The Properties of Chondrocyte Membrane Reservoirs and Their Role in Impact-Induced Cell Death

Impact loading of articular cartilage causes extensive chondrocyte death. Cell membranes have a limited elastic range of 3–4% strain but are protected from direct stretch during physiological loading by their membrane reservoir, an intricate pattern of membrane folds. Using a finite-element model, we suggested previously that access to the membrane reservoir is strain-rate-dependent and that during impact loading, the accessible membrane reservoir is drastically decreased, so that strains applied to chondrocytes are directly transferred to cell membranes, which fail when strains exceed 3–4%. However, experimental support for this proposal is lacking. The purpose of this study was to measure the accessible membrane reservoir size for different membrane strain rates using membrane tethering techniques with atomic force microscopy. We conducted atomic force spectroscopy on isolated chondrocytes (n = 87). A micron-sized cantilever was used to extract membrane tethers from cell surfaces at constant pulling rates. Membrane tethers could be identified as force plateaus in the resulting force-displacement curves. Six pulling rates were tested (1, 5, 10, 20, 40, and 80 μm/s). The size of the membrane reservoir, represented by the membrane tether surface areas, decreased exponentially with increasing pulling rates. The current results support our theoretical findings that chondrocytes exposed to impact loading die because of membrane ruptures caused by high tensile membrane strain rates.     

Multiple membrane tethers probed by atomic force microscopy

Using the atomic force microscope to locally probe the cell membrane, we observed the formation of multiple tethers (thin nanotubes, each requiring a similar pulling force) as reproducible features within force profiles recorded on individual cells. Forces obtained with Chinese hamster ovary cells, a malignant human brain tumor cell line, and human endothelial cells (EA hy926) were found to be 28 +/- 10 pN, 29 +/- 9 pN, and 29 +/- 10 pN, respectively, independent of the nature of attachment to the cantilever. The rather large variation of the tether pulling forces measured at several locations on individual cells points to the existence of heterogeneity in the membrane properties of a morphologically homogeneous cell. Measurement of the summary lengths of the simultaneously extracted tethers provides a measure of the size of the available membrane reservoir through which co-existing tethers are associated. As expected, partial disruption of the actin cytoskeleton and removal of the hyaluronan backbone of the glycocalyx were observed to result in a marked decrease (30-50%) in the magnitude and a significant sharpening of the force distribution indicating reduced heterogeneity of membrane properties. Taken together, our results demonstrate the ability of the plasma membrane to locally produce multiple interdependent tethers-a process that could play an important role in the mechanical association of cells with their environment.     

Cell cytoskeleton and tether extraction

We perform a detailed investigation of the force × deformation curve in tether extraction from 3T3 cells by optical tweezers. Contrary to conventional wisdom about tethers extracted from cells, we find that actin filaments are present within them, so that a revised theory of tether pulling from cells is called for. We also measure steady and maximum tether force values significantly higher than previously published ones for 3T3 cells. Possible explanations for these differences are investigated. Further experimental support of the theory of force barriers for membrane tube extension is obtained. The potential of studies on tether pulling force × deformation for retrieving information on membrane-cytoskeleton interaction is emphasized.     

Mechanical behaviour of in-situ chondrocytes subjected to different loading rates: a finite element study

Experimental findings indicate that in-situ chondrocytes die readily following impact loading, but remain essentially unaffected at low (non-impact) strain rates. This study was aimed at identifying possible causes for cell death in impact loading by quantifying chondrocyte mechanics when cartilage was subjected to a 5% nominal tissue strain at different strain rates. Multi-scale modelling techniques were used to simulate cartilage tissue and the corresponding chondrocytes residing in the tissue. Chondrocytes were modelled by accounting for the cell membrane, pericellular matrix and pericellular capsule. The results suggest that cell deformations, cell fluid pressures and fluid flow velocity through cells are highest at the highest (impact) strain rate, but they do not reach damaging levels. Tangential strain rates of the cell membrane were highest at the highest strain rate and were observed primarily in superficial tissue cells. Since cell death following impact loading occurs primarily in superficial zone cells, we speculate that cell death in impact loading is caused by the high tangential strain rates in the membrane of superficial zone cells causing membrane rupture and loss of cell content and integrity.     

The mechanical microenvironment of high concentration agarose for applying deformation to primary chondrocytes

Cartilage and chondrocytes experience loading that causes alterations in chondrocyte biological activity. In vivo chondrocytes are surrounded by a pericellular matrix with a stiffness of ~25–200 kPa. Understanding the mechanical loading environment of the chondrocyte is of substantial interest for understanding chondrocyte mechanotransduction. The first objective of this study was to analyze the spatial variability of applied mechanical deformations in physiologically stiff agarose on cellular and sub-cellular length scales. Fluorescent microspheres were embedded in physiologically stiff agarose hydrogels. Microsphere positions were measured via confocal microscopy and used to calculate displacement and strain fields as a function of spatial position. The second objective was to assess the feasibility of encapsulating primary human chondrocytes in physiologically stiff agarose. The third objective was to determine if primary human chondrocytes could deform in high-stiffness agarose gels. Primary human chondrocyte viability was assessed using live–dead imaging following 24 and 72 h in tissue culture. Chondrocyte shape was measured before and after application of 10% compression. These data indicate that (1) displacement and strain precision are ~1% and 6.5% respectively, (2) high-stiffness agarose gels can maintain primary human chondrocyte viability of >95%, and (3) compression of chondrocytes in 4.5% agarose can induce shape changes indicative of cellular compression. Overall, these results demonstrate the feasibility of using high-concentration agarose for applying in vitro compression to chondrocytes as a model for understanding how chondrocytes respond to in vivo loading.     

Antibody-unfolding and metastable-state binding in force spectroscopy and recognition imaging

Force spectroscopy and recognition imaging are important techniques for characterizing and mapping molecular interactions. In both cases, an antibody is pulled away from its target in times that are much less than the normal residence time of the antibody on its target. The distribution of pulling lengths in force spectroscopy shows the development of additional peaks at high loading rates, indicating that part of the antibody frequently unfolds. This propensity to unfold is reversible, indicating that exposure to high loading rates induces a structural transition to a metastable state. Weakened interactions of the antibody in this metastable state could account for reduced specificity in recognition imaging where the loading rates are always high. The much weaker interaction between the partially unfolded antibody and target, while still specific (as shown by control experiments), results in unbinding on millisecond timescales, giving rise to rapid switching noise in the recognition images. At the lower loading rates used in force spectroscopy, we still find discrepancies between the binding kinetics determined by force spectroscopy and those determined by surface plasmon resonance—possibly a consequence of the short tethers used in recognition imaging. Recognition imaging is nonetheless a powerful tool for interpreting complex atomic force microscopy images, so long as specificity is calibrated in situ, and not inferred from equilibrium binding kinetics.     

Eukaryotic membrane tethers revisited using magnetic tweezers

Membrane nanotubes, under physiological conditions, typically form en masse. We employed magnetic tweezers (MTW) to extract tethers from human brain tumor cells and compared their biophysical properties with tethers extracted after disruption of the cytoskeleton and from a strongly differing cell type, Chinese hamster ovary cells. In this method, the constant force produced with the MTW is transduced to cells through super-paramagnetic beads attached to the cell membrane. Multiple sudden jumps in bead velocity were manifest in the recorded bead displacement-time profiles. These discrete events were interpreted as successive ruptures of individual tethers. Observation with scanning electron microscopy supported the simultaneous existence of multiple tethers. The physical characteristics, in particular, the number and viscoelastic properties of the extracted tethers were determined from the analytic fit to bead trajectories, provided by a standard model of viscoelasticity. Comparison of tethers formed with MTW and atomic force microscopy (AFM), a technique where the cantilever-force transducer is moved at constant velocity, revealed significant differences in the two methods of tether formation. Our findings imply that extreme care must be used to interpret the outcome of tether pulling experiments performed with single molecular techniques (MTW, AFM, optical tweezers, etc). First, the different methods may be testing distinct membrane structures with distinct properties. Second, as soon as a true cell membrane (as opposed to that of a vesicle) can attach to a substrate, upon pulling on it, multiple nonspecific membrane tethers may be generated. Therefore, under physiological conditions, distinguishing between tethers formed through specific and nonspecific interactions is highly nontrivial if at all possible.     

Membrane tether formation from outer hair cells with optical tweezers

Optical tweezers were used to characterize the mechanical properties of the outer hair cell (OHC) plasma membrane by pulling tethers with 4.5-microm polystyrene beads. Tether formation force and tether force were measured in static and dynamic conditions. A greater force was required for tether formations from OHC lateral wall (499 +/- 152 pN) than from OHC basal end (142 +/- 49 pN). The difference in the force required to pull tethers is consistent with an extensive cytoskeletal framework associated with the lateral wall known as the cortical lattice. The apparent plasma membrane stiffness, estimated under the static conditions by measuring tether force at different tether length, was 3.71 pN/microm for OHC lateral wall and 4.57 pN/microm for OHC basal end. The effective membrane viscosity was measured by pulling tethers at different rates while continuously recording the tether force, and estimated in the range of 2.39 to 5.25 pN x s/microm. The viscous force most likely results from the viscous interactions between plasma membrane lipids and the OHC cortical lattice and/or integral membrane proteins. The information these studies provide on the mechanical properties of the OHC lateral wall is important for understanding the mechanism of OHC electromotility.     

Dynamics of Membrane Tethers Reveal Novel Aspects of Cytoskeleton-Membrane Interactions in Axons

Mechanical properties of cell membranes are known to be significantly influenced by the underlying cortical cytoskeleton. The technique of pulling membrane tethers from cells is one of the most effective ways of studying the membrane mechanics and the membrane-cortex interaction. In this article, we show that axon membranes make an interesting system to explore as they exhibit both free membrane-like behavior where the tether-membrane junction is movable on the surface of the axons (unlike many other cell membranes) as well as cell-like behavior where there are transient and spontaneous eruptions in the tether force that vanish when F-actin is depolymerized. We analyze the passive and spontaneous responses of axonal membrane tethers and propose theoretical models to explain the observed behavior.     

Membrane-based actuation for high-speed single molecule force spectroscopy studies using AFM

Atomic force microscopy (AFM)-based dynamic force spectroscopy of single molecular interactions involves characterizing unbinding/unfolding force distributions over a range of pulling speeds. Owing to their size and stiffness, AFM cantilevers are adversely affected by hydrodynamic forces, especially at pulling speeds >10 μm/s, when the viscous drag becomes comparable to the unbinding/unfolding forces. To circumvent these adverse effects, we have fabricated polymer-based membranes capable of actuating commercial AFM cantilevers at speeds ≥100 μm/s with minimal viscous drag effects. We have used FLUENT^®, a computational fluid dynamics (CFD) software, to simulate high-speed pulling and fast actuation of AFM cantilevers and membranes in different experimental configurations. The simulation results support the experimental findings on a variety of commercial AFM cantilevers and predict significant reduction in drag forces when membrane actuators are used. Unbinding force experiments involving human antibodies using these membranes demonstrate that it is possible to achieve bond loading rates ≥10⁶ pN/s, an order of magnitude greater than that reported with commercial AFM cantilevers and systems.     

Cell protrusions and tethers: a unified approach

Low pulling forces applied locally to cell surface membranes produce viscoelastic cell surface protrusions. As the force increases, the membrane can locally separate from the cytoskeleton and a tether forms. Tethers can grow to great lengths exceeding the cell diameter. The protrusion-to-tether transition is known as the crossover. Here we propose a unified approach to protrusions and tethers providing, to our knowledge, new insights into their biomechanics. We derive a necessary and sufficient condition for a crossover to occur, a formula for predicting the crossover time, conditions for a tether to establish a dynamic equilibrium (characterized by constant nonzero pulling force and tether extension rate), a general formula for the tether material after crossover, and a general modeling method for tether pulling experiments. We introduce two general protrusion parameters, the spring constant and effective viscosity, valid before and after crossover. Their first estimates for neutrophils are 50 pN μm⁻¹ and 9 pN s μm⁻¹, respectively. The tether elongation after crossover is described as elongation of a viscoelastic-like material with a nonlinearly decaying spring (NLDs-viscoelastic material). Our model correctly describes the results of the published protrusion and tether pulling experiments, suggesting that it is universally applicable to such experiments.     

Uncoiling Mechanics of Escherichia coli Type I Fimbriae Are Optimized for Catch Bonds

We determined whether the molecular structures through which force is applied to receptor–ligand pairs are tuned to optimize cell adhesion under flow. The adhesive tethers of our model system, Escherichia coli, are type I fimbriae, which are anchored to the outer membrane of most E. coli strains. They consist of a fimbrial rod (0.3–1.5 μm in length) built from a helically coiled structural subunit, FimA, and an adhesive subunit, FimH, incorporated at the fimbrial tip. Previously reported data suggest that FimH binds to mannosylated ligands on the surfaces of host cells via catch bonds that are enhanced by the shear-originated tensile force. To understand whether the mechanical properties of the fimbrial rod regulate the stability of the FimH–mannose bond, we pulled the fimbriae via a mannosylated tip of an atomic force microscope. Individual fimbriae rapidly elongate for up to 10 μm at forces above 60 pN and rapidly contract again at forces below 25 pN. At intermediate forces, fimbriae change length more slowly, and discrete 5.0 ± 0.3–nm changes in length can be observed, consistent with uncoiling and coiling of the helical quaternary structure of one FimA subunit at a time. The force range at which fimbriae are relatively stable in length is the same as the optimal force range at which FimH–mannose bonds are longest lived. Higher or lower forces, which cause shorter bond lifetimes, cause rapid length changes in the fimbria that help maintain force at the optimal range for sustaining the FimH–mannose interaction. The modulation of force and the rate at which it is transmitted from the bacterial cell to the adhesive catch bond present a novel physiological role for the fimbrial rod in bacterial host cell adhesion. This suggests that the mechanical properties of the fimbrial shaft have codeveloped to optimize the stability of the terminal adhesive under flow.     

In situ deformation of growth plate chondrocytes in stress-controlled static vs dynamic compression

Longitudinal bone growth in children/adolescents occurs through endochondral ossification at growth plates and is influenced by mechanical loading, where increased compression decreases growth (i.e., Hueter-Volkmann Law). Past in vivo studies on static vs dynamic compression of growth plates indicate that factors modulating growth rate might lie at the cellular level. Here, in situ viscoelastic deformation of hypertrophic chondrocytes in growth plate explants undergoing stress-controlled static vs dynamic loading conditions was investigated. Growth plate explants from the proximal tibia of pre-pubertal rats were subjected to static vs dynamic stress-controlled mechanical tests. Stained hypertrophic chondrocytes were tracked before and after mechanical testing with a confocal microscope to derive volumetric, axial and lateral cellular strains. Axial strain in hypertrophic chondrocytes was similar for all groups, supporting the mean applied compressive stress’s correlation with bone growth rate and hypertrophic chondrocyte height in past studies. However, static conditions resulted in significantly higher lateral (p < 0.001) and volumetric cellular strains (p ≤ 0.015) than dynamic conditions, presumably due to the growth plate’s viscoelastic nature. Sustained compression in stress-controlled static loading results in continued time-dependent cellular deformation; conversely, dynamic groups have less volumetric strain because the cyclically varying stress limits time-dependent deformation. Furthermore, high frequency dynamic tests showed significantly lower volumetric strain (p = 0.002) than low frequency conditions. Mechanical loading protocols could be translated into treatments to correct or halt progression of bone deformities in children/adolescents. Mimicking physiological stress-controlled dynamic conditions may have beneficial effects at the cellular level as dynamic tests are associated with limited lateral and volumetric cellular deformation.     

Probing the energy landscape of the membrane protein bacteriorhodopsin

The folding and stability of transmembrane proteins is a fundamental and unsolved biological problem. Here, single bacteriorhodopsin molecules were mechanically unfolded from native purple membranes using atomic force microscopy and force spectroscopy. The energy landscape of individual transmembrane alpha helices and polypeptide loops was mapped by monitoring the pulling speed dependence of the unfolding forces and applying Monte Carlo simulations. Single helices formed independently stable units stabilized by a single potential barrier. Mechanical unfolding of the helices was triggered by 3.9-7.7 A extension, while natural unfolding rates were of the order of 10(-3) s(-1). Besides acting as individually stable units, helices associated pairwise, establishing a collective potential barrier. The unfolding pathways of individual proteins reflect distinct pulling speed-dependent unfolding routes in their energy landscapes. These observations support the two-stage model of membrane protein folding in which alpha helices insert into the membrane as stable units and then assemble into the functional protein.     

Atomic force microscope spectroscopy reveals a hemifusion intermediate during soluble N-ethylmaleimide-sensitive factor-attachment protein receptors-mediated membrane fusion

This study investigated the effect of soluble N-ethylmaleimide-sensitive factor-attachment protein (SNAP) receptors (SNAREs) on the fusion of egg L-α-phosphatidylcholine bilayers using atomic force microscope (AFM) spectroscopy. AFM measurements of the fusion force under compression were acquired to reveal the energy landscape of the fusion process. A single main energy barrier governing the fusion process was identified in the absence and presence of SNAREs in the bilayers. Under compression, a significant downward shift in the fusion dynamic force spectrum was observed when cognate v- and t-SNAREs were present in the opposite bilayers. The presence of vesicle-associated membrane protein (VAMP) and binary syntaxin and SNAP 25 in the apposed bilayers resulted in a reduction in the height of the activation potential by ∼1.3 k_BT and a >2-fold increase in the width of the energy barrier. The widening of the energy barrier in the presence SNAREs is interpreted as an increase in the compressibility of the membranes, which translates to a greater ease in the bilayer deformation and subsequently the fusion of the membranes under compression. Facilitation of membrane fusion was observed only when SNAREs were present in both bilayers. Moreover, addition of the soluble cytoplasmic domain of VAMP, which interferes with the interaction between opposing v- and t-SNAREs, prevented such facilitation. These observations implicated the interaction between the cytoplasmic domains of opposing SNAREs in the observed fusion facilitation, possibly by destabilizing the bilayers through pulling on their transmembrane segments. Our AFM compression measurements revealed that SNARE-mediated membrane fusion proceeded through a sequence of two ∼5 nm collapses of the membrane, an observation that is consistent with the existence of a hemifused state during the fusion process.     

Single-molecule adhesion forces and attachment lifetimes of myosin-I phosphoinositide interactions

Phosphoinositides regulate the activities and localization of many cytoskeletal proteins involved in crucial biological processes, including membrane-cytoskeleton adhesion. Yet little is known about the mechanics of protein-phosphoinositide interactions, or about the membrane-attachment mechanics of any peripheral membrane proteins. Myosin-Ic (myo1c) is a molecular motor that links membranes to the cytoskeleton via phosphoinositide binding, so it is particularly important to understand the mechanics of its membrane attachment. We used optical tweezers to measure the strength and attachment lifetime of single myo1c molecules as they bind beads coated with a bilayer of 2% phosphatidylinositol 4,5-bisphosphate and 98% phosphatidylcholine. Adhesion forces measured under ramp-load ranged between 5.5 and 16 pN at loading rates between 250 and 1800 pN/s. Dissociation rates increased linearly with constant force (0.3-2.5 pN), with rates exceeding 360 s⁻¹ at 2.5 pN. Attachment lifetimes calculated from adhesion force measurements were loading-rate-dependent, suggesting nonadiabatic behavior during pulling. The adhesion forces of myo1c with phosphoinositides are greater than the motors stall forces and are within twofold of the force required to extract a lipid molecule from the membrane. However, attachment durations are short-lived, suggesting that phosphoinositides alone do not provide the mechanical stability required to anchor myo1c to membranes during multiple ATPase cycles.     

Hydrodynamic effects in fast AFM single-molecule force measurements

Atomic force microscopy (AFM) allows the critical forces that unfold single proteins and rupture individual receptor–ligand bonds to be measured. To derive the shape of the energy landscape, the dynamic strength of the system is probed at different force loading rates. This is usually achieved by varying the pulling speed between a few nm/s and a few m/s, although for a more complete investigation of the kinetic properties higher speeds are desirable. Above 10 m/s, the hydrodynamic drag force acting on the AFM cantilever reaches the same order of magnitude as the molecular forces. This has limited the maximum pulling speed in AFM single-molecule force spectroscopy experiments. Here, we present an approach for considering these hydrodynamic effects, thereby allowing a correct evaluation of AFM force measurements recorded over an extended range of pulling speeds (and thus loading rates). To support and illustrate our theoretical considerations, we experimentally evaluated the mechanical unfolding of a multi-domain protein recorded at 30 m/s pulling speed.Abbrevations AFM atomic force micrcoscopy - pN piconewton - BR bacteriorhodopsin - DFS dynamic force spectroscopy - Ig27 immunoglobulin 27 - If27-8 immunoglobulin 27 octameric construct - BFP biomembrane force probe     

Importance of phospholipid bilayer integrity in the analysis of protein–lipid interactions

The integrity of supported phospholipid bilayer membranes is of crucial importance for the investigation of lipid–protein interactions. Therefore we recorded the formation of supported membranes on SiO₂ and mica by quartz crystal microbalance and controlled the integrity by atomic force microscopy. This study aims to analyze how membrane defects affect protein–lipid interactions. The experiments focused on a lipid mixture of POPC/DOPC/Chol/POPS/PI(4,5)P₂ (37:20:20:20:3) and the binding of the peripheral membrane associated protein annexin A2. We found that formation of a continuous undisturbed bilayer is an indispensable precondition for a reliable determination and quantification of lipid–protein-interactions. If membrane defects were present, protein adsorption causes membrane disruption and lipid detachment on a support thus leading to false determination of binding constants. Our results obtained for PI(4,5)P₂ and cholesterol containing supported membranes yield new knowledge to construct functional surfaces that may cover nanoporous substrates, form free standing membranes or may be used for lab-on-a-chip applications.     

Experimental and finite element analysis of strains induced by axial tibial compression in young-adult and old female C57Bl/6 mice

Axial compression of the mouse tibia is used to study strain-adaptive bone (re)modeling. In some studies, comparisons between mice of different ages are of interest. We characterized the tibial deformation and force–strain relationships in female C57Bl/6 mice at 5-, 12- and 22-months age. A three-gauge experimental method was used to determine the strain distribution at the mid-diaphysis, while specimen-specific finite element analysis was used to examine strain distribution along the tibial length. The peak strains in the tibial mid-diaphyseal cross-section are compressive and occur at the postero-lateral apex. The magnitudes of these peak compressive strains are 1.5 to 2 times those on the opposite, antero-medial face (a site often used for strain gauge placement). For example, −10 N force applied to a 5-months old mouse engenders a peak compressive strain of −2800 µε and a tensile strain on the antero-medial face of +1450 µε. The orientation of the neutral axis at the mid-diaphysis did not differ with age (p=0.46), indicating a similar deformation mode in young and old tibiae. On the other hand, from 5- to 22-months there is a 25% reduction in cortical thickness and moment of inertia (p<0.05), resulting in significantly greater tibial strain magnitudes in older mice for equivalent applied force (p<0.05). We conclude that comparisons of tibial loading responses in young-adult and old C57Bl/6 tibiae are facilitated by similar deformation pattern across ages, but that modest adjustment of force levels is required to engender matching peak strains.