Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than ～15% of global cell deformation in cell compression tests, or more than ～3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.     

An integrated laser trap/flow control video microscope for the study of single biomolecules

We have developed an integrated laser trap/flow control video microscope for mechanical manipulation of single biopolymers. The instrument is automated to maximize experimental throughput. A single-beam optical trap capable of trapping micron-scale polystyrene beads in the middle of a 200-microm-deep microchamber is used, making it possible to insert a micropipette inside this chamber to hold a second bead by suction. Together, these beads function as easily exchangeable surfaces between which macromolecules of interest can be attached. A computer-controlled flow system is used to exchange the liquid in the chamber and to establish a flow rate with high precision. The flow and the optical trap can be used to exert forces on the beads, the displacements of which can be measured either by video microscopy or by laser deflection. To test the performance of this instrument, individual biotinylated DNA molecules were assembled between two streptavidin beads, and the DNA elasticity was characterized using both laser trap and flow forces. DNA extension under varying forces was measured by video microscopy. The combination of the flow system and video microscopy is a versatile design that is particularly useful for the study of systems susceptible to laser-induced damage. This capability was demonstrated by following the translocation of transcribing RNA polymerase up to 650 s.     

Single-molecule manipulation of double-stranded DNA using optical tweezers: interaction studies of DNA with RecA and YOYO-1.

By using optical tweezers and a specially designed flow cell with an integrated glass micropipette, we constructed a setup similar to that of Smith et al. (Science 271:795-799, 1996) in which an individual double-stranded DNA (dsDNA) molecule can be captured between two polystyrene beads. The first bead is immobilized by the optical tweezers and the second by the micropipette. Movement of the micropipette allows manipulation and stretching of the DNA molecule, and the force exerted on it can be monitored simultaneously with the optical tweezers. We used this setup to study elongation of dsDNA by RecA protein and YOYO-1 dye molecules. We found that the stability of the different DNA-ligand complexes and their binding kinetics were quite different. The length of the DNA molecule was extended by 45% when RecA protein was added. Interestingly, the speed of elongation was dependent on the external force applied to the DNA molecule. In experiments in which YOYO-1 was added, a 10-20% extension of the DNA molecule length was observed. Moreover, these experiments showed that a change in the applied external force results in a time-dependent structural change of the DNA-YOYO-1 complex, with a time constant of approximately 35 s (1/e2). Because the setup provides an oriented DNA molecule, we determined the orientation of the transition dipole moment of YOYO-1 within DNA by using fluorescence polarization. The angle of the transition dipole moment with respect to the helical axis of the DNA molecule was 69 degrees +/- 3.     

Mechanical Characterization of Protein L in the Low-Force Regime by Electromagnetic Tweezers/Evanescent Nanometry

Mechanical manipulation at the single molecule level of proteins exhibiting mechanical stability poses a technical challenge that has been almost exclusively approached by atomic force microscopy (AFM) techniques. However, due to mechanical drift limitations, AFM techniques are restricted to experimental recordings that last less than a minute in the high-force regime. Here we demonstrate a novel combination of electromagnetic tweezers and evanescent nanometry that readily captures the forced unfolding trajectories of protein L at pulling forces as low as 10 ∼ 15 pN. Using this approach, we monitor unfolding and refolding cycles of the same polyprotein for a period of time longer than 30 min. From such long-lasting recordings, we obtain ensemble averages of unfolding step sizes and rates that are consistent with single-molecule AFM data obtained at higher stretching forces. The unfolding kinetics of protein L at low stretching forces confirms and extends the observations that the mechanical unfolding rate is exponentially dependent on the pulling force within a wide range of stretching forces spanning from 13 pN up to 120 pN. Our experiments demonstrate a novel approach for the mechanical manipulation of single proteins for extended periods of time in the low-force regime.     

Reversible and irreversible unfolding of mitotic newt chromosomes by applied force

The force-extension behavior of individual mitotic newt chromosomes was studied, using micropipette surgery and manipulation, for elongations up to 80 times native length. After elongations up to five times, chromosomes return to their native length. In this regime chromosomes have linear elasticity, requiring approximately 1 nN of force to be stretched to two times native length. After more than five times stretching, chromosomes are permanently elongated, with force hysteresis during relaxation. If a chromosome is repeatedly stretched to approximately 10 times native length and relaxed, a series of hysteresis loops are obtained that converge to a single reversible elastic response. For further elongations, the linear dependence of force on extension terminates at a force "plateau" of approximately 15-20 nN, near 30 times extension. After >30 times extensions, the elastic moduli of chromosomes can be reduced by more than 20-fold, and they appear as "ghosts": swollen, elongated, and with reduced optical contrast under both phase and differential interference contrast imaging. Antibody labeling indicates that histone proteins are not being lost during even extreme extensions. Results are interpreted in terms of extension and failure of chromatin-tethering elements; the force data allow estimates of the number and size of such connectors in a chromosome.     

Reversible mechanical unfolding of single ubiquitin molecules

Single-molecule manipulation techniques have enabled the characterization of the unfolding and refolding process of individual protein molecules, using mechanical forces to initiate the unfolding transition. Experimental and computational results following this approach have shed new light on the mechanisms of the mechanical functions of proteins involved in several cellular processes, as well as revealed new information on the protein folding/unfolding free-energy landscapes. To investigate how protein molecules of different folds respond to a stretching force, and to elucidate the effects of solution conditions on the mechanical stability of a protein, we synthesized polymers of the protein ubiquitin and characterized the force-induced unfolding and refolding of individual ubiquitin molecules using an atomic-force-microscope-based single-molecule manipulation technique. The ubiquitin molecule was highly resistant to a stretching force, and the mechanical unfolding process was reversible. A model calculation based on the hydrogen-bonding pattern in the native structure was performed to explain the origin of this high mechanical stability. Furthermore, pH effects were studied and it was found that the forces required to unfold the protein remained constant within a pH range around the neutral value, and forces decreased as the solution pH was lowered to more acidic values.     

Effects of carpal tunnel syndrome on adaptation of multi-digit forces to object weight for whole-hand manipulation

The delicate tuning of digit forces to object properties can be disrupted by a number of neurological and musculoskeletal diseases. One such condition is Carpal Tunnel Syndrome (CTS), a compression neuropathy of the median nerve that causes sensory and motor deficits in a subset of digits in the hand. Whereas the effects of CTS on median nerve physiology are well understood, the extent to which it affects whole-hand manipulation remains to be addressed. CTS affects only the lateral three and a half digits, which raises the question of how the central nervous system integrates sensory feedback from affected and unaffected digits to plan and execute whole-hand object manipulation. We addressed this question by asking CTS patients and healthy controls to grasp, lift, and hold a grip device (445, 545, or 745 g) for several consecutive trials. We found that CTS patients were able to successfully adapt grip force to object weight. However, multi-digit force coordination in patients was characterized by lower discrimination of force modulation to lighter object weights, higher across-trial digit force variability, the consistent use of excessively large digit forces across consecutive trials, and a lower ability to minimize net moments on the object. Importantly, the mechanical requirement of attaining equilibrium of forces and torques caused CTS patients to exert excessive forces at both CTS-affected digits and digits with intact sensorimotor capabilities. These findings suggest that CTS-induced deficits in tactile sensitivity interfere with the formation of accurate sensorimotor memories of previous manipulations. Consequently, CTS patients use compensatory strategies to maximize grasp stability at the expense of exerting consistently larger multi-digit forces than controls. These behavioral deficits might be particularly detrimental for tasks that require fine regulation of fingertip forces for manipulating light or fragile objects.     

The human erythrocyte membrane skeleton may be an ionic gel. III. Micropipette aspiration of unswollen erythrocytes

We have carried out a theoretical analysis of micropipette aspiration of unswollen erythrocytes using the protein-gel-lipid-bilayer membrane model and taking into account that the modulus of area compression of the membrane skeleton may depend on the environmental conditions. Our analysis shows that the aspiration pressure needed to obtain a certain membrane projection length is strongly dependent on the ratio between the membrane skeleton modulus of area compression and the elastic shear modulus. Our analysis therefore predicts that micropipette aspiration of unswollen erythrocytes may be a sensitive method for detection of changes in this ratio. The analysis thus also shows that micropipette aspiration of unswollen erythrocytes can not be used to determine the membrane shear modulus unless something is known about the membrane skeleton modulus of area compression.     

Evidence for a second valve system in lymphatics: endothelial microvalves.

The mechanism for interstitial fluid uptake into the lymphatics remains speculative and unresolved. A system of intralymphatic valves exists that prevents reflow along the length of the lymphatic channels. However, these valves are not sufficient to provide unidirectional flow at the level of the initial lymphatics. We investigate here the hypothesis that initial lymphatics have a second, separate valve system that permits fluid to enter from the interstitium into the initial lymph channels but prevents escape back out into the tissue. The transport of fluorescent microspheres (0.31 microm) across endothelium of initial lymphatics in rat cremaster muscle was investigated with micropipette manipulation techniques. The results indicate that microspheres can readily pass from the interstitium across the endothelium into the lumen of the initial lymphatics. Once inside the lymphatic lumen, the microspheres cannot be forced out of the lumen even after elevation of the lymphatic pressure by outflow obstruction. Reaspiration of the microspheres inside the lymphatic lumen with a micropipette is blocked by the lymphatic endothelium. This blockade exists whether the aspiration is carried out at the microsphere entry site or anywhere along the initial lymphatics. Nevertheless, puncture of the initial lymphatic endothelium with the micropipette leads to rapid aspiration of intralymphatic microspheres. Investigation of lymphatic endothelial sections fixed during lymph pumping shows open interendothelial junctions not found in resting initial lymphatics. These results suggest that initial lymphatics have a (primary) valve system at the level of the endothelium. In conjunction with the classical (secondary) intralymphatic valves, the primary valves provide the mechanism that facilitates the unidirectional flow during periodic compression and expansion of initial lymphatics.     

Unraveling proteins: a molecular mechanics study

An internal coordinate molecular mechanics study of unfolding peptide chains by external stretching has been carried out to predict the type of force spectra that may be expected from single-molecule manipulation experiments currently being prepared. Rather than modeling the stretching of a given protein, we have looked at the behavior of simple secondary structure elements (alpha-helix, beta-ribbon, and interacting alpha-helices) to estimate the magnitude of the forces involved in their unfolding or separation and the dependence of these forces on the way pulling is carried out as well as on the length of the structural elements. The results point to a hierarchy of forces covering a surprisingly large range and to important orientational effects in the response to external stress.     

Single-cell adhesion tests against functionalized microspheres arrayed on AFM cantilevers confirm heterophilic E- and N-cadherin binding

We assess the cross-reactivity of both cellular as well as recombinant E- and N-cadherins using functionalized bead arrays assembled on atomic-force-microscope cantilevers. This new approach builds upon and enhances the utility of a recently developed force probe that integrates a custom-built, horizontal atomic force microscope with micropipette manipulation. It enables us to test multiple biomolecular interactions of the same cell in a swift sequential or cyclic manner and thus to resolve subtle differences between individual interactions that otherwise would be obscured by cell-cell baseline variability. For each cell, we contrast heterophilic E:N-cadherin binding with the respective homophilic bonds and with a suitable control. Clarifying previous literature reports, we establish that specific bonds between E- and N-cadherins form readily, albeit less frequently than homophilic bonds of either cadherin. We support this assessment with a rough estimate of the ratio of on-rate constants of E/N-cadherin binding.     

Old,socially housed rhesus monkeys manipulate objects

Recent research has indicated that old, individually housed monkeys show little interest in novel objects. Yet unanswered is whether this effect is caused primarily by age or housing condition. The purpose of this study was to assess the role of social living in promoting responsiveness to objects. We measured the rates of object manipulation in older animals, assessed responsiveness over time to particular objects as a measure of habituation, and examined social influences on object use. Several social groups of rhesus monkeys that contained older adults were studied. These groups were housed in indoor pens or in an outdoor enclosure, and all monkeys had continuous access to a variety of objects in their home environment. In contrast to previous studies of individually housed monkeys, our group-housed monkeys showed sustained interest in objects. Old monkeys manipulated objects extensively, and this response was all the more significant, given that the objects were not novel. Monkeys housed in an outdoor enclosure showed object manipulation patterns that were not different from monkeys housed in indoor pens. However, females exhibited much higher object-related responses than males. Social facilitation played a role in the reactions of some monkeys to objects. Patterns of social facilitation as well as avoidance were present in two of the three indoor groups that were observed. Failure to manipulate objects in rhesus macaques appears to be more a function of individual housing than of old age. Factors such as environmental complexity, social needs, and early experience should be considered in order to understand why individually housed rhesus monkeys are unresponsive to objects. © 1993 Wiley-Liss, Inc.     

Toward a molecular understanding of the anisotropic response of proteins to external forces: insights from elastic network models

With recent advances in single-molecule manipulation techniques, it is now possible to measure the mechanical resistance of proteins to external pulling forces applied at specific positions. Remarkably, such recent studies demonstrated that the pulling/stretching forces required to initiate unfolding vary considerably depending on the location of the application of the forces, unraveling residue/position-specific response of proteins to uniaxial tension. Here we show that coarse-grained elastic network models based on the topology of interresidue contacts in the native state can satisfactory explain the relative sizes of such stretching forces exerted on different residue pairs. Despite their simplicity, such models presumably capture a fundamental property that dominates the observed behavior: deformations that can be accommodated by the relatively lower frequency modes of motions intrinsically favored by the structure require weaker forces and vice versa. The mechanical response of proteins to external stress is therefore shown to correlate with the anisotropic fluctuation dynamics intrinsically accessible in the folded state. The dependence on the overall fold implies that evolutionarily related proteins sharing common structural features tend to possess similar mechanical properties. However, the theory cannot explain the differences observed in a number of structurally similar but sequentially distant domains, such as the fibronectin domains.     

'Single molecule': theory and experiments,an introduction

At scales below micrometers, Brownian motion dictates most of the behaviors. The simple observation of a colloid is striking: a permanent and random motion is seen, whereas inertial forces play a negligible role. This Physics, where velocity is proportional to force, has opened new horizons in biology. The random feature is challenged in living systems where some proteins - molecular motors - have a directed motion whereas their passive behaviors of colloid should lead to a Brownian motion. Individual proteins, polymers of living matter such as DNA, RNA, actin or microtubules, molecular motors, all these objects can be viewed as chains of colloids. They are submitted to shocks from molecules of the solvent. Shapes taken by these biopolymers or dynamics imposed by motors can be measured and modeled from single molecules to their collective effects. Thanks to the development of experimental methods such as optical tweezers, Atomic Force Microscope (AFM), micropipettes, and quantitative fluorescence (such as Förster Resonance Energy Transfer, FRET), it is possible to manipulate these individual biomolecules in an unprecedented manner: experiments allow to probe the validity of models; and a new Physics has thereby emerged with original biological insights. Theories based on statistical mechanics are needed to explain behaviors of these systems. When force-extension curves of these molecules are extracted, the curves need to be fitted with models that predict the deformation of free objects or submitted to a force. When velocity of motors is altered, a quantitative analysis is required to explain the motions of individual molecules under external forces. This lecture will give some elements of introduction to the lectures of the session 'Nanophysics for Molecular Biology'.     

Analyzing forced unfolding of protein tandems by ordered variates, 1: Independent unfolding times

Most of the mechanically active proteins are organized into tandems of identical repeats, (D)N, or heterogeneous tandems, D1-D2-...-DN. In current atomic force microscopy experiments, conformational transitions of protein tandems can be accessed by employing constant stretching force f (force-clamp) and by analyzing the recorded unfolding times of individual domains. Analysis of unfolding data for homogeneous tandems relies on the assumption that unfolding times are independent and identically distributed, and involves inference of the (parent) probability density of unfolding times from the histogram of the combined unfolding times. This procedure cannot be used to describe tandems characterized by interdomain interactions, or heteregoneous tandems. In this article, we introduce an alternative approach that is based on recognizing that the observed data are ordered, i.e., first, second, third, etc., unfolding times. The approach is exemplified through the analysis of unfolding times for a computer model of the homogeneous and heterogeneous tandems, subjected to constant force. We show that, in the experimentally accessible range of stretching forces, the independent and identically distributed assumption may not hold. Specifically, the uncorrelated unfolding transitions of individual domains at lower force may become correlated (dependent) at elevated force levels. The proposed formalism can be used in atomic force microscopy experiments to infer the unfolding time distributions of individual domains from experimental histograms of ordered unfolding times, and it can be extended to analyzing protein tandems that exhibit interdomain interactions.     

Determination of the Poisson's ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration

Chondrocytes in articular cartilage are regularly subjected to compression and recovery due to dynamic loading of the joint. Previous studies have investigated the elastic and viscoelastic properties of chondrocytes using micropipette aspiration techniques, but in order to calculate cell properties, these studies have generally assumed that cells are incompressible with a Poisson's ratio of 0.5. The goal of this study was to measure the Poisson's ratio and recovery properties of the chondrocyte by combining theoretical modeling with experimental measures of complete cellular aspiration and release from a micropipette. Chondrocytes isolated from non-osteoarthritic and osteoarthritic cartilage were fully aspirated into a micropipette and allowed to reach mechanical equilibrium. Cells were then extruded from the micropipette and cell volume and morphology were measured throughout the experiment. This experimental procedure was simulated with finite element analysis, modeling the chondrocyte as either a compressible two-mode viscoelastic solid, or as a biphasic viscoelastic material. By fitting the experimental data to the theoretically predicted cell response, the Poisson's ratio and the viscoelastic recovery properties of the cell were determined. The Poisson's ratio of chondrocytes was found to be 0.38 for non-osteoarthritic cartilage and 0.36 for osteoarthritic chondrocytes (no significant difference). Osteoarthritic chondrocytes showed an increased recovery time following full aspiration. In contrast to previous assumptions, these findings suggest that chondrocytes are compressible, consistent with previous studies showing cell volume changes with compression of the extracellular matrix.     

An Apparatus for Measuring Volumes of Small Objects

An apparatus for measuring volumes of small objects such as tissue blocks is described. The apparatus measures volumes by fluid displacement and consists of a micropipette adapted to fit the mouth of an Erleiuneyer flask, a Luer adaptor fused to the side of the flask, and a glass syringe. When assembled with fluid enclosed, the fluid rises to a low level in the micropipette. Withdrawal of fluid into the syringe lowers the fluid level below the mouth of the flask. The micropipette is raised, the object to be measured is placed in the flask, and the micropipette is joined to the flask again. Fluid returned to the flask from the syringe rises to a higher level in the micropipette. The difference between the two fluid levels equals the volume of the object measured.

This apparatus gives reproducible measurements and can be calibrated for absolute volume determination. It is inexpensive to construct and easy to use.     

A power-law rheology-based finite element model for single cell deformation

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.     

Unfolding individual nucleosomes by stretching single chromatin fibers with optical tweezers.

Single chromatin fibers were assembled directly in the flow cell of an optical tweezers setup. A single lambda phage DNA molecule, suspended between two polystyrene beads, was exposed to a Xenopus laevis egg extract, leading to chromatin assembly with concomitant apparent shortening of the DNA molecule. Assembly was force-dependent and could not take place at forces exceeding 10 pN. The assembled single chromatin fiber was subjected to stretching by controlled movement of one of the beads with the force generated in the molecule continuously monitored with the second bead trapped in the optical trap. The force displayed discrete, sudden drops upon fiber stretching, reflecting discrete opening events in fiber structure. These opening events were quantized at increments in fiber length of approximately 65 nm and are attributed to unwrapping of the DNA from around individual histone octamers. Repeated stretching and relaxing of the fiber in the absence of egg extract showed that the loss of histone octamers was irreversible. The forces measured for individual nucleosome disruptions are in the range of 20-40 pN, comparable to forces reported for RNA- and DNA-polymerases.