Francesco Pedaci

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 tethers 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.

Excitable particles in an optical torque wrench

The optical torque wrench is a laser trapping technique capable of applying and directly measuring torque on microscopic birefringent particles using spin momentum transfer, and has found application in the measurement of static torsional properties of biological molecules such as single DNAs. Motivated by the potential of the optical torque wrench to access the fast rotational dynamics of biological systems, a result of its all-optical manipulation and detection, we focus on the angular dynamics of the trapped birefringent particle, demonstrating its excitability in the vicinity of a critical point. This links the optical torque wrench to nonlinear dynamical systems such as neuronal and cardiovascular tissues, nonlinear optics and chemical reactions, all of which display an excitable binary (‘all-or-none’) response to input perturbations. On the basis of this dynamical feature, we devise and implement a conceptually new sensing technique capable of detecting single perturbation events with high signal-to-noise ratio and continuously adjustable sensitivity.

Torque spectroscopy for the study of rotary motion in biological systems.

Systems Jan Lipfert,†,‡ Maarten M. van Oene,‡ Mina Lee,‡ Francesco Pedaci,‡,§ and Nynke H. Dekker*,‡ †Department of Physics, Nanosystems Initiative Munich, and Center for NanoScience (CeNS), Ludwig-Maximilian-University Munich, Amalienstrasse 54, 80799 Munich, Germany ‡Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands Department of Single-Molecule Biophysics, Centre de Biochimie Structurale, UMR 5048 CNRS, 34090 Montpellier, France

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.

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 s 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.

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.

Catch bond drives stator mechanosensitivity in the bacterial flagellar motor

Significance The bacterial flagellar motor (BFM) is the rotary motor powering swimming of many motile bacteria. Many of the components of this molecular machine are dynamic, a property which allows the cell to optimize its behavior in accordance with the surrounding environment. A prime example is the stator unit, a membrane-bound ion channel that is responsible for applying torque to the rotor. The stator units are mechanosensitive, with the number of engaged units dependent on the viscous load on the motor. We measure the kinetics of the stators as a function of the viscous load and find that the mechanosensitivity of the BFM is governed by a catch bond: a counterintuitive type of bond that becomes stronger under force. 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.

Modal switching in quantum-well semiconductor lasers with weak optical feedback

We analyze theoretically and experimentally how the modal dynamics of quantum-well semiconductor lasers is affected by weak optical feedback. Without feedback, these lasers exhibit a regular switching among several longitudinal modes, following a well determined modal sequence and leaving the total intensity output constant. Using a multimode theoretical model we have identified the four wave mixing as the dominant mechanism at the origin of these intriguing dynamics, while the asymmetry of the susceptibility function of semiconductor materials allows to explain the modal sequence. In this manuscript we show that these dynamics, which is almost insensitive to current noise or modulation, is instead extremely sensitive to optical feedback. The experimental results are satisfactorily compared with the numerical predictions of the model, properly adapted for including weak optical feedback.

Fabrication of quartz microcylinders by laser interference lithography for angular optical tweezers

Abstract. The use of optical tweezers (OTs) and spin angular momentum transfer to birefringent particles allows new mechanical measurements in systems where torque and rotation are relevant parameters at the single-molecule level. There is a growing interest in developing simple, fast, and inexpensive protocols to produce a large number of submicron scale cylinders of quartz, a positive uniaxial birefringent crystal, to be employed for such angular measurements in OTs. Here, we show that laser interference lithography, a method well known for its simplicity, fulfills these requirements and produces quartz cylindrical particles that we successfully use to apply and measure optical torque in the piconewton nm range in an optical torque wrench.