Spatiotemporal dynamics of the proton motive force on single bacterial cells.

Electrochemical gradients across biological membranes are vital for cellular bioenergetics. In bacteria, the proton motive force (PMF) drives essential processes like adenosine triphosphate production and motility. Traditionally viewed as temporally and spatially stable, recent research reveals a dynamic PMF behavior at both single-cell and community levels. Moreover, the observed lateral segregation of respiratory complexes could suggest a spatial heterogeneity of the PMF. Using a light-activated proton pump and detecting the activity of the bacterial flagellar motor, we perturb and probe the PMF of single cells. Spatially homogeneous PMF perturbations reveal millisecond-scale temporal dynamics and an asymmetrical capacitive response. Localized perturbations show a rapid lateral PMF homogenization, faster than proton diffusion, akin to the electrotonic potential spread observed in passive neurons, explained by cable theory. These observations imply a global coupling between PMF sources and consumers along the membrane, precluding sustained PMF spatial heterogeneity but allowing for rapid temporal changes.

Dynamic stiffening of the flagellar hook.

For many bacteria, motility stems from one or more flagella, each rotated by the bacterial flagellar motor, a powerful rotary molecular machine. The hook, a soft polymer at the base of each flagellum, acts as a universal joint, coupling rotation between the rigid membrane-spanning rotor and rigid flagellum. In multi-flagellated species, where thrust arises from a hydrodynamically coordinated flagellar bundle, hook flexibility is crucial, as flagella rotate significantly off-axis. However, consequently, the thrust applies a significant bending moment. Therefore, the hook must simultaneously be compliant to enable bundle formation yet rigid to withstand large hydrodynamical forces. Here, via high-resolution measurements and analysis of hook fluctuations under dynamical conditions, we elucidate how it fulfills this double functionality: the hook shows a dynamic increase in bending stiffness under increasing torsional stress. Such strain-stiffening allows the system to be flexible when needed yet reduce deformation under high loads, enabling high speed motility.

The Dynamic Ion Motive Force Powering the Bacterial Flagellar Motor.

The bacterial flagellar motor (BFM) is a rotary molecular motor embedded in the cell membrane of numerous bacteria. It turns a flagellum which acts as a propeller, enabling bacterial motility and chemotaxis. The BFM is rotated by stator units, inner membrane protein complexes that stochastically associate to and dissociate from individual motors at a rate which depends on the mechanical and electrochemical environment. Stator units consume the ion motive force (IMF), the electrochemical gradient across the inner membrane that results from cellular respiration, converting the electrochemical energy of translocated ions into mechanical energy, imparted to the rotor. Here, we review some of the main results that form the base of our current understanding of the relationship between the IMF and the functioning of the flagellar motor. We examine a series of studies that establish a linear proportionality between IMF and motor speed, and we discuss more recent evidence that the stator units sense the IMF, altering their rates of dynamic assembly. This, in turn, raises the question of to what degree the classical dependence of motor speed on IMF is due to stator dynamics vs. the rate of ion flow through the stators. Finally, while long assumed to be static and homogeneous, there is mounting evidence that the IMF is dynamic, and that its fluctuations control important phenomena such as cell-to-cell signaling and mechanotransduction. Within the growing toolbox of single cell bacterial electrophysiology, one of the best tools to probe IMF fluctuations may, ironically, be the motor that consumes it. Perfecting our incomplete understanding of how the BFM employs the energy of ion flow will help decipher the dynamical behavior of the bacterial IMF.

High-Resolution Photonic Force Microscopy Based on Sharp Nanofabricated Tips.

Although near-field imaging techniques reach sub-nanometer resolution on rigid samples, it remains extremely challenging to image soft interfaces, such as biological membranes, due to the deformations induced by the probe. In photonic force microscopy, optical tweezers are used to manipulate and measure the scanning probe, allowing imaging of soft materials without force-induced artifacts. However, the size of the optically trapped probe still limits the maximum resolution. Here, we show a novel and simple nanofabrication protocol to massively produce optically trappable quartz particles which mimic the sharp tips of atomic force microscopy. Imaging rigid nanostructures with our tips, we resolve features smaller than 80 nm. Scanning the membrane of living malaria-infected red blood cells reveals, with no visible artifacts, submicron features termed knobs, related to the parasite activity. The use of nanoengineered particles in photonic force microscopy opens the way to imaging soft samples at high resolution.

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.

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

This corrects the article DOI: 10.1038/srep43285.

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.

Catch bond drives stator mechanosensitivity in the bacterial flagellar motor.

The bacterial flagellar motor (BFM) is the rotary motor that rotates each bacterial flagellum, powering the swimming and swarming of many motile bacteria. The torque is provided by stator units, ion motive force-powered ion channels known to assemble and disassemble dynamically in the BFM. This turnover is mechanosensitive, with the number of engaged units dependent on the viscous load experienced by the motor through the flagellum. However, the molecular mechanism driving BFM mechanosensitivity is unknown. Here, we directly measure the kinetics of arrival and departure of the stator units in individual motors via analysis of high-resolution recordings of motor speed, while dynamically varying the load on the motor via external magnetic torque. The kinetic rates obtained, robust with respect to the details of the applied adsorption model, indicate that the lifetime of an assembled stator unit increases when a higher force is applied to its anchoring point in the cell wall. This provides strong evidence that a catch bond (a bond strengthened instead of weakened by force) drives mechanosensitivity of the flagellar motor complex. These results add the BFM to a short, but growing, list of systems demonstrating catch bonds, suggesting that this "molecular strategy" is a widespread mechanism to sense and respond to mechanical stress. We propose that force-enhanced stator adhesion allows the cell to adapt to a heterogeneous environmental viscosity and may ultimately play a role in surface-sensing during swarming and biofilm formation.

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.

Optical Torque Wrench Design and Calibration.

Expanding the capabilities of optical traps with angular control of the trapped particle has numerous potential applications in all fields where standard linear optical tweezers are employed. Here we describe in detail the construction, alignment, and calibration of the Optical Torque Wrench, a mode of function that can be added to linear optical tweezers to simultaneously apply and measure both force and torque on birefringent microscopic cylindrical particles. The interaction between the linear polarization of the laser and the birefringent cylinder creates an angular trap for the particle orientation, described by a periodic potential. As a consequence of the experimental control of the tilt of the periodic potential, the dynamical excitability of the system can be observed. Angular optical tweezers remain less widespread than their linear counterpart. We hope this technical guide can foster their development and new applications.

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.

Efficient illumination for microsecond tracking microscopy.

The possibility to observe microsecond dynamics at the sub-micron scale, opened by recent technological advances in fast camera sensors, will affect many biophysical studies based on particle tracking in optical microscopy. A main limiting factor for further development of fast video microscopy remains the illumination of the sample, which must deliver sufficient light to the camera to allow microsecond exposure times. Here we systematically compare the main illumination systems employed in holographic tracking microscopy, and we show that a superluminescent diode and a modulated laser diode perform the best in terms of image quality and acquisition speed, respectively. In particular, we show that the simple and inexpensive laser illumination enables less than 1 µs camera exposure time at high magnification on a large field of view without coherence image artifacts, together with a good hologram quality that allows nm-tracking of microscopic beads to be performed. This comparison of sources can guide in choosing the most efficient illumination system with respect to the specific application.

Calibration of the optical torque wrench.

The optical torque wrench is a laser trapping technique that expands the capability of standard optical tweezers to torque manipulation and measurement, using the laser linear polarization to orient tailored microscopic birefringent particles. The ability to measure torque of the order of kBT (∼4 pN nm) is especially important in the study of biophysical systems at the molecular and cellular level. Quantitative torque measurements rely on an accurate calibration of the instrument. Here we describe and implement a set of calibration approaches for the optical torque wrench, including methods that have direct analogs in linear optical tweezers as well as introducing others that are specifically developed for the angular variables. We compare the different methods, analyze their differences, and make recommendations regarding their implementations.

Freely orbiting magnetic tweezers to directly monitor changes in the twist of nucleic acids.

The double-stranded nature of DNA links its replication, transcription and repair to rotational motion and torsional strain. Magnetic tweezers (MT) are a powerful single-molecule technique to apply both forces and torques to individual DNA or RNA molecules. However, conventional MT do not track rotational motion directly and constrain the free rotation of the nucleic acid tether. Here we present freely orbiting MT (FOMT) that allow the measurement of equilibrium fluctuations and changes in the twist of tethered nucleic acid molecules. Using a precisely aligned vertically oriented magnetic field, FOMT enable tracking of the rotation angle from straight forward (x,y)-position tracking and permits the application of calibrated stretching forces, without biasing the tether's free rotation. We utilize FOMT to measure the force-dependent torsional stiffness of DNA from equilibrium rotational fluctuations and to follow the assembly of recombination protein A filaments on DNA.

Electron beam fabrication of birefringent microcylinders.

Numerous biological and biotechnological applications rely on the use of micrometer- and nanometer-scale particles, benefiting tremendously from quantitative control of their physical and chemical properties. Here, we describe the use of electron beam lithography for the design, fabrication, and functionalization of micrometer-scale birefringent quartz cylinders for use in sensing and detection. We demonstrate excellent control of the cylinders' geometry, fabricating cylinders with heights of 0.5-2 µm and diameters of 200-500 nm with high precision while maintaining control of their side-wall angle. The flexible fabrication allows cylinders to be selectively shaped into conical structures or to include centered protrusions for the selective attachment of biomolecules. The latter is facilitated by straightforward functionalization targeted either to a cylinder's face or to the centered protrusion alone. The fabricated quartz cylinders are characterized in an optical torque wrench, permitting correlation of their geometrical properties to measured torques. Lastly, we tether individual DNA molecules to the functionalized cylinders and demonstrate the translational and rotational control required for single-molecule studies.

Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser.

We analyze theoretically and experimentally the influence of current noise on the longitudinal mode hopping dynamics of a bulk semiconductor laser. It is shown that the mean residence times on each mode have different sensitivity to external noise added to the bias current. In particular, an increase of the noise level enhances the residence time on the longitudinal mode that dominates at low current, evidencing the multiplicative nature of the stochastic process. A two-mode rate equation model for a semiconductor laser is able to reproduce the experimental findings. Under a suitable separation of the involved time scales, the model can be reduced to a one-dimensional bistable potential system with a multiplicative stochastic term related to the current noise strength. The reduced model clarifies the influence of the different noise sources on the hopping dynamics.

Stochastic resonance in bulk semiconductor lasers.

The stochastic time scale of the mode hopping in a bulk semiconductor laser can be varied maintaining the symmetry of the residence times by a proper tuning of the laser substrate temperature and pumping current. While the addition of external noise to the pumping current affects the symmetry of the mode-hopping process, a sinusoidal modulation does not, providing that the modulation amplitude is below a critical value. In this case, we observe stochastic resonance in the modal intensities of the laser. We show the occurrence of the phenomenon in the spectral domain, and we characterize it by a statistical analysis based on the residence times probability distributions. The evidence of bona fide resonance is also provided, varying the modulation frequency and analyzing a proper statistical indicator. Changing the temperature of the laser substrate we show that resonance occurs at different modulation periods always equal to the double of the average residence time measured without modulation.