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.     

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.     

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.     

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.     

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.     

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.     

NAP1-Assisted Nucleosome Assembly on DNA Measured in Real Time by Single-Molecule Magnetic Tweezers

While many proteins are involved in the assembly and (re)positioning of nucleosomes, the dynamics of protein-assisted nucleosome formation are not well understood. We study NAP1 (nucleosome assembly protein 1) assisted nucleosome formation at the single-molecule level using magnetic tweezers. This method allows to apply a well-defined stretching force and supercoiling density to a single DNA molecule, and to study in real time the change in linking number, stiffness and length of the DNA during nucleosome formation. We observe a decrease in end-to-end length when NAP1 and core histones (CH) are added to the dsDNA. We characterize the formation of complete nucleosomes by measuring the change in linking number of DNA, which is induced by the NAP1-assisted nucleosome assembly, and which does not occur for non-nucleosomal bound histones H3 and H4. By rotating the magnets, the supercoils formed upon nucleosome assembly are removed and the number of assembled nucleosomes can be counted. We find that the compaction of DNA at low force is about 56 nm per assembled nucleosome. The number of compaction steps and associated change in linking number indicate that NAP1-assisted nucleosome assembly is a two-step process.     

Calibration of Optical Tweezers for In Vivo Force Measurements: How do Different Approaches Compare?

There is significant interest in quantifying force production inside cells, but since conditions in vivo are less well controlled than those in vitro, in vivo measurements are challenging. In particular, the in vivo environment may vary locally as far as its optical properties, and the organelles manipulated by the optical trap frequently vary in size and shape. Several methods have been proposed to overcome these difficulties. We evaluate the relative merits of these methods and directly compare two of them, a refractive index matching method, and a light-momentum-change method. Since in vivo forces are frequently relatively high (e.g., can exceed 15 pN for lipid droplets), a high-power laser is employed. We discover that this high-powered trap induces local temperature changes, and we develop an approach to compensate for uncertainties in the magnitude of applied force due to such temperature variations.     

Blind Predictions of DNA and RNA Tweezers Experiments with Force and Torque

Single-molecule tweezers measurements of double-stranded nucleic acids (dsDNA and dsRNA) provide unprecedented opportunities to dissect how these fundamental molecules respond to forces and torques analogous to those applied by topoisomerases, viral capsids, and other biological partners. However, tweezers data are still most commonly interpreted post facto in the framework of simple analytical models. Testing falsifiable predictions of state-of-the-art nucleic acid models would be more illuminating but has not been performed. Here we describe a blind challenge in which numerical predictions of nucleic acid mechanical properties were compared to experimental data obtained recently for dsRNA under applied force and torque. The predictions were enabled by the HelixMC package, first presented in this paper. HelixMC advances crystallography-derived base-pair level models (BPLMs) to simulate kilobase-length dsDNAs and dsRNAs under external forces and torques, including their global linking numbers. These calculations recovered the experimental bending persistence length of dsRNA within the error of the simulations and accurately predicted that dsRNA''s “spring-like” conformation would give a two-fold decrease of stretch modulus relative to dsDNA. Further blind predictions of helix torsional properties, however, exposed inaccuracies in current BPLM theory, including three-fold discrepancies in torsional persistence length at the high force limit and the incorrect sign of dsRNA link-extension (twist-stretch) coupling. Beyond these experiments, HelixMC predicted that ‘nucleosome-excluding’ poly(A)/poly(T) is at least two-fold stiffer than random-sequence dsDNA in bending, stretching, and torsional behaviors; Z-DNA to be at least three-fold stiffer than random-sequence dsDNA, with a near-zero link-extension coupling; and non-negligible effects from base pair step correlations. We propose that experimentally testing these predictions should be powerful next steps for understanding the flexibility of dsDNA and dsRNA in sequence contexts and under mechanical stresses relevant to their biology.     

DNA芯片技术及应用

DNA芯片技术是随着人类基因组计划的实施发展起来的一项高新技术。本文介绍了DNA芯片的基本原理,并对近年来DNA芯片技术的应用进行了综述。     

Analysis and Optimization of Pulse Dynamics for Magnetic Stimulation

Magnetic stimulation is a standard tool in brain research and has found important clinical applications in neurology, psychiatry, and rehabilitation. Whereas coil designs and the spatial field properties have been intensively studied in the literature, the temporal dynamics of the field has received less attention. Typically, the magnetic field waveform is determined by available device circuit topologies rather than by consideration of what is optimal for neural stimulation. This paper analyzes and optimizes the waveform dynamics using a nonlinear model of a mammalian axon. The optimization objective was to minimize the pulse energy loss. The energy loss drives power consumption and heating, which are the dominating limitations of magnetic stimulation. The optimization approach is based on a hybrid global-local method. Different coordinate systems for describing the continuous waveforms in a limited parameter space are defined for numerical stability. The optimization results suggest that there are waveforms with substantially higher efficiency than that of traditional pulse shapes. One class of optimal pulses is analyzed further. Although the coil voltage profile of these waveforms is almost rectangular, the corresponding current shape presents distinctive characteristics, such as a slow low-amplitude first phase which precedes the main pulse and reduces the losses. Representatives of this class of waveforms corresponding to different maximum voltages are linked by a nonlinear transformation. The main phase, however, scales with time only. As with conventional magnetic stimulation pulses, briefer pulses result in lower energy loss but require higher coil voltage than longer pulses.     

Nano-Precision Tweezers for Mechanosensitive Proteins and Beyond

Mechanical forces play pivotal roles in regulating cell shape, function, and fate. Key players that govern the mechanobiological interplay are the mechanosensitive proteins found on cell membranes and in cytoskeleton. Their unique nanomechanics can be interrogated using single-molecule tweezers, which can apply controlled forces to the proteins and simultaneously measure the ensuing structural changes. Breakthroughs in high-resolution tweezers have enabled the routine monitoring of nanometer-scale, millisecond dynamics as a function of force. Undoubtedly, the advancement of structural biology will be further fueled by integrating static atomic-resolution structures and their dynamic changes and interactions observed with the force application techniques. In this minireview, we will introduce the general principles of single-molecule tweezers and their recent applications to the studies of force-bearing proteins, including the synaptic proteins that need to be categorized as mechanosensitive in a broad sense. We anticipate that the impact of nano-precision approaches in mechanobiology research will continue to grow in the future.     

A General Method for Modeling Population Dynamics and Its Applications

Studying populations, be it a microbe colony or mankind, is important for understanding how complex systems evolve and exist. Such knowledge also often provides insights into evolution, history and different aspects of human life. By and large, populations’ prosperity and decline is about transformation of certain resources into quantity and other characteristics of populations through growth, replication, expansion and acquisition of resources. We introduce a general model of population change, applicable to different types of populations, which interconnects numerous factors influencing population dynamics, such as nutrient influx and nutrient consumption, reproduction period, reproduction rate, etc. It is also possible to take into account specific growth features of individual organisms. We considered two recently discovered distinct growth scenarios: first, when organisms do not change their grown mass regardless of nutrients availability, and the second when organisms can reduce their grown mass by several times in a nutritionally poor environment. We found that nutrient supply and reproduction period are two major factors influencing the shape of population growth curves. There is also a difference in population dynamics between these two groups. Organisms belonging to the second group are significantly more adaptive to reduction of nutrients and far more resistant to extinction. Also, such organisms have substantially more frequent and lesser in amplitude fluctuations of population quantity for the same periodic nutrient supply (compared to the first group). Proposed model allows adequately describing virtually any possible growth scenario, including complex ones with periodic and irregular nutrient supply and other changing parameters, which present approaches cannot do.     

Single-Stranded DNA within Nanopores: Conformational Dynamics and Implications for Sequencing; a Molecular Dynamics Simulation Study

Engineered protein nanopores, such as those based on α-hemolysin from Staphylococcus aureus have shown great promise as components of next-generation DNA sequencing devices. However, before such protein nanopores can be used to their full potential, the conformational dynamics and translocation pathway of the DNA within them must be characterized at the individual molecule level. Here, we employ atomistic molecular dynamics simulations of single-stranded DNA movement through a model α-hemolysin pore under an applied electric field. The simulations enable characterization of the conformations adopted by single-stranded DNA, and allow exploration of how the conformations may impact on translocation within the wild-type model pore and a number of mutants. Our results show that specific interactions between the protein nanopore and the DNA can have a significant impact on the DNA conformation often leading to localized coiling, which in turn, can alter the order in which the DNA bases exit the nanopore. Thus, our simulations show that strategies to control the conformation of DNA within a protein nanopore would be a distinct advantage for the purposes of DNA sequencing.     

Axial Optical Traps: A New Direction for Optical Tweezers

Optical tweezers have revolutionized our understanding of the microscopic world. Axial optical tweezers, which apply force to a surface-tethered molecule by directly moving either the trap or the stage along the laser beam axis, offer several potential benefits when studying a range of novel biophysical phenomena. This geometry, although it is conceptually straightforward, suffers from aberrations that result in variation of the trap stiffness when the distance between the microscope coverslip and the trap focus is being changed. Many standard techniques, such as back-focal-plane interferometry, are difficult to employ in this geometry due to back-scattered light between the bead and the coverslip, whereas the noise inherent in a surface-tethered assay can severely limit the resolution of an experiment. Because of these complications, precision force spectroscopy measurements have adapted alternative geometries such as the highly successful dumbbell traps. In recent years, however, most of the difficulties inherent in constructing a precision axial optical tweezers have been solved. This review article aims to inform the reader about recent progress in axial optical trapping, as well as the potential for these devices to perform innovative biophysical measurements.     

Protein Sliding along DNA: Dynamics and Structural Characterization

Efficient search of DNA by proteins is fundamental to the control of cellular regulatory processes. It is currently believed that protein sliding, hopping, and transfer between adjacent DNA segments, during which the protein nonspecifically interacts with DNA, are central to the speed of their specific recognition. In this study, we focused on the structural and dynamic features of proteins when they scan the DNA. Using a simple computational model that represents protein-DNA interactions by electrostatic forces, we identified that the protein makes use of identical binding interfaces for both nonspecific and specific DNA interactions. Accordingly, in its one-dimensional diffusion along the DNA, the protein is bound at the major groove and performs a helical motion, which is stochastic and driven by thermal diffusion. A microscopic structural insight into sliding from our model, which is governed by electrostatic forces, corroborates previous experimental studies suggesting that the active site of some regulatory proteins continually faces the interior of the DNA groove while sliding along sugar-phosphate rails. The diffusion coefficient of spiral motion along the major groove of the DNA is not affected by salt concentration, but the efficiency of the search can be significantly enhanced by increasing salt concentration due to a larger number of hopping events. We found that the most efficient search comprises ∼ 20% sliding along the DNA and ∼ 80% hopping and three-dimensional diffusion. The presented model that captures various experimental features of facilitated diffusion has the potency to address other questions regarding the nature of DNA search, such as the sliding characteristics of oligomeric and multidomain DNA-binding proteins that are ubiquitous in the cell.     

Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics

Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles’ size distribution and moment and the applied field’s amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter.     

磁性氧化铁纳米颗粒及其磁共振成像应用

磁性氧化铁纳米颗粒在磁共振成像方面的应用,已经在全世界范围内得到了广泛的关注,相关研究也被各国科学家高度重视.目前,磁性氧化铁纳米颗粒正在从早期的基于被动识别的肝部磁共振造影,快速转向基于主动识别的磁共振分子影像应用.本文将围绕磁性氧化铁纳米颗粒的生物体内应用,着重介绍磁性纳米颗粒的制备及其在疾病诊断,尤其是在肿瘤早期...