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.     

Quantitative Modeling and Optimization of Magnetic Tweezers

Magnetic tweezers are a powerful tool to manipulate single DNA or RNA molecules and to study nucleic acid-protein interactions in real time. Here, we have modeled the magnetic fields of permanent magnets in magnetic tweezers and computed the forces exerted on superparamagnetic beads from first principles. For simple, symmetric geometries the magnetic fields can be calculated semianalytically using the Biot-Savart law. For complicated geometries and in the presence of an iron yoke, we employ a finite-element three-dimensional PDE solver to numerically solve the magnetostatic problem. The theoretical predictions are in quantitative agreement with direct Hall-probe measurements of the magnetic field and with measurements of the force exerted on DNA-tethered beads. Using these predictive theories, we systematically explore the effects of magnet alignment, magnet spacing, magnet size, and of adding an iron yoke to the magnets on the forces that can be exerted on tethered particles. We find that the optimal configuration for maximal stretching forces is a vertically aligned pair of magnets, with a minimal gap between the magnets and minimal flow cell thickness. Following these principles, we present a configuration that allows one to apply ≥40 pN stretching forces on ≈1-μm tethered beads.     

Magnetic tweezers: micromanipulation and force measurement at the molecular level

Cantilevers and optical tweezers are widely used for micromanipulating cells or biomolecules for measuring their mechanical properties. However, they do not allow easy rotary motion and can sometimes damage the handled material. We present here a system of magnetic tweezers that overcomes those drawbacks while retaining most of the previous dynamometers properties. Electromagnets are coupled to a microscope-based particle tracking system through a digital feedback loop. Magnetic beads are first trapped in a potential well of stiffness approximately 10(-7) N/m. Thus, they can be manipulated in three dimensions at a speed of approximately 10 microm/s and rotated along the optical axis at a frequency of 10 Hz. In addition, our apparatus can work as a dynamometer relying on either usual calibration against the viscous drag or complete calibration using Brownian fluctuations. By stretching a DNA molecule between a magnetic particle and a glass surface, we applied and measured vertical forces ranging from 50 fN to 20 pN. Similarly, nearly horizontal forces up to 5 pN were obtained. From those experiments, we conclude that magnetic tweezers represent a low-cost and biocompatible setup that could become a suitable alternative to the other available micromanipulators.     

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.     

Using Optics to Measure Biological Forces and Mechanics

Spanning all size levels, regulating biological forces and transport are fundamental life processes. Used by various investigators over the last dozen years, optical techniques offer unique advantages for studying biological forces. The most mature of these techniques, optical tweezers, or the single-beam optical trap, is commercially available and is used by numerous investigators. Although technical innovations have improved the versatility of optical tweezers, simple optical tweezers continue to provide insights into cell biology. Two new, promising optical technologies, laser-tracking microrheology and the optical stretcher, allow mechanical measurements that are not possible with optical tweezers. Here, I review these various optical technologies and their roles in understanding mechanical forces in cell biology.     

Optical tweezers in biology and medicine

Optical trapping techniques provide unique means to manipulate biological particles such as virus, living cells and subcellular organelles. Another area of interest is the measurement of mechanical (elastic) properties of cell membranes, long strands of single DNA molecule, and filamentous proteins. One of the most attractive applications is the study of single motor molecules. With optical tweezers traps, one can measure the forces generated by single motor molecules such as kinesin and myosin, in the piconewton range and, for the first time, resolve their detailed stepping motion.     

Magnetic torque tweezers: measuring torsional stiffness in DNA and RecA-DNA filaments

We introduce magnetic torque tweezers, which enable direct single-molecule measurements of torque. Our measurements of the effective torsional stiffness C of dsDNA indicated a substantial force dependence, with C = approximately 40 nm at low forces up to C = approximately 100 nm at high forces. The initial torsional stiffness of RecA filaments was nearly twofold larger than that for dsDNA, yet at moderate torques further build-up of torsional strain was prevented.     

Single cell analytics for nanobiology

Single cell analytics allows quantitative investigation of single biological cells from a structural, functional and proteomics point of view and opens possibilities to a novel unamplified cell analysis inherently insensitive to ensemble-averaging, cell-cycle or cell-population effects. We report on three different experimental methods and their application to cellular systems with single molecule sensitivity at the single cell level. Firstly, atomic force microscopy (AFM) can be used to elucidate the surface structure of living bacteria down to the nanometer scale where identification of irregular surface areas and 2D-arrays of regular protein s-layers is possible. Secondly, single cell manipulation and probing experiments with optical tweezers (OT) force spectroscopy allows quantitative identification of individual recognition events of membrane bound receptors. And thirdly, a novel, single cell analysis for protein fingerprinting in structured microfluidic device format will allow a future (label-free) on-chip electrophoretical protein separation of single cells without preamplification.     

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.     

Force unfolding kinetics of RNA using optical tweezers. II. Modeling experiments

By exerting mechanical force, it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a mesoscopic model to analyze the hopping kinetics of RNA hairpins in an optical tweezers setup. The model includes different elements of the experimental setup (beads, handles, and RNA sequence) and limitations of the instrument (time lag of the force-feedback mechanism and finite bandwidth of data acquisition). We investigated the influence of the instrument on the measured hopping rates. Results from the model are in good agreement with the experiments reported in the companion article. The comparison between theory and experiments allowed us to infer the values of the intrinsic molecular rates of the RNA hairpin alone and to search for the optimal experimental conditions to do the measurements. We conclude that the longest handles and softest traps that allow detection of the folding/unfolding signal (handles approximately 5-10 Kbp and traps approximately 0.03 pN/nm) represent the best conditions to obtain the intrinsic molecular rates. The methodology and rationale presented here can be applied to other experimental setups and other molecules.     

Multiplexed Single-molecule Force Proteolysis Measurements Using Magnetic Tweezers

The generation and detection of mechanical forces is a ubiquitous aspect of cell physiology, with direct relevance to cancer metastasis¹, atherogenesis² and wound healing³. In each of these examples, cells both exert force on their surroundings and simultaneously enzymatically remodel the extracellular matrix (ECM). The effect of forces on ECM has thus become an area of considerable interest due to its likely biological and medical importance^4-7.Single molecule techniques such as optical trapping⁸, atomic force microscopy⁹, and magnetic tweezers^10,11 allow researchers to probe the function of enzymes at a molecular level by exerting forces on individual proteins. Of these techniques, magnetic tweezers (MT) are notable for their low cost and high throughput. MT exert forces in the range of ~1-100 pN and can provide millisecond temporal resolution, qualities that are well matched to the study of enzyme mechanism at the single-molecule level¹². Here we report a highly parallelizable MT assay to study the effect of force on the proteolysis of single protein molecules. We present the specific example of the proteolysis of a trimeric collagen peptide by matrix metalloproteinase 1 (MMP-1); however, this assay can be easily adapted to study other substrates and proteases.     

Twisting and untwisting a single DNA molecule covered by RecA protein

We study dsDNA-RecA interactions by exerting forces in the pN range on single DNA molecules while the interstrand topological state is controlled owing to a magnetic tweezers setup. We show that unwinding a duplex DNA molecule induces RecA polymerization even at moderate force. Once initial polymerization has nucleated, the extent of RecA coverage still depends on the degree of supercoiling: exerting a positive or negative torsional constraint on the fiber forces partial depolymerization, with a strikingly greater stability when ATPgammaS is used as a cofactor instead of ATP. This nucleofilament's sensitivity to topology might be a way for the bacterial cell to limit consumption of precious RecA monomers when DNA damage is addressed through homologous recombination repair.     

Magnetic tweezers: a sensitive tool to study DNA and chromatin at the single-molecule level.

The advent of single-molecule biology has allowed unprecedented insight into the dynamic behavior of biological macromolecules and their complexes. Unexpected properties, masked by the asynchronous behavior of myriads of molecules in bulk experiments, can be revealed; equally importantly, individual members of a molecular population often exhibit distinct features in their properties. Finally, the single-molecule approaches allow us to study the behavior of biological macromolecules under applied tension or torsion; understanding the mechanical properties of these molecules helps us understand how they function in the cell. In this review, we summarize the application of magnetic tweezers (MT) to the study of DNA behavior at the single-molecule level. MT can be conveniently used to stretch DNA and introduce controlled levels of superhelicity into the molecule and to follow to a high definition the action of different types of topoisomerases. Its potential for chromatin studies is also enormous, and we will briefly present our first chromatin results.     

Portable magnetic tweezers device enables visualization of the three-dimensional microscale deformation of soft biological materials

We have designed and built a magnetic tweezers device that enables the application of calibrated stresses to soft materials while simultaneously measuring their microscale deformation using confocal microscopy. Unlike previous magnetic tweezers designs, our device is entirely portable, allowing easy use on microscopes in core imaging facilities or in collaborators' laboratories. The imaging capabilities of the microscope are unimpaired, enabling the 3-D structures of fluorescently labeled materials to be precisely determined under applied load. With this device, we can apply a large range of forces (~1-1200 pN) over micron-scale contact areas to beads that are either embedded within 3-D matrices or attached to the surface of thin slab gels. To demonstrate the usefulness of this instrument, we have studied two important and biologically relevant materials: polyacrylamide-based hydrogel films typical of those used in cell traction force microscopy, and reconstituted networks of microtubules, essential cytoskeletal filaments.     

Versatile laser‐based cell manipulator

Here we describe a two‐photon microscope and laser ablation setup combined with optical tweezers. We tested the setup on the fission yeast Schizosaccharomyces pombe, a commonly used model organism. We show that long‐term imaging can be achieved without significant photo‐bleaching or damage of the sample. The setup can precisely ablate sub‐micrometer structures, such as microtubules and mitotic spindles, inside living cells, which remain viable after the manipulation. Longer exposure times lead to ablation, while shorter exposures lead to photo‐bleaching of the target structure. We used optical tweezers to trap intracellular particles and to displace the cell nucleus. Two‐photon fluorescence imaging of the manipulated cell can be performed simultaneously with trapping. The combination of techniques described here may help to solve a variety of problems in cell biology, such as positioning of organelles and the forces exerted by the cytoskeleton. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence

Optical tweezers have emerged as a powerful technique for micromanipulation of living cells. Although the technique often has been claimed to be nonintrusive, evidence has appeared that this is not always the case. This work presents evidence that near-infrared continuous-wave laser light from optical tweezers can produce stress in Caenorhabditis elegans. A transgenic strain of C. elegans, carrying an integrated heat-shock-responsive reporter gene, has been exposed to laser light under a variety of illumination conditions. It was found that gene expression was most often induced by light of 760 nm, and least by 810 nm. The stress response increased with laser power and irradiation time. At 810 nm, significant gene expression could be observed at 360 mW of illumination, which is more than one order of magnitude above that normally used in optical tweezers. In the 700-760-nm range, the results show that the stress response is caused by photochemical processes, whereas at 810 nm, it mainly has a photothermal origin. These results give further evidence that the 700-760-nm wavelength region is unsuitable for optical tweezers and suggest that work at 810 nm at normal laser powers does not cause stress at the cellular level.     

Invincible DNA tethers: covalent DNA anchoring for enhanced temporal and force stability in magnetic tweezers experiments

Magnetic tweezers are a powerful single-molecule technique that allows real-time quantitative investigation of biomolecular processes under applied force. High pulling forces exceeding tens of picoNewtons may be required, e.g. to probe the force range of proteins that actively transcribe or package the genome. Frequently, however, the application of such forces decreases the sample lifetime, hindering data acquisition. To provide experimentally viable sample lifetimes in the face of high pulling forces, we have designed a novel anchoring strategy for DNA in magnetic tweezers. Our approach, which exploits covalent functionalization based on heterobifunctional poly(ethylene glycol) crosslinkers, allows us to strongly tether DNA while simultaneously suppressing undesirable non-specific adhesion. A complete force and lifetime characterization of these covalently anchored DNA-tethers demonstrates that, compared to more commonly employed anchoring strategies, they withstand 3-fold higher pulling forces (up to 150 pN) and exhibit up to 200-fold higher lifetimes (exceeding 24 h at a constant force of 150 pN). This advance makes it possible to apply the full range of biologically relevant force scales to biomolecular processes, and its straightforward implementation should extend its reach to a multitude of applications in the field of single-molecule force spectroscopy.     

Directed positioning of nuclei in living Paramecium tetraurelia: Use of the laser optical force trap for developmental biology

We have constructed a laser optical force trap (“laser tweezers”) by coupling an Nd:YAG laser to an optical microscope with a high numerical aperture objective. The laser beam (approximately 0.1 W power) is focused to a diffraction-limited spot at the specimen plane of the objective: the wavelength chosen (1,064 nm) is not strongly absorbed by most biological materials and is thus not ablative. Because the intensity of the laser beam increases towards the center of the focal spot, small particles brought near the spot will be attracted to the center and held there. Movement of the laser beam will tend to move any trapped particles with it. The laser tweezers can permit precise, nondestructive repositioning of small structures inside a living cell, without recourse to micromanipulators. Initial work has involved the use of laser tweezers on cells of Paramecium tet-raurelia held by a rotocompressor. We have been able to trap and reposition small organelles, especially the highly refractile structures known as crystals. Using a trapped crystal as a “tool”, we have been able to push micronuclei and other structures for many micrometers to virtually any desired location in a cell. In spite of extended exposure of specific structures and of individual cells to the laser beam, no damage has been detectible. Exposed cells, which were removed from the rotocompres-sor and cultured, showed complete viabilty. The laser tweezers technique shows tremendous potential for applications to the study of many fundamental cellular and developmental phenomena in paramecia and other ciliates. For example, we intend to use this technique to investigate temporal and spatial characteristics of nuclear determining regions during sexual reorganization in Paramecium. © 1992 Wiley-Liss, Inc.     

On the feasibility of obtaining multiple muscular maximal voluntary excitation levels from test exertions: A shoulder example

Currently, contrasting views exist regarding which body and arm postures are most effective for eliciting maximal voluntary exertions in the shoulder muscles. Informed exertion standardization may improve comparisons between subjects and muscle groups for normalized electromyography values. Additionally, identifying exertions that can produce equivalent maximal electrical activity values can reduce experimental setup time and reduce the likelihood of fatigue development. This research study examined twelve posture and force direction defined test exertions to identify those that elicited maximal electrical activity from the deltoid (anterior and middle fibres) and pectoralis major (clavicular and sternal heads). Further, the question of whether a single test exertion could obtain maximal electrical activity from multiple muscle fascicles was explored. Maximal activation was demonstrated for the deltoid during several exertions that incorporated an upward force exertion and the pectoralis major for multiple exertions that included an inward force direction. Finally, two test exertions produced maximal electrical activity from both muscles of interest. This research supports the notion that a range of exertions can elicit maximal electrical activity from a muscle, rather than one specific exertion. This suggests that researchers may be able to leverage a smaller set of test exertions to evaluate multiple muscles simultaneously without loss of data quality, and thereby decrease overall experimental data collection time while maintaining high fidelity data.     

活细胞染色体切割（光刀）和光捕捉（光钳）的研究

本文报道了光捕捉活细胞染色体的最新实验结果。对ＰＴＫ＿２有丝分裂细胞的染色体先围激光刀切割,再用光钳捕捉使该切割的染色体片断的行为发生改变。光捕捉中期切割的染色体片断有可能使它们整合到同一个子细胞中或丢失在分裂沟中。光捕捉后期切割的染色体可使该切割片断或掺入相反的细胞中或丢失在分裂沟中或回到原有的相应子细胞中。光捕捉操纵染色体去水螈肺上支子细胞中不仅同样有效,还可以在纺缍体的边缘,即纺缍体和间丝笼之间的细胞质清澈区域内用光钳操纵染色体片断移动,旋转。根据细胞和染色体形态和行为,对７００－８４０ｎｍ波长范围内的各种波长的光捕捉进行了比较,结果表明,７００ｎｍ或８００－８２０ｎｍ波长操纵的细胞,出现最少的异常细胞百分率,７６０ｎｍ则诱发百分之百的异常细胞率。根据各方面的综合比较,７００ｎｍ为最佳波长,共次为１０６０和８００ｎｍ。７６０ｎｍ损伤细胞最严重,应避免使用。文中并讨论了光捕捉染色体的应用前景。