Abstract

Optical tweezers combined with various microscopy techniques are a versatile tool for single-molecule force spectroscopy. However, some combinations may compromise measurements. Here, we combined optical tweezers with total-internal-reflection-fluorescence (TIRF) and interference-reflection microscopy (IRM). Using a light-emitting diode (LED) for IRM illumination, we show that single microtubules can be imaged with high contrast. Furthermore, we converted the IRM interference pattern of an upward bent microtubule to its three-dimensional (3D) profile calibrated against the optical tweezers and evanescent TIRF field. In general, LED-based IRM is a powerful method for high-contrast 3D microscopy.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

To apply force on a wide range of samples and measure the response down to single biological molecules, optical tweezers are widely used in physics, material science, and biology [1]. In the optical trap, the momentum of light is used to apply forces onto trapped cells or particles. For example, microspheres are often used as sensor probes to measure the mechanochemical interaction of individual molecular machines with their tracks or substrate. In case of cytoskeletal motor proteins, either actin filaments or microtubules are immobilized on surfaces [1]. During an experiment, such filaments need to be imaged for extended periods. To this end, optical tweezers are often combined with various label-free microscopy contrast methods ranging from bright-field, via differential interference contrast (DIC) [2,3], or less common, phase-contrast [4], dark field [5] and rotating-coherent-scattering microscopy (ROCS) [6] to fluorescence microscopy including among others epi-, TIRF, confocal, or stimulated emission depletion (STED) configurations [7–11]. Because fluorescence microscopy requires labeling of proteins, is phototoxic, and has photobleaching, and brightfield microscopy has low contrast or involves considerable post-processing of the images [12], the technique of choice for visualizing microtubules is often video-enhanced DIC [2,13]. However, due to the shear axis of the Nomarski prisms, simple DIC implementations are direction dependent [14] and limit the polarization and power of optical tweezers. Only linearly polarized trapping lasers with the polarization direction aligned with the Nomarski prism’s shear axis pass the prims without changing the polarization. Linearly polarized trapping light induces an asymmetry in the force field of the optical trap [15], which may lead to artifacts for 2D and 3D experiments [16,17], and makes experiments that utilize the transfer of angular momentum of the trapping light to trapped particles difficult [18]. In addition, the trapping power may be reduced for near infrared lasers. Despite these limitations, DIC is often the technique of choice for microtubule-based, optical-tweezers assays.

To eliminate these restrictions, we combined our optical tweezers with label-free IRM. In addition, we integrated TIRF into the system to allow for single-molecule fluorescence microscopy. IRM provides high, three-dimensional (3D) contrast, can be realized with a simple, cost-efficient optical design, and, in comparison to differential interference contrast (DIC), is orientation independent and does not compromise the polarization state or the power of optical tweezers. Furthermore, since IRM works in reflection, the half space above the objective is free for other manipulation or detection techniques. IRM was first used by Curtis et al. [19] to measure cell-substrate distances during cell adhesion. These distances were inferred from interference fringes that occur because the back-scattered (or reflected) light of the specimen interferes with the reflected “reference” light from the glass–water interface converting a phase into an amplitude contrast. This contrast changes axially within λ/(4n)—where λ is the used wavelength for illumination and n is the refractive index of the sample medium—from dark (destructive interference) to bright (constructive interference). Moreover, the contrast was improved significantly by reducing the amount of unwanted reflected light from other optical elements by crossed polarizers and an “Antiflex” objective (reflection interference contrast microscopy (RICM) [20]). Independent of the implementation, a quantitative analysis of separation distances and optical thicknesses is possible [21] providing 3D information about the sample with exquisite axial precision allowing, for example, ångström precision surface stabilization by tracking immobilized microspheres [22]. Recently, the detection limits of the technique have been pushed further, utilizing the technical improvements of digital cameras, processing power, and lasers for illumination (interferometric scattering microscopy (iSCAT) [23,24]) allowing for the detection of single unlabeled molecules sufficiently separated either in space or time [25,26]. Single microtubules were imaged in a confocal configuration [27], more recently with high spatiotemporal precision using iSCAT [28], or a solid-state-white-light illumination in an inverted epi-fluorescence microscope [29].

In our combination with optical tweezers, we used a high-power LED as a light source and show that single, isolated microtubules can be visualized with a signal-to-noise (SNR) ratio comparable to DIC. We measured and optimized the microtubule contrast in terms of photon flux, frame-averaging, and illumination numerical aperture. Furthermore, using the optical tweezers and the height-dependent interference patterns of an upward bent microtubule, we measured its 3D profile. We used this profile to calibrate the evanescent field of the TIRF microscope. The short coherence length of the LED compared to lasers has the advantage that no speckles and etalon fringes arise, which simplifies image analysis procedures and improves contrast. In general, LED-based IRM is a simple, but powerful microscopy contrast method compatible with many other techniques allowing for high-contrast 3D microscopy. Our combination can be applied to a wide range of biological systems and allows versatile imaging and force spectroscopy down to single molecules.

2. Materials and methods

2.1. Experimental setup

The setup combines optical tweezers with TIRF microscopy and IRM (Fig. 1) described in more detail below. The assembly is custom-built and placed in a vibration-isolated walk-in chamber inside an air-conditioned room. The temperature of the chamber itself is not actively controlled, but isolates the device from outside noise and heat sources. All components that generate heat inside the chamber are constantly on such that the chamber equilibrates to a constant temperature. Chambers are only entered to exchange samples. During an experiment, all adjustments are done via motorized components. All components are placed on a 1.2 m × 1 m × 0.2 m optical table (Standa, Lithuania), which is mechanically stabilized by an active vibration isolation system (VarioBasic-60, Accurion, Germany). Overall, the system had a tracking precision (Allan deviation) of a fixed microsphere of less than 5 nm and 10 nm for the lateral and axial direction, respectively, measured over a duration of 1000 s. Over a minute, the tracking precision was better than 1 nm in all directions. Thus, thermal drift was not a problem for the current study. In the following subsections, we describe the optical tweezers, the IRM, and TIRF implementation.

 

Fig. 1 Schematic of the combined IRM–TIRF-microscope–optical-tweezers setup.

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2.1.1. Optical tweezers setup

The optical tweezers setup uses a diode-pumped solid state YVO4-laser that continuously emits 3 W at 1064 nm (Smart Laser Systems, Germany). The laser passes a Faraday isolator to avoid back-reflections and etalon fringes. The half-wave plate (HWP) matches the laser polarization with the following mirror axes to preserve the linear polarization of the trapping laser. The 3-lens Galilean telescope increases the beam diameter to 5 mm. Adjustment of the laser power is realized by a combination of a HWP and a polarizing beam splitter (PBS) cube. Unwanted laser light passes the PBS and reaches a beam dump, whereas the reflected light passes a quarter-wave plate (QWP) and is reflected by a deformable mirror (MMDM10-1-focus, OKO Technologies, The Netherlands). This mirror enables fast axial steering of the trap in the sample relative to the imaging plane of the microscope [30]. After the reflection, the laser passes the QWP a second time resulting in a 90° rotation of the linear polarization direction. Thus, the laser is transmitted by the PBS and passes two Keplerian telescopes. A dichroic mirror (F33-725, AHF Analysentechnik, Germany) reflects the laser beam to the objective lens (CFI Apo TIRF 60x oil, NA 1.49, Nikon Instruments, Japan). The two telescopes relay the optical plane of the deformable mirror into the back-focal plane (BFP) of the objective lens and magnify the laser beam diameter to 8.8 mm corresponding to an overfilling ratio of α = 1.0 [31]. The objective tightly focuses the laser and forms a trap in the sample chamber. The sample is mounted on a long-range open-loop (MX-35, Mechonics, Germany) and a short-range, high-precision, closed-loop piezo-driven stage (PI Hera 620 XYZ, Physik Instrumente, Germany). The transmitted laser light is collected by a condenser lens (D-CUO Achr.-Apl. NA 1.4, Nikon Instruments, Japan). The image of the BFP of the condenser is de-magnified and projected onto a quadrant photo diode (QP154-Q-HVSD, First Sensor AG, Germany) by a relay lens. To ensure thermal stability in the sample, both the objective and condenser lens temperature are set to 29.000 °C controlled by a millikelvin-precision temperature feedback [3].

2.1.2. Interference reflection microscope

The LED-based interference reflection microscope consists of a few simple optical components (Fig. 2). For illumination a blue LED (Royal-Blue LUXEON Rebel LED, Lumileds, Germany; λ ± Δλ ≈ 450 ± 20 nm with 525 mW at 700 mA) was used. To provide thermal stability— especially at high currents, the LED was mounted on a large aluminum heat sink (Fisher Elektronik, Germany). The driving current is provided by a DC power supply (Agilent E3648A, Keysight, Böblingen, Germany). An image of the LED is magnified by two telescopes and projected into the BFP of the objective lens to Köhler-illuminate the sample. An aperture iris is placed at the first image plane of the LED, which is conjugate to the BFP. This iris truncates the LED image and thus, avoids total internal reflection. With the aperture iris, the illumination numerical aperture (INA) can also be adjusted. Note that a large INA and a curved sample affects the coherence of the reflected light [21]. A field iris limits the illumination area in the sample-plane, i.e. the front-focal plane of the objective. The detection and illumination light path are separated by a 50/50 beam splitter plate (BS) (F21-000, AHF Analysentechnik, Germany). Half the reflected light from the sample passes the beam splitter and a filter blocks the infrared light from the optical trap. A 200 mm tube lens and a zoom (S5LPJ7073, Sill Optics, Germany) magnify the sample image about 165× and project it onto a CCD camera (LU135-M, Lumenera, Canada). Note that the use of an Antiflex objective and linearly polarized light did not improve the image contrast significantly.

 

Fig. 2 Schematic of the IRM design and principle. The optical path is drawn to scale and shows the marginal rays of the LED (blue lines), the sample (black lines), and the field iris (dashed gray lines). The inset shows the principle of the IRM contrast formation. The incident light of the Köhler-illuminated sample, here a microtubule, is reflected from the glass-water interface (reference) and the specimen (sample), which interfere to form the final IRM signal.

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2.1.3. Total internal reflection fluorescence (TIRF) microscope

The objective-type TIRF microscope uses a 488 nm diode-laser with a maximum power of 80 mW (PhoxX 488-80, Omicron-Laserage, Germany). The laser is magnified by a telescope and cleaned up by a Fourier-filter with a diameter of 30 μm. To focus the laser into the objective’s BFP, a lens and a small, millimeter-sized mirror [32] are mounted on a closed-loop piezo-driven stage (M3-L, NewScale Technologies, USA) underneath the objective. The piezo-driven stage allows to precisely position the laser at a certain distance from the optical axis. Thus, the angle of incidence can be precisely tuned to achieve total internal reflection at the glass–water interface. Reflected excitation light is coupled out by a second small mirror that is also motorized by the same piezo stage as used for the other small mirror. Fluorescent light is collected by the objective lens and reflected by a dichroic mirror (F73-510, AHF Analysentechnik, Germany) toward the fluorescence detection path. A 160 mm tube-lens forms an image of the sample and an adjustable slit (Spalte SP 40, Owis, Germany) confines the field of view. The following unit is a color splitter, independently developed and similar in design to the one by Jiang et al. [33]. The fluorescent light is split into a “green” and “red” path by the usage of a dichroic mirror (F38-560, AHF Analysentechnik, Germany) and focuses both colors independently onto an electron multiplying CCD camera (iXon3, Andor Technology, UK).

2.2. Sample preparation

2.2.1. Polymerization of microtubules

Porcine α/β-tubulin was purified according to [34]. Microtubules were polymerized from a 30 μM tubulin solution that contained, 4 mM MgCl2, 1 mM GTP, and 5 % DMSO in BRB80 [80 mM PIPES (1,4-piperazinediethanesulfonic acid, Sigma-Aldrich) pH adjusted to 6.9 using KOH, 1 mM MgCl2, 1 mM EGTA (ethylene glycol-bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid, Sigma-Aldrich)]. For the fluorescence experiments, 10 % rhodamine-labeled (TAMRA, SE; 5-(and-6)-carboxytetramethylrhodamine, succinimidyl ester (5(6)-TAMRA, SE), Invitrogen, emission peak: 578 nm) tubulin was used. The solution was incubated for 30 min at 37 °C. The polymerized microtubules were then centrifuged and suspended in a 0.1 % taxol–BRB80 solution.

2.2.2. Microsphere functionalization

Polystyrene (PS) microspheres with a diameter of 590 nm (Bangs Laboratories, USA) were functionalized as described in Bugiel et al. [35] except that the green fluorescent protein (GFP) antibody was replaced with a nanobody: a GFP-binding-protein (GBP), which is a 13 kDa GFP-binding fragment derived from a llama single-chain antibody [36]. A protein solution of a truncated rat kinesin-1 motor protein (his6-rkin430-eGFP) was then mixed with the microsphere solution. The protein solution contained BRB80, 112.5 mM casein, 1 mM 5′-adenylyl-imidodiphosphate (AMPPNP, a non-hydrolyzable analog of ATP ensuring a rigor kinesin-microtubule attachment), and an oxygen scavenger system (20 mM D-glucose, 20 μg/ml glucose oxidase, 8 μg/ml, and 0.1 % β-mercaptoethanol).

2.2.3. Sample chamber preparation

The sample flow cells were constructed of Parafilm sandwiched between two cover slips (22 mm × 22 mm, # 1.5, Corning, and 18 mm × 18 mm, # 0, Menzel Gläser), which were cleaned and treated with chlorotrimethylsilane vapor under vacuum to generate a hydrophobic surface. The flow chamber was first filled with a solution containing anti-β-tubulin I antibodies (Sigma-Aldrich). For the microtubule bending experiment, we decreased the concentration of anti-β-tubulin about 1000×. Non-specific binding was prevented by incubating the flow chamber for 10 min with a 1 % aqueous solution of Pluronic F-127 (Sigma-Aldrich). Afterwards, the microtubule solution was flowed in. To bend a microtubule, the solution of functionalized microspheres was added after the microtubules were bound to the surface.

2.3. Image processing

2.3.1. Background measurement

Inhomogeneous illumination of the sample is a common problem in microscopy and is accounted for by subtraction of a so-called background image. In IRM, the background strongly depends on the vertical position of the reference plane, i.e. the glass–water interface relative to the focal or imaging plane. Therefore, it is necessary to move the reference into the focal plane to measure a background image. To avoid any (static) sample of being considered as background, we moved the sample laterally, sufficiently fast, while recording a set of ≈400 images at a frame rate of 25 Hz. A median of this set approximates the static, uneven illumination of the field of view well and is considered as background. This background image is subtracted from the raw IRM images [Fig. 3(A)]. After background subtraction, the resulting images show the interference contrast as a positive (white) or negative (black) IRM signal on an even background (gray). Note that the nominal values depend on the bit depth of the recorded images and should be normalized by this depth if raw signal values need to be compared. All IRM images presented have the background subtracted unless stated otherwise.

 

Fig. 3 Background subtraction and SNR measurement of a microtubule. (A) Raw IRM image (top) of microtubules on a glass surface and background image (middle). Background subtraction leads to the image of the IRM signal (bottom). Note that microtubules are visible without background subtraction. Also note the signature of an interference pattern: a partially unbound microtubule has black and white regions (arrows in (A) top and bottom). (B) Region of interest of the microtubule indicated in A. The black spots are impurities. (C) Median-intensity profile calculated along the microtubule axis of B (black) and a Gaussian fit (orange). (D) Residual noise image after subtraction of the Gaussian fit shown in C from each column of the microtubule image in B. Values above or below the threshold (vertical, dashed lines in C) are indicated in red or blue, respectively. (E) Histogram of the gray values in D (light gray bars). The image noise was calculated from the gray values within the threshold (dark gray bars) excluding signals from impurities. The threshold (*) was calculated as ±1.5× the interquartile range around the median gray level.

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2.3.2. Measuring the signal-to-noise ratio

To compare different images of the IRM signal it is necessary to use a standard signal-generating sample. Here, we used the contrast generated by a single, isolated microtubule bound to a glass surface. One way of measuring a microtubule’s signal is based on an intensity profile of a line across the microtubule. The difference between the highest and lowest intensity would be the signal. However, this approach is error-prone because the IRM signal depends on the probe’s height above the surface and potential irregularities as well as dirt on the glass surface. The latter, in particular, could result in large errors in the signal value.

Here, the signal of a microtubule was extracted from a Gaussian-fit to a median intensity profile calculated along the microtubule axis. First, a part of a microtubule was cut out, using Fiji’s segmented-line in combination with the “Straighten” tool [37] [Fig. 3(B)]. While we used nearly straight microtubules, in principle, the analysis could also be performed on laterally bent samples. Then, the median intensity profile along the microtubule axis was calculated [Fig. 3(C)]. The microtubule signal, I0, was then extracted from a Gaussian-fit I(x) = I0 exp(−(xx0)2/2σ2) + Ioffset to the median profile. The noise was calculated from a residual image. An image of the IRM signal contains noise, whereby the major intrinsic contribution of noise is shot noise. Other contrast generating content, such as dirt, drift, or fluctuations in illumination intensity add to the total noise. To mainly extract the shot noise, a residual image was calculated by subtracting the Gaussian-fit from every column of a region of interest centered around a microtubule [Fig. 3(D)]. A direct calculation of the standard deviation of the intensity distribution of the residual image usually overestimates the perceptual noise because dirt or irregularities in the glass surface increase the variance. To minimize the overestimation, we applied a threshold to the noise histogram. The threshold was set at Q1 − 1.5 IQR and Q3 + 1.5 IQR, where Q1 and Q3 are the first and the third quartile of the intensity distribution and IQR is its interquartile range [Fig. 3(E)]. The resulting intensity distribution of the filtered residuals was then fitted to another Gaussian. Its standard deviation was taken as a measure for the noise. The ratio between the signal and the noise was then taken as the measure for the IRM signal quality or SNR.

3. Results and discussion

3.1. Optimizing the signal-to-noise ratio

The SNR of a microtubule increases with the amount of light reaching the camera. To investigate how the signal of a microtubule can be improved, we kept the exposure time constant at 0.04 s and consecutively increased the illumination light power by increasing the LED current until we saturated the CCD camera [Fig. 4(A)]. The SNR increased in a power-law manner with an exponent 0.44 ± 0.03. This increase approximately follows the theoretical behavior in the shot noise limit with an exponent of 0.5. Deviations may be due to small nonlinearities in the LED power-current relationship and heating of the LED with increased currents. In these experiments, the SNR did not saturate. Therefore, the pixel well depth of our camera was limiting the SNR because higher LED currents saturated the camera. Next, we investigated the influence of frame averaging.

 

Fig. 4 Optimization of the IRM signal-to-noise ratio. (A) Analyzed microtubule images (top) and residual images (middle) at varying LED currents. The measured SNR is plotted versus the applied LED current (bottom). A power-law fit (dashed line) showed near shot-noise limited imaging. Inset: Measured noise vs. LED current. The noise scaled with an exponent 0.46 ± 0.1. (B) Analyzed microtubule images (top) and residual images (middle) for an increasing number N of averaged frames. The solid line indicates a power-law slope with exponent 0.5. Inset: IRM signal vs. number of averages. (C) Top 2 panels: section 10 images of the microtubule shown in D with increasing INA and the respective residual images. Bottom panels: Legend of sections. Signal of all microtubule-sections (indicated in D) and the corresponding noise is plotted vs. INA. The averaged SNR is normalized by the SNR at INA = 1.3 at the very bottom. (D) An averaged image of a microtubule (N = 50), its line intensity profile (bottom left) and the corresponding histogram (bottom right). The analyzed microtubule-sections of C are indicated (dashed lines).

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In the shot-noise limit, the SNR improves by averaging consecutive frames. In our experiments, the SNR of a microtubule increased with the number of averaged frames, but was limited by other contrast-generating irregularities in the sample [Fig. 4(B)]. We recorded a set of ≈900 images of a single microtubule at a frame rate of 25 Hz using a LED current of 0.2 A and measured its SNR as a function of the number of averaged frames. In one frame, a single microtubule had a SNR of ≈5.6. Upon averaging, the SNR doubled at N = 8 frames (SNR ≈ 11.4), but leveled off to ≈17.2 for N ≥ 128 frames. Because the measured IRM signal of the microtubule was also constant (Fig. 4(B), bottom, inset), the saturation was due to the effective image noise becoming constant. While for a single frame, shot-noise was the dominant noise, the signal of contrast-generating irregularities surpassed the shot-noise for a high number of averages. Therefore, the increase of the SNR was limited by the cleanliness of the sample and the roughness of the glass cover slips. In analogy to the procedure reported for iSCAT imaging [25,26], the background could be reduced by dynamic background image acquisition and subtraction.

The SNR could be further improved by using a high illumination numerical aperture (INA). By opening and closing the aperture iris, we varied the INA and, thereby, the LED image size in the BFP of the objective. To account for the change in average intensity on the CCD, we adjusted the LED current to a constant mean CCD intensity. We imaged one long microtubule, averaged 50 consecutive frames, and measured the signal and the image noise of 10 different microtubule sections [Fig. 4(C) and (D)]. The signal of a microtubule-section and its image noise increased with increasing INA (Fig. 4(C), middle). The resulting SNR of all microtubule-sections increased up to an INA of 1.14 and leveled off for higher INAs (Fig. 4(C), bottom). Increasing the illumination angle improved the IRM signal, but also increased the image noise. The increase of the image noise might again be caused by an increased visibility of irregularities on the glass surface. However, the increase of the IRM signal with increasing INA was unexpected based on theory (compare Eq. (1) below). A quantitative comparison of the INA dependence for samples located directly at the glass surface (h = 0) or at varying heights did not account well for the increase in the SNR. The measurements might be explained by other effects, e.g. by empty-aperture, for which high-order spherical aberrations lead to an effective loss of NA [38]. A non-uniform scattering field of small molecules like microtubules, which was recently utilized to improve iSCAT contrast [39,40], may also contribute to the effect even though the imaging NA was unchanged during our experiments.

IRM could distinguish between single and bundled microtubules. Some microtubules (e.g. Fig. 4D) showed a patchy IRM signal. In IRM, differences in the signal could occur due to height differences of the specimen or different mass for sub-diffraction-limited objects. In the former, changes in height typically occur gradually. In the latter, the signal changed in a stepwise fashion within the lateral resolution limit. The histogram of a line profile along the microtubule in Fig. 4D showed a discrete distribution. The discrete peaks suggests that several microtubules were bundled consistent with previous observations [41].

3.2. Quantitative 3D-IRM

To test whether the IRM signal can be used for precise 3D measurements of samples and calibration of the evanescent TIRF field, we used optical tweezers to bend a microtubule upward in a controlled and calibrated fashion [Fig. 5(A)]. To this end, we trapped a microsphere that was functionalized to bind microtubules (see Methods 2.2.2), attached the microsphere to a microtubule end, and pulled the microtubule end upward by displacing the optical trap in 200-nm vertical steps using the deformable mirror (Fig. 1). Since the other microtubule end was bound to the glass surface, the microtubule bent with increasing applied force. The increasing vertical position of the microtubule caused a phase change between the reference and scattered field and, therefore, an amplitude change of the IRM signal. With increasing optical trap heights, the microtubule IRM image showed black and white regions along its length characteristic for interference contrast methods [42]. To quantify this IRM amplitude change and microtubule deformation, we recorded the IRM and TIRF signals [Fig. 5(B)]. Subsequently, we measured the line-intensity profiles along the microtubule and determined its 3D profile, h(x) [Fig. 5(C) and (E)]. The microtubule height h(x) as a function of lateral position x is related to the IRM signal or intensity I(x) according to [21,43]

I(x)=BDsinyycos(2kh(x)[1sin2(α2)]),
where B is the background gray-level intensity, which—after background subtraction—should be close to zero, D is the peak-to-peak interference amplitude, k = 2πnw/λ is the wave number with the refractive index of water, nw, and the illumination wavelength, λ. The parameter y = 2kh(x) sin2 (α/2) models the objective’s point spread function, where α = arcsin (INA/nw) is the half angle of the INA cone. The interference amplitude D can also be related to the maximum iSCAT signal by D = 2srIinc, with Iinc being the incident intensity, r is the reflectivity given by the refractive index mismatch between the glass–water interface and s is the scattering amplitude [23]. The microtubule itself can be modeled as a cantilevered beam of length L = xtx0, where xt = 0 μm is the position of the trap and x0 is the position, at which the microtubule is attached to the surface. The beam equation in the small angle approximation is given by [44]
h(x)=A(xtx02(xx0)2(xx0)36),
where A = EI/F is the shape defining parameter given by the ratio of the flexural rigidity, i.e. the product of the elastic modulus E and the geometrical moment of inertia I, and the applied force F, which is provided by the optical trap.

 

Fig. 5 IRM and evanescent field calibration using bent microtubules. (A) Schematic drawing not to scale. A microsphere functionalized with non-motile kinesin-1–GFP motor proteins is trapped and attached to a loose microtubule end, which is pulled upward by the trap. (B) TIRF (red channel, left) and IRM images (right) of a bent microtubule and attached microsphere at increasing trap heights. Note that the bright intensity around the microsphere is due to scattering of the illumination light and not due to the trapping laser. The latter is blocked by an infrared filter. Scale bar: 2 μm. (C) IRM line profiles along the microtubule shown in B (symbols) and the global fit of Eq. (1) (solid lines). The trap height and axial force are indicated. For clarity, data points are offset vertically. (D) Weighted linear fit (dashed line) to the microtubule tip height hMT (circles) plotted versus the trap height htrap (error bars are SEM, gray lines). Inset: Calculated microtubule profile vs. height. (E) Fluorescence intensity line profiles along the microtubule shown in B for different tip heights. (F) Normalized fluorescence intensity line profiles (symbols). Profiles were normalized to the average intensity of the first 20 points and to the line profile at ht = 0.0 μm (shaded area and blue circles in E, respectively). A global fit (solid lines) of the data to Eq. (3) determined the depth of the evanescent field.

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A global nonlinear least-squares fit using Eqs. (1) and (2) to the microtubule IRM profiles [Fig. 5(C)] resulted in the height of the microtubule with respect to its lateral position along the microtubule axis. The best fit parameters are listed in Table 1. Because axial optical tweezers force measurements require significant background correction, which make small-force measurements unreliable in particular for large trap-surface variations [15,45], we estimated the force F that was acting on the microtubule based on its flexural rigidity of 20 × 10−24 Nm2 [44,46]. Equation (2) allowed us to determine the height of the microtubule tip hMT = h(xt) and the corresponding height profile of the microtubule [Fig. 5(D)]. A linear fit of the microtubule tip height hMT with respect to the height of the trap htrap showed the expected slope of unity and an offset of (−320 ± 10) nm. The offset roughly corresponds to the microsphere radius (≈295 nm) plus the linker size (≈35 nm). The axial displacement of the microsphere within the trap in the nanometer range was negligible compared to the tip height in the micrometer range. With the maximum force of Fz ≈ 0.8 pN and a trap stiffness κz in the vertical direction of (0.05 ± 0.01) pN/nm, the displacement was Δz = Fz/κz ≈ (16±4) nm. The agreement between the IRM-based microtubule tip height and predefined optical trap height confirms that the IRM signal can be used for quantitative 3D measurements.

Tables Icon

Table 1. Fit parameters of the global fit to the IRM and TIRF intensity profiles.

As a further quantitative control for the accuracy of the IRM-based height profiles, we tested whether the height profiles are consistent with the exponential decay of the TIRF field. In addition, we can use the profiles to measure the evanescent field depth. The TIRF intensity of the profiles [Fig. 5(B) and (E)] depend on both the fluorophore labeling density and the fluorophore height above the surface. To account for the inhomogeneous labeling and photo-bleaching, we normalized the TIRF intensity profiles [Fig. 5(F)]. The normalized profiles were consistent with an exponentially decreasing TIRF intensity ITIRF(x) with increasing distance from the glass–water interface

ITIRF(x)=exp[h(x)/δ],
where δ is the evanescent field depth. With the known shape of the microtubule, the decay of fluorescence intensity solely depends on the depth of the evanescent field, δ. A global fit of the normalized fluorescence intensity profiles to Eq. (3) with h = h(x, x0, A) and the evanescent field depth as common parameter resulted in δ = (165 ± 4) nm, which is in good agreement with our experimental design. In summary, the microtubule IRM signal quantitatively agreed in 3D with both the optical trap and TIRF-based height determination.

4. Conclusion

Using LED-IRM, we were able to measure the 3D profile of a single, isolated microtubule with high contrast and precision. To characterize the quality of the IRM signal, we developed a robust method to measure the SNR of a single microtubule. Our method accounts for overestimation of the microtubule signal due to contrast generating structures that might lie underneath the microtubule. It also accounts for overestimation of image noise by avoiding high-contrast signals in the residual image that result from other contrast generating structures. LED-IRM is limited by shot noise as the SNR scales with the light intensity and is, thus, limited by the electron well depth of the camera. The SNR of a single microtubule in one frame was about 5.6. This SNR is comparable to the one achieved with DIC (SNR ≈ 3.4 [2]). The value is also consistent with recent work using IRM in comparison to different microscopy techniques [29]. IRM interference fringes give information about the height of a specimen. Although the quantitative interpretation of the fringes, in general, is a non-trivial task, especially for arbitrary objects [43], in cases where the structure of interest is simple, such as a bent microtubule, it is possible to determine the axial position of an object and thus, the 3D profile with high precision on the order of a few tens of nanometers. This knowledge we used to determine the depth of the evanescent field of the TIRF microscope, thus, providing yet another method to characterize its excitation field [47].

LED-IRM is a cheap and simple, high-contrast 3D microscopy method. The method can be easily integrated into existing optical setups providing a viable alternative to commonly used microscopy techniques. LED-IRM does not require expensive nor complicated optical elements like lasers or polarizing optics. In particular for single-molecule force spectroscopy using optical tweezers, LED-IRM has considerable advantages compared to DIC microscopy. First, there is no trapping power loss—DIC prisms may reduce the trapping power in our case by up to 10 % per prism. Second, whereas the SNR of a microtubule is comparable to the one achieved in DIC [2], IRM outcompetes DIC with its simple optical design, cheap components and its orientation-independent contrast. Third, in contrast to DIC, IRM does not restrict the optical tweezers design to a linearly polarized trapping laser. Therefore, any polarization state like circularly polarized light is possible allowing the use of an optical microprotractor, torsion balance, or torque wrench [18,48]. Also, because IRM illumination and detection is done via the objective lens, the sample is in principle freely accessible from the top for other manipulation or imaging techniques. For free upper access in our combination of IRM with optical tweezers, position detection would have to be implemented in reflection [49,50]. Furthermore, LED-based illumination provides long-term intensity stability, if a sufficiently stable power supply and heat sink are used. In contrast to laser-based illumination, where long coherence lengths can cause etalon fringes, i.e. “unwanted” interference effects, light emitted from a LED had a coherence length of λ2λ ≈ 10 μm. This short coherence length prevents long-range interference between reflected rays, which could compromise the reference field and degrade the measurable IRM signal. In comparison to most iSCAT implementations, IRM provides a larger field of view limited by the size of the camera chip and not the scan range of the laser. Our SNR was limited by contrast-generating structures on the glass surface to a SNR of about 17 for a single microtubule when averaging 100 frames. Increasing the LED power, frame rate, and using a dynamic background subtraction provides avenues for further improvement in contrast.

Funding

Deutsche Forschungsgemeinschaft (DFG; Emmy Noether Program and CRC 1101, Project A04); European Research Council (ERC Starting Grant 2010, Nanomech 260875); Technische Universität Dresden; and Universität Tübingen.

Acknowledgments

The authors thank U. Rothbauer for providing the GFP-binding protein and M. Bugiel, A. Jannasch, M. Mahamdeh and Q.T. Davis for discussions and critical reading of the manuscript. This work was done by use of free and open software. S.S. wants to acknowledge the following projects in particular: Python [51], Scipy [52], matplotlib [53] and lmfit [54].

Contributions

S.S. designed, constructed, and assembled the instrument, prepared samples for the SNR measurements and performed all experiments. M.K.A. prepared the quantitative IRM experiments, i.e. functionalization of microspheres and the flow cell preparation. G.H. helped in the design and assembly of the TIRF microscope. S.S. and E.S. conceived and designed the experiments, analyzed the data, and wrote the manuscript.

References and links

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2. V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007). [CrossRef]   [PubMed]  

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

4. L. Kong, P. Zhang, P. Setlow, and Y.-Q. Li, “Characterization of Bacterial Spore Germination Using Integrated Phase Contrast Microscopy, Raman Spectroscopy, and Optical Tweezers,” Anal. Chem. 82, 3840–3847 (2010). [CrossRef]   [PubMed]  

5. I. Fedosov, “Particle image velocimetry for visualizing laser-induced motion of nanoparticles,” SPIE Newsroom pp. 8–10 (2007).

6. M. D. Koch and A. Rohrbach, “Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping,” Biophys. J. 114, 168–177 (2018). [CrossRef]   [PubMed]  

7. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef]   [PubMed]  

8. M. J. Lang, P. M. Fordyce, and S. M. Block, “Combined optical trapping and single-molecule fluorescence,” J. Biol. 2, 6 (2003). [CrossRef]   [PubMed]  

9. M. J. Comstock, T. Ha, and Y. R. Chemla, “Ultrahigh-resolution optical trap with single-fluorophore sensitivity,” Nat. Methods 8, 335–340 (2011). [CrossRef]   [PubMed]  

10. K. Visscher, G. J. Brakenhoff, and J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993). [CrossRef]  

11. I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013). [CrossRef]   [PubMed]  

12. B. Gutiérrez-Medina and S. M. Block, “Visualizing individual microtubules by bright field microscopy,” Am. J. Phys. 78, 1152 (2010). [CrossRef]  

13. R. A. Walker, E. T. O’Brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon, “Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies,” J. Cell Biol. 107, 1437–1448 (1988). [CrossRef]   [PubMed]  

14. M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469 (2006). [CrossRef]   [PubMed]  

15. V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008). [CrossRef]   [PubMed]  

16. M. Bugiel, A. Jannasch, and E. Schäffer, “Implementation and tuning of an optical tweezers force-clamp feedback system,” Methods Mol. Biol. 1486, 109–136 (2017). [CrossRef]  

17. M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018). [CrossRef]   [PubMed]  

18. A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017). [PubMed]  

19. A. S. G. Curtis, “A Study by Interference Reflection Microscopy,” J. Cell Biol. 20, 199–215 (1964). [CrossRef]   [PubMed]  

20. J. Ploem, “Reflection-contrast microscopy as tool for investigation of the attachment of living cells to a glass surface,” in “Mononuclear Phagocytes In Immunity Infection Pathology,”, R. Van Furth, ed. (Blackwell Scientific, 1975), pp. 405–421.

21. J. Rädler and E. Sackmann, “Imaging optical thicknesses and separation distances of phospholipid vesicles at solid surfaces,” J. Phys. II France 3, 727–748 (1993). [CrossRef]  

22. K. Kim and O. A. Saleh, “Stabilizing method for reflection interference contrast microscopy,” Appl. Opt. 47, 2070–2075 (2008). [CrossRef]   [PubMed]  

23. V. Jacobsen, P. Stoller, C. Brunner, V. Vogel, and V. Sandoghdar, “Interferometric optical detection and tracking of very small gold nanoparticles at a water-glass interface,” Opt. Express 14, 405–414 (2006). [CrossRef]   [PubMed]  

24. J. Ortega-Arroyo and P. Kukura, “Interferometric scattering microscopy (iSCAT): new frontiers in ultrafast and ultrasensitive optical microscopy,” Phys. Chem. Chem. Phys. 14, 15625–15636 (2012). [CrossRef]   [PubMed]  

25. J. Ortega Arroyo, J. Andrecka, K. M. Spillane, N. Billington, Y. Takagi, J. R. Sellers, and P. Kukura, “Label-free, all-optical detection, imaging, and tracking of a single protein,” Nano Lett. 14, 2065–2070 (2014). [CrossRef]   [PubMed]  

26. M. Piliarik and V. Sandoghdar, “Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites,” Nat. Commun. 5, 1–8 (2014). [CrossRef]  

27. L. A. Amos and W. B. Amos, “The bending of sliding microtubules imaged by confocal light microscopy and negative stain electron microscopy,” J. Cell Sci. Suppl. 14, 95–101 (1991). [CrossRef]  

28. J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016). [CrossRef]   [PubMed]  

29. M. Mahamdeh, S. Simmert, A. Luchniak, E. Schaeffer, and J. Howard, “Label-free high-speed wide-field imaging of single microtubules using interference reflection microscopy,” bioRxiv (2018). DOI: https://doi.org/10.1101/273086.

30. Y. Huang, J. Wan, M. C. Cheng, Z. Zhang, S. M. Jhiang, and C. H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 1–8 (2009). [CrossRef]  

31. M. Mahamdeh, C. P. Campos, and E. Schäffer, “Under-filling trapping objectives optimizes the use of the available laser power in optical tweezers,” Opt. Express 19, 11759–11768 (2011). [CrossRef]   [PubMed]  

32. L. J. Friedman, J. Chung, and J. Gelles, “Viewing dynamic assembly of molecular complexes by multi-wavelength single-molecule fluorescence,” Biophys. J. 91, 1023–1031 (2006). [CrossRef]   [PubMed]  

33. C. Jiang, N. Kaul, J. Campbell, and E. Meyhofer, “A novel dual-color bifocal imaging system for single-molecule studies,” Rev. Sci. Instrum. 88, 053705 (2017). [CrossRef]   [PubMed]  

34. M. Castoldi and A. V. Popov, “Purification of brain tubulin through two cycles of polymerization–depolymerization in a high-molarity buffer,” Protein Expr. Purif. 32, 83– 88 (2003). [CrossRef]   [PubMed]  

35. M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015). [CrossRef]  

36. U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008). [CrossRef]  

37. J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012). [CrossRef]   [PubMed]  

38. R. Juškaitis, “Measuring the real point spread function of high numerical aperture microscope objective lenses,” in “Handb. Biol. Confocal Microsc.”, (SpringerUS, 2006), book section 11, pp. 239–250.

39. K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011). [CrossRef]  

40. M. Liebel, J. T. Hugall, and N. F. van Hulst, “Ultrasensitive label-free nanosensing and high-speed tracking of single proteins,” Nano Lett. 17, 1277–1281 (2017). [CrossRef]   [PubMed]  

41. R. Oldenbourg, E. Salmon, and P. Tran, “Birefringence of Single and Bundled Microtubules,” Biophys. J. 74, 645–654 (1998). [CrossRef]   [PubMed]  

42. J. Kerssemakers, J. Howard, H. Hess, and S. Diez, “The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy,” Proc. Natl. Acad. Sci. U. S. A. 103, 15812 (2006). [CrossRef]   [PubMed]  

43. L. Limozin and K. Sengupta, “Quantitative Reflection Interference Contrast Microscopy (RICM) in Soft Matter and Cell Adhesion,” ChemPhysChem 10, 2752–2768 (2009). [CrossRef]   [PubMed]  

44. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Associates, Inc., 2001).

45. E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007). [CrossRef]   [PubMed]  

46. F. Gittes, B. Mickey, J. Nettleton, and J. Howard, “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape,” J. Cell Biol. 120, 923–934 (1993). [CrossRef]   [PubMed]  

47. C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009). [CrossRef]   [PubMed]  

48. A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004). [CrossRef]   [PubMed]  

49. 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, 7112–7116 (1996). [CrossRef]   [PubMed]  

50. A. Sischka, C. Kleimann, W. Hachmann, M. M. Schäfer, I. Seuffert, K. Tönsing, and D. Anselmetti, “Single beam optical tweezers setup with backscattered light detection for three-dimensional measurements on dna and nanopores,” Rev. Sci. Instrum. 79, 063702 (2008). [CrossRef]   [PubMed]  

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References

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  1. A. Gennerich, Optical Tweezers: Methods and Protocols, vol. 1486 of Methods Mol. Biol. (Springer, 2017).
    [Crossref]
  2. V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
    [Crossref] [PubMed]
  3. M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17, 17190–17199 (2009).
    [Crossref] [PubMed]
  4. L. Kong, P. Zhang, P. Setlow, and Y.-Q. Li, “Characterization of Bacterial Spore Germination Using Integrated Phase Contrast Microscopy, Raman Spectroscopy, and Optical Tweezers,” Anal. Chem. 82, 3840–3847 (2010).
    [Crossref] [PubMed]
  5. I. Fedosov, “Particle image velocimetry for visualizing laser-induced motion of nanoparticles,” SPIE Newsroom pp. 8–10 (2007).
  6. M. D. Koch and A. Rohrbach, “Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping,” Biophys. J. 114, 168–177 (2018).
    [Crossref] [PubMed]
  7. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [Crossref] [PubMed]
  8. M. J. Lang, P. M. Fordyce, and S. M. Block, “Combined optical trapping and single-molecule fluorescence,” J. Biol. 2, 6 (2003).
    [Crossref] [PubMed]
  9. M. J. Comstock, T. Ha, and Y. R. Chemla, “Ultrahigh-resolution optical trap with single-fluorophore sensitivity,” Nat. Methods 8, 335–340 (2011).
    [Crossref] [PubMed]
  10. K. Visscher, G. J. Brakenhoff, and J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
    [Crossref]
  11. I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013).
    [Crossref] [PubMed]
  12. B. Gutiérrez-Medina and S. M. Block, “Visualizing individual microtubules by bright field microscopy,” Am. J. Phys. 78, 1152 (2010).
    [Crossref]
  13. R. A. Walker, E. T. O’Brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon, “Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies,” J. Cell Biol. 107, 1437–1448 (1988).
    [Crossref] [PubMed]
  14. M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469 (2006).
    [Crossref] [PubMed]
  15. V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
    [Crossref] [PubMed]
  16. M. Bugiel, A. Jannasch, and E. Schäffer, “Implementation and tuning of an optical tweezers force-clamp feedback system,” Methods Mol. Biol. 1486, 109–136 (2017).
    [Crossref]
  17. M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
    [Crossref] [PubMed]
  18. A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017).
    [PubMed]
  19. A. S. G. Curtis, “A Study by Interference Reflection Microscopy,” J. Cell Biol. 20, 199–215 (1964).
    [Crossref] [PubMed]
  20. J. Ploem, “Reflection-contrast microscopy as tool for investigation of the attachment of living cells to a glass surface,” in “Mononuclear Phagocytes In Immunity Infection Pathology,”, R. Van Furth, ed. (Blackwell Scientific, 1975), pp. 405–421.
  21. J. Rädler and E. Sackmann, “Imaging optical thicknesses and separation distances of phospholipid vesicles at solid surfaces,” J. Phys. II France 3, 727–748 (1993).
    [Crossref]
  22. K. Kim and O. A. Saleh, “Stabilizing method for reflection interference contrast microscopy,” Appl. Opt. 47, 2070–2075 (2008).
    [Crossref] [PubMed]
  23. V. Jacobsen, P. Stoller, C. Brunner, V. Vogel, and V. Sandoghdar, “Interferometric optical detection and tracking of very small gold nanoparticles at a water-glass interface,” Opt. Express 14, 405–414 (2006).
    [Crossref] [PubMed]
  24. J. Ortega-Arroyo and P. Kukura, “Interferometric scattering microscopy (iSCAT): new frontiers in ultrafast and ultrasensitive optical microscopy,” Phys. Chem. Chem. Phys. 14, 15625–15636 (2012).
    [Crossref] [PubMed]
  25. J. Ortega Arroyo, J. Andrecka, K. M. Spillane, N. Billington, Y. Takagi, J. R. Sellers, and P. Kukura, “Label-free, all-optical detection, imaging, and tracking of a single protein,” Nano Lett. 14, 2065–2070 (2014).
    [Crossref] [PubMed]
  26. M. Piliarik and V. Sandoghdar, “Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites,” Nat. Commun. 5, 1–8 (2014).
    [Crossref]
  27. L. A. Amos and W. B. Amos, “The bending of sliding microtubules imaged by confocal light microscopy and negative stain electron microscopy,” J. Cell Sci. Suppl. 14, 95–101 (1991).
    [Crossref]
  28. J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016).
    [Crossref] [PubMed]
  29. M. Mahamdeh, S. Simmert, A. Luchniak, E. Schaeffer, and J. Howard, “Label-free high-speed wide-field imaging of single microtubules using interference reflection microscopy,” bioRxiv (2018). DOI: https://doi.org/10.1101/273086 .
  30. Y. Huang, J. Wan, M. C. Cheng, Z. Zhang, S. M. Jhiang, and C. H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 1–8 (2009).
    [Crossref]
  31. M. Mahamdeh, C. P. Campos, and E. Schäffer, “Under-filling trapping objectives optimizes the use of the available laser power in optical tweezers,” Opt. Express 19, 11759–11768 (2011).
    [Crossref] [PubMed]
  32. L. J. Friedman, J. Chung, and J. Gelles, “Viewing dynamic assembly of molecular complexes by multi-wavelength single-molecule fluorescence,” Biophys. J. 91, 1023–1031 (2006).
    [Crossref] [PubMed]
  33. C. Jiang, N. Kaul, J. Campbell, and E. Meyhofer, “A novel dual-color bifocal imaging system for single-molecule studies,” Rev. Sci. Instrum. 88, 053705 (2017).
    [Crossref] [PubMed]
  34. M. Castoldi and A. V. Popov, “Purification of brain tubulin through two cycles of polymerization–depolymerization in a high-molarity buffer,” Protein Expr. Purif. 32, 83– 88 (2003).
    [Crossref] [PubMed]
  35. M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
    [Crossref]
  36. U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
    [Crossref]
  37. J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
    [Crossref] [PubMed]
  38. R. Juškaitis, “Measuring the real point spread function of high numerical aperture microscope objective lenses,” in “Handb. Biol. Confocal Microsc.”, (SpringerUS, 2006), book section 11, pp. 239–250.
  39. K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
    [Crossref]
  40. M. Liebel, J. T. Hugall, and N. F. van Hulst, “Ultrasensitive label-free nanosensing and high-speed tracking of single proteins,” Nano Lett. 17, 1277–1281 (2017).
    [Crossref] [PubMed]
  41. R. Oldenbourg, E. Salmon, and P. Tran, “Birefringence of Single and Bundled Microtubules,” Biophys. J. 74, 645–654 (1998).
    [Crossref] [PubMed]
  42. J. Kerssemakers, J. Howard, H. Hess, and S. Diez, “The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy,” Proc. Natl. Acad. Sci. U. S. A. 103, 15812 (2006).
    [Crossref] [PubMed]
  43. L. Limozin and K. Sengupta, “Quantitative Reflection Interference Contrast Microscopy (RICM) in Soft Matter and Cell Adhesion,” ChemPhysChem 10, 2752–2768 (2009).
    [Crossref] [PubMed]
  44. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Associates, Inc., 2001).
  45. E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
    [Crossref] [PubMed]
  46. F. Gittes, B. Mickey, J. Nettleton, and J. Howard, “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape,” J. Cell Biol. 120, 923–934 (1993).
    [Crossref] [PubMed]
  47. C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009).
    [Crossref] [PubMed]
  48. A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
    [Crossref] [PubMed]
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2018 (2)

M. D. Koch and A. Rohrbach, “Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping,” Biophys. J. 114, 168–177 (2018).
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M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
[Crossref] [PubMed]

2017 (4)

A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017).
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M. Bugiel, A. Jannasch, and E. Schäffer, “Implementation and tuning of an optical tweezers force-clamp feedback system,” Methods Mol. Biol. 1486, 109–136 (2017).
[Crossref]

C. Jiang, N. Kaul, J. Campbell, and E. Meyhofer, “A novel dual-color bifocal imaging system for single-molecule studies,” Rev. Sci. Instrum. 88, 053705 (2017).
[Crossref] [PubMed]

M. Liebel, J. T. Hugall, and N. F. van Hulst, “Ultrasensitive label-free nanosensing and high-speed tracking of single proteins,” Nano Lett. 17, 1277–1281 (2017).
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2016 (1)

J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016).
[Crossref] [PubMed]

2015 (1)

M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
[Crossref]

2014 (2)

J. Ortega Arroyo, J. Andrecka, K. M. Spillane, N. Billington, Y. Takagi, J. R. Sellers, and P. Kukura, “Label-free, all-optical detection, imaging, and tracking of a single protein,” Nano Lett. 14, 2065–2070 (2014).
[Crossref] [PubMed]

M. Piliarik and V. Sandoghdar, “Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites,” Nat. Commun. 5, 1–8 (2014).
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2013 (1)

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013).
[Crossref] [PubMed]

2012 (2)

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[Crossref] [PubMed]

J. Ortega-Arroyo and P. Kukura, “Interferometric scattering microscopy (iSCAT): new frontiers in ultrafast and ultrasensitive optical microscopy,” Phys. Chem. Chem. Phys. 14, 15625–15636 (2012).
[Crossref] [PubMed]

2011 (3)

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
[Crossref]

M. Mahamdeh, C. P. Campos, and E. Schäffer, “Under-filling trapping objectives optimizes the use of the available laser power in optical tweezers,” Opt. Express 19, 11759–11768 (2011).
[Crossref] [PubMed]

M. J. Comstock, T. Ha, and Y. R. Chemla, “Ultrahigh-resolution optical trap with single-fluorophore sensitivity,” Nat. Methods 8, 335–340 (2011).
[Crossref] [PubMed]

2010 (2)

L. Kong, P. Zhang, P. Setlow, and Y.-Q. Li, “Characterization of Bacterial Spore Germination Using Integrated Phase Contrast Microscopy, Raman Spectroscopy, and Optical Tweezers,” Anal. Chem. 82, 3840–3847 (2010).
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B. Gutiérrez-Medina and S. M. Block, “Visualizing individual microtubules by bright field microscopy,” Am. J. Phys. 78, 1152 (2010).
[Crossref]

2009 (4)

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

Y. Huang, J. Wan, M. C. Cheng, Z. Zhang, S. M. Jhiang, and C. H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 1–8 (2009).
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L. Limozin and K. Sengupta, “Quantitative Reflection Interference Contrast Microscopy (RICM) in Soft Matter and Cell Adhesion,” ChemPhysChem 10, 2752–2768 (2009).
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C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009).
[Crossref] [PubMed]

2008 (4)

A. Sischka, C. Kleimann, W. Hachmann, M. M. Schäfer, I. Seuffert, K. Tönsing, and D. Anselmetti, “Single beam optical tweezers setup with backscattered light detection for three-dimensional measurements on dna and nanopores,” Rev. Sci. Instrum. 79, 063702 (2008).
[Crossref] [PubMed]

K. Kim and O. A. Saleh, “Stabilizing method for reflection interference contrast microscopy,” Appl. Opt. 47, 2070–2075 (2008).
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U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
[Crossref]

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[Crossref] [PubMed]

2007 (3)

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[Crossref] [PubMed]

J. D. Hunter, “Matplotlib: A 2D graphics environment,” Comput. Sci. Eng. 9, 90–95 (2007).
[Crossref]

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[Crossref] [PubMed]

2006 (4)

J. Kerssemakers, J. Howard, H. Hess, and S. Diez, “The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy,” Proc. Natl. Acad. Sci. U. S. A. 103, 15812 (2006).
[Crossref] [PubMed]

M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469 (2006).
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V. Jacobsen, P. Stoller, C. Brunner, V. Vogel, and V. Sandoghdar, “Interferometric optical detection and tracking of very small gold nanoparticles at a water-glass interface,” Opt. Express 14, 405–414 (2006).
[Crossref] [PubMed]

L. J. Friedman, J. Chung, and J. Gelles, “Viewing dynamic assembly of molecular complexes by multi-wavelength single-molecule fluorescence,” Biophys. J. 91, 1023–1031 (2006).
[Crossref] [PubMed]

2004 (1)

A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[Crossref] [PubMed]

2003 (2)

M. Castoldi and A. V. Popov, “Purification of brain tubulin through two cycles of polymerization–depolymerization in a high-molarity buffer,” Protein Expr. Purif. 32, 83– 88 (2003).
[Crossref] [PubMed]

M. J. Lang, P. M. Fordyce, and S. M. Block, “Combined optical trapping and single-molecule fluorescence,” J. Biol. 2, 6 (2003).
[Crossref] [PubMed]

1998 (1)

R. Oldenbourg, E. Salmon, and P. Tran, “Birefringence of Single and Bundled Microtubules,” Biophys. J. 74, 645–654 (1998).
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1996 (1)

1993 (3)

F. Gittes, B. Mickey, J. Nettleton, and J. Howard, “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape,” J. Cell Biol. 120, 923–934 (1993).
[Crossref] [PubMed]

K. Visscher, G. J. Brakenhoff, and J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
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J. Rädler and E. Sackmann, “Imaging optical thicknesses and separation distances of phospholipid vesicles at solid surfaces,” J. Phys. II France 3, 727–748 (1993).
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1991 (1)

L. A. Amos and W. B. Amos, “The bending of sliding microtubules imaged by confocal light microscopy and negative stain electron microscopy,” J. Cell Sci. Suppl. 14, 95–101 (1991).
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1988 (1)

R. A. Walker, E. T. O’Brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon, “Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies,” J. Cell Biol. 107, 1437–1448 (1988).
[Crossref] [PubMed]

1986 (1)

1964 (1)

A. S. G. Curtis, “A Study by Interference Reflection Microscopy,” J. Cell Biol. 20, 199–215 (1964).
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Amos, L. A.

L. A. Amos and W. B. Amos, “The bending of sliding microtubules imaged by confocal light microscopy and negative stain electron microscopy,” J. Cell Sci. Suppl. 14, 95–101 (1991).
[Crossref]

Amos, W. B.

L. A. Amos and W. B. Amos, “The bending of sliding microtubules imaged by confocal light microscopy and negative stain electron microscopy,” J. Cell Sci. Suppl. 14, 95–101 (1991).
[Crossref]

Ander, M.

Andrecka, J.

J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016).
[Crossref] [PubMed]

J. Ortega Arroyo, J. Andrecka, K. M. Spillane, N. Billington, Y. Takagi, J. R. Sellers, and P. Kukura, “Label-free, all-optical detection, imaging, and tracking of a single protein,” Nano Lett. 14, 2065–2070 (2014).
[Crossref] [PubMed]

Anselmetti, D.

A. Sischka, C. Kleimann, W. Hachmann, M. M. Schäfer, I. Seuffert, K. Tönsing, and D. Anselmetti, “Single beam optical tweezers setup with backscattered light detection for three-dimensional measurements on dna and nanopores,” Rev. Sci. Instrum. 79, 063702 (2008).
[Crossref] [PubMed]

Arganda-Carreras, I.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[Crossref] [PubMed]

Ashkin, A.

Berndt, M.

C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009).
[Crossref] [PubMed]

Billington, N.

J. Ortega Arroyo, J. Andrecka, K. M. Spillane, N. Billington, Y. Takagi, J. R. Sellers, and P. Kukura, “Label-free, all-optical detection, imaging, and tracking of a single protein,” Nano Lett. 14, 2065–2070 (2014).
[Crossref] [PubMed]

Bjorkholm, J. E.

Block, S. M.

B. Gutiérrez-Medina and S. M. Block, “Visualizing individual microtubules by bright field microscopy,” Am. J. Phys. 78, 1152 (2010).
[Crossref]

M. J. Lang, P. M. Fordyce, and S. M. Block, “Combined optical trapping and single-molecule fluorescence,” J. Biol. 2, 6 (2003).
[Crossref] [PubMed]

Bormuth, V.

M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
[Crossref]

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[Crossref] [PubMed]

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[Crossref] [PubMed]

Brakenhoff, G. J.

K. Visscher, G. J. Brakenhoff, and J. J. Krol, “Micromanipulation by “multiple” optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,” Cytometry 14, 105–114 (1993).
[Crossref]

Broekmans, O. D.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013).
[Crossref] [PubMed]

Brunner, C.

Bugiel, M.

M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
[Crossref] [PubMed]

A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017).
[PubMed]

M. Bugiel, A. Jannasch, and E. Schäffer, “Implementation and tuning of an optical tweezers force-clamp feedback system,” Methods Mol. Biol. 1486, 109–136 (2017).
[Crossref]

M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
[Crossref]

Campbell, J.

C. Jiang, N. Kaul, J. Campbell, and E. Meyhofer, “A novel dual-color bifocal imaging system for single-molecule studies,” Rev. Sci. Instrum. 88, 053705 (2017).
[Crossref] [PubMed]

Campos, C. P.

Cardona, A.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[Crossref] [PubMed]

Cardoso, M. C.

U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
[Crossref]

Castoldi, M.

M. Castoldi and A. V. Popov, “Purification of brain tubulin through two cycles of polymerization–depolymerization in a high-molarity buffer,” Protein Expr. Purif. 32, 83– 88 (2003).
[Crossref] [PubMed]

Chemla, Y. R.

M. J. Comstock, T. Ha, and Y. R. Chemla, “Ultrahigh-resolution optical trap with single-fluorophore sensitivity,” Nat. Methods 8, 335–340 (2011).
[Crossref] [PubMed]

Chen, X. W.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
[Crossref]

Cheng, M. C.

Y. Huang, J. Wan, M. C. Cheng, Z. Zhang, S. M. Jhiang, and C. H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 1–8 (2009).
[Crossref]

Chu, S.

Chung, J.

L. J. Friedman, J. Chung, and J. Gelles, “Viewing dynamic assembly of molecular complexes by multi-wavelength single-molecule fluorescence,” Biophys. J. 91, 1023–1031 (2006).
[Crossref] [PubMed]

Comstock, M. J.

M. J. Comstock, T. Ha, and Y. R. Chemla, “Ultrahigh-resolution optical trap with single-fluorophore sensitivity,” Nat. Methods 8, 335–340 (2011).
[Crossref] [PubMed]

Cross, R.

J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016).
[Crossref] [PubMed]

Curtis, A. S. G.

A. S. G. Curtis, “A Study by Interference Reflection Microscopy,” J. Cell Biol. 20, 199–215 (1964).
[Crossref] [PubMed]

Dearden, E. W.

Diez, S.

M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
[Crossref] [PubMed]

C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009).
[Crossref] [PubMed]

J. Kerssemakers, J. Howard, H. Hess, and S. Diez, “The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy,” Proc. Natl. Acad. Sci. U. S. A. 103, 15812 (2006).
[Crossref] [PubMed]

Dziedzic, J. M.

Eghlidi, H.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
[Crossref]

Eliceiri, K.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[Crossref] [PubMed]

Enderlein, J.

C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009).
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R. A. Walker, E. T. O’Brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon, “Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies,” J. Cell Biol. 107, 1437–1448 (1988).
[Crossref] [PubMed]

Fantana, H.

M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
[Crossref]

Farge, G.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013).
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M. J. Lang, P. M. Fordyce, and S. M. Block, “Combined optical trapping and single-molecule fluorescence,” J. Biol. 2, 6 (2003).
[Crossref] [PubMed]

Friedman, L. J.

L. J. Friedman, J. Chung, and J. Gelles, “Viewing dynamic assembly of molecular complexes by multi-wavelength single-molecule fluorescence,” Biophys. J. 91, 1023–1031 (2006).
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Frise, E.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
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Gell, C.

C. Gell, M. Berndt, J. Enderlein, and S. Diez, “TIRF microscopy evanescent field calibration using tilted fluorescent microtubules,” J. Microsc. 234, 38–46 (2009).
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Gelles, J.

L. J. Friedman, J. Chung, and J. Gelles, “Viewing dynamic assembly of molecular complexes by multi-wavelength single-molecule fluorescence,” Biophys. J. 91, 1023–1031 (2006).
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M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
[Crossref] [PubMed]

Gittes, F.

F. Gittes, B. Mickey, J. Nettleton, and J. Howard, “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape,” J. Cell Biol. 120, 923–934 (1993).
[Crossref] [PubMed]

Götzinger, S.

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
[Crossref]

Gutiérrez-Medina, B.

B. Gutiérrez-Medina and S. M. Block, “Visualizing individual microtubules by bright field microscopy,” Am. J. Phys. 78, 1152 (2010).
[Crossref]

Ha, T.

M. J. Comstock, T. Ha, and Y. R. Chemla, “Ultrahigh-resolution optical trap with single-fluorophore sensitivity,” Nat. Methods 8, 335–340 (2011).
[Crossref] [PubMed]

Hachmann, W.

A. Sischka, C. Kleimann, W. Hachmann, M. M. Schäfer, I. Seuffert, K. Tönsing, and D. Anselmetti, “Single beam optical tweezers setup with backscattered light detection for three-dimensional measurements on dna and nanopores,” Rev. Sci. Instrum. 79, 063702 (2008).
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Hartenstein, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
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J. Kerssemakers, J. Howard, H. Hess, and S. Diez, “The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy,” Proc. Natl. Acad. Sci. U. S. A. 103, 15812 (2006).
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Y. Huang, J. Wan, M. C. Cheng, Z. Zhang, S. M. Jhiang, and C. H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 1–8 (2009).
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M. D. Koch and A. Rohrbach, “Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping,” Biophys. J. 114, 168–177 (2018).
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U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
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J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016).
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M. Liebel, J. T. Hugall, and N. F. van Hulst, “Ultrasensitive label-free nanosensing and high-speed tracking of single proteins,” Nano Lett. 17, 1277–1281 (2017).
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M. Mahamdeh, S. Simmert, A. Luchniak, E. Schaeffer, and J. Howard, “Label-free high-speed wide-field imaging of single microtubules using interference reflection microscopy,” bioRxiv (2018). DOI: https://doi.org/10.1101/273086 .

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Menges, C.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013).
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Y. Huang, J. Wan, M. C. Cheng, Z. Zhang, S. M. Jhiang, and C. H. Menq, “Three-axis rapid steering of optically propelled micro/nanoparticles,” Rev. Sci. Instrum. 80, 1–8 (2009).
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C. Jiang, N. Kaul, J. Campbell, and E. Meyhofer, “A novel dual-color bifocal imaging system for single-molecule studies,” Rev. Sci. Instrum. 88, 053705 (2017).
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F. Gittes, B. Mickey, J. Nettleton, and J. Howard, “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape,” J. Cell Biol. 120, 923–934 (1993).
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M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
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U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
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F. Gittes, B. Mickey, J. Nettleton, and J. Howard, “Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape,” J. Cell Biol. 120, 923–934 (1993).
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E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
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J. Andrecka, J. Ortega Arroyo, K. Lewis, R. Cross, and P. Kukura, “Label-free imaging of microtubules with sub-nm precision using interferometric scattering microscopy,” Biophys. J. 110, 214–217 (2016).
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J. Ortega-Arroyo and P. Kukura, “Interferometric scattering microscopy (iSCAT): new frontiers in ultrafast and ultrasensitive optical microscopy,” Phys. Chem. Chem. Phys. 14, 15625–15636 (2012).
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I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10, 910–916 (2013).
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R. A. Walker, E. T. O’Brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon, “Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies,” J. Cell Biol. 107, 1437–1448 (1988).
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A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017).
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K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
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M. D. Koch and A. Rohrbach, “Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping,” Biophys. J. 114, 168–177 (2018).
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Rothbauer, U.

U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
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A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017).
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Rueden, C.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
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J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
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J. Rädler and E. Sackmann, “Imaging optical thicknesses and separation distances of phospholipid vesicles at solid surfaces,” J. Phys. II France 3, 727–748 (1993).
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Salmon, E.

R. Oldenbourg, E. Salmon, and P. Tran, “Birefringence of Single and Bundled Microtubules,” Biophys. J. 74, 645–654 (1998).
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Salmon, E. D.

R. A. Walker, E. T. O’Brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P. Erickson, and E. D. Salmon, “Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies,” J. Cell Biol. 107, 1437–1448 (1988).
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Sandoghdar, V.

M. Piliarik and V. Sandoghdar, “Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites,” Nat. Commun. 5, 1–8 (2014).
[Crossref]

K. G. Lee, X. W. Chen, H. Eghlidi, P. Kukura, R. Lettow, A. Renn, V. Sandoghdar, and S. Götzinger, “A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency,” Nat. Photonics 5, 166 (2011).
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M. Mahamdeh, S. Simmert, A. Luchniak, E. Schaeffer, and J. Howard, “Label-free high-speed wide-field imaging of single microtubules using interference reflection microscopy,” bioRxiv (2018). DOI: https://doi.org/10.1101/273086 .

Schäfer, M. M.

A. Sischka, C. Kleimann, W. Hachmann, M. M. Schäfer, I. Seuffert, K. Tönsing, and D. Anselmetti, “Single beam optical tweezers setup with backscattered light detection for three-dimensional measurements on dna and nanopores,” Rev. Sci. Instrum. 79, 063702 (2008).
[Crossref] [PubMed]

Schäffer, E.

M. Bugiel, A. Mitra, S. Girardo, S. Diez, and E. Schäffer, “Measuring microtubule supertwist and defects by three-dimensional-force-clamp tracking of single kinesin-1 motors,” Nano Lett. 18, 1290–1295 (2018).
[Crossref] [PubMed]

A. Ramaiya, B. Roy, M. Bugiel, and E. Schäffer, “Kinesin rotates unidirectionally and generates torque while walking on microtubules,” Proc. Natl. Acad. Sci. U. S. A. 114, 10894–10899 (2017).
[PubMed]

M. Bugiel, A. Jannasch, and E. Schäffer, “Implementation and tuning of an optical tweezers force-clamp feedback system,” Methods Mol. Biol. 1486, 109–136 (2017).
[Crossref]

M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
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M. Mahamdeh, C. P. Campos, and E. Schäffer, “Under-filling trapping objectives optimizes the use of the available laser power in optical tweezers,” Opt. Express 19, 11759–11768 (2011).
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M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17, 17190–17199 (2009).
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V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[Crossref] [PubMed]

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[Crossref] [PubMed]

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[Crossref] [PubMed]

Schepers, A.

U. Rothbauer, K. Zolghadr, S. Muyldermans, A. Schepers, M. C. Cardoso, and H. Leonhardt, “A versatile nanotrap for biochemical and functional studies with fluorescent fusion proteins,” Mol. Cell. Proteomics 7, 282–289 (2008).
[Crossref]

Schiemann, F.

M. Bugiel, H. Fantana, V. Bormuth, F. Schiemann, J. Howard, E. Schäffer, and A. Jannasch, “Versatile microsphere attachment of GFP-labeled proteins with preserved functionality Microsphere preparation,” J. Biol. Methods 2, 1–12 (2015).
[Crossref]

Schindelin, J.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
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Schmid, B.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
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Sellers, J. R.

J. Ortega Arroyo, J. Andrecka, K. M. Spillane, N. Billington, Y. Takagi, J. R. Sellers, and P. Kukura, “Label-free, all-optical detection, imaging, and tracking of a single protein,” Nano Lett. 14, 2065–2070 (2014).
[Crossref] [PubMed]

Sengupta, K.

L. Limozin and K. Sengupta, “Quantitative Reflection Interference Contrast Microscopy (RICM) in Soft Matter and Cell Adhesion,” ChemPhysChem 10, 2752–2768 (2009).
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A. Sischka, C. Kleimann, W. Hachmann, M. M. Schäfer, I. Seuffert, K. Tönsing, and D. Anselmetti, “Single beam optical tweezers setup with backscattered light detection for three-dimensional measurements on dna and nanopores,” Rev. Sci. Instrum. 79, 063702 (2008).
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Figures (5)

Fig. 1
Fig. 1 Schematic of the combined IRM–TIRF-microscope–optical-tweezers setup.
Fig. 2
Fig. 2 Schematic of the IRM design and principle. The optical path is drawn to scale and shows the marginal rays of the LED (blue lines), the sample (black lines), and the field iris (dashed gray lines). The inset shows the principle of the IRM contrast formation. The incident light of the Köhler-illuminated sample, here a microtubule, is reflected from the glass-water interface (reference) and the specimen (sample), which interfere to form the final IRM signal.
Fig. 3
Fig. 3 Background subtraction and SNR measurement of a microtubule. (A) Raw IRM image (top) of microtubules on a glass surface and background image (middle). Background subtraction leads to the image of the IRM signal (bottom). Note that microtubules are visible without background subtraction. Also note the signature of an interference pattern: a partially unbound microtubule has black and white regions (arrows in (A) top and bottom). (B) Region of interest of the microtubule indicated in A. The black spots are impurities. (C) Median-intensity profile calculated along the microtubule axis of B (black) and a Gaussian fit (orange). (D) Residual noise image after subtraction of the Gaussian fit shown in C from each column of the microtubule image in B. Values above or below the threshold (vertical, dashed lines in C) are indicated in red or blue, respectively. (E) Histogram of the gray values in D (light gray bars). The image noise was calculated from the gray values within the threshold (dark gray bars) excluding signals from impurities. The threshold (*) was calculated as ±1.5× the interquartile range around the median gray level.
Fig. 4
Fig. 4 Optimization of the IRM signal-to-noise ratio. (A) Analyzed microtubule images (top) and residual images (middle) at varying LED currents. The measured SNR is plotted versus the applied LED current (bottom). A power-law fit (dashed line) showed near shot-noise limited imaging. Inset: Measured noise vs. LED current. The noise scaled with an exponent 0.46 ± 0.1. (B) Analyzed microtubule images (top) and residual images (middle) for an increasing number N of averaged frames. The solid line indicates a power-law slope with exponent 0.5. Inset: IRM signal vs. number of averages. (C) Top 2 panels: section 10 images of the microtubule shown in D with increasing INA and the respective residual images. Bottom panels: Legend of sections. Signal of all microtubule-sections (indicated in D) and the corresponding noise is plotted vs. INA. The averaged SNR is normalized by the SNR at INA = 1.3 at the very bottom. (D) An averaged image of a microtubule (N = 50), its line intensity profile (bottom left) and the corresponding histogram (bottom right). The analyzed microtubule-sections of C are indicated (dashed lines).
Fig. 5
Fig. 5 IRM and evanescent field calibration using bent microtubules. (A) Schematic drawing not to scale. A microsphere functionalized with non-motile kinesin-1–GFP motor proteins is trapped and attached to a loose microtubule end, which is pulled upward by the trap. (B) TIRF (red channel, left) and IRM images (right) of a bent microtubule and attached microsphere at increasing trap heights. Note that the bright intensity around the microsphere is due to scattering of the illumination light and not due to the trapping laser. The latter is blocked by an infrared filter. Scale bar: 2 μm. (C) IRM line profiles along the microtubule shown in B (symbols) and the global fit of Eq. (1) (solid lines). The trap height and axial force are indicated. For clarity, data points are offset vertically. (D) Weighted linear fit (dashed line) to the microtubule tip height hMT (circles) plotted versus the trap height htrap (error bars are SEM, gray lines). Inset: Calculated microtubule profile vs. height. (E) Fluorescence intensity line profiles along the microtubule shown in B for different tip heights. (F) Normalized fluorescence intensity line profiles (symbols). Profiles were normalized to the average intensity of the first 20 points and to the line profile at ht = 0.0 μm (shaded area and blue circles in E, respectively). A global fit (solid lines) of the data to Eq. (3) determined the depth of the evanescent field.

Tables (1)

Tables Icon

Table 1 Fit parameters of the global fit to the IRM and TIRF intensity profiles.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

I ( x ) = B D sin y y cos ( 2 k h ( x ) [ 1 sin 2 ( α 2 ) ] ) ,
h ( x ) = A ( x t x 0 2 ( x x 0 ) 2 ( x x 0 ) 3 6 ) ,
I TIRF ( x ) = exp [ h ( x ) / δ ] ,

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