Quantifying the Precision of Single-Molecule Torque and Twist Measurements Using Allan Variance.

Single-molecule manipulation techniques have provided unprecedented insights into the structure, function, interactions, and mechanical properties of biological macromolecules. Recently, the single-molecule toolbox has been expanded by techniques that enable measurements of rotation and torque, such as the optical torque wrench (OTW) and several different implementations of magnetic (torque) tweezers. Although systematic analyses of the position and force precision of single-molecule techniques have attracted considerable attention, their angle and torque precision have been treated in much less detail. Here, we propose Allan deviation as a tool to systematically quantitate angle and torque precision in single-molecule measurements. We apply the Allan variance method to experimental data from our implementations of (electro)magnetic torque tweezers and an OTW and find that both approaches can achieve a torque precision better than 1 pN · nm. The OTW, capable of measuring torque on (sub)millisecond timescales, provides the best torque precision for measurement times ≲10 s, after which drift becomes a limiting factor. For longer measurement times, magnetic torque tweezers with their superior stability provide the best torque precision. Use of the Allan deviation enables critical assessments of the torque precision as a function of measurement time across different measurement modalities and provides a tool to optimize measurement protocols for a given instrument and application.

Publisher's Note: Biological Magnetometry: Torque on Superparamagnetic Beads in Magnetic Fields [Phys. Rev. Lett. 114, 218301 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.114.218301.

Biological magnetometry: torque on superparamagnetic beads in magnetic fields.

Superparamagnetic beads are widely used in biochemistry and single-molecule biophysics, but the nature of the anisotropy that enables the application of torques remains controversial. To quantitatively investigate the torques experienced by superparamagnetic particles, we use a biological motor to rotate beads in a magnetic field and demonstrate that the underlying potential is π periodic. In addition, we tether a bead to a single DNA molecule and show that the angular trap stiffness increases nonlinearly with magnetic field strength. Our results indicate that the superparamagnetic beads' anisotropy derives from a nonuniform intrabead distribution of superparamagnetic nanoparticles.

Single-Crystal Rutile TiO2 Nanocylinders are Highly Effective Transducers of Optical Force and Torque.

Optical trapping of (sub)micron-sized particles is broadly employed in nanoscience and engineering. The materials commonly employed for these particles, however, have physical properties that limit the transfer of linear or angular momentum (or both). This reduces the magnitude of forces and torques, and the spatiotemporal resolution, achievable in linear and angular traps. Here, we overcome these limitations through the use of single-crystal rutile TiO2, which has an exceptionally large optical birefringence, a high index of refraction, good chemical stability, and is amenable to geometric control at the nanoscale. We show that rutile TiO2 nanocylinders form powerful joint force and torque transducers in aqueous environments by using only moderate laser powers to apply nN·nm torques at kHz rotational frequencies to tightly trapped particles. In doing so, we demonstrate how rutile TiO2 nanocylinders outperform other materials and offer unprecedented opportunities to expand the control of optical force and torque at the nanoscale.

Corrigendum: Applying torque to the Escherichia coli flagellar motor using magnetic tweezers.

This corrects the article DOI: 10.1038/srep43285.

Applying torque to the Escherichia coli flagellar motor using magnetic tweezers.

The bacterial flagellar motor of Escherichia coli is a nanoscale rotary engine essential for bacterial propulsion. Studies on the power output of single motors rely on the measurement of motor torque and rotation under external load. Here, we investigate the use of magnetic tweezers, which in principle allow the application and active control of a calibrated load torque, to study single flagellar motors in Escherichia coli. We manipulate the external load on the motor by adjusting the magnetic field experienced by a magnetic bead linked to the motor, and we probe the motor's response. A simple model describes the average motor speed over the entire range of applied fields. We extract the motor torque at stall and find it to be similar to the motor torque at drag-limited speed. In addition, use of the magnetic tweezers allows us to force motor rotation in both forward and backward directions. We monitor the motor's performance before and after periods of forced rotation and observe no destructive effects on the motor. Our experiments show how magnetic tweezers can provide active and fast control of the external load while also exposing remaining challenges in calibration. Through their non-invasive character and straightforward parallelization, magnetic tweezers provide an attractive platform to study nanoscale rotary motors at the single-motor level.

Tunable top-down fabrication and functional surface coating of single-crystal titanium dioxide nanostructures and nanoparticles.

Titanium dioxide (TiO2) is a key component of diverse optical and electronic applications that exploit its exceptional material properties. In particular, the use of TiO2 in its single-crystalline phase can offer substantial advantages over its amorphous and polycrystalline phases for existing and yet-to-be-developed applications. However, the implementation of single-crystal TiO2 has been hampered by challenges in its fabrication and subsequent surface functionalization. Here, we introduce a novel top-down approach that allows for batch fabrication of uniform high-aspect-ratio single-crystal TiO2 nanostructures with targeted sidewall profiles. We complement our fabrication approach with a functionalization strategy that achieves dense, uniform, and area-selective coating with a variety of biomolecules. This allows us to fabricate single-crystal rutile TiO2 nanocylinders tethered with individual DNA molecules for use as force- and torque-transducers in an optical torque wrench. These developments provide the means for increased exploitation of the superior material properties of single-crystal TiO2 at the nanoscale.

A force calibration standard for magnetic tweezers.

To study the behavior of biological macromolecules and enzymatic reactions under force, advances in single-molecule force spectroscopy have proven instrumental. Magnetic tweezers form one of the most powerful of these techniques, due to their overall simplicity, non-invasive character, potential for high throughput measurements, and large force range. Drawbacks of magnetic tweezers, however, are that accurate determination of the applied forces can be challenging for short biomolecules at high forces and very time-consuming for long tethers at low forces below ∼1 piconewton. Here, we address these drawbacks by presenting a calibration standard for magnetic tweezers consisting of measured forces for four magnet configurations. Each such configuration is calibrated for two commonly employed commercially available magnetic microspheres. We calculate forces in both time and spectral domains by analyzing bead fluctuations. The resulting calibration curves, validated through the use of different algorithms that yield close agreement in their determination of the applied forces, span a range from 100 piconewtons down to tens of femtonewtons. These generalized force calibrations will serve as a convenient resource for magnetic tweezers users and diminish variations between different experimental configurations or laboratories.