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.     

Signaling through the phosphatidylinositol 3-kinase regulates mechanotaxis induced by local low magnetic forces in Entamoeba histolytica

In micro-organisms, as well as in metazoan cells, cellular polarization and directed migration are finely regulated by external stimuli, including mechanical stresses. The mechanisms sustaining the transduction of such external stresses into intracellular biochemical signals remain mainly unknown. Using an external magnetic tip, we generated a magnetic field gradient that allows migration analysis of cells submitted to local low-intensity magnetic forces (50 pN). We applied our system to the amoeba Entamoeba histolytica. Indeed, motility and chemotaxis are key activities that allow this parasite to invade and destroy the human tissues during amoebiasis. The magnetic force was applied either inside the cytoplasm or externally at the rear pole of the amoeba. We observed that the application of an intracellular force did not affect cell polarization and migration, whereas the application of the force at the rear pole of the cell induced a persistent polarization and strongly directional motion, almost directly opposed to the magnetic force. This phenomenon was completely abolished when phosphatidylinositol 3-kinase activity was inhibited by wortmanin. This result demonstrated that the applied mechanical stimulus was transduced and amplified into an intracellular biochemical signal, a process that allows such low-intensity force to strongly modify the migration behavior of the cell.     

Inhibitor binding increases the mechanical stability of staphylococcal nuclease

Staphylococcal nuclease (SNase) catalyzes the hydrolysis of DNA and RNA in a calcium-dependent fashion. We used AFM-based single-molecule force spectroscopy to investigate the mechanical stability of SNase alone and in its complex with an SNase inhibitor, deoxythymidine 3′,5′-bisphosphate. We found that the enzyme unfolds in an all-or-none fashion at ∼26 pN. Upon binding to the inhibitor, the mechanical unfolding forces of the enzyme-inhibitor complex increase to ∼50 pN. This inhibitor-induced increase in the mechanical stability of the enzyme is consistent with the increased thermodynamical stability of the complex over that of SNase. Because of its strong mechanical response to inhibitor binding, SNase, a model protein folding system, offers a unique opportunity for studying the relationship between enzyme mechanics and catalysis.     

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.     

The effects of macromolecular crowding on the mechanical stability of protein molecules

Macromolecular crowding, a common phenomenon in the cellular environments, can significantly affect the thermodynamic and kinetic properties of proteins. A single-molecule method based on atomic force microscopy (AFM) was used to investigate the effects of macromolecular crowding on the forces required to unfold individual protein molecules. It was found that the mechanical stability of ubiquitin molecules was enhanced by macromolecular crowding from added dextran molecules. The average unfolding force increased from 210 pN in the absence of dextran to 234 pN in the presence of 300 g/L dextran at a pulling speed of 0.25 microm/sec. A theoretical model, accounting for the effects of macromolecular crowding on the native and transition states of the protein molecule by applying the scaled-particle theory, was used to quantitatively explain the crowding-induced increase in the unfolding force. The experimental results and interpretation presented could have wide implications for the many proteins that experience mechanical stresses and perform mechanical functions in the crowded environment of the cell.     

Improved resolution of tertiary structure elasticity in muscle protein

Rearrangement of tertiary structure in response to mechanical force (termed tertiary structure elasticity) in the tandem Ig chain is the first mode of elastic response for muscle protein titin. Tertiary structure elasticity occurs at low stretching forces (few tens of pN), and was described at atomic resolution in a recent molecular dynamics study, in which an originally crescent-shaped six-Ig chain was stretched into a linear chain. However, the force-extension profile that resulted from this explicit solvent simulation was dominated by the hydrodynamic drag force, and effects of tertiary structure elasticity only manifested for stretching forces above 20 pN. Here we report a slow pulling 100-ns simulation (along with other auxiliary simulations), in which hydrodynamic drag force is seen to reduce to near 0 pN, such that tertiary structure elasticity could be characterized over a 0–200 pN range. Statistical mechanical analysis showed that the stretching velocity was sufficiently low such that the protein remained significantly relaxed during the major part of its extension.     

Dictyostelium cells' cytoplasm as an active viscoplastic body

We applied a recently developed microrheology technique based on colloidal magnetic tweezers to measure local viscoelastic moduli and active forces in cells of Dictyostelium discoideum. The active transport of nonmagnetic beads taken up by phagocytosis was analyzed by single particle tracking, which allowed us to measure the length of straight steps and the corresponding velocities of the movements. The motion consists of a superposition of nearly straight long-range steps (step length in the micrometer range) and local random walks (step widths about 0.1 microm). The velocities for the former type of motion range from 1 to 3 microm/s. They decrease with increasing bead size and are attributed to rapid active transport along microtubuli. The short-range local motions exhibit velocities of less than 0.5 microm/s and reflect the internal dynamics of the cytoplasm. Viscoelastic response curves were measured by application of force pulses with amplitudes varying between 50 pN and 400 pN. Analysis of the response curves in terms of mechanical equivalent circuits yielded cytoplasmic viscosities varying between 10 and 350 Pa s. Simultaneous analysis of the response curves and of the bead trajectories showed that the motion of the beads is determined by the local yield stress within the cytoplasmic scaffold and cisternae, which varies between sigma = 30 Pa and 250 Pa. The motion of intracellular particles is interpreted in terms of viscoplastic behavior and the apparent viscosity is a measure of the reciprocal rate of bond breakage within the cytoplasmatic network. The viscoelastic moduli are interpreted as dynamic quantities which depend sensitively on the amplitude of the forces, and the rate of bond breakage is determined by the Arrhenius-Kramers law with the activation energy being reduced by the work performed by the applied force. In agreement with previous work, we provide evidence that the myosin II-deficient cells exhibit higher yield stresses, suggesting that the function of myosin II as a cross-linker is taken over by the other (non-active) cross-linkers.     

Transmission of Mechanical Stresses within the Cytoskeleton of Adherent Cells: A Theoretical Analysis Based on a Multi-Component Cell Model

How environmental mechanical forces affect cellular functions is a central problem in cell biology. Theoretical models of cellular biomechanics provide relevant tools for understanding how the contributions of deformable intracellular components and specific adhesion conditions at the cell interface are integrated for determining the overall balance of mechanical forces within the cell. We investigate here the spatial distributions of intracellular stresses when adherent cells are probed by magnetic twisting cytometry. The influence of the cell nucleus stiffness on the simulated nonlinear torque-bead rotation response is analyzed by considering a finite element multi-component cell model in which the cell and its nucleus are considered as different hyperelastic materials. We additionally take into account the mechanical properties of the basal cell cortex, which can be affected by the interaction of the basal cell membrane with the extracellular substrate. In agreement with data obtained on epithelial cells, the simulated behaviour of the cell model relates the hyperelastic response observed at the entire cell scale to the distribution of stresses and strains within the nucleus and the cytoskeleton, up to cell adhesion areas. These results, which indicate how mechanical forces are transmitted at distant points through the cytoskeleton, are compared to recent data imaging the highly localized distribution of intracellular stresses.     

Analysis of the Precision,Robustness, and Speed of Elastic Resonator Interference Stress Microscopy

Localization-microscopy-based methods are widely used to map the forces that cells apply to their substrates and to study important questions of cellular biomechanics. By contrast, elastic resonator interference stress microscopy (ERISM) uses an interference-based approach, which requires low light intensity and facilitates imaging of cellular forces with extreme precision (down to pN forces) and robustness (e.g., for continuous force monitoring over weeks). Here, the measurement trade-offs and numerical considerations required to optimize the performance of ERISM are described. The crucial parts of the fitting algorithm and the computational tools used to evaluate the data are explained in detail, and the precision and accuracy achievable with ERISM are analyzed. Additional features that can improve the robustness of ERISM further are discussed. The implementation of the analysis algorithm is verified with simulated test data and with experimental data. In addition, an approach to increase the acquisition speed of ERISM by a factor of four compared to the original implementation is described. In combination, these strategies allow us to measure the forces generated by a neural growth cone with high temporal resolution and continuously over several hours.     

Nanomechanical properties of desmin intermediate filaments

Desmin intermediate filaments play important role in the mechanical integrity and elasticity of muscle cells. The mechanisms of how desmin contributes to cellular mechanics are little understood. Here, we explored the nanomechanics of desmin by manipulating individual filaments with atomic force microscopy. In complex, hierarchical force responses we identified recurring features which likely correspond to distinct properties and structural transitions related to desmin's extensibility and elasticity. The most frequently observed feature is an initial unbinding transition that corresponds to the removal of approximately 45-nm-long coiled-coil dimers from the filament surface with 20-60 pN forces in usually two discrete steps. In tethers longer than 60 nm we most often observed force plateaus studded with bumps spaced approximately 16 nm apart, which are likely caused by a combination of protofilament unzipping, dimer-dimer sliding and coiled-coil-domain unfolding events. At high stresses and strains non-linear, entropic elasticity was dominant, and sometimes repetitive sawtooth force transitions were seen which might arise because of slippage within the desmin protofilament. A model is proposed in which mechanical yielding is caused by coiled-coil domain unfolding and dimer-dimer sliding/slippage, and strain hardening by the entropic elasticity of partially unfolded protofilaments.     

A novel patterned magnetic micropillar array substrate for analysis of cellular mechanical responses

Traction forces generated at cellular focal adhesions (FAs) play an essential role in regulating various cellular functions. These forces (1–100 nN) can be measured by observing the local displacement of a flexible substrate upon which cells have been plated. Approaches employing this method include using microfabricated arrays of poly(dimethylsiloxane) (PDMS) micropillars that bend by cellular traction forces. A tool capable of applying a force to FAs independently, by actively moving the micropillars, should become a powerful tool to delineate the cellular mechanotransduction mechanisms. Here, we developed a patterned magnetic micropillar array PDMS substrate that can be used for the mechanical stimulation of cellular FAs and the measurement of associated traction forces. The diameter, length, and center-to-center spacing of the micropillars were 3, 9, and 9 µm, respectively. Iron particles were embedded into the micropillars, enabling the pillars to bend in response to an external magnetic field, which also controlled their location on the substrate. Applying a magnetic field of 0.3 T bent the pillars by ∼4 µm and allowed transfer of external forces to the actin cytoskeleton through FAs formed on the pillar top. Using this approach, we investigated the traction force changes in cultured aortic smooth muscle cells (SMCs) after local compressive stimuli to release cell pretension. The mechanical responses of SMCs were roughly classified into two types: almost a half of the cells showed a little decrease of traction force at each pillar following compressive stimulation, although cell area increased significantly; and the rest showed the opposite, with increased forces and a simultaneous decrease in area. The traction forces of SMCs fluctuated markedly during the local compression. The root mean square of traction forces significantly increased during the compression, and returned to the baseline level after its release. These results suggest that the fluctuation of forces may be caused by active reorganization of the actin cytoskeleton and/or its dynamic interaction with myosin molecules. Thus, our magnetic micropillar substrate would be useful in investigating the mechanotransduction mechanisms of cells.     

The force-driven conformations of heparin studied with single molecule force microscopy

Using single molecule force spectroscopy we examine the response of heparin chains to mechanical stretching. We find that at forces below 200 pN heparin behaves as a simple entropic spring. At approximately 200 pN heparin displays a large enthalpic elasticity, which is evident as a pronounced plateau in the force-extension relationship. We determine that this enthalpic elasticity is produced by sugar rings of heparin flipping to more energetic and more extended conformations. We estimate that in vivo, the forces which stretch heparin are comparable to the forces that trigger conformational transitions in our single molecule atomic force microscopy measurements. We hypothesize that these conformational transitions have biological significance in that they provide a mechanism to finely regulate the affinity of various ligands toward heparin, for example, in secretory granules undergoing exocytosis and during the mechanical interactions between cells and the extracellular matrix.     

Micropipet-based pico force transducer: in depth analysis and experimental verification.

Measurements of forces in the piconewton range are very important for the study of molecular adhesion and mechanics. Recently, a micropipet-based force transducer for this type of experiment was presented (E. Evans, K. Ritchie, and R. Merkel, 1995, Biophys. J., 68:2580-2587). In the present article we give a detailed mechanical analysis of this transducer, including nonlinear effects. An analytical expression for the transducer stiffness at small elongations is given. Using magnetic tweezers (F. Ziemann, J. Rädler, and E. Sackmann, 1994, Biophys. J., 66:2210-2216), we were able to determine the force displacement relation of this transducer experimentally. Forces from approximately 10 pN to 500 pN were applied. Theoretical predictions and experimental results coincide remarkably well.     

Molecular Tension Probes to Quantify Cell-Generated Mechanical Forces

Living cells generate, sense, and respond to mechanical forces through their interaction with neighboring cells or extracellular matrix, thereby regulating diverse cellular processes such as growth, motility, differentiation, and immune responses. Dysregulation of mechanosensitive signaling pathways is found associated with the development and progression of various diseases such as cancer. Yet, little is known about the mechanisms behind mechano-regulation, largely due to the limited availability of tools to study it at the molecular level. The recent development of molecular tension probes allows measurement of cellular forces exerted by single ligand-receptor interaction, which has helped in revealing the hitherto unknown mechanistic details of various mechanosensitive processes in living cells. Here, we provide an introductory overview of two methods based on molecular tension probes, tension gauge tether (TGT), and molecular tension fluorescence microscopy (MTFM). TGT utilizes the irreversible rupture of double-stranded DNA tether upon application of force in the piconewton (pN) range, whereas MTFM utilizes the reversible extension of molecular springs such as polymer or single-stranded DNA hairpin under applied pN forces. Specifically, the underlying principle of how molecular tension probes measure cell-generated mechanical forces and their applications to mechanosensitive biological processes are described.     

Magnetic targeting of mechanosensors in bone cells for tissue engineering applications

Mechanical signalling plays a pivotal role in maintaining bone cell function and remodelling of the skeleton. Our previous work has highlighted the potential role of mechano-induction in tissue engineering applications. In particular, we have highlighted the potential for using magnetic particle techniques for tissue engineering applications. Previous studies have shown that manipulation of integrin attached magnetic particles leads to changes in intracellular calcium signalling within osteoblasts. However, due to the phenomenon of particle internalisation, previous studies have typically focused on short-term stimulation experiments performed within 1-2 h of particle attachment. For tissue engineering applications, bone tissue growth occurs over a period of 3-5 weeks. To date, no study has investigated the cellular responses elicited from osteoblasts over time following stimulation with internalised magnetic particles. Here, we demonstrate the long-term biocompatibility of 4.5 microm RGD-coated particles with osteoblasts up to 21 days in culture, and detail a time course of responses elicited from osteoblasts following mechanical stimulation with integrin attached magnetic particles (<2h post attachment) and internalised particles (>48h post attachment). Mechanical manipulation of both integrin attached and internalised particles were found to induce intracellular calcium signalling. It is concluded that magnetic particles offer a tool for applying controlled mechanical forces to osteoblasts, and can be used to stimulate intracellular calcium signalling over prolonged periods of time. Magnetic particle technology presents a potentially valuable tool for tissue engineering which permits the delivery of highly localised mechano-inductive forces directly to cells.     

Force microscopy imaging of individual protein molecules with sub-pico Newton force sensitivity

The capability of atomic force microscopes (AFM) to generate atomic or nanoscale resolution images of surfaces has deeply transformed the study of materials. However, high resolution imaging of biological systems has proved more difficult than obtaining atomic resolution images of crystalline surfaces. In many cases, the forces exerted by the tip on the molecules (1-10 nN) either displace them laterally or break the noncovalent bonds that hold the biomolecules together. Here, we apply a force microscope concept based on the simultaneous excitation of the first two flexural modes of the cantilever. The coupling of the modes generated by the tip-molecule forces enables imaging under the application of forces ( approximately 35 pN) which are smaller than those needed to break noncovalent bonds. With this instrument we have resolved the intramolecular structure of antibodies in monomer and pentameric forms. Furthermore, the instrument has a force sensitivity of 0.2 pN which enables the identification of compositional changes along the protein fragments.     

Live en face imaging of aortic valve leaflets under mechanical stress

Soft tissues, such as tendons, skin, arteries, or lung, are constantly subject to mechanical stresses in vivo. None more so than the aortic heart valve that experiences an array of forces including shear stress, cyclic pressure, strain, and flexion. Anisotropic biaxial cyclic stretch maintains valve homeostasis; however, abnormal forces are implicated in disease progression. The response of the valve endothelium to deviations from physiological levels has not been fully characterized. Here, we show the design and validation of a novel stretch apparatus capable of applying biaxial stretch to viable heart valve tissue, while simultaneously allowing for live en face endothelial cell imaging via confocal laser scanning microscopy (CLSM). Real-time imaging of tissue is possible while undergoing highly characterized mechanical conditions and maintaining the native extracellular matrix. Thus, it provides significant advantages over traditional cell culture or in vivo animal models. Planar biaxial tissue stretching with simultaneous live cell imaging could prove useful in studying the mechanobiology of any soft tissue.     

Cytoskeletal forces produced by extremely low‐frequency electric fields acting on extracellular glycoproteins

The physical mechanism by which cells transduce an applied electric field is not well understood. This article establishes for the first time a direct, quantitative model that links the field to cytoskeletal forces. In a previous article, applied electric fields of physiological strength were shown to produce significant mechanical torques at the cellular level. In this article, the corresponding forces exerted on the cytoskeleton are computed and found to be comparable in magnitude to mechanical forces known to produce physiological effects. In addition to the electrical force, the viscous drag force exerted by the surrounding medium and the restoring force exerted by the neighboring structures are considered in the analysis. For an applied electric field of 10 V/m, the force transmitted to the CD44 receptor of a hyaluronan chain in cartilage is about 1 pN at 10 Hz and 7 pN at 1 Hz. For an applied electric field of 100 V/m, the force transmitted to the cytoskeleton at one focus of the glycocalyx is about 0.5 pN at 10 Hz and 1.3 pN at 1 Hz. Mechanical forces of similar magnitude have been observed to produce physiological effects. Hence, this electromechanical transduction process is a plausible mechanism for the production of physiological effects by such electric fields. Bioelectromagnetics 31:77–84, 2010. © 2009 Wiley‐Liss, Inc.     

Improved high-force magnetic tweezers for stretching and refolding of proteins and short DNA

Although magnetic tweezers have many unique advantages in terms of specificity, throughput, and force stability, this tool has had limited application on short tethers because accurate measurement of force has been difficult for short tethers under large tension. Here, we report a method that allows us to apply magnetic tweezers to stretch short biomolecules with accurate force calibration over a wide range of up to 100 pN. We demonstrate the use of the method by overstretching of a short DNA and unfolding/refolding a protein of filamin A immunoglobulin domains 1–8. Other potential applications of this method are also discussed.     

Ligand binding modulates the mechanical stability of dihydrofolate reductase

We use single-molecule force spectroscopy to demonstrate that the mechanical stability of the enzyme dihydrofolate reductase (DHFR) is modulated by ligand binding. In the absence of bound ligands, DHFR extends at very low forces, averaging 27 pN, without any characteristic mechanical fingerprint. By contrast, in the presence of micromolar concentrations of the ligands methotrexate, nicotinamide adenine dihydrogen phosphate, or dihydrofolate, much higher forces are required (82 +/- 18 pN, 98 +/- 15 pN, and 83 +/- 16 pN, respectively) and a characteristic fingerprint is observed in the force-extension curves. The increased mechanical stability triggered by these ligands is not additive. Our results explain the large reduction in the degradation rate of DHFR, in the presence of its ligands. Our observations support the view that the rate-limiting step in protein degradation by adenosine triphosphate-dependent proteases is the mechanical unfolding of the target protein.