Magnetic Tweezers Experiments Research Articles

Theoretical study of the nonlinear force-loading control in single-molecule stretching experiments

Force spectrum measurements with constant loading rates are widely used in single-molecule manipulation experiments to study the mechanical stability and force response of biomolecules. Force-dependent transition rates can be obtained from the transition force distribution, but it is limited to the force range with non-zero force distribution. Although constant loading rate control can be realized with magnetic tweezers, the loading rate range is limited due to the slow movement of permanent magnets. Non-linear exponential and exponential squared force loading functions are more feasible in magnetic tweezers, while there is no theoretical result available for these two kinds of non-linear force loading functions. In this study, we solved the unfolding process of a protein following Bell’s model under nonlinear exponential and exponential squared force loading functions, which offer a broader range of unfolding force distribution compared to the traditional constant loading rate experiments. Furthermore, we derived two force loading functions, which can produce uniform unfolding force distribution. This research contributes fundamental equations for the analysis of experimental data obtained through single-molecule manipulation under nonlinear force loading controls, paving the way for the use of nonlinear force control in magnetic tweezer experiments.

Temperature-Dependent Twist of Double-Stranded RNA Probed by Magnetic Tweezer Experiments and Molecular Dynamics Simulations.

RNA plays critical roles in the transmission and regulation of genetic information and is increasingly used in biomedical and biotechnological applications. Functional RNAs contain extended double-stranded regions, and the structure of double-stranded RNA (dsRNA) has been revealed at high resolution. However, the dependence of the properties of the RNA double helix on environmental effects, notably temperature, is still poorly understood. Here, we use single-molecule magnetic tweezer measurements to determine the dependence of the dsRNA twist on temperature. We find that dsRNA unwinds with increasing temperature, even more than DNA, with ΔTwRNA = -14.4 ± 0.7°/(°C·kbp), compared to ΔTwDNA = -11.0 ± 1.2°/(°C·kbp). All-atom molecular dynamics (MD) simulations using a range of nucleic acid force fields, ion parameters, and water models correctly predict that dsRNA unwinds with rising temperature but significantly underestimate the magnitude of the effect. These MD data, together with additional MD simulations involving DNA and DNA-RNA hybrid duplexes, reveal a linear correlation between the twist temperature decrease and the helical rise, in line with DNA but at variance with RNA experimental data. We speculate that this discrepancy might be caused by some unknown bias in the RNA force fields tested or by as yet undiscovered transient alternative structures in the RNA duplex. Our results provide a baseline to model more complex RNA assemblies and to test and develop new parametrizations for RNA simulations. They may also inspire physical models of the temperature-dependent dsRNA structure.

Unravelling DNA Organization with Single-Molecule Force Spectroscopy Using Magnetic Tweezers.

Genomes carry the genetic blueprint of all living organisms. Their organization requires strong condensation as well as carefully regulated accessibility to specific genes for proper functioning of their hosts. The study of the structure and dynamics of the proteins that organize the genome has benefited tremendously from the development of single-molecule force spectroscopy techniques that allow for real-time, nanometer accuracy measurements of the compaction of DNA and manipulation with pico-Newton scale forces. Magnetic tweezers, in particular, have the unique ability to complement such force spectroscopy with the control over the linking number of the DNA molecule, which plays an important role when DNA-organizing proteins form or release wraps, loops, and bends in DNA. Here, we describe all the necessary steps to prepare DNA substrates for magnetic tweezers experiments, assemble flow cells, tether DNA to a magnetic bead inside a flow cell, and manipulate and record the extension of such DNA tethers. Furthermore, we explain how mechanical parameters of nucleoprotein filaments can be extracted from the data.

Allosteric activation of vinculin by talin

The talin-vinculin axis is a key mechanosensing component of cellular focal adhesions. How talin and vinculin respond to forces and regulate one another remains unclear. By combining single-molecule magnetic tweezers experiments, Molecular Dynamics simulations, actin-bundling assays, and adhesion assembly experiments in live cells, we here describe a two-ways allosteric network within vinculin as a regulator of the talin-vinculin interaction. We directly observe a maturation process of vinculin upon talin binding, which reinforces the binding to talin at a rate of 0.03 s−1. This allosteric transition can compete with force-induced dissociation of vinculin from talin only at forces up to 10 pN. Mimicking the allosteric activation by mutation yields a vinculin molecule that bundles actin and localizes to focal adhesions in a force-independent manner. Hence, the allosteric switch confines talin-vinculin interactions and focal adhesion build-up to intermediate force levels. The ‘allosteric vinculin mutant’ is a valuable molecular tool to further dissect the mechanical and biochemical signalling circuits at focal adhesions and elsewhere.

Universality in RNA and DNA deformations induced by salt, temperature change, stretching force, and protein binding

Nucleic acid deformations play important roles in many biological processes. The physical understanding of nucleic acid deformation by environmental stimuli is limited due to the challenge in the precise measurement of RNA and DNA deformations and the complexity of interactions in RNA and DNA. Magnetic tweezers experiments provide an excellent opportunity to precisely measure DNA and RNA twist changes induced by environmental stimuli. In this work, we applied magnetic tweezers to measure double-stranded RNA twist changes induced by salt and temperature changes. We observed RNA unwinds when lowering salt concentration, or increasing temperature. Our molecular dynamics simulations revealed the mechanism: lowering salt concentration or increasing temperature enlarges RNA major groove width, which causes twist decrease through twist-groove coupling. Combining these results with previous results, we found some universality in RNA and DNA deformations induced by three different stimuli: salt change, temperature, and stretching force. For RNA, these stimuli first modify the major groove width, which is transduced into twist change through twist-groove coupling. For DNA, these stimuli first modify diameter, which is transduced into twist change through twist-diameter coupling. Twist-groove coupling and twist-diameter coupling appear to be utilized by protein binding to reduce DNA and RNA deformation energy cost upon protein binding.

Digital holography-based 3D particle localization for single-molecule tweezer techniques

We present a three-dimensional (3D) imaging technique for the fast tracking of microscopic objects in a fluid environment. Our technique couples digital holographic microscopy with three-dimensional localization via parabolic masking. Compared with existing approaches, our method reconstructs 3D volumes from single-plane images, which greatly simplifies image acquisition, reduces the demand on microscope hardware, and facilitates tracking higher densities of microscopic particles while maintaining similar levels of precision. We demonstrate utility of this method in magnetic tweezer experiments, opening their use to multiplexed single-molecule force spectroscopy assays, which were previously limited by particle crowding and fast dissociation times. We propose that our technique will also be useful in other applications that involve the tracking of microscopic objects in three dimensions, such as studies of microorganism motility and 3D flow characterization of microfluidic devices.

Twisting DNA by salt.

The structure and properties of DNA depend on the environment, in particular the ion atmosphere. Here, we investigate how DNA twist -one of the central properties of DNA- changes with concentration and identity of the surrounding ions. To resolve how cations influence the twist, we combine single-molecule magnetic tweezer experiments and extensive all-atom molecular dynamics simulations. Two interconnected trends are observed for monovalent alkali and divalent alkaline earth cations. First, DNA twist increases monotonously with increasing concentration for all ions investigated. Second, for a given salt concentration, DNA twist strongly depends on cation identity. At 100 mM concentration, DNA twist increases as Na+ < K+ < Rb+ < Ba2+ < Li+ ≈ Cs+ < Sr2+ < Mg2+ < Ca2+. Our molecular dynamics simulations reveal that preferential binding of the cations to the DNA backbone or the nucleobases has opposing effects on DNA twist and provides the microscopic explanation of the observed ion specificity. However, the simulations also reveal shortcomings of existing force field parameters for Cs+ and Sr2+. The comprehensive view gained from our combined approach provides a foundation for understanding and predicting cation-induced structural changes both in nature and in DNA nanotechnology.

Twist-diameter coupling drives DNA twist changes with salt and temperature.

DNA deformations upon environmental changes, e.g., salt and temperature, play crucial roles in many biological processes and material applications. Here, our magnetic tweezers experiments observed that the increase in NaCl, KCl, or RbCl concentration leads to substantial DNA overwinding. Our simulations and theoretical calculation quantitatively explain the salt-induced twist change through the mechanism: More salt enhances the screening of interstrand electrostatic repulsion and hence reduces DNA diameter, which is transduced to twist increase through twist-diameter coupling. We determined that the coupling constant is 4.5 ± 0.8 kBT/(degrees∙nm) for one base pair. The coupling comes from the restraint of the contour length of DNA backbone. On the basis of this coupling constant and diameter-dependent DNA conformational entropy, we predict the temperature dependence of DNA twist Δωbp/ΔT ≈ −0.01 degree/°C, which agrees with our and previous experimental results. Our analysis suggests that twist-diameter coupling is a common driving force for salt- and temperature-induced DNA twist changes.

Multivalent Cations Reverse the Twist-Stretch Coupling of RNA.

When stretched, both DNA and RNA duplexes change their twist angles through twist-stretch coupling. The coupling is negative for DNA but positive for RNA, which is not yet completely understood. Here, our magnetic tweezers experiments show that the coupling of RNA reverses from positive to negative by multivalent cations. Combining with the previously reported tension-induced negative-to-positive coupling reversal of DNA, we propose a unified mechanism of the couplings of both RNA and DNA based on molecular dynamics simulations. Two deformation pathways are competing when stretched: shrinking the radius causes positive couplings but widening the major groove causes negative couplings. For RNA whose major groove is clamped by multivalent cations and canonical DNA, their radii shrink when stretched, thus exhibiting positive couplings. For elongated DNA whose radius already shrinks to the minimum and canonical RNA, their major grooves are widened when stretched, thus exhibiting negative couplings.

Elasticity of single flexible polymer chains in good and poor solvents

Force versus extension curves measure entropic elasticity of single polymer chain in force spectroscopy experiments. A Worm-like Chain model is used to describe force extension experiments with an intrinsic chain parameter called persistence length, which is a measure of local bending flexibility. For flexible polymers, there is a discrepancy in estimates of persistence length in various force regimes. For instance, Atomic Force Microscopy (AFM) based pulling experiments report anomaly low values which are also inconsistent with magnetic tweezers experiments. To understand this, we investigate the role of coupling between microscopic force probe and intrinsic elasticity of polyethylene glycol chain in AFM-based experiments. We perform experiments using oscillatory rheology by providing an external excitation of fixed frequency to the probe. We show that a proper quantification of elastic response measured directly by oscillatory technique deviates significantly from conventional force-extension curves. The persistence length obtained by fitting WLC to stiffness extension data matches well with equilibrium tweezers experiments. In addition, for polystyrene chain in poor solvent no deviation in elastic response is observed between oscillatory and constant velocity pulling experiments. However, such deviation is seen for polystyrene in good solvent. We attribute this to hydrophobic interaction between monomers of polystyrene in water. Our results suggest that oscillatory rheology on single polymer chains provide quantitative estimate of its elastic response. The consistency in values of persistence length using magnetic tweezers experiments in low force regime and the AFM experiments in high force regime suggests that WLC is successful in describing the polymer elasticity in the force range typically probed in AFM experiments.

CTP promotes efficient ParB-dependent DNA condensation by facilitating one-dimensional diffusion from parS.

Faithful segregation of bacterial chromosomes relies on the ParABS partitioning system and the SMC complex. In this work, we used single-molecule techniques to investigate the role of cytidine triphosphate (CTP) binding and hydrolysis in the critical interaction between centromere-like parS DNA sequences and the ParB CTPase. Using a combined optical tweezers confocal microscope, we observe the specific interaction of ParB with parS directly. Binding around parS is enhanced by the presence of CTP or the non-hydrolysable analogue CTPγS. However, ParB proteins are also detected at a lower density in distal non-specific DNA. This requires the presence of a parS loading site and is prevented by protein roadblocks, consistent with one-dimensional diffusion by a sliding clamp. ParB diffusion on non-specific DNA is corroborated by direct visualization and quantification of movement of individual quantum dot labelled ParB. Magnetic tweezers experiments show that the spreading activity, which has an absolute requirement for CTP binding but not hydrolysis, results in the condensation of parS-containing DNA molecules at low nanomolar protein concentrations.

High-yield purification of exceptional-quality, single-molecule DNA substrates

Single-molecule studies involving DNA or RNA, require homogeneous preparations of nucleic acid substrates of exceptional quality. Over the past several years, a variety of methods have been published describing different purification methods but these are frustratingly inconsistent with variable yields even in the hands of experienced bench scientists. To address these issues, we present an optimized and straightforward, column-based approach that is reproducible and produces high yields of substrates or substrate components of exceptional quality. Central to the success of the method presented is the use of a non-porous anion exchange resin. In addition to the use of this resin, we encourage the optimization of each step in the construction of substrates. The fully optimized method produces high yields of a hairpin DNA substrate of exceptional quality. While this substrate is suitable for single-molecule, magnetic tweezer experiments, the described method is readily adaptable to the production of DNA substrates for the majority of single-molecule studies involving nucleic acids ranging in size from 70–15000 bp.

Understanding the paradoxical mechanical response of in-phase A-tracts at different force regimes.

A-tracts are A:T rich DNA sequences that exhibit unique structural and mechanical properties associated with several functions in vivo. The crystallographic structure of A-tracts has been well characterized. However, the mechanical properties of these sequences is controversial and their response to force remains unexplored. Here, we rationalize the mechanical properties of in-phase A-tracts present in the Caenorhabditis elegans genome over a wide range of external forces, using single-molecule experiments and theoretical polymer models. Atomic Force Microscopy imaging shows that A-tracts induce long-range (∼200 nm) bending, which originates from an intrinsically bent structure rather than from larger bending flexibility. These data are well described with a theoretical model based on the worm-like chain model that includes intrinsic bending. Magnetic tweezers experiments show that the mechanical response of A-tracts and arbitrary DNA sequences have a similar dependence with monovalent salt supporting that the observed A-tract bend is intrinsic to the sequence. Optical tweezers experiments reveal a high stretch modulus of the A-tract sequences in the enthalpic regime. Our work rationalizes the complex multiscale flexibility of A-tracts, providing a physical basis for the versatile character of these sequences inside the cell.

A polymer model of bacterial supercoiled DNA including structural transitions of the double helix

DNA supercoiling, the under or overwinding of DNA, is a key physical mechanism both participating to compaction of bacterial genomes and making genomic sequences adopt various structural forms. DNA supercoiling may lead to the formation of braided superstructures (plectonemes), or it may locally destabilize canonical B-DNA to generate denaturation bubbles, left-handed Z-DNA and other functional alternative forms. Prediction of the relative fraction of these structures has been limited because of a lack of predictive polymer models that can capture the multiscale properties of long DNA molecules. In this work, we address this issue by extending the self-avoiding rod-like chain model of DNA so that every site of the chain is allocated with an additional structural degree of freedom reflecting variations of DNA forms. Efficient simulations of the model reveal its relevancy to capture multiscale properties of long chains (here up to 21 kb) as reported in magnetic tweezers experiments. Well-controlled approximations further lead to accurate analytical estimations of thermodynamic properties in the high force regime, providing, in combination with experiments, a simple, yet powerful framework to infer physical parameters describing alternative forms. In this regard, using simulated data, we find that extension curves at forces above 2 pN may lead, alone, to erroneous parameter estimations as a consequence of an underdetermination problem. We thus revisit published data in light of these findings and discuss the relevancy of previously proposed sets of parameters for both denatured and left-handed DNA forms. Altogether, our work paves the way for a scalable quantitative model of bacterial DNA.

Structure and Dynamics of the Telomeric Nucleosome and Chromatin

Eukaryotic genomic DNA is condensed into chromatin: 146bp DNA wraps around the histone octamer (HO) comprising two copies each of the core histones H2A, H2B, H3 and H4 forming the nucleosome core particle (NCP). A string of nucleosomes folds into the so-called called “30nm” chromatin fibre, which compacts into metaphase chromosomes. Human telomeres constitute the protective structure at the end of the chromosomes with repetitive TTAGGG sequences that are about 10kbp. Little is known about the consequences of this unique sequence for chromatin structural and dynamic properties. Although it is established that telomeric DNA is packaged in chromatin with an unusually short (157 bp) nucleosome repeat length (NRL) and can form nucleosomes and chromatin, almost nothing is known about the telomeric nucleosome core and telomeric chromatin structure at the detailed molecular level. We have characterised the telomeric human HO 145 bp DNA NCP (Telo-NCP), using biophysical methods and determined its structure at 2.1 Å resolution with X-ray crystallography. Although the structure is largely similar to the well-known published atomic resolution NCP structures, several differences can be identified, e.g. DNA stretching on the Telo-NCP is different from that of the “601” (high-affinity nucleosome positioning sequence) and alpha satellite NCPs of the same length. We have designed and prepared 20×157 bp telomeric DNA template repeats, reconstituted these with human HO and performed characterisation of the structural and dynamic properties of the telomeric chromatin fibres with EM and single molecule magnetic tweezer experiments. Telomeric chromatin fibres are considerably more homogeneous than corresponding 157 bp repeat fibres reconstituted from 601-DNA array templates. However, the structural and dynamic properties of individual telomeric arrays saturated with 20 nucleosomes, appear similar to equivalent 601 chromatin fibres under the influence of force in single molecule pulling experiment.

Correction-free force calibration for magnetic tweezers experiments

Magnetic tweezers are a powerful technique to perform high-throughput and high-resolution force spectroscopy experiments at the single-molecule level. The camera-based detection of magnetic tweezers enables the observation of hundreds of magnetic beads in parallel, and therefore the characterization of the mechanochemical behavior of hundreds of nucleic acids and enzymes. However, magnetic tweezers experiments require an accurate force calibration to extract quantitative data, which is limited to low forces if the deleterious effect of the finite camera open shutter time (τsh) is not corrected. Here, we provide a simple method to perform correction-free force calibration for high-throughput magnetic tweezers at low image acquisition frequency (fac). By significantly reducing τsh to at most 1/4 the characteristic time of the tethered magnetic bead, we accurately evaluated the variance of the magnetic bead position along the axis parallel to the magnetic field, estimating the force with a relative error of ~10% (standard deviation), being only limited by the bead-to-bead difference. We calibrated several magnets - magnetic beads configurations, covering a force range from ~50 fN to ~60 pN. In addition, for the presented configurations, we provide a table with the mathematical expressions that describe the force as a function of the magnets position.

Kinetic Pathway of Torsional DNA Buckling.

In magnetic tweezers experiments, we observe that torsional DNA buckling rates and transition state distances are insensitive to base-pairing defects. This is surprising because defects are expected to kink DNA and lower the energy of a localized loop. Nonetheless, base-pairing defects lead to pinning of buckled structures at the defects, which may be important for DNA repair in vivo. We find that the decrease in entropy from pinning roughly balances the decrease in bending energy, explaining why defects have little effect on buckling rates. Our data are generally consistent with elastic rod theory, which predicts that the transition state structure for torsional buckling is a localized wave with a specific shape ("soliton"). The transition state soliton decays to a metastable looped intermediate ("curl") that is separated from the final, fully buckled state by a second, low energy barrier. DNAs with base mismatch defects buckle at lower torque, where elastic rod theory predicts the loop structure is more stable, and manifest an intermediate buckling structure consistent with such a loop. We estimate that, under our high force, high salt experimental conditions, the soliton barrier is approximately 10 kB T and, to reach this transition state from the unbuckled state, the system torque instantaneously decreases by approximately 1 pN·nm for DNA with or without a small defect.

Defect-facilitated buckling in supercoiled double-helix DNA.

We present a statistical-mechanical model for stretched twisted double-helix DNA, where thermal fluctuations are treated explicitly from a Hamiltonian without using any scaling hypotheses. Our model applied to defect-free supercoiled DNA describes the coexistence of multiple plectoneme domains in long DNA molecules at physiological salt concentrations (≈0.1MNa^{+}) and stretching forces (≈1pN). We find a higher (lower) number of domains at lower (higher) ionic strengths and stretching forces, in accord with experimental observations. We use our model to study the effect of an immobile point defect on the DNA contour that allows a localized kink. The degree of the kink is controlled by the defect size, such that a larger defect further reduces the bending energy of the defect-facilitated kinked end loop. We find that a defect can spatially pin a plectoneme domain via nucleation of a kinked end loop, in accord with experiments and simulations. Our model explains previously reported magnetic tweezer experiments [A. Dittmore etal., Phys. Rev. Lett. 119, 147801 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.147801] showing two buckling signatures: buckling and "rebuckling" in supercoiled DNA with a base-unpaired region. Comparing with experiments, we find that under 1 pN force, a kinked end loop nucleated at a base-mismatched site reduces the bending energy by ≈0.7k_{B}T per unpaired base. Our model predicts the coexistence of three states at the buckling and rebuckling transitions, which warrants new experiments.

The Work of Titin Protein Folding as a Major Driver in Muscle Contraction

Single-molecule atomic force microscopy and magnetic tweezers experiments have demonstrated that titin immunoglobulin (Ig) domains are capable of folding against a pulling force, generating mechanical work that exceeds that produced by a myosin motor. We hypothesize that upon muscle activation, formation of actomyosin cross bridges reduces the force on titin, causing entropic recoil of the titin polymer and triggering the folding of the titin Ig domains. In the physiological force range of 4-15 pN under which titin operates in muscle, the folding contraction of a single Ig domain can generate 200% of the work of entropic recoil and occurs at forces that exceed the maximum stalling force of single myosin motors. Thus, titin operates like a mechanical battery, storing elastic energy efficiently by unfolding Ig domains and delivering the charge back by folding when the motors are activated during a contraction. We advance the hypothesis that titin folding and myosin activation act as inextricable partners during muscle contraction.

Nucleation of Multiple Buckled Structures in Intertwined DNA Double Helices.

We study the statistical-mechanical properties of intertwined double-helical DNAs (DNA braids). In magnetic tweezers experiments, we find that torsionally stressed stretched braids supercoil via an abrupt buckling transition, which is associated with the nucleation of a braid end loop, and that the buckled braid is characterized by a proliferation of multiple domains. Differences between the mechanics of DNA braids and supercoiled single DNAs can be understood as an effect of the increased bulkiness in the structure of the former. The experimental results are in accord with the predictions of a statistical-mechanical model.