optical traps, atomic force microscopy, and optical microscopy, including super-resolution techniques.

© 2015 Optical Society of America

1. Introduction

Single-molecule techniques, such as optical traps [1] and atomic force microscopy (AFM) [2], have long been capable of measuring Ångstrom-scale (1 Å) displacement. Coupling this precision with Å-scale stability has opened the door to a variety of exciting biophysical applications [39]. For instance, the development of a dual-trap assay [Fig. 1(a)] for RNA polymerase (RNAP) [10] enabled real-time detection of RNAP’s fundamental step size of 1-base-pair (1 bp = 3.4 Å) [11]. In addition to determining the step sizes of various nucleic acid enzymes [1215], high-precision optical-trapping assays can yield insight into complex kinetic pathways by detecting intermediates in protein folding [1618] and pauses in enzymatic motion [11, 1922]. Notwithstanding the substantial effort invested in improving the stability of optical traps [11, 2326], it remains challenging to detect more than a handful of 1-bp steps in register over an extended period of time (~5–30 s) due, in part, to instrumental drift [6]. The underlying opto-mechanical stability typically needs to be ~3-fold better than the required biological precision [6, 11, 24]. In other words, a detection system with 1-Å precision and stability is needed to measure 1-bp steps along DNA. To be most useful, such performance metrics need to be complemented with high-bandwidth detection (~100 kHz); high bandwidth enables accurate stiffness calibrations based upon power spectral analysis [1] and detection of short-lived states (e.g., sub-ms protein-folding intermediates [18]). Hence, an ideal opto-mechanical measurement platform for single-molecule biophysics would have sub-Å precision and stability coupled with high bandwidth.

 figure: Fig. 1

Fig. 1 A wide variety of microscopy techniques can benefit from improved Ångstrom-scale precision and stability, including (a) a dual-beam optical-trap, (b) a surface-coupled optical trap, (c) atomic force microscopy, and (d) optical microscopy, particularly super-resolution techniques. In the first two assays, two focused lasers are used to measure opposite ends of a stretched molecule via scattered light. The ultimate limit to the precision of the position measurement is the differential-pointing stability between the lasers. This technique can be extended to actively stabilize the sample position for surface-coupled assays (b-d) using a reference mark attached to the sample.

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Sub-Å precision is critical to improving the detection of 1-bp steps RNAP [11], particularly in a standard surface-coupled optical-trapping assay [27], because the pioneering work to detect RNAP’s steps used a unique trap geometry called a passive optical force clamp [28]. Among its benefits, the passive force clamp improves positional precision by eliminating the attenuation between biologically induced motion and detected bead motion. This reduction arises because biomolecules are elastic. Quantitatively, this attenuation is given by kbio/(kbio + ktrap) [29] where kbio is the effective stiffness determined by slope of the force-extension curve at a given F. For example, the attenuation is 0.7 when measuring a 1,000-nm long DNA at a moderate force (8 pN) (kbio = F/x|F=8pN = 0.24 pN/nm and ktrap = 0.11 pN/nm). Hence, an opto-mechanical precision of 0.7 Å is needed in a traditional optical-trapping assay to equal the state-of-the-art results by Abbondanzieri et al. in a passive force clamp.

To be most effective, sub-Å precision needs to be complemented with equal stability. Yet over long time scales, sub-Å stability remains challenging [6]. A key insight that led to the success of the dual-trap assay was that the mechanical drift of the microscope stage limited instrumental performance [10]. By decoupling the assay from the coverslip [Fig. 1(a)], stability is limited by the differential stability between a pair of laser foci, which forms a local optical reference frame. Each of the two laser foci measures the position of one end of the molecule under tension. The use of such a differential reference frame eliminates common-mode noise sources, such as motion of the microscope objective or air currents in regions where the two lasers are co-linear. To improve upon the near base-pair stability of the original dual-trap RNAP assay [10], Abbondanzieri et al. enclosed their optics in helium to achieve 1-bp stability over tens of seconds in select RNAP records [11]. Our goal was to develop an opto-mechanical detection system with comparable performance but without the day-to-day complexity of using a helium buffer gas or a passive force clamp. Moreover, we wanted the instrument to achieve this stability routinely to avoid convolving variability in the instrument performance with complexity of the biological assay. Finally, a wide range of single-molecule assays (optical traps [Fig. 1(b)], AFMs [Fig. 1(c)], and super-resolution techniques [Fig. 1(d)]) are coupled to surfaces, so we wanted to demonstrate these performance metrics in a surface-coupled assay by stabilizing an optical-trapping microscope.

Success in applying an optical reference frame to surface-coupled assays requires precise measurement of unwanted stage motion. Such motion can be detected by imaging a bead stuck to a coverslip [30, 31]. Although the bandwidth of the video detection continues to improve [32], laser-based detection offers higher bandwidth and precision than image-based techniques [1, 33]. In the short term, unwanted stage motion can be subtracted out with 1-Å precision in 1 ms [34]. However, stuck beads move relative to the coverslip on the sub-nm scale [35]. To overcome this problem, we developed firmly attached, nanofabricated fiducial marks that accurately reflect coverslip position [24, 35]. Stability is achieved by active feedback through a 3-axis piezo-electric (PZT) stage [35]. Such active feedback enabled us to achieve 1-bp stability in a surface-coupled optical-trapping assay [Fig. 1(b)] when detecting forward-scattered light [24]. To extend optical stabilization to AFM [Fig. 1(c)] [36], we enhanced back-scattered detection (BSD) [37] to achieve 1 Å in 3D [38] and thereby stabilize tip-sample lateral position to 4 Å over 80 min of imaging [36]. Such success relied upon reducing low-frequency (f) noise by enhancing laser stability and minimizing non-common mode noise [35]. Laser stability was enhanced by active techniques (see Methods). Decreased non-common mode noise was achieved by launching both lasers from the same fiber so that the pointing noise associated with the fiber was suppressed in our differential measurement [38]. To avoid the use of helium, the beam paths—especially for non-common mode beam paths—were minimized. However, our previous designs still incorporated separate quadrant photodiodes (QPDs) for position detection. Differential motion of these separate detectors degrades instrumental performance. Additionally, small thermal variations in the electronics, even in a temperature-regulated room ( ± 0.3 C), decrease long-term stability.

In this paper, we significantly enhanced the long-term stability of BSD while achieving high-temporal bandwidth (100 kHz). To do so, we used a single QPD to detect both laser beams, suppressing the residual motion of the QPD. Each laser was modulated at a separate frequency (1 and 2.5 MHz) using an acousto-optic modulator (AOM). The resulting QPD signal was deconvolved using lock-in amplifiers [39]. Besides enabling the separation of two signals on a single detector, lock-in amplification excels at suppressing low-frequency noise, including a recent application to optical traps [40]. Ångstrom-scale vertical sensitivity, which relies upon excellent intensity stability, was preserved by implementing active intensity control of the modulated laser beams. To demonstrate the performance of this enhanced system, we stabilized the sample of an optical-trapping microscope in 3D with one laser while measuring the resulting stability with a second laser as an out-of-loop monitor. Lateral stability is a key metric for molecular-motor and protein-folding assays, and we achieved a 0.2-Å lateral stability over 100 s based on an Allan deviation analysis (see Fig. 6). Moreover, sub-Å stability was common and reproducible; analysis of a 28-h record showed 100% of sequential 100-s segments achieved a 0.7-Å lateral stability. Our enhanced BSD with lock-in detection improved 3D stabilities as well. We achieved 1-Å stability in 3D over 1,000 s and 1 nm over ~15 h, primarily limited by fluctuations in room temperature. A variety of high-precision single-molecule assays, including optical traps, AFM, magnetic tweezers, and even super resolution techniques [41], can immediately benefit from this enhanced performance.

2. Methods

Using a single QPD to simultaneously measure two separate signals required modulated lasers and lock-in amplifiers. We first discuss the optical apparatus (§2.1), the specifics of intensity stabilization of modulated lasers (§2.2), the details of high-bandwidth detection using lock-in amplifiers (§2.3), and the data acquisition and position calibration procedures (§2.4). Overall system performance was tested by stabilizing an optical-trapping microscope and quantifying the residual motion with a second laser as an out-of-loop monitor (§2.5).

2.1 Experimental layout

The design strategy and overall optical setup (Fig. 2) was similar to our prior work on BSD [38]. Briefly, two diode lasers (845 and 945 nm, Lumics) were actively stabilized (see §2.2) by the combination of optics shown in the gray-dashed box in Fig. 2. This set of optics enhanced stability by converting a variety of noise sources (pointing, mode, and polarization) into intensity noise that, in turn, was minimized using an AOM inside an analog feedback loop [35]. Each laser was independently translated in the imaging plane by mirrors conjugate to the objective’s back aperture. The diameters of the beams at the back aperture were 3.3 mm (FWHM), purposely too small a diameter for trapping, and had a laser power of ~1 mW at the sample plane. The foci of the two lasers were aligned to each other in 3D and then, via a three axis PZT stage (P561.3DD, PI) to a fiducial mark on the surface. The fiducial marks consisted of a two-dimensional array of silicon posts (650-nm dia., 80-nm high; for a detailed protocol on parallel fabrication of metallic posts, see [42]). Finally, the combination of the polarizing beam splitter (PBS) and quarter-waveplate (λ/4) led to highly efficient BSD.

 figure: Fig. 2

Fig. 2 Schematic of back-scattered detection (BSD) apparatus. Two laser diodes (LD) were modulated and actively stabilized by a combination of elements in the gray-dashed box. Each laser focus was translated laterally in the sample plane by mirrors positioned conjugate to the back focal plane of the objective (blue). The polarizing beam splitter cube (PBS) and quarter-wave plate (λ/4) acted as an optical isolator for efficient collection of back-scattered light. Back-scattered light was detected by a single quadrant photodiode (QPD). Acronyms represent the following: stabilized, modulated diode lasers (SMDL), acousto-optic modulator (AOM), photodiode (PD), lock-in amplifiers (LI), dichroic (DC), neutral density filters (ND), beam-sampler (BS), and piezo-electric (PZT).

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The current setup has both beams detected by a common QPD, distinct from our prior work where the signals were split by wavelength and detected on separate QPDs [38]. However, both BSD signals still needed to be independently centered on the QPD to achieve the maximum spatial sensitivity. This centering was done using a custom-built mount designed for stability and minimizing the non-common mode beam path, identical in design to the mount used to translate the beams in the imaging plane. Wavelength separation by dichroic mirrors is not 100%, so optical bandpass filters were added to each arm to block the stray leaked light. The recombined beams were detected with a larger area QPD [dia. = 11.2 mm (YAG-444-4A, EG&G)] reverse biased at −105 V to increase bandwidth [43]. This QPD, and the photodiode for intensity control, were connected to a heat sink to minimize the adverse thermal effects arising from the relatively high reverse bias.

2.2 Intensity stabilization of modulated lasers

When using BSD to detect motion in 3D [38], fluctuations in laser intensity directly appear as spurious variations in z. Hence, we needed to actively stabilize the laser intensity to achieve 1-Å vertical precision and stability [35]. In our earlier work, the bandwidth of the intensity stabilization feedback loop was ~250 kHz. In the present work, the bandwidth of the demodulated signal was limited by the modulation frequency and the accompanying electronics. Initially, we used modulation frequencies of 65 and 550 kHz, but the resulting bandwidths of the intensity servos were too slow (~1 and ~10 kHz, respectively). As a result, we achieved relatively modest reductions in intensity noise. To increase the bandwidth of the demodulated signal, we raised the modulation frequencies to 1 and 2.5 MHz, relatively high frequencies for our large area (11.2 mm dia.) photodiode. This large area, in combination with known signal filtering of wavelengths beyond the silicon band gap when using a silicon photodiode [43], necessitated a substantial reverse bias (180 V) to achieve high-bandwidth. This increased bandwidth significantly improved our intensity stabilization as well as allowing for ~100 kHz of bandwidth for conventional AFM and optical-trapping applications (see §3.1).

2.3 Multiplexed position detection using lock-in amplifiers

Position measurements were deduced from voltage signals on the QPD. We first demodulated each quadrant. The resulting lateral signals (Vx and Vy) for each laser were amplified from the normalized difference signals from each half of the QPD, and the raw vertical signals were deduced from variations in the total light falling upon the four quadrants of the QPD. To improve precision, the initial vertical signals were offset amplified to yield final vertical signals (Vz) that better matched to the input voltage range of the data acquisition system [35].

Thermal stability of the electronics was critical to attaining long-term stability. While the lock-in design was standard, component selection for our custom-built lock-in amplifiers and associated electronics focused on minimizing the effects of thermal variation. For instance, we used thermally stable voltage references (LM399, Linear Technology). We also minimized thermal heating of the electronics by improving the passive air cooling to the pre-amplifier housed on the back of the QPD and to the main electronic boards (amplifiers, filters, lock-in amplifiers, etc). Finally, we lowered the reverse bias voltage on the QPD—but not the PD used for intensity stabilization—from −180 V to −105 V to improve long-term stability without significant loss of temporal bandwidth. Bandwidth for the two separate lock-in signals was determined by measuring normalized peak-to-peak amplitude after demodulation of a blinking light-emitting diode (LED) placed in front of the QPD.

2.4 Data acquisition and position calibration

Precise position determination required compensating for crosstalk in the BSD signals. In other words, a motion of the sample x led not only to a change in Vx, but also Vy and Vz. To quantify this crosstalk, we scanned the fiducial mark in a 3D volume (e.g., 25 × 25 × 25 nm) while measuring the BSD signals (Vx, Vy, and Vz) at each stage position (xstage, ystage, and zstage). The resulting data set was analyzed using an algorithm adapted from optical trapping [44] to create a 3D position calibration and a set of 35 calibration coefficients (aijkx) per axis of the form

x(Vx,Vy,Vz)=i,j,k=0i+j+k=4aijkxVxiVyjVzk.
Fits were quantified using the residual RMS error per axis, with a typical value of 2–4 Å/axis.

To rapidly compensate for this optical crosstalk, we used a field programmable gate array [FPGA (PXI-7854R, National Instruments)] to digitize the signal, linearize the response, and move the sample via a 3D PZT stage to hold the sample stable with respect to laser focus. For this experiment, we digitized the signal at 5 kHz after using a 2.4 kHz adjustable antialiasing filter (828L8E-Y, Frequency Devices). A standard PI control loop (Labview 2012, National Instruments) implemented on the FPGA then maintained a constant position. The feedback loop communicated at 5 kHz with the stage controller using a 16-bit parallel digital interface. We limited position updates to 500 Hz since the PZT stage took ~2 ms to respond to nm-sized steps. The position data from both lasers were transferred from the FPGA to the computer using a FIFO (first in, first out) memory structure.

2.5 Stabilizing an optical-trapping microscope in 3D

Our preferred metric for characterizing the opto-mechanical performance of our system is to stabilize an optical-trapping microscope with one laser and use the other laser as an out-of-loop monitor [Fig. 3]. This out-of-loop detector helps identify problems hidden when only analyzing the in-loop error signal. For example, motion of the 845-nm laser focus in the imaging plane—the laser used for stabilizing—is indistinguishable from stage motion. Hence, in such a scenario, the feedback loop compensates for this false displacement, leading to unwanted sample motion. By using a sensor outside of the feedback loop (the out-of-loop sensor), we detected such spurious motion. The differential stability reported by this assay is the same stability needed in subsequent optical-trapping applications [6]: each laser detects one end of the molecule, and the difference reports on the extension of the molecule.

 figure: Fig. 3

Fig. 3 Schematic of stabilization procedure using an out-of-loop monitor. Two modulated lasers scattered light from the same fiducial marker. The scattered light was detected on a common QPD, and the signals were electronically separated using lock-in amplifiers. After filtering and amplification, the signals were digitized by an FPGA, which used the signals to calculate the position of the sample. The 2.5-MHz signal stabilized the sample, while the 1-MHz signal provided an out-of-loop measurement. White boxes denote analog electronics. Grey boxes denote field programmable gate array (FPGA).

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To test our performance using this metric, we stabilized an optical-trapping microscope in 3D by measuring the position of a silicon post with one laser (845 nm modulated at 2.5 MHz), while quantifying this stability with the second laser (945 nm modulated at 1 MHz). The resulting position measurements by both lasers were recorded at 5 kHz. For presentation, the data were filtered to 10 Hz unless otherwise noted. For quantification, we used the Allan deviation (σ), which was determined using

σx(τ)=12(xi+1xi)2τ,
where τ is the time interval, and xi is the mean value of the data over the ith time interval.

3. Results

State-of-the-art single-molecule experiments are advanced by providing high-bandwidth detection coupled with atomic-scale stability and precision. After first proving high-bandwidth detection (§3.1), we stabilized a microscope in 3D over 28 h. Analysis shows that lateral stability over any 100-s period was better than 0.7 Å. Moreover, we achieved 3D stabilities of 1 Å over 1,000 s and 1 nm over 15 h (§3.2). Finally, atomic-scale sensitivity was demonstrated by generating and then detecting 1-Å steps (§3.3).

3.1 High-bandwidth, multiplexed detection

High-bandwidth position detection is critical to biophysical studies using optical traps and atomic force microscopy. Both techniques rely on power spectral analysis of thermal fluctuations to deduce the stiffness of the force probe. High bandwidth also allows for detection of briefly populated states, including short-lived (<1 ms) protein-folding intermediates [18] and more effective averaging of Brownian motion for Å-scale precision.

The bandwidth of our present system was limited by the lock-in detection used to separate the two position signals detected on a common QPD. To measure the performance of our system, we rapidly turned a LED on and off and plotted the peak-to-peak amplitude, normalized by the low-frequency response, as a function of blinking frequency [Fig. 4]. The data shows ~100 kHz of bandwidth, with the more rapidly modulated signal showing slightly faster response, as expected. This relatively high bandwidth is sufficient for typical optical-trapping and AFM-based single-molecule force spectroscopy applications.

 figure: Fig. 4

Fig. 4 Simultaneous high-bandwidth detection of two lasers on a common detector. The normalized peak-to-peak voltage response of the detection system after demodulation is plotted as a function of the blinking rate of an LED placed immediately in front of the QPD.

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Besides this signal separation, our application benefited from lock-in detection’s suppression of low-frequency noise. Lock-in detection—developed in the 1940s [39]—is ubiquitously used in a relatively narrow bandwidth around its modulation frequency to isolate a weak signal in the presence of low-frequency noise. For instance, in AMO physics, it is common to modulate a signal detected on a photodiode at a moderately high frequency (e.g., 50 kHz) to suppress spurious signals, including room lights and thermal variation. In contrast, we optimized our lock-in electronics for stability and responsivity over a broad frequency range.

3.2 Sub-nanometer stability in 3D over multiple hours

Our primary goal in developing multiplexed back-scattered detection was to assure that the smallest fundamental motions in biology [e.g., 1 bp (3.4 Å)] would not be masked by instrumental instability over a long period (~100 s). In other words, we strived for Å-scale stability not just over occasional 100-s periods but overall 100-s periods. To demonstrate our resulting instrumental performance, we stabilized a microscope in 3D over 28 h and analyzed the resulting data. More specifically, we used one laser beam to stabilize the sample and a second laser as an out-of-loop detector to quantify performance, as outlined in Fig. 3. For clarity, we show the full record averaged and decimated to 0.1 Hz [Fig. 5(a)]. Over the first ~15 hours, all 3 dimensions showed less than 1 nm of drift, with slightly increased drift over the last 13 h. While sections of this 28-h record show more drift, a more detailed inspection of different 100-s periods shows excellent Å-scale stability over 100 s [Figs. 5(b)5(d)]. We note that the y-axis consistently outperformed the other two axes. The exact origin of this increased performance is not known, but we attribute it to the higher sensitivity to motion in the y-axis than the x-axis.

 figure: Fig. 5

Fig. 5 Stabilization of an optical-trapping microscope to better than 1 nm in 3D over multiple hours. (a) Sample position versus time plotted during active stabilization as quantified by the out-of-loop detection laser [x (green), y (red), and z (blue)]. Data smoothed to 0.1 Hz for clarity. (b–d) Position-versus-time traces detail different 100-s time periods, emphasizing the Å-scale stability over any given 100-s period. Data smoothed to 10 Hz and offset vertically for clarity.

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To quantify instrumental performance, we used the Allan variance [45]. The Allan variance analysis is a particularly useful metric for single-molecule applications like optical trapping [46], since it shows how effectively one can trade off temporal resolution for improved spatial precision by averaging the signal until the instrumental performance is limited by low-frequency drift. We computed the Allan variance—or, more technically, the Allan deviation as described in the methods—from data shown in Fig. 5. The resulting plot of Allan deviation versus averaging time shows sub-Å precision over approximately four decades of averaging time (~0.1–1,000 s). More generally, on short times scales (< 1 s), the spatial precision improves with longer averaging times for all 3 axes, following a t-1/2 dependence that is typical for averaging noise [Fig. 6, dashed line)]. Over intermediate time scales (1–100 s), the Allan deviation stops decreasing and remains near 0.2, 0.1, and 0.4 Å for x, y, and z, respectively. On long time scales (>100 s), the Allan deviation increases with increasing averaging time. Notwithstanding this decreased stability over such extended periods, the Allan deviation stayed below 1 Å up to approximately 2500, 6600, and 2500 s for x, y, and z, respectively. Moreover, the Allan deviation is below 1 nm for all 3 spatial dimensions up to 50,000 s (~14 h), as expected from visual inspection of Fig. 5(a).

 figure: Fig. 6

Fig. 6 Sub-Å precision and stability over extended periods. The Allan deviation for the out-of-loop position record [Fig. 5(a)] plotted as function of averaging time for all 3 axes [x (green), y (red), and z (blue)]. The dashed line represents the expected improvement for averaging random noise.

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Our lab’s thermal stability limited the instrumental performance over extended periods (hours). Variations in temperature often, but not always, correlated with both lateral and vertical drift. While our lab temperature was stabilized, the temperature could vary from ~0.1–1 °C over an 8-h period, depending on outside ambient conditions and other external parameters. For the traces shown in Fig. 5(a), the room temperature slowly increased by ~0.2 °C over 15 h but changed sign and then decreased by 0.4 °C over the last 6 h. Hence, improved long-term stability could be attained by better control of room temperature. Notwithstanding such drift over hours, we emphasize that even during relatively rapid changes in the out-of-loop position shown in Fig. 5 (t = 20–28 h), the stabilization over any 100-s period remained excellent [Figs. 5(b)5(d)].

3.3 Detecting 1-Å steps

To demonstrate Å-scale precision of our multiplexed detection scheme, we moved the sample in a series of 1-Å steps and detected the resulting motion. More specifically, we actively stabilized stage position in 3D at 500 Hz (see §2.5) and then increased the lateral set point by 1 Å every 2 s while measuring the resulting motion with the out-of-loop detection laser. We note that this step size is 2-fold lower than the manufacturer’s specified precision of our 3-axis PZT stage.

To highlight the importance of an out-of-loop measurement, we plot both the in-loop and out-of-loop signal [Fig. 7(a)]. The in-loop signal is much quieter, as expected. Care should be taken in interpreting this in-loop result, since a properly functioning feedback loop necessarily drives the signal to the set point. Hence, we based our analysis on the out-of-loop measurement. Albeit noisier, this measurement gives a more accurate representation of what to expect in a typical biophysical application. The statistical significance of the detected steps is computed from the Fourier transform of pair-wise distance difference (PDD) [30] between all pairs of points [Fig. 5(b)]. The primary spatial frequency component was 1 ± 0.25 Å−1 (peak ± HWHM), implying a SNR ≅ 5 based on 1 σ = FWHM/2.35 for data smoothed to 5 Hz.

 figure: Fig. 7

Fig. 7 Generation and detection of 1-Å steps. (a) Records of position versus time showing 1-Å steps detected with the out-of-loop laser (blue) as the stabilization set point of the in-loop signal (red) was updated by 1 Å every 2 s. (b) The Fourier transform of the pairwise distance difference between all pairs of points for both signals.

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4. Conclusions

We have developed a versatile ultrastable measurement platform that has sub-Å stability in 3D over any 100-s period and sub-nm stability over hours for a surface-coupled assay. This platform is compatible with a variety of applications, including AFM, optical trapping, and super-resolution microscopy. We expect this ultrastable platform to enable more robust and routine detection of the smallest unitary steps along DNA (1 bp), allowing researchers to focus on their biological application rather than variability in instrumental performance. In particular, extension of this detection scheme to dual-beam optical-trapping assay [Fig. 1(a)] should yield even better performance, since mechanical noise from stage motion does not degrade the assay. Finally, this extreme stability should open the door to studying a wide range of Å-scale dynamics of single proteins beyond those that show discrete, repeatedly sized motions.

Acknowledgments

This work was supported by a fellowship from the National Research Council (R.W.), the National Science Foundation (DBI-1353987, Phys-1125844) and NIST. Mention of commercial products is for information only; it does not imply NIST’s recommendation or endorsement. TTP is a staff member of NIST’s Quantum Physics Division.

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19. K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002). [CrossRef]   [PubMed]  

20. T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003). [CrossRef]   [PubMed]  

21. K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003). [CrossRef]   [PubMed]  

22. K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008). [CrossRef]   [PubMed]  

23. J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006). [CrossRef]   [PubMed]  

24. A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009). [CrossRef]   [PubMed]  

25. W. Cheng, X. Hou, and F. Ye, “Use of tapered amplifier diode laser for biological-friendly high-resolution optical trapping,” Opt. Lett. 35(17), 2988–2990 (2010). [CrossRef]   [PubMed]  

26. M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17(19), 17190–17199 (2009). [CrossRef]   [PubMed]  

27. M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998). [CrossRef]   [PubMed]  

28. W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005). [CrossRef]   [PubMed]  

29. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993). [CrossRef]   [PubMed]  

30. 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]  

31. M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005). [CrossRef]  

32. B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013). [CrossRef]   [PubMed]  

33. A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999). [CrossRef]   [PubMed]  

34. L. Nugent-Glandorf and T. T. Perkins, “Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection,” Opt. Lett. 29(22), 2611–2613 (2004). [CrossRef]   [PubMed]  

35. A. R. Carter, G. M. King, T. A. Ulrich, W. Halsey, D. Alchenberger, and T. T. Perkins, “Stabilization of an optical microscope to 0.1 nm in three dimensions,” Appl. Opt. 46(3), 421–427 (2007). [CrossRef]   [PubMed]  

36. G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009). [CrossRef]   [PubMed]  

37. M. E. J. Friese, H. Rubinsztein-Dunlop, N. R. Heckenberg, and E. W. Dearden, “Determination of the force constant of a single-beam gradient trap by measurement of backscattered light,” Appl. Opt. 35(36), 7112–7116 (1996). [CrossRef]   [PubMed]  

38. A. R. Carter, G. M. King, and T. T. Perkins, “Back-scattered detection provides atomic-scale localization precision, stability, and registration in 3D,” Opt. Express 15(20), 13434–13445 (2007). [CrossRef]   [PubMed]  

39. W. C. Michels and N. L. Curtis, “A pentode lock‐in amplifier of high frequency selectivity,” Rev. Sci. Instrum. 12(9), 444–447 (1941). [CrossRef]  

40. M. A. Taylor, J. Knittel, and W. P. Bowen, “Optical lock-in particle tracking in optical tweezers,” Opt. Express 21(7), 8018–8024 (2013). [CrossRef]   [PubMed]  

41. S. H. Lee, M. Baday, M. Tjioe, P. D. Simonson, R. Zhang, E. Cai, and P. R. Selvin, “Using fixed fiduciary markers for stage drift correction,” Opt. Express 20(11), 12177–12183 (2012). [CrossRef]   [PubMed]  

42. D. H. Paik and T. T. Perkins, “Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts,” Methods Mol. Biol. 875, 335–356 (2012). [PubMed]  

43. E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003). [CrossRef]  

44. M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002). [CrossRef]   [PubMed]  

45. D. B. Sullivan, D. W. Allan, D. A. Howe, and E. L. Walls, eds., Characterization of Clocks and Oscillators (U.S. Government Printing Office, 1990).

46. F. Czerwinski, A. C. Richardson, and L. B. Oddershede, “Quantifying noise in optical tweezers by allan variance,” Opt. Express 17(15), 13255–13269 (2009). [CrossRef]   [PubMed]  

References

  • View by:

  1. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
    [Crossref] [PubMed]
  2. D. J. Müller and Y. F. Dufrêne, “Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology,” Nat. Nanotechnol. 3(5), 261–269 (2008).
    [Crossref] [PubMed]
  3. W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 171–190 (2007).
    [Crossref] [PubMed]
  4. K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
    [Crossref] [PubMed]
  5. Y. R. Chemla and D. E. Smith, “Single-molecule studies of viral DNA packaging,” Adv. Exp. Med. Biol. 726, 549–584 (2012).
    [PubMed]
  6. T. T. Perkins, “Ångström-precision optical traps and applications,” Annu Rev Biophys 43(1), 279–302 (2014).
    [Crossref] [PubMed]
  7. J. M. Fernandez and H. Li, “Force-clamp spectroscopy monitors the folding trajectory of a single protein,” Science 303(5664), 1674–1678 (2004).
    [Crossref] [PubMed]
  8. C. A. Bippes and D. J. Muller, “High-resolution atomic force microscopy and spectroscopy of native membrane proteins,” Rep. Prog. Phys. 74(8), 086601 (2011).
    [Crossref]
  9. T. Hoffmann and L. Dougan, “Single molecule force spectroscopy using polyproteins,” Chem. Soc. Rev. 41(14), 4781–4796 (2012).
    [Crossref] [PubMed]
  10. J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
    [Crossref] [PubMed]
  11. E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
    [Crossref] [PubMed]
  12. S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
    [Crossref] [PubMed]
  13. J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
    [Crossref] [PubMed]
  14. J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
    [Crossref] [PubMed]
  15. W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
    [Crossref] [PubMed]
  16. C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
    [Crossref] [PubMed]
  17. J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
    [Crossref] [PubMed]
  18. H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
    [Crossref] [PubMed]
  19. K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
    [Crossref] [PubMed]
  20. T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
    [Crossref] [PubMed]
  21. K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
    [Crossref] [PubMed]
  22. K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008).
    [Crossref] [PubMed]
  23. J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
    [Crossref] [PubMed]
  24. A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009).
    [Crossref] [PubMed]
  25. W. Cheng, X. Hou, and F. Ye, “Use of tapered amplifier diode laser for biological-friendly high-resolution optical trapping,” Opt. Lett. 35(17), 2988–2990 (2010).
    [Crossref] [PubMed]
  26. M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17(19), 17190–17199 (2009).
    [Crossref] [PubMed]
  27. M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
    [Crossref] [PubMed]
  28. W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
    [Crossref] [PubMed]
  29. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
    [Crossref] [PubMed]
  30. 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]
  31. M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005).
    [Crossref]
  32. B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
    [Crossref] [PubMed]
  33. A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
    [Crossref] [PubMed]
  34. L. Nugent-Glandorf and T. T. Perkins, “Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection,” Opt. Lett. 29(22), 2611–2613 (2004).
    [Crossref] [PubMed]
  35. A. R. Carter, G. M. King, T. A. Ulrich, W. Halsey, D. Alchenberger, and T. T. Perkins, “Stabilization of an optical microscope to 0.1 nm in three dimensions,” Appl. Opt. 46(3), 421–427 (2007).
    [Crossref] [PubMed]
  36. G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
    [Crossref] [PubMed]
  37. M. E. J. Friese, H. Rubinsztein-Dunlop, N. R. Heckenberg, and E. W. Dearden, “Determination of the force constant of a single-beam gradient trap by measurement of backscattered light,” Appl. Opt. 35(36), 7112–7116 (1996).
    [Crossref] [PubMed]
  38. A. R. Carter, G. M. King, and T. T. Perkins, “Back-scattered detection provides atomic-scale localization precision, stability, and registration in 3D,” Opt. Express 15(20), 13434–13445 (2007).
    [Crossref] [PubMed]
  39. W. C. Michels and N. L. Curtis, “A pentode lock‐in amplifier of high frequency selectivity,” Rev. Sci. Instrum. 12(9), 444–447 (1941).
    [Crossref]
  40. M. A. Taylor, J. Knittel, and W. P. Bowen, “Optical lock-in particle tracking in optical tweezers,” Opt. Express 21(7), 8018–8024 (2013).
    [Crossref] [PubMed]
  41. S. H. Lee, M. Baday, M. Tjioe, P. D. Simonson, R. Zhang, E. Cai, and P. R. Selvin, “Using fixed fiduciary markers for stage drift correction,” Opt. Express 20(11), 12177–12183 (2012).
    [Crossref] [PubMed]
  42. D. H. Paik and T. T. Perkins, “Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts,” Methods Mol. Biol. 875, 335–356 (2012).
    [PubMed]
  43. E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
    [Crossref]
  44. M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
    [Crossref] [PubMed]
  45. D. B. Sullivan, D. W. Allan, D. A. Howe, and E. L. Walls, eds., Characterization of Clocks and Oscillators (U.S. Government Printing Office, 1990).
  46. F. Czerwinski, A. C. Richardson, and L. B. Oddershede, “Quantifying noise in optical tweezers by allan variance,” Opt. Express 17(15), 13255–13269 (2009).
    [Crossref] [PubMed]

2014 (1)

T. T. Perkins, “Ångström-precision optical traps and applications,” Annu Rev Biophys 43(1), 279–302 (2014).
[Crossref] [PubMed]

2013 (2)

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

M. A. Taylor, J. Knittel, and W. P. Bowen, “Optical lock-in particle tracking in optical tweezers,” Opt. Express 21(7), 8018–8024 (2013).
[Crossref] [PubMed]

2012 (5)

S. H. Lee, M. Baday, M. Tjioe, P. D. Simonson, R. Zhang, E. Cai, and P. R. Selvin, “Using fixed fiduciary markers for stage drift correction,” Opt. Express 20(11), 12177–12183 (2012).
[Crossref] [PubMed]

D. H. Paik and T. T. Perkins, “Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts,” Methods Mol. Biol. 875, 335–356 (2012).
[PubMed]

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Y. R. Chemla and D. E. Smith, “Single-molecule studies of viral DNA packaging,” Adv. Exp. Med. Biol. 726, 549–584 (2012).
[PubMed]

T. Hoffmann and L. Dougan, “Single molecule force spectroscopy using polyproteins,” Chem. Soc. Rev. 41(14), 4781–4796 (2012).
[Crossref] [PubMed]

2011 (3)

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

C. A. Bippes and D. J. Muller, “High-resolution atomic force microscopy and spectroscopy of native membrane proteins,” Rep. Prog. Phys. 74(8), 086601 (2011).
[Crossref]

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (5)

M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17(19), 17190–17199 (2009).
[Crossref] [PubMed]

A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
[Crossref] [PubMed]

F. Czerwinski, A. C. Richardson, and L. B. Oddershede, “Quantifying noise in optical tweezers by allan variance,” Opt. Express 17(15), 13255–13269 (2009).
[Crossref] [PubMed]

2008 (4)

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

D. J. Müller and Y. F. Dufrêne, “Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology,” Nat. Nanotechnol. 3(5), 261–269 (2008).
[Crossref] [PubMed]

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (2)

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[Crossref] [PubMed]

2005 (4)

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
[Crossref] [PubMed]

M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005).
[Crossref]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
[Crossref] [PubMed]

2004 (2)

J. M. Fernandez and H. Li, “Force-clamp spectroscopy monitors the folding trajectory of a single protein,” Science 303(5664), 1674–1678 (2004).
[Crossref] [PubMed]

L. Nugent-Glandorf and T. T. Perkins, “Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection,” Opt. Lett. 29(22), 2611–2613 (2004).
[Crossref] [PubMed]

2003 (4)

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
[Crossref] [PubMed]

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
[Crossref] [PubMed]

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[Crossref]

2002 (2)

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[Crossref] [PubMed]

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

1999 (1)

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

1998 (1)

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

1996 (1)

1994 (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[Crossref] [PubMed]

1988 (1)

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]

1941 (1)

W. C. Michels and N. L. Curtis, “A pentode lock‐in amplifier of high frequency selectivity,” Rev. Sci. Instrum. 12(9), 444–447 (1941).
[Crossref]

Aathavan, K.

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

Abbondanzieri, E. A.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
[Crossref] [PubMed]

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
[Crossref] [PubMed]

Adelman, K.

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

Alchenberger, D.

Anderson, D. L.

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

Arunajadai, S. G.

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

Asbury, C. L.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[Crossref] [PubMed]

Baday, M.

Beran, R. K.

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

Bippes, C. A.

C. A. Bippes and D. J. Muller, “High-resolution atomic force microscopy and spectroscopy of native membrane proteins,” Rep. Prog. Phys. 74(8), 086601 (2011).
[Crossref]

Block, S. M.

K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 171–190 (2007).
[Crossref] [PubMed]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
[Crossref] [PubMed]

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
[Crossref] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
[Crossref] [PubMed]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[Crossref] [PubMed]

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[Crossref] [PubMed]

Bowen, W. P.

Brigley, A. M.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Bustamante, C.

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[Crossref] [PubMed]

C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
[Crossref] [PubMed]

Cai, E.

Capitanio, M.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005).
[Crossref]

Carter, A. R.

G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
[Crossref] [PubMed]

A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009).
[Crossref] [PubMed]

A. R. Carter, G. M. King, T. A. Ulrich, W. Halsey, D. Alchenberger, and T. T. Perkins, “Stabilization of an optical microscope to 0.1 nm in three dimensions,” Appl. Opt. 46(3), 421–427 (2007).
[Crossref] [PubMed]

A. R. Carter, G. M. King, and T. T. Perkins, “Back-scattered detection provides atomic-scale localization precision, stability, and registration in 3D,” Opt. Express 15(20), 13434–13445 (2007).
[Crossref] [PubMed]

Cecconi, C.

C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
[Crossref] [PubMed]

Chemla, Y. R.

Y. R. Chemla and D. E. Smith, “Single-molecule studies of viral DNA packaging,” Adv. Exp. Med. Biol. 726, 549–584 (2012).
[PubMed]

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[Crossref] [PubMed]

Cheng, W.

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

W. Cheng, X. Hou, and F. Ye, “Use of tapered amplifier diode laser for biological-friendly high-resolution optical trapping,” Opt. Lett. 35(17), 2988–2990 (2010).
[Crossref] [PubMed]

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

Churnside, A. B.

G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
[Crossref] [PubMed]

Cicchi, R.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005).
[Crossref]

Curtis, N. L.

W. C. Michels and N. L. Curtis, “A pentode lock‐in amplifier of high frequency selectivity,” Rev. Sci. Instrum. 12(9), 444–447 (1941).
[Crossref]

Czerwinski, F.

Dalal, R. V.

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
[Crossref] [PubMed]

Dearden, E. W.

Dittmore, A.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

Dougan, L.

T. Hoffmann and L. Dougan, “Single molecule force spectroscopy using polyproteins,” Chem. Soc. Rev. 41(14), 4781–4796 (2012).
[Crossref] [PubMed]

Dufrêne, Y. F.

D. J. Müller and Y. F. Dufrêne, “Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology,” Nat. Nanotechnol. 3(5), 261–269 (2008).
[Crossref] [PubMed]

Dumont, S.

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

Eberle, L. S.

G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
[Crossref] [PubMed]

Fernandez, J. M.

J. M. Fernandez and H. Li, “Force-clamp spectroscopy monitors the folding trajectory of a single protein,” Science 303(5664), 1674–1678 (2004).
[Crossref] [PubMed]

Florin, E.-L.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

Friese, M. E. J.

Gebhardt, J. C. M.

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

Gelles, J.

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

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]

Gieseke, A.

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

Greenleaf, W. J.

K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 171–190 (2007).
[Crossref] [PubMed]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
[Crossref] [PubMed]

Grimes, S.

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

Gupta, A. N.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Halsey, W.

Heckenberg, N. R.

Herbert, K. M.

K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008).
[Crossref] [PubMed]

Hodges, C.

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

Hoffmann, T.

T. Hoffmann and L. Dougan, “Single molecule force spectroscopy using polyproteins,” Chem. Soc. Rev. 41(14), 4781–4796 (2012).
[Crossref] [PubMed]

Hörber, J. K. H.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

Hou, X.

Izhaky, D.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[Crossref] [PubMed]

Jardine, P. J.

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

Kapitein, L. C.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[Crossref]

King, G. M.

Knittel, J.

La Porta, A.

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

Lancaster, L.

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

Landick, R.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
[Crossref] [PubMed]

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

Lang, M. J.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[Crossref] [PubMed]

Lansdorp, B. M.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

Lee, S. H.

Li, H.

J. M. Fernandez and H. Li, “Force-clamp spectroscopy monitors the folding trajectory of a single protein,” Science 303(5664), 1674–1678 (2004).
[Crossref] [PubMed]

Lis, J. T.

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

Liu, X.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Mahamdeh, M.

Marqusee, S.

C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
[Crossref] [PubMed]

Michels, W. C.

W. C. Michels and N. L. Curtis, “A pentode lock‐in amplifier of high frequency selectivity,” Rev. Sci. Instrum. 12(9), 444–447 (1941).
[Crossref]

Mitsis, P. G.

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
[Crossref] [PubMed]

Moffitt, J. R.

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[Crossref] [PubMed]

Muller, D. J.

C. A. Bippes and D. J. Muller, “High-resolution atomic force microscopy and spectroscopy of native membrane proteins,” Rep. Prog. Phys. 74(8), 086601 (2011).
[Crossref]

Müller, D. J.

D. J. Müller and Y. F. Dufrêne, “Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology,” Nat. Nanotechnol. 3(5), 261–269 (2008).
[Crossref] [PubMed]

Nagy, A.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

Neuman, K. C.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

Neupane, K.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Noller, H. F.

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

Nugent-Glandorf, L.

Oddershede, L. B.

Paik, D. H.

D. H. Paik and T. T. Perkins, “Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts,” Methods Mol. Biol. 875, 335–356 (2012).
[PubMed]

Pavone, F. S.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005).
[Crossref]

Perkins, T. T.

T. T. Perkins, “Ångström-precision optical traps and applications,” Annu Rev Biophys 43(1), 279–302 (2014).
[Crossref] [PubMed]

D. H. Paik and T. T. Perkins, “Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts,” Methods Mol. Biol. 875, 335–356 (2012).
[PubMed]

G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
[Crossref] [PubMed]

A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009).
[Crossref] [PubMed]

A. R. Carter, G. M. King, T. A. Ulrich, W. Halsey, D. Alchenberger, and T. T. Perkins, “Stabilization of an optical microscope to 0.1 nm in three dimensions,” Appl. Opt. 46(3), 421–427 (2007).
[Crossref] [PubMed]

A. R. Carter, G. M. King, and T. T. Perkins, “Back-scattered detection provides atomic-scale localization precision, stability, and registration in 3D,” Opt. Express 15(20), 13434–13445 (2007).
[Crossref] [PubMed]

L. Nugent-Glandorf and T. T. Perkins, “Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection,” Opt. Lett. 29(22), 2611–2613 (2004).
[Crossref] [PubMed]

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
[Crossref] [PubMed]

Peterman, E. J. G.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[Crossref]

Pralle, A.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

Prummer, M.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

Pyle, A. M.

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

Richardson, A. C.

Rief, M.

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

Roberts, J. W.

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

Rubinsztein-Dunlop, H.

Saleh, O. A.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

Santangelo, T. J.

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

Schäffer, E.

Schmidt, C. F.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[Crossref]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[Crossref] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[Crossref] [PubMed]

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]

Schnitzer, M. J.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

Selvin, P. R.

Seol, Y.

A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009).
[Crossref] [PubMed]

Serebrov, V.

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

Shaevitz, J. W.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
[Crossref] [PubMed]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[Crossref] [PubMed]

Shank, E. A.

C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
[Crossref] [PubMed]

Sheetz, M. P.

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]

Simonson, P. D.

Smith, D. E.

Y. R. Chemla and D. E. Smith, “Single-molecule studies of viral DNA packaging,” Adv. Exp. Med. Biol. 726, 549–584 (2012).
[PubMed]

Solanki, A.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Sosova, I.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Stelzer, E. H. K.

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

Stigler, J.

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[Crossref] [PubMed]

Tabrizi, S. J.

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

Taylor, M. A.

Tinoco, I.

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

Tjioe, M.

Ulrich, T. A.

van Dijk, M. A.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[Crossref]

Wang, M. D.

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

Wen, J. D.

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

Woodside, M. T.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 171–190 (2007).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
[Crossref] [PubMed]

Ye, F.

Yin, H.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

Yoshimura, S. H.

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

Yu, H.

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

Zeri, A. C.

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

Zhang, R.

Ziegler, F.

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

Adv. Exp. Med. Biol. (1)

Y. R. Chemla and D. E. Smith, “Single-molecule studies of viral DNA packaging,” Adv. Exp. Med. Biol. 726, 549–584 (2012).
[PubMed]

Annu Rev Biophys (1)

T. T. Perkins, “Ångström-precision optical traps and applications,” Annu Rev Biophys 43(1), 279–302 (2014).
[Crossref] [PubMed]

Annu. Rev. Biochem. (1)

K. M. Herbert, W. J. Greenleaf, and S. M. Block, “Single-molecule studies of RNA polymerase: Motoring along,” Annu. Rev. Biochem. 77(1), 149–176 (2008).
[Crossref] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (2)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

W. J. Greenleaf, M. T. Woodside, and S. M. Block, “High-resolution, single-molecule measurements of biomolecular motion,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 171–190 (2007).
[Crossref] [PubMed]

Appl. Opt. (2)

Biophys. J. (2)

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, “An automated two-dimensional optical force clamp for single molecule studies,” Biophys. J. 83(1), 491–501 (2002).
[Crossref] [PubMed]

A. R. Carter, Y. Seol, and T. T. Perkins, “Precision surface-coupled optical-trapping assay with one-basepair resolution,” Biophys. J. 96(7), 2926–2934 (2009).
[Crossref] [PubMed]

Cell (1)

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, “Ubiquitous transcriptional pausing is independent of RNA polymerase backtracking,” Cell 115(4), 437–447 (2003).
[Crossref] [PubMed]

Chem. Soc. Rev. (1)

T. Hoffmann and L. Dougan, “Single molecule force spectroscopy using polyproteins,” Chem. Soc. Rev. 41(14), 4781–4796 (2012).
[Crossref] [PubMed]

Eur. Phys. J. B (1)

M. Capitanio, R. Cicchi, and F. S. Pavone, “Position control and optical manipulation for nanotechnology applications,” Eur. Phys. J. B 46(1), 1–8 (2005).
[Crossref]

Methods Mol. Biol. (1)

D. H. Paik and T. T. Perkins, “Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts,” Methods Mol. Biol. 875, 335–356 (2012).
[PubMed]

Microsc. Res. Tech. (1)

A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999).
[Crossref] [PubMed]

Nano Lett. (1)

G. M. King, A. R. Carter, A. B. Churnside, L. S. Eberle, and T. T. Perkins, “Ultrastable atomic force microscopy: Atomic-scale stability and registration in ambient conditions,” Nano Lett. 9(4), 1451–1456 (2009).
[Crossref] [PubMed]

Nat. Methods (1)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

D. J. Müller and Y. F. Dufrêne, “Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology,” Nat. Nanotechnol. 3(5), 261–269 (2008).
[Crossref] [PubMed]

Nature (7)

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, “Backtracking by single RNA polymerase molecules observed at near-base-pair resolution,” Nature 426(6967), 684–687 (2003).
[Crossref] [PubMed]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, “Direct observation of base-pair stepping by RNA polymerase,” Nature 438(7067), 460–465 (2005).
[Crossref] [PubMed]

S. Dumont, W. Cheng, V. Serebrov, R. K. Beran, I. Tinoco, A. M. Pyle, and C. Bustamante, “RNA translocation and unwinding mechanism of HCV NS3 helicase and its coordination by ATP,” Nature 439(7072), 105–108 (2006).
[Crossref] [PubMed]

J. D. Wen, L. Lancaster, C. Hodges, A. C. Zeri, S. H. Yoshimura, H. F. Noller, C. Bustamante, and I. Tinoco, “Following translation by single ribosomes one codon at a time,” Nature 452(7187), 598–603 (2008).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, K. Aathavan, S. Grimes, P. J. Jardine, D. L. Anderson, and C. Bustamante, “Intersubunit coordination in a homomeric ring ATPase,” Nature 457(7228), 446–450 (2009).
[Crossref] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365(6448), 721–727 (1993).
[Crossref] [PubMed]

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]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

W. J. Greenleaf, M. T. Woodside, E. A. Abbondanzieri, and S. M. Block, “Passive all-optical force clamp for high-resolution laser trapping,” Phys. Rev. Lett. 95(20), 208102 (2005).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (3)

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, “Differential detection of dual traps improves the spatial resolution of optical tweezers,” Proc. Natl. Acad. Sci. U.S.A. 103(24), 9006–9011 (2006).
[Crossref] [PubMed]

H. Yu, X. Liu, K. Neupane, A. N. Gupta, A. M. Brigley, A. Solanki, I. Sosova, and M. T. Woodside, “Direct observation of multiple misfolding pathways in a single prion protein molecule,” Proc. Natl. Acad. Sci. U.S.A. 109(14), 5283–5288 (2012).
[Crossref] [PubMed]

K. Adelman, A. La Porta, T. J. Santangelo, J. T. Lis, J. W. Roberts, and M. D. Wang, “Single molecule analysis of RNA polymerase elongation reveals uniform kinetic behavior,” Proc. Natl. Acad. Sci. U.S.A. 99(21), 13538–13543 (2002).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

C. A. Bippes and D. J. Muller, “High-resolution atomic force microscopy and spectroscopy of native membrane proteins,” Rep. Prog. Phys. 74(8), 086601 (2011).
[Crossref]

Rev. Sci. Instrum. (3)

B. M. Lansdorp, S. J. Tabrizi, A. Dittmore, and O. A. Saleh, “A high-speed magnetic tweezer beyond 10,000 frames per second,” Rev. Sci. Instrum. 84(4), 044301 (2013).
[Crossref] [PubMed]

W. C. Michels and N. L. Curtis, “A pentode lock‐in amplifier of high frequency selectivity,” Rev. Sci. Instrum. 12(9), 444–447 (1941).
[Crossref]

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[Crossref]

Science (6)

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

T. T. Perkins, R. V. Dalal, P. G. Mitsis, and S. M. Block, “Sequence-dependent pausing of single lambda exonuclease molecules,” Science 301(5641), 1914–1918 (2003).
[Crossref] [PubMed]

J. M. Fernandez and H. Li, “Force-clamp spectroscopy monitors the folding trajectory of a single protein,” Science 303(5664), 1674–1678 (2004).
[Crossref] [PubMed]

W. Cheng, S. G. Arunajadai, J. R. Moffitt, I. Tinoco, and C. Bustamante, “Single-base pair unwinding and asynchronous RNA release by the hepatitis C virus NS3 helicase,” Science 333(6050), 1746–1749 (2011).
[Crossref] [PubMed]

C. Cecconi, E. A. Shank, C. Bustamante, and S. Marqusee, “Direct observation of the three-state folding of a single protein molecule,” Science 309(5743), 2057–2060 (2005).
[Crossref] [PubMed]

J. Stigler, F. Ziegler, A. Gieseke, J. C. M. Gebhardt, and M. Rief, “The complex folding network of single calmodulin molecules,” Science 334(6055), 512–516 (2011).
[Crossref] [PubMed]

Other (1)

D. B. Sullivan, D. W. Allan, D. A. Howe, and E. L. Walls, eds., Characterization of Clocks and Oscillators (U.S. Government Printing Office, 1990).

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Figures (7)

Fig. 1
Fig. 1 A wide variety of microscopy techniques can benefit from improved Ångstrom-scale precision and stability, including (a) a dual-beam optical-trap, (b) a surface-coupled optical trap, (c) atomic force microscopy, and (d) optical microscopy, particularly super-resolution techniques. In the first two assays, two focused lasers are used to measure opposite ends of a stretched molecule via scattered light. The ultimate limit to the precision of the position measurement is the differential-pointing stability between the lasers. This technique can be extended to actively stabilize the sample position for surface-coupled assays (b-d) using a reference mark attached to the sample.
Fig. 2
Fig. 2 Schematic of back-scattered detection (BSD) apparatus. Two laser diodes (LD) were modulated and actively stabilized by a combination of elements in the gray-dashed box. Each laser focus was translated laterally in the sample plane by mirrors positioned conjugate to the back focal plane of the objective (blue). The polarizing beam splitter cube (PBS) and quarter-wave plate (λ/4) acted as an optical isolator for efficient collection of back-scattered light. Back-scattered light was detected by a single quadrant photodiode (QPD). Acronyms represent the following: stabilized, modulated diode lasers (SMDL), acousto-optic modulator (AOM), photodiode (PD), lock-in amplifiers (LI), dichroic (DC), neutral density filters (ND), beam-sampler (BS), and piezo-electric (PZT).
Fig. 3
Fig. 3 Schematic of stabilization procedure using an out-of-loop monitor. Two modulated lasers scattered light from the same fiducial marker. The scattered light was detected on a common QPD, and the signals were electronically separated using lock-in amplifiers. After filtering and amplification, the signals were digitized by an FPGA, which used the signals to calculate the position of the sample. The 2.5-MHz signal stabilized the sample, while the 1-MHz signal provided an out-of-loop measurement. White boxes denote analog electronics. Grey boxes denote field programmable gate array (FPGA).
Fig. 4
Fig. 4 Simultaneous high-bandwidth detection of two lasers on a common detector. The normalized peak-to-peak voltage response of the detection system after demodulation is plotted as a function of the blinking rate of an LED placed immediately in front of the QPD.
Fig. 5
Fig. 5 Stabilization of an optical-trapping microscope to better than 1 nm in 3D over multiple hours. (a) Sample position versus time plotted during active stabilization as quantified by the out-of-loop detection laser [x (green), y (red), and z (blue)]. Data smoothed to 0.1 Hz for clarity. (b–d) Position-versus-time traces detail different 100-s time periods, emphasizing the Å-scale stability over any given 100-s period. Data smoothed to 10 Hz and offset vertically for clarity.
Fig. 6
Fig. 6 Sub-Å precision and stability over extended periods. The Allan deviation for the out-of-loop position record [Fig. 5(a)] plotted as function of averaging time for all 3 axes [x (green), y (red), and z (blue)]. The dashed line represents the expected improvement for averaging random noise.
Fig. 7
Fig. 7 Generation and detection of 1-Å steps. (a) Records of position versus time showing 1-Å steps detected with the out-of-loop laser (blue) as the stabilization set point of the in-loop signal (red) was updated by 1 Å every 2 s. (b) The Fourier transform of the pairwise distance difference between all pairs of points for both signals.

Equations (2)

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x( V x , V y , V z )= i,j,k=0 i+j+k=4 a ijk x V x i V y j V z k .
σ x ( τ )= 1 2 ( x i+1 x i ) 2 τ ,

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