Choosing orientation: influence of cargo geometry and ActA polarization on actin comet tails

Networks of polymerizing actin filaments can propel intracellular pathogens and drive movement of artificial particles in reconstituted systems. While biochemical mechanisms activating actin network assembly have been well characterized, it remains unclear how particle geometry and large-scale force balance affect emergent properties of movement. We reconstituted actin-based motility using ellipsoidal beads resembling the geometry of Listeria monocytogenes. Beads coated uniformly with the L. monocytogenes ActA protein migrated equally well in either of two distinct orientations, with their long axes parallel or perpendicular to the direction of motion, while intermediate orientations were unstable. When beads were coated with a fluid lipid bilayer rendering ActA laterally mobile, beads predominantly migrated with their long axes parallel to the direction of motion, mimicking the orientation of motile L. monocytogenes. Generating an accurate biophysical model to account for our observations required the combination of elastic-propulsion and tethered-ratchet actin-polymerization theories. Our results indicate that the characteristic orientation of L. monocytogenes must be due to polarized ActA rather than intrinsic actin network forces. Furthermore, viscoelastic stresses, forces, and torques produced by individual actin filaments and lateral movement of molecular complexes must all be incorporated to correctly predict large-scale behavior in the actin-based movement of nonspherical particles.     

Propagation of mechanical stress through the actin cytoskeleton toward focal adhesions: model and experiment

We investigate both theoretically and experimentally how stress is propagated through the actin cytoskeleton of adherent cells and consequentially distributed at sites of focal adhesions (FAs). The actin cytoskeleton is modeled as a two-dimensional cable network with different lattice geometries. Both prestrain, resulting from actomyosin contractility, and central application of external force, lead to finite forces at the FAs that are largely independent of the lattice geometry, but strongly depend on the exact spatial distribution of the FAs. The simulation results compare favorably with experiments with adherent fibroblasts onto which lateral force is exerted using a microfabricated pillar. For elliptical cells, central application of external force along the long axis leads to two large stress regions located obliquely opposite to the pulling direction. For elliptical cells pulled along the short axis as well as for circular cells, there is only one region of large stress opposite to the direction of pull. If in the computer simulations FAs are allowed to rupture under force for elliptically elongated and circular cell shapes, then morphologies arise which are typical for migrating fibroblasts and keratocytes, respectively. The same effect can be obtained also by internally generated force, suggesting a mechanism by which cells can control their migration morphologies.     

Large colloidal probes for atomic force microscopy: Fabrication and calibration issues

Atomic force microscopy (AFM) is a powerful tool to investigate interaction forces at the micro and nanoscale. Cantilever stiffness, dimensions and geometry of the tip can be chosen according to the requirements of the specific application, in terms of spatial resolution and force sensitivity. Colloidal probes (CPs), obtained by attaching a spherical particle to a tipless (TL) cantilever, offer several advantages for accurate force measurements: tunable and well‐characterisable radius; higher averaging capabilities (at the expense of spatial resolution) and sensitivity to weak interactions; a well‐defined interaction geometry (sphere on flat), which allows accurate and reliable data fitting by means of analytical models. The dynamics of standard AFM probes has been widely investigated, and protocols have been developed for the calibration of the cantilever spring constant. Nevertheless, the dynamics of CPs, and in particular of large CPs, with radius well above 10 μm and mass comparable, or larger, than the cantilever mass, is at present still poorly characterized. Here we describe the fabrication and calibration of (large) CPs. We describe and discuss the peculiar dynamical behaviour of CPs, and present an alternative protocol for the accurate calibration of the spring constant.     

A novel method for measuring tension generated in stress fibers by applying external forces

The distribution of contractile forces generated in cytoskeletal stress fibers (SFs) contributes to cellular dynamic functions such as migration and mechanotransduction. Here we describe a novel (to our knowledge) method for measuring local tensions in SFs based on the following procedure: 1), known forces of different magnitudes are applied to an SF in the direction perpendicular to its longitudinal axis; 2), force balance equations are used to calculate the resulting tensions in the SF from changes in the SF angle; and 3), the relationship between tension and applied force thus established is extrapolated to an applied force of zero to determine the preexisting tension in the SF. In this study, we measured tensions in SFs by attaching magnetic particles to them and applying known forces with an electromagnetic needle. Fluorescence microscopy was used to capture images of SFs fluorescently labeled with myosin II antibodies, and analysis of these images allowed the tension in the SFs to be measured. The average tension measured in this study was comparable to previous reports, which indicates that this method may become a powerful tool for elucidating the mechanisms by which cytoskeletal tensions affect cellular functions.     

Design of bio-mimetic particles with enhanced vascular interaction

The majority of particle-based delivery systems for the ‘smart’ administration of therapeutic and imaging agents have a spherical shape, are made by polymeric or lipid materials, have a size in the order of few hundreds of nanometers and a negligibly small relative density to aqueous solutions. In the microcirculation and deep airways of the lungs, where the creeping flow assumption holds, such small spheres move by following the flow stream lines and are not affected by external volume force fields. A delivery system should be designed to drift across the stream lines and interact repeatedly with the vessel walls, so that vascular interaction could be enhanced. The numerical approach presented in [Gavze, E., Shapiro, M., 1997. Particles in a shear flow near a solid wall: effect of nonsphericity on forces and velocities. International Journal of Multiphase Flow 23, 155–182.] is, here, proposed as a tool to analyze the dynamics of arbitrarily shaped particles in a creeping flow, and has been extended to include the contribution of external force fields. As an example, ellipsoidal particles with aspect ratio 0.5 are considered. In the absence of external volume forces, a net lateral drift (margination) of the particles has been observed for Stokes number larger than unity (St>1); whereas, for smaller St, the particles oscillate with no net lateral motion. Under these conditions, margination is governed solely by particle inertia (geometry and particle-to-fluid density ratio). In the presence of volume forces, even for fairly small St, margination is observed but in a direction dictated by the external force field. It is concluded that a fine balance between size, shape and density can lead to EVI particles (particles with enhanced vascular interaction) that are able to sense endothelial cells for biological and biophysical abnormalities, mimicking circulating platelets and leukocytes.     

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.     

Magnetic tweezers: micromanipulation and force measurement at the molecular level

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

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.     

Interaction forces between red cells agglutinated by antibody. I. Theoretical.

A general method of calculating forces, torques, and translational and rotational velocities of rigid, neutrally buoyant spheres suspended in viscous liquids undergoing a uniform shear flow has been given by Arp and Mason (1977). The method is based on the matrix formulation of hydrodynamic resistances in creeping flow by Brenner and O'Neill (1972). We describe the solution of the Brenner-O'Neill force-torque vector equation in terms of the particle and external flow field coordinates and derive expressions for the normal force acting along, and the shear force acting perpendicular to, the axis of the doublet of spheres, the latter explicitly given for the first time. The equations consist of a term comprising force and torque coefficients obtained from the matrices of the hydrodynamic resistances (functions of the distance h between sphere surfaces which have been computed), and terms comprising the orientation of the doublet axis relative to the coordinates of the external flow field and the shear stress (which can be experimentally determined). We have applied the theory to a system of doublets of sphered, hardened human red cells of group A or B antigenic type cross-linked by the corresponding antibody at a fixed interparticle distance. Working from studies of the breakup of doublets of red cells in an accelerating Poiseuille flow, given in the succeeding paper, we are able to compute the hydrodynamic force required to separate the two spheres. Previous work has shown that the theory can be applied to doublets in a variable shear, Poiseuille flow, provided the ratio of particle to tube diameter is small. In calculating the force-torque coefficients it was assumed that the cells are crosslinked by antibody with h = 20 nm.     

Subcellular tension fields and mechanical resistance of the lamella front related to the direction of locomotion

Keratocytes derived from the epidermis of aquatic vertebrates are now widely used for investigation of the mechanism of cell locomotion. One of the main topics under discussion is the question of driving force development and concomitantly subcellular force distribution. Do cells move by actin polymerization-driven extension of the lamella, or is the lamella edge extended at regions of weakness by a flow of cytoplasm generated by hydrostatic pressure? Thus, elasticity changes were followed and the stiffness of the leading front of the lamella was manipulated by local application of phalloidin and cytochalasin D (CD). In scanning acoustic microscopy (SAM), elasticity is revealed from the propagation velocity of longitudinal sound waves (1 GHz). The lateral resolution of SAM is in the micrometer range. Using this method, subcellular tension fields with different stiffnesses (elasticity) can be determined. A typical pattern of subcellular stiffness distribution is related to the direction of migration. Cells forced to change their direction of movement by exposure to DC electric fields of varying polarity alter their pattern of subcellular stiffness in relationship to the new direction. The cells spread into the direction of low stiffness and retract at zones of high stiffness. The pattern of subcellular stiffness distribution reveals force distribution in migrating cells; i.e., if a cell moves exactly in a direction perpendicular to its long axis, then the contractile forces are largest along the long axis and decrease toward the short axis. Locomotion in any angle oblique to this axis requires an asymmetric stiffness distribution. Inhibition of actomyosin contractions by La³⁺ (2 mM), which inhibits Ca²⁺ influx, reduces cytoplasmic stiffness accompanied by an immediate cessation of locomotion and a change of cell shape. Local release of CD in front of a progressing lamella activates a cell to follow the CD gradient: The lamella thickens locally and is extended toward the tip of the microcapillary. Release of phalloidin stops extension of the lamella, and the cell turns away from the releasing microcapillary. The response to CD is assumed to be the result of local weakening of the cytoplasm due to severing of the actin fibrils. Phalloidin is supposed to stabilize the leading front by inhibition of F-actin depolymerization. These observations are in favor of the assumption that migration is due to an extension of the cell into the direction of minimum stiffness, and they are consistent with the hypothesis that local release of hydrostatic pressure provides the driving force for the flux of cytoplasm.     

A three-dimensional mathematical model of the human masticatory system predicting maximum possible bite forces

A three-dimensional mathematical model of the human masticatory system, containing 16 muscle forces and two joint reaction forces, is described. The model allows simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. The system parameters for the model were obtained from a cadaver head. Maximum possible bite forces were computed using optimization techniques; the optimization criterion we used was the minimizing of the relative activity of the most active muscle. The model predicts that at each specific bite point, bite forces can be generated in a wide range of directions, and that the magnitude of the maximum bite force depends on its direction. The relationship between bite force direction and its maximum magnitude depends on bite point location and mandibular position. In general, the direction of the largest possible bite force does not coincide with the direction perpendicular to the occlusal plane.     

Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion

An optical force measurement system for quantitating forces in the pN range between micrometer-sized objects has been developed. The system was based upon optical tweezers in combination with a sensitive position detection system and constructed around an inverted microscope. A trapped particle in the focus of the high numerical aperture microscope-objective behaves like an omnidirectional mechanical spring in response to an external force. The particle's displacement from the equilibrium position is therefore a direct measure of the exerted force. A weak probe laser beam, focused directly below the trapping focus, was used for position detection of the trapped particle (a polystyrene bead). The bead and the condenser focus the light to a distinct spot in the far field, monitored by a position sensitive detector. Various calibration procedures were implemented in order to provide absolute force measurements. The system has been used to measure the binding forces between Escherichia coli bacterial adhesins and galabiose-functionalized beads.     

Vertical and lateral forces applied to the bar during the bench press in novice lifters

The purpose of this study was to determine the vertical and lateral forces applied to the bar during a maximal and a submaximal effort bench press lifts. For this study, 10 male and 8 female recreational lifters were recruited (mean height: 1.71 ± 0.08 m; mass: 73.7 ± 13.6 kg) and were asked to perform a maximal and submaximal (80% of maximal lift) bench press. These lifts were performed with a bar instrumented to record forces applied to it, via the hands, in the vertical direction and along the long axis of the bar. To determine the position of the bar and timing of events, 3D kinematic data were recorded and analyzed for both lifts. The subjects in this study averaged a maximal lift of 63 ± 29 kg (90 ± 31% bodyweight). The peak vertical force was 115 ± 22% (percentage of load), whereas for the submaximal condition it was 113 ± 20%; these forces were statistically different between conditions; they were not when expressed as a percentage of the load (p > 0.05). During all the lifts, the lateral forces were always outward along the bar. The lateral force profile was similar to that of the vertical force, albeit at a lesser magnitude. During the lift phase, the peak lateral force was on average 26.3 ± 3.9% of the vertical force for the maximal lift and 23.7 ± 3.9% of the vertical force for the submaximal lift. Given that the amount of force applied laterally to the bar was a similar percentage of vertical force irrespective of load, it appears that the generation of lateral forces during the bench press is a result of having the muscles engaged in generating vertical force.     

Stability of particle motions in a narrow channel flow

Single rows or two rows of identical circular cylinders spaced regularly in a narrow channel flow have been shown to be capable of steady flow provided the cylinders are located at equal lateral positions and with equal spacings in the flow direction. The stability of such steady flows of circular cylinders is studied for periodic perturbations of the particle positions, assuming that every other cylinder is equally perturbed in lateral position and spacing along the channel. This results in two rows which are not symmetrically placed. The suspending fluid is assumed to be an incompressible Newtonian fluid. It is assumed that no external forces or moments act on the cylinders and the effects of inertia forces on the motion of the fluid and the cylinders are negligible. The velocity field of the suspending fluid and the instantaneous velocities of the cylinders are computed by the finite element method. The translational velocities of the cylinders are obtained for a large number of particle positions, from which the trajectories of their relative motion are determined for various initial positions near the regular single-file and two-file arrangements. It is shown that when the initial arrangements of the cylinders are slightly perturbed from the regular (alternating) two-file flows, the trajectories of their relative motions become small closed loops around the regular two-file arrangements. In contrast, such small closed trajectories are not obtained when they start from the arrangements near the regular single-file flows or regular (symmetric) double-file flows, suggesting that these flows are unstable under the conditions examined.     

Force Generation of Curved Actin Gels Characterized by Combined AFM-Epifluorescence Measurements

Polymerization of actin into branched filaments is the driving force behind active migration of eukaryotic cells and motility of intracellular organelles. The site-directed assembly of a polarized branched array forms an expanding gel that generates the force that pushes the membrane. Here, we use atomic force microscopy to understand the relation between actin polymerization and the produced force. Functionalized spherical colloidal probes of varying size and curvature are attached to the atomic force microscopy cantilever and initiate the formation of a polarized actin gel in a solution mimicking the in vivo context. The gel growth is recorded by epifluorescence microscopy both against the cantilever and in the perpendicular (lateral) nonconstrained direction. In this configuration, the gel growth stops simultaneously in both directions at the stall force, which corresponds to a pressure of 0.15 nN/μm². The results show that the growth of the gel is limited laterally, in the absence of external force, by internal mechanical stresses resulting from a combination of the curved geometry and the molecular mechanism of site-directed assembly of a cohesive branched filament array.     

Orientation of paramecium swimming in a DC magnetic field

We found that a ciliated protozoan, Paramecium, swam perpendicular to a static (DC) magnetic field (0.68 T). The swimming orientation was similar even when the ionic current through the cell membrane disappeared after saponin treatment. To determine the diamagnetic anisotropy of intracellular organs, macronuclei, cilia, and secretory vesicles, trichocysts, were selectively isolated. Both cilia and trichocysts tended to align their long axis parallel to the magnetic field (0.78 T). Paramecium mutants that lack trichocysts also swam perpendicular to the magnetic field, although the proportion fraction was smaller than the normal population. Since large numbers of cilia and trichocysts are arranged at right angles to the long axis of the cell, the diamagnetic anisotropies of cilia and trichocysts cause the long axis of the cell to align perpendicular to the magnetic field. In contrast to the DC magnetic field, an alternative (AC) magnetic field (60 Hz, 0.65 T) had almost no effect on the swimming orientation of Paramecium.     

Transport properties of particles with segmental flexibility. I. Hydrodynamic resistance and diffusion coefficients of a freely hinged particle

Expressions are derived for the hydrodynamic resistance tensor and the diffusion tensor of a particle consisting of two rigid subunits connected by a free hinge. No restrictions are placed on the shapes of the subunits. The resistance tensor is obtained by using two independent approaches: first, from the Rayleigh dissipation function and, second, from an examination of the generalized forces for the appropriate seven-dimensional coordinate system. For the derivation of the generalized Einstein equation connecting the diffusion and resistance tensors, the Brownian motion is treated as a stochastic process. That derivation is based on the assumption that the restoring force for bending is negligible, and the Einstein relation holds instantaneously only if that assumption is true. The relationship between these tensors and the macroscopically observable parameters is discussed, and it is shown that the separate measurement of resistance and diffusion coefficients can be used to detect macromolecular flexibility. One example is treated, the diffusion of a particle composed of two long rods joined at a free hinge. Those calculations are carried out with the first-order assumption of negligible hydrodynamic interactions between the subunits. For the hinged rod, the bending degree of freedom produces a 34% increase in the translational diffusion coefficient over that of a stiff rod of the same total length, while the rotational diffusion coefficient about the axis perpendicular to the plane of bending is increased by 125%.     

Mechanical unbinding of abeta peptides from amyloid fibrils

Using the experimental structures of Abeta amyloid fibrils and all-atom molecular dynamics, we study the force-induced unbinding of Abeta peptides from the fibril. We show that the mechanical dissociation of Abeta peptides is highly anisotropic and proceeds via different pathways when force is applied in parallel or perpendicular direction with respect to the fibril axis. The threshold forces associated with lateral unbinding of Abeta peptides exceed those observed during the mechanical dissociation along the fibril axis. In addition, Abeta fibrils are found to be brittle in the lateral direction of unbinding and soft along the fibril axis. Lateral mechanical unbinding and the unbinding along the fibril axis load different types of fibril interactions. Lateral unbinding is primarily determined by the cooperative rupture of fibril backbone hydrogen bonds. The unbinding along the fibril axis largely depends on the interpeptide Lys-Asp electrostatic contacts and the hydrophobic interactions formed by the Abeta C terminal. Due to universality of the amyloid beta structure, the anisotropic mechanical dissociation observed for Abeta fibrils is likely to be applicable to other amyloid assemblies. The estimates of equilibrium forces required to dissociate Abeta peptide from the amyloid fibril suggest that these supramolecular structures are mechanically stronger than most protein domains.     

Detection of intracellular macromolecule behavior under strong magnetic fields by linearly polarized light

Strong static magnetic fields on the order of 10 T have a diamagnetic force on cell components and generate a clear alignment of a smooth muscle cell assembly, parallel to the direction of the magnetic fields within an exposure period of 3 days. This work shows the effects of diamagnetic torque forces on cell component motion. Linearly polarized light was utilized to detect the displacement of intracellular macromolecules. The polarized light passed through a mass of cells in a magnetic field, and transmission of the light increased and reached a plateau 2 h after the beginning of magnetic field exposure at 14 T. However, no distinct change was observed in transmission of the light under zero magnetic field exposure. The change in polarized light intensity through the lamellar cell assembly under magnetic fields corresponds to behavioral changes in cell components. It was speculated that intracellular macromolecules rotated and showed a displacement due to diamagnetic torque forces during 2-3 h of magnetic field exposure at 14 T.