Magnetic forces and DNA mechanics in multiplexed magnetic tweezers

Magnetic tweezers (MT) are a powerful tool for the study of DNA-enzyme interactions. Both the magnet-based manipulation and the camera-based detection used in MT are well suited for multiplexed measurements. Here, we systematically address challenges related to scaling of multiplexed magnetic tweezers (MMT) towards high levels of parallelization where large numbers of molecules (say 10³) are addressed in the same amount of time required by a single-molecule measurement. We apply offline analysis of recorded images and show that this approach provides a scalable solution for parallel tracking of the xyz-positions of many beads simultaneously. We employ a large field-of-view imaging system to address many DNA-bead tethers in parallel. We model the 3D magnetic field generated by the magnets and derive the magnetic force experienced by DNA-bead tethers across the large field of view from first principles. We furthermore experimentally demonstrate that a DNA-bead tether subject to a rotating magnetic field describes a bicircular, Limaçon rotation pattern and that an analysis of this pattern simultaneously yields information about the force angle and the position of attachment of the DNA on the bead. Finally, we apply MMT in the high-throughput investigation of the distribution of the induced magnetic moment, the position of attachment of DNA on the beads, and DNA flexibility. The methods described herein pave the way to kilo-molecule level magnetic tweezers experiments.     

Eukaryotic membrane tethers revisited using magnetic tweezers

Membrane nanotubes, under physiological conditions, typically form en masse. We employed magnetic tweezers (MTW) to extract tethers from human brain tumor cells and compared their biophysical properties with tethers extracted after disruption of the cytoskeleton and from a strongly differing cell type, Chinese hamster ovary cells. In this method, the constant force produced with the MTW is transduced to cells through super-paramagnetic beads attached to the cell membrane. Multiple sudden jumps in bead velocity were manifest in the recorded bead displacement-time profiles. These discrete events were interpreted as successive ruptures of individual tethers. Observation with scanning electron microscopy supported the simultaneous existence of multiple tethers. The physical characteristics, in particular, the number and viscoelastic properties of the extracted tethers were determined from the analytic fit to bead trajectories, provided by a standard model of viscoelasticity. Comparison of tethers formed with MTW and atomic force microscopy (AFM), a technique where the cantilever-force transducer is moved at constant velocity, revealed significant differences in the two methods of tether formation. Our findings imply that extreme care must be used to interpret the outcome of tether pulling experiments performed with single molecular techniques (MTW, AFM, optical tweezers, etc). First, the different methods may be testing distinct membrane structures with distinct properties. Second, as soon as a true cell membrane (as opposed to that of a vesicle) can attach to a substrate, upon pulling on it, multiple nonspecific membrane tethers may be generated. Therefore, under physiological conditions, distinguishing between tethers formed through specific and nonspecific interactions is highly nontrivial if at all possible.     

Scanning a DNA Molecule for Bound Proteins Using Hybrid Magnetic and Optical Tweezers

The functional state of the genome is determined by its interactions with proteins that bind, modify, and move along the DNA. To determine the positions and binding strength of proteins localized on DNA we have developed a combined magnetic and optical tweezers apparatus that allows for both sensitive and label-free detection. A DNA loop, that acts as a scanning probe, is created by looping an optically trapped DNA tether around a DNA molecule that is held with magnetic tweezers. Upon scanning the loop along the λ-DNA molecule, EcoRI proteins were detected with ∼17 nm spatial resolution. An offset of 33±5 nm for the detected protein positions was found between back and forwards scans, corresponding to the size of the DNA loop and in agreement with theoretical estimates. At higher applied stretching forces, the scanning loop was able to remove bound proteins from the DNA, showing that the method is in principle also capable of measuring the binding strength of proteins to DNA with a force resolution of 0.1 pN/. The use of magnetic tweezers in this assay allows the facile preparation of many single-molecule tethers, which can be scanned one after the other, while it also allows for direct control of the supercoiling state of the DNA molecule, making it uniquely suitable to address the effects of torque on protein-DNA interactions.     

Nucleosome Assembly Depends on the Torsion in the DNA Molecule: A Magnetic Tweezers Study

We have used magnetic tweezers to study nucleosome assembly on topologically constrained DNA molecules. Assembly was achieved using chicken erythrocyte core histones and histone chaperone protein Nap1 under constant low force. We have observed only partial assembly when the DNA was topologically constrained and much more complete assembly on unconstrained (nicked) DNA tethers. To verify our hypothesis that the lack of full nucleosome assembly on topologically constrained tethers was due to compensatory accumulation of positive supercoiling in the rest of the template, we carried out experiments in which we mechanically relieved the positive supercoiling by rotating the external magnetic field at certain time points of the assembly process. Indeed, such rotation did lead to the same nucleosome saturation level as in the case of nicked tethers. We conclude that levels of positive supercoiling in the range of 0.025-0.051 (most probably in the form of twist) stall the nucleosome assembly process.     

Magnetic Tweezers for the Measurement of Twist and Torque

Single-molecule techniques make it possible to investigate the behavior of individual biological molecules in solution in real time. These techniques include so-called force spectroscopy approaches such as atomic force microscopy, optical tweezers, flow stretching, and magnetic tweezers. Amongst these approaches, magnetic tweezers have distinguished themselves by their ability to apply torque while maintaining a constant stretching force. Here, it is illustrated how such a “conventional” magnetic tweezers experimental configuration can, through a straightforward modification of its field configuration to minimize the magnitude of the transverse field, be adapted to measure the degree of twist in a biological molecule. The resulting configuration is termed the freely-orbiting magnetic tweezers. Additionally, it is shown how further modification of the field configuration can yield a transverse field with a magnitude intermediate between that of the “conventional” magnetic tweezers and the freely-orbiting magnetic tweezers, which makes it possible to directly measure the torque stored in a biological molecule. This configuration is termed the magnetic torque tweezers. The accompanying video explains in detail how the conversion of conventional magnetic tweezers into freely-orbiting magnetic tweezers and magnetic torque tweezers can be accomplished, and demonstrates the use of these techniques. These adaptations maintain all the strengths of conventional magnetic tweezers while greatly expanding the versatility of this powerful instrument.     

Cell cytoskeleton and tether extraction

We perform a detailed investigation of the force × deformation curve in tether extraction from 3T3 cells by optical tweezers. Contrary to conventional wisdom about tethers extracted from cells, we find that actin filaments are present within them, so that a revised theory of tether pulling from cells is called for. We also measure steady and maximum tether force values significantly higher than previously published ones for 3T3 cells. Possible explanations for these differences are investigated. Further experimental support of the theory of force barriers for membrane tube extension is obtained. The potential of studies on tether pulling force × deformation for retrieving information on membrane-cytoskeleton interaction is emphasized.     

Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy

Single-molecule force spectroscopy has emerged as a powerful tool to investigate the forces and motions associated with biological molecules and enzymatic activity. The most common force spectroscopy techniques are optical tweezers, magnetic tweezers and atomic force microscopy. Here we describe these techniques and illustrate them with examples highlighting current capabilities and limitations.     

Quantitative Guidelines for Force Calibration through Spectral Analysis of Magnetic Tweezers Data

Single-molecule techniques are powerful tools that can be used to study the kinetics and mechanics of a variety of enzymes and their complexes. Force spectroscopy, for example, can be used to control the force applied to a single molecule and thereby facilitate the investigation of real-time nucleic acid-protein interactions. In magnetic tweezers, which offer straightforward control and compatibility with fluorescence measurements or parallel tracking modes, force-measurement typically relies on the analysis of positional fluctuations through video microscopy. Significant errors in force estimates, however, may arise from incorrect spectral analysis of the Brownian motion in the magnetic tweezers. Here we investigated physical and analytical optimization procedures that can be used to improve the range over which forces can be reliably measured. To systematically probe the limitations of magnetic tweezers spectral analysis, we have developed a magnetic tweezers simulator, whose outcome was validated with experimental data. Using this simulator, we evaluate methods to correctly perform force experiments and provide guidelines for correct force calibration under configurations that can be encountered in typical magnetic tweezers experiments.     

Interrogating Biology with Force: Single Molecule High-Resolution Measurements with Optical Tweezers

Single molecule force spectroscopy methods, such as optical and magnetic tweezers and atomic force microscopy, have opened up the possibility to study biological processes regulated by force, dynamics of structural conformations of proteins and nucleic acids, and load-dependent kinetics of molecular interactions. Among the various tools available today, optical tweezers have recently seen great progress in terms of spatial resolution, which now allows the measurement of atomic-scale conformational changes, and temporal resolution, which has reached the limit of the microsecond-scale relaxation times of biological molecules bound to a force probe. Here, we review different strategies and experimental configurations recently developed to apply and measure force using optical tweezers. We present the latest progress that has pushed optical tweezers’ spatial and temporal resolution down to today’s values, discussing the experimental variables and constraints that are influencing measurement resolution and how these can be optimized depending on the biological molecule under study.     

Interrogating Biology with Force: Single Molecule High-Resolution Measurements with Optical Tweezers

Single molecule force spectroscopy methods, such as optical and magnetic tweezers and atomic force microscopy, have opened up the possibility to study biological processes regulated by force, dynamics of structural conformations of proteins and nucleic acids, and load-dependent kinetics of molecular interactions. Among the various tools available today, optical tweezers have recently seen great progress in terms of spatial resolution, which now allows the measurement of atomic-scale conformational changes, and temporal resolution, which has reached the limit of the microsecond-scale relaxation times of biological molecules bound to a force probe. Here, we review different strategies and experimental configurations recently developed to apply and measure force using optical tweezers. We present the latest progress that has pushed optical tweezers’ spatial and temporal resolution down to today’s values, discussing the experimental variables and constraints that are influencing measurement resolution and how these can be optimized depending on the biological molecule under study.     

Membrane tether formation from outer hair cells with optical tweezers

Optical tweezers were used to characterize the mechanical properties of the outer hair cell (OHC) plasma membrane by pulling tethers with 4.5-microm polystyrene beads. Tether formation force and tether force were measured in static and dynamic conditions. A greater force was required for tether formations from OHC lateral wall (499 +/- 152 pN) than from OHC basal end (142 +/- 49 pN). The difference in the force required to pull tethers is consistent with an extensive cytoskeletal framework associated with the lateral wall known as the cortical lattice. The apparent plasma membrane stiffness, estimated under the static conditions by measuring tether force at different tether length, was 3.71 pN/microm for OHC lateral wall and 4.57 pN/microm for OHC basal end. The effective membrane viscosity was measured by pulling tethers at different rates while continuously recording the tether force, and estimated in the range of 2.39 to 5.25 pN x s/microm. The viscous force most likely results from the viscous interactions between plasma membrane lipids and the OHC cortical lattice and/or integral membrane proteins. The information these studies provide on the mechanical properties of the OHC lateral wall is important for understanding the mechanism of OHC electromotility.     

Coalescence of membrane tethers: experiments, theory, and applications

Tethers are nanocylinders of lipid bilayer membrane, arising in situations ranging from micromanipulation experiments on synthetic vesicles to the formation of dynamic tubular networks in the Golgi apparatus. Relying on the extensive theoretical and experimental works aimed to understand the physics of individual tethers formation, we addressed the problem of the interaction between two nanotubes. By using a combination of micropipette manipulation and optical tweezers, we quantitatively studied the process of coalescence that occurred when the separation distance between both vesicle-tether junctions became smaller than a threshold length. Our experiments, which were supported by an original theoretical analysis, demonstrated that the measurements of the tether force and angle between tethers at coalescence directly yield the bending rigidity, kappa, and the membrane tension, sigma, of the vesicles. Contrary to other methods used to probe the bending rigidity of vesicles, the proposed approach permits a direct measurement of kappa without requiring any control of the membrane tension. Finally, after validation of the method and proposal of possible applications, we experimentally investigated the dynamics of the coalescence process.     

单细胞机械性能检测方法与应用研究进展

细胞机械性能与细胞的生理状态与功能存在密切联系。早期对于细胞机械性能的研究受制于技术条件,只能获得细胞群的弹性或剪切模量,使得少量异质细胞的机械表型被淹没。近年来,单细胞机械性能检测技术得到了蓬勃发展。原子力显微镜、微吸管技术、光镊与光学拉伸、磁扭转流变仪与磁镊等单细胞机械性能检测技术展现出非常高的检测精度,但检测通量相对较低。新型微流控高通量检测方法的出现使检测通量呈几何式增长,有望解决大样本快速检测的需求。本文首先综述原子力显微镜、微吸管、光镊与光学拉伸和磁扭转流变仪与磁镊等单细胞机械性能检测技术。在此基础上,重点介绍细胞过孔、剪切诱导细胞变形和拉伸诱导细胞变形3种新兴微流控高通量检测技术的工作原理及最新研究进展,探讨各类方法的优缺点。最后,本文展望单细胞机械性能检测技术的未来发展方向。     

Force Spectroscopy with Dual-Trap Optical Tweezers: Molecular Stiffness Measurements and Coupled Fluctuations Analysis

Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies.     

Subpiconewton dynamic force spectroscopy using magnetic tweezers

We introduce a simple method for dynamic force spectroscopy with magnetic tweezers. This method allows application of subpiconewton force and twist control by calibration of the applied force from the height of the magnets. Initial dynamic force spectroscopy experiments on DNA molecules revealed a large hysteresis that is caused by viscous drag on the magnetic bead and will conceal weak interactions. When smaller beads are used, this hysteresis is sufficiently reduced to reveal intramolecular interactions at subpiconewton forces. Compared with typical quasistatic force spectroscopy, a significant reduction of measurement time is achieved, allowing the real-time study of transient structures and reaction intermediates. As a proof of principle, nucleosome-nucleosome interactions on a subsaturated chromatin fiber were analyzed.     

Extending the Range for Force Calibration in Magnetic Tweezers

Magnetic tweezers are a wide-spread tool used to study the mechanics and the function of a large variety of biomolecules and biomolecular machines. This tool uses a magnetic particle and a strong magnetic field gradient to apply defined forces to the molecule of interest. Forces are typically quantified by analyzing the lateral fluctuations of the biomolecule-tethered particle in the direction perpendicular to the applied force. Since the magnetic field pins the anisotropy axis of the particle, the lateral fluctuations follow the geometry of a pendulum with a short pendulum length along and a long pendulum length perpendicular to the field lines. Typically, the short pendulum geometry is used for force calibration by power-spectral-density (PSD) analysis, because the movement of the bead in this direction can be approximated by a simple translational motion. Here, we provide a detailed analysis of the fluctuations according to the long pendulum geometry and show that for this direction, both the translational and the rotational motions of the particle have to be considered. We provide analytical formulas for the PSD of this coupled system that agree well with PSDs obtained in experiments and simulations and that finally allow a faithful quantification of the magnetic force for the long pendulum geometry. We furthermore demonstrate that this methodology allows the calibration of much larger forces than the short pendulum geometry in a tether-length-dependent manner. In addition, the accuracy of determination of the absolute force is improved. Our force calibration based on the long pendulum geometry will facilitate high-resolution magnetic-tweezers experiments that rely on short molecules and large forces, as well as highly parallelized measurements that use low frame rates.     

Effects of chlorpromazine on mechanical properties of the outer hair cell plasma membrane

An optical tweezers system was used to characterize the effects of chlorpromazine (CPZ) on the mechanical properties of the mammalian outer hair cell (OHC) through the formation of plasma membrane tethers. Such tethers exhibited force relaxation when held at a constant length for several minutes. We used a second-order generalized Kelvin body to model tether-force behavior from which several mechanical parameters were then calculated including stiffness, viscosity-associated measures, and force relaxation time constants. The results of the analysis portray a two-part relaxation process characterized by significantly different rates of force decay, which we propose is due to the local reorganization of lipids within the tether and the flow of external lipid into the tether. We found that CPZ's effect was limited to the latter phenomenon since only the second phase of relaxation was significantly affected by the drug. This finding coupled with an observed large reduction in overall tether forces implies a common basis for the drug's effects, the plasma membrane-cytoskeleton interaction. The CPZ-induced changes in tether viscoelastic behavior suggest that alterations in the mechanical properties of the OHC lateral wall could play a role in the modulation of OHC electromotility by CPZ.     

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$\mathrm{?}$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.