High Spatiotemporal-Resolution Magnetic Tweezers: Calibration and Applications for DNA Dynamics

The observation of biological processes at the molecular scale in real time requires high spatial and temporal resolution. Magnetic tweezers are straightforward to implement, free of radiation or photodamage, and provide ample multiplexing capability, but their spatiotemporal resolution has lagged behind that of other single-molecule manipulation techniques, notably optical tweezers and AFM. Here, we present, to our knowledge, a new high-resolution magnetic tweezers apparatus. We systematically characterize the achievable spatiotemporal resolution for both incoherent and coherent light sources, different types and sizes of beads, and different types and lengths of tethered molecules. Using a bright coherent laser source for illumination and tracking at 6 kHz, we resolve 3 Å steps with a 1 s period for surface-melted beads and 5 Å steps with a 0.5 s period for double-stranded-dsDNA-tethered beads, in good agreement with a model of stochastic bead motion in the magnetic tweezers. We demonstrate how this instrument can be used to monitor the opening and closing of a DNA hairpin on millisecond timescales in real time, together with attendant changes in the hairpin dynamics upon the addition of deoxythymidine triphosphate. Our approach opens up the possibility of observing biological events at submillisecond timescales with subnanometer resolution using camera-based detection.     

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.     

Nano-mechanical measurements of protein-DNA interactions with a silicon nitride pulley

Proteins adhere to DNA at locations and with strengths that depend on the protein conformation, the underlying DNA sequence and the ionic content of the solution. A facile technique to probe the positions and strengths of protein-DNA binding would aid in understanding these important interactions. Here, we describe a ‘DNA pulley’ for position-resolved nano-mechanical measurements of protein-DNA interactions. A molecule of λ DNA is tethered by one end to a glass surface, and by the other end to a magnetic bead. The DNA is stretched horizontally by a magnet, and a nanoscale knife made of silicon nitride is manipulated to contact, bend and scan along the DNA. The mechanical profile of the DNA at the contact with the knife is probed via nanometer-precision optical tracking of the magnetic bead. This system enables detection of protein bumps on the DNA and localization of their binding sites. We study theoretically the technical requirements to detect mechanical heterogeneities in the DNA itself.     

Kinesin velocity increases with the number of motors pulling against viscoelastic drag

Although the properties of single kinesin molecular motors are well understood, it is not clear whether multiple motors pulling a single vesicle in a cell cooperate or interfere with one another. To learn how small numbers of motors interact, microtubule gliding assays were carried out with full-length Drosophila kinesin in a novel motility medium containing xanthan, a stiff, water-soluble polysaccharide. At 2 mg/ml xanthan, the zero-shear viscosity of this medium is 1,000 times the viscosity of water, similar to cellular viscosity. To mimic the rheological drag force on the motors when attached to a vesicle in a cell, we attached a 2 μm bead to one end of the microtubule (MT). During gliding assays in our novel medium, the moving bead exerted a drag force of 4–15 pN on the kinesins pulling the MT. The velocity of MTs with an attached bead increased with MT length and with kinesin concentration. The increase with MT length arose because the number of motors is directly proportional to MT length. Our results show that small numbers of kinesins cooperate constructively when pulling against a viscoelastic drag. In the absence of a bead but still in the viscous medium, MT velocity was independent of MT length and kinesin concentration because the thin MT, like a snake moving through grass, was able to move between xanthan molecules with little resistance. A minimal shared-load model in which the number of motors is proportional to MT length fits the observed dependence of gliding velocity on MT length and kinesin concentration.     

Quantitative measurements of force and displacement using an optical trap.

We combined a single-beam gradient optical trap with a high-resolution photodiode position detector to show that an optical trap can be used to make quantitative measurements of nanometer displacements and piconewton forces with millisecond resolution. When an external force is applied to a micron-sized bead held by an optical trap, the bead is displaced from the center of the trap by an amount proportional to the applied force. When the applied force is changed rapidly, the rise time of the displacement is on the millisecond time scale, and thus a trapped bead can be used as a force transducer. The performance can be enhanced by a feedback circuit so that the position of the trap moves by means of acousto-optic modulators to exert a force equal and opposite to the external force applied to the bead. In this case the position of the trap can be used to measure the applied force. We consider parameters of the trapped bead such as stiffness and response time as a function of bead diameter and laser beam power and compare the results with recent ray-optic calculations.     

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer.

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G'(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G'(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.     

Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position.

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.     

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.     

Multiplexed Nanometric 3D Tracking of Microbeads Using an FFT-Phasor Algorithm

Many single-molecule biophysical techniques rely on nanometric tracking of microbeads to obtain quantitative information about the mechanical properties of biomolecules such as chromatin fibers. Their three-dimensional (3D) position can be resolved by holographic analysis of the diffraction pattern in wide-field imaging. Fitting this diffraction pattern to Lorenz-Mie scattering theory yields the bead’s position with nanometer accuracy in three dimensions but is computationally expensive. Real-time multiplexed bead tracking therefore requires a more efficient tracking method, such as comparison with previously measured diffraction patterns, known as look-up tables. Here, we introduce an alternative 3D phasor algorithm that provides robust bead tracking with nanometric localization accuracy in a z range of over 10 μm under nonoptimal imaging conditions. The algorithm is based on a two-dimensional cross correlation using fast Fourier transforms with computer-generated reference images, yielding a processing rate of up to 10,000 regions of interest per second. We implemented the technique in magnetic tweezers and tracked the 3D position of over 100 beads in real time on a generic CPU. The accuracy of 3D phasor tracking was extensively tested and compared to a look-up table approach using Lorenz-Mie simulations, avoiding experimental uncertainties. Its easy implementation, efficiency, and robustness can improve multiplexed biophysical bead-tracking applications, especially when high throughput is required and image artifacts are difficult to avoid.     

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.     

Measuring single cardiac myocyte contractile force via moving a magnetic bead

One of the biggest problems of heart failure is the heart's inability to effectively pump blood to meet the body's demands, which may be caused by disease-induced alterations in contraction properties (such as contractile force and Young's modulus). Thus, it is very important to measure contractile properties at single cardiac myocyte level that can lay the foundation for quantitatively understanding the mechanism of heart failure and understanding molecular alterations in diseased heart cells. In this article, we report a novel single cardiac myocyte contractile force measurement technique based on moving a magnetic bead. The measuring system is mainly composed of 1), a high-power inverted microscope with video output and edge detection; and 2), a moving magnetic bead based magnetic force loading module. The main measurement procedures are as follows: 1), record maximal displacement of single cardiac myocyte during contraction; 2), attach a magnetic bead on one end of the myocyte that will move with myocyte during the contraction; 3), repeat step 1 and record contraction processes under different magnitudes of magnetic force loading by adjusting the magnetic field applied on the magnetic bead; and 4), derive the myocyte contractile force base on the maximal displacement of cell contraction and magnetic loading force. The major advantages of this unique approach are: 1), measuring the force without direct connections to the cell specimen (i.e., "remote sensing", a noninvasive/minimally invasive approach); 2), high sensitivity and large dynamic range (force measurement range: from pico Newton to micro Newton); 3), a convenient and cost-effective approach; and 4), more importantly, it can be used to study the contractile properties of heart cells under different levels of external loading forces by adjusting the magnitude of applied magnetic field, which is very important for studying disease induced alterations in contraction properties. Experimental results demonstrated the feasibility of proposed approach.     

Impact-Free Measurement of Microtubule Rotations on Kinesin and Cytoplasmic-Dynein Coated Surfaces

Knowledge about the three-dimensional stepping of motor proteins on the surface of microtubules (MTs) as well as the torsional components in their power strokes can be inferred from longitudinal MT rotations in gliding motility assays. In previous studies, optical detection of these rotations relied on the tracking of rather large optical probes present on the outer MT surface. However, these probes may act as obstacles for motor stepping and may prevent the unhindered rotation of the gliding MTs. To overcome these limitations, we devised a novel, impact-free method to detect MT rotations based on fluorescent speckles within the MT structure in combination with fluorescence-interference contrast microscopy. We (i) confirmed the rotational pitches of MTs gliding on surfaces coated by kinesin-1 and kinesin-8 motors, (ii) demonstrated the superiority of our method over previous approaches on kinesin-8 coated surfaces at low ATP concentration, and (iii) identified MT rotations driven by mammalian cytoplasmic dynein, indicating that during collective motion cytoplasmic dynein side-steps with a bias in one direction. Our novel method is easy to implement on any state-of-the-art fluorescence microscope and allows for high-throughput experiments.     

Behavior of supercoiled DNA.

We study DNA supercoiling in a quantitative fashion by micromanipulating single linear DNA molecules with a magnetic field gradient. By anchoring one end of the DNA to multiple sites on a magnetic bead and the other end to multiple sites on a glass surface, we were able to exert torsional control on the DNA. A rotating magnetic field was used to induce rotation of the magnetic bead, and reversibly over- and underwind the molecule. The magnetic field was also used to increase or decrease the stretching force exerted by the magnetic bead on the DNA. The molecule's degree of supercoiling could therefore be quantitatively controlled and monitored, and tethered-particle motion analysis allowed us to measure the stretching force acting on the DNA. Experimental results indicate that this is a very powerful technique for measuring forces at the picoscale. We studied the effect of stretching forces ranging from 0.01 pN to 100 pN on supercoiled DNA (-0.1 < sigma < 0.2) in a variety of ionic conditions. Other effects, such as stretching-relaxing hysteresis and the braiding of two DNA molecules, are discussed.     

Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods

Single particle tracking is widely used to study protein movement with high spatiotemporal resolution both in vitro and in cells. Quantum dots, which are semiconductor nanoparticles, have recently been employed in single particle tracking because of their intense and stable fluorescence. Although single particles inside cells have been tracked in three spatial dimensions (X, Y, Z), measurement of the angular orientation of a molecule being tracked would significantly enhance our understanding of the molecule’s function. In this study, we synthesized highly polarized, rod-shaped quantum dots (Qrods) and developed a coating method that optimizes the Qrods for biological imaging. We describe a Qrod-based single particle tracking technique that blends optical nanometry with nanomaterial science to simultaneously measure the three-dimensional and angular movements of molecules. Using Qrods, we spatially tracked a membrane receptor in living cells in four dimensions with precision close to the single-digit range in nanometers and degrees.     

Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods

Single particle tracking is widely used to study protein movement with high spatiotemporal resolution both in vitro and in cells. Quantum dots, which are semiconductor nanoparticles, have recently been employed in single particle tracking because of their intense and stable fluorescence. Although single particles inside cells have been tracked in three spatial dimensions (X, Y, Z), measurement of the angular orientation of a molecule being tracked would significantly enhance our understanding of the molecule’s function. In this study, we synthesized highly polarized, rod-shaped quantum dots (Qrods) and developed a coating method that optimizes the Qrods for biological imaging. We describe a Qrod-based single particle tracking technique that blends optical nanometry with nanomaterial science to simultaneously measure the three-dimensional and angular movements of molecules. Using Qrods, we spatially tracked a membrane receptor in living cells in four dimensions with precision close to the single-digit range in nanometers and degrees.     

Theoretical modeling of aging effects in microtubule dynamics

The microtubule (MT) network, an important part of the cytoskeleton, is constantly remodeled by alternating phases of growth and shrinkage of individual filaments. Plus-end tracking proteins (+TIPs) interact with the MT and in many cases alter its dynamics. Although it is established that some +TIPs modify MT dynamics by increasing rescues, the plus-end tracking mechanism is still under debate. We present a model for MT dynamics in which a rescue factor is dynamically added to the filament during growth. As a consequence, the filament shows aging behavior that should be experimentally accessible and thus allow one to exclude some hypothesized models regarding the inclusion of rescue factors at the MT plus end. This result is not limited to +TIPs and can be extended to any kind of mechanism shifting the parameters of dynamic instability. Additionally, we show that the cell geometry has a strong influence on the quantitative results.     

Mapping the organization of axis of motion selective features in human area MT using high-field fMRI

Functional magnetic resonance imaging (fMRI) at high magnetic fields has made it possible to investigate the columnar organization of the human brain in vivo with high degrees of accuracy and sensitivity. Until now, these results have been limited to the organization principles of early visual cortex (V1). While the middle temporal area (MT) has been the first identified extra-striate visual area shown to exhibit a columnar organization in monkeys, evidence of MT's columnar response properties and topographic layout in humans has remained elusive. Research using various approaches suggests similar response properties as in monkeys but failed to provide direct evidence for direction or axis of motion selectivity in human area MT. By combining state of the art pulse sequence design, high spatial resolution in all three dimensions (0.8 mm isotropic), optimized coil design, ultrahigh field magnets (7 Tesla) and novel high resolution cortical grid sampling analysis tools, we provide the first direct evidence for large-scale axis of motion selective feature organization in human area MT closely matching predictions from topographic columnar-level simulations.     

The motion of a single molecule,the lambda-receptor,in the bacterial outer membrane

Using optical tweezers and single particle tracking, we have revealed the motion of a single protein, the lambda-receptor, in the outer membrane of living Escherichia coli bacteria. We genetically modified the lambda-receptor placing a biotin on an extracellular site of the receptor in vivo. The efficiency of this in vivo biotinylation is very low, thus enabling the attachment of a streptavidin-coated bead binding specifically to a single biotinylated lambda-receptor. The bead was used as a handle for the optical tweezers and as a marker for the single particle tracking routine. We propose a model that allows extraction of the motion of the protein from measurements of the mobility of the bead-molecule complex; these results are equally applicable to analyze bead-protein complexes in other membrane systems. Within a domain of radius approximately 25 nm, the receptor diffuses with a diffusion constant of (1.5 +/- 1.0) x 10(-9) cm(2)/s and sits in a harmonic potential as if it were tethered by an elastic spring of spring constant of ~1.0 x 10(-2) pN/nm to the bacterial membrane. The purpose of the protein motion might be to facilitate transport of maltodextrins through the outer bacterial membrane.     

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.     

Tuning microtubule-based transport through filamentous MAPs: the problem of dynein

We recently proposed that regulating the single-to-multiple motor transition was a likely strategy for regulating kinesin-based transport in vivo . In this study, we use an in vitro bead assay coupled with an optical trap to investigate how this proposed regulatory mechanism affects dynein-based transport. We show that tau's regulation of kinesin function can proceed without interfering with dynein-based transport. Surprisingly, at extremely high tau levels – where kinesin cannot bind microtubules (MTs) – dynein can still contact MTs. The difference between tau's effects on kinesin- and dynein-based motility suggests that tau can be used to tune relative amounts of plus-end and minus-end-directed transport. As in the case of kinesin, we find that the 3RS isoform of tau is a more potent inhibitor of dynein binding to MTs. We show that this isoform-specific effect is not because of steric interference of tau's projection domains but rather because of tau's interactions with the motor at the MT surface. Nonetheless, we do observe a modest steric interference effect of tau away from the MT and discuss the potential implications of this for molecular motor structure.