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.     

Power-law rheology analysis of cells undergoing micropipette aspiration

Accurate quantification of the mechanical properties of living cells requires the combined use of experimental techniques and theoretical models. In this paper, we investigate the viscoelastic response of suspended NIH 3T3 fibroblasts undergoing micropipette aspiration using power-law rheology model. As an important first step, we examine the pipette size effect on cell deformation and find that pipettes larger than ~7 μm are more suitable for bulk rheological measurements than smaller ones and the cell can be treated as effectively continuum. When the large pipettes are used to apply a constant pressure to a cell, the creep deformation is better fitted with the power-law rheology model than with the liquid drop or spring-dashpot models; magnetic twisting cytometry measurement on the rounded cell confirms the power-law behavior. This finding is further extended to suspended cells treated with drugs targeting their cytoskeleton. As such, our results suggest that the application of relatively large pipettes can provide more effective assessment of the bulk material properties as well as support application of power-law rheology to cells in suspension.     

Characterizing Cell Adhesion by Using Micropipette Aspiration

We have developed a technique to directly quantify cell-substrate adhesion force using micropipette aspiration. The micropipette is positioned perpendicular to the surface of an adherent cell and a constant-rate aspiration pressure is applied. Since the micropipette diameter and the aspiration pressure are our control parameters, we have direct knowledge of the aspiration force, whereas the cell behavior is monitored either in brightfield or interference reflection microscopy. This setup thus allows us to explore a range of geometric parameters, such as projected cell area, adhesion area, or pipette size, as well as dynamical parameters such as the loading rate. We find that cell detachment is a well-defined event occurring at a critical aspiration pressure, and that the detachment force scales with the cell adhesion area (for a given micropipette diameter and loading rate), which defines a critical stress. Taking into account the cell adhesion area, intrinsic parameters of the adhesion bonds, and the loading rate, a minimal model provides an expression for the critical stress that helps rationalize our experimental results.     

Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration

The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.     

Stability analysis of micropipette aspiration of neutrophils

During micropipette aspiration, neutrophil leukocytes exhibit a liquid-drop behavior, i.e., if a neutrophil is aspirated by a pressure larger than a certain threshold pressure, it flows continuously into the pipette. The point of the largest aspiration pressure at which the neutrophil can still be held in a stable equilibrium is called the critical point of aspiration. Here, we present a theoretical analysis of the equilibrium behavior and stability of a neutrophil during micropipette aspiration with the aim to rigorously characterize the critical point. We take the energy minimization approach, in which the critical point is well defined as the point of the stability breakdown. We use the basic liquid-drop model of neutrophil rheology extended by considering also the neutrophil elastic area expansivity. Our analysis predicts that the behavior at large pipette radii or small elastic area expansivity is close to the one predicted by the basic liquid-drop model, where the critical point is attained slightly before the projection length reaches the pipette radius. The effect of elastic area expansivity is qualitatively different at smaller pipette radii, where our analysis predicts that the critical point is attained at the projection lengths that may significantly exceed the pipette radius.     

Mechanical properties of the cell nucleus and the effect of emerin deficiency

Nuclear structure and mechanics are gaining recognition as important factors that affect gene expression, development, and differentiation in normal function and disease, yet the physical mechanisms that govern nuclear mechanical stability remain unclear. Here we examined the physical properties of the cell nucleus by imaging fluorescently labeled components of the inner nucleus (chromatin and nucleoli) and the nuclear envelope (lamins and membranes) in nuclei deformed by micropipette aspiration (confocal imaged microdeformation). We investigated nuclei, both isolated and in intact, living cells, and found that nuclear volume significantly decreased by 60-70% during aspiration. While nuclear membranes exhibited blebbing and fluid characteristics during aspiration, the nuclear lamina exhibited behavior of a solid-elastic shell. Under large deformations of GFP-lamin A-labeled nuclei, we observed a decay of fluorescence intensity into the tip of the deformed tongue that we interpreted in terms of nonlinear, two-dimensional elasticity theory. Here we applied this method to study nuclear envelope stability in disease and found that mouse embryo fibroblasts lacking the inner nuclear membrane protein, emerin, had a significantly decreased ratio of the area expansion to shear moduli (K/mu) compared to wild-type cells (2.1 +/- 0.2 versus 5.1 +/- 1.3). These data suggest that altered nuclear envelope elasticity caused by loss of emerin could contribute to increased nuclear fragility in Emery-Dreifuss muscular dystrophy patients with mutations in the emerin gene. Based on our experimental results and theoretical considerations, we present a model describing how the nucleus is stabilized in the pipette. Such a model is essential for interpreting the results of any micropipette study of the nucleus and porous materials in general.     

Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation

The micropipette aspiration technique was used to investigate the deformation properties of a panel of nontransformed and transformed rat fibroblasts derived from the same normal cell line. In this method, a step negative pressure is applied to the cell via a micropipette and the aspiration distance into the pipette as a function of time is determined using video techniques. A standard solid viscoelastic model was then used to analyze the viscoelastic properties of the cell. From these results, it is concluded that a direct correlation exists between an increase in deformability and progression of the transformed phenotype from a nontumorigenic cell line into a tumorigenic, metastatic cell line.     

Micropipette Aspiration of Substrate-attached Cells to Estimate Cell Stiffness

Growing number of studies show that biomechanical properties of individual cells play major roles in multiple cellular functions, including cell proliferation, differentiation, migration and cell-cell interactions. The two key parameters of cellular biomechanics are cellular deformability or stiffness and the ability of the cells to contract and generate force. Here we describe a quick and simple method to estimate cell stiffness by measuring the degree of membrane deformation in response to negative pressure applied by a glass micropipette to the cell surface, a technique that is called Micropipette Aspiration or Microaspiration.Microaspiration is performed by pulling a glass capillary to create a micropipette with a very small tip (2-50 μm diameter depending on the size of a cell or a tissue sample), which is then connected to a pneumatic pressure transducer and brought to a close vicinity of a cell under a microscope. When the tip of the pipette touches a cell, a step of negative pressure is applied to the pipette by the pneumatic pressure transducer generating well-defined pressure on the cell membrane. In response to pressure, the membrane is aspirated into the pipette and progressive membrane deformation or "membrane projection" into the pipette is measured as a function of time. The basic principle of this experimental approach is that the degree of membrane deformation in response to a defined mechanical force is a function of membrane stiffness. The stiffer the membrane is, the slower the rate of membrane deformation and the shorter the steady-state aspiration length.The technique can be performed on isolated cells, both in suspension and substrate-attached, large organelles, and liposomes.Analysis is performed by comparing maximal membrane deformations achieved under a given pressure for different cell populations or experimental conditions. A "stiffness coefficient" is estimated by plotting the aspirated length of membrane deformation as a function of the applied pressure. Furthermore, the data can be further analyzed to estimate the Young''s modulus of the cells (E), the most common parameter to characterize stiffness of materials. It is important to note that plasma membranes of eukaryotic cells can be viewed as a bi-component system where membrane lipid bilayer is underlied by the sub-membrane cytoskeleton and that it is the cytoskeleton that constitutes the mechanical scaffold of the membrane and dominates the deformability of the cellular envelope. This approach, therefore, allows probing the biomechanical properties of the sub-membrane cytoskeleton.     

The behavior of human neutrophils during flow through capillary pores

The passage times of individual human neutrophils through single capillary-sized pores in polycarbonate membranes were measured with the resistive pulse technique, and results were compared to those obtained from the micropipette aspiration of entire cells. Pore transit measurement serves as a useful means to screen populations of cells, and allows for protocols that measure time dependent changes to the population. Neutrophils exhibited a highly linear pressure/flow rate relationship at aspiration pressures from 200 Pa to 1,500 Pa in both the pore and pipette systems. Cellular viscosity, as determined by the method of Hochmuth and Needham, was 89.0 Pa.s for the pore systems and 134.9 Pa.s for the pipette systems. These results are in general agreement with recent values of neutrophil viscosity published in the literature. Extrapolation of the observed linear flow response revealed an apparent minimum pressure for whole cell aspiration significantly above the threshold pressure predicted by Evans' liquid drop model. However, whole cell aspiration was achieved in both the pore and pipette systems at pressures below this extrapolated minimum, although the calculated cellular viscosity was greatly increased. The implications of these two regimes of cell deformation is unclear. This behavior could be explained by shear thinning of the material in the cell body. However the origin of this phenomenon may be in the cortical region of the cell, which exhibits an elastic tension that may be deformation rate dependent.     

Passive mechanical properties of human leukocytes.

Micropipette experiments are used to determine the rheological properties of human leukocytes. Individual cells in EDTA are subjected to a known aspiration pressure via a micropipette, and their surface deformation from the undeformed spherical shape is recorded on a television monitor. The cells are mathematically modeled as homogeneous spheres, and a standard solid viscoelastic model is found to describe accurately the deformation of the cell for small strains. These experimental and theoretical studies provide the basis for further investigations of leukocyte rheology in health and disease.     

Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties

The viscoelastic deformation of porcine aortic endothelial cells grown under static culture conditions was measured using the micropipette technique. Experiments were conducted both for control cells (mechanically or trypsin detached from the substrate) and for cells in which cytoskeletal elements were disrupted by cytochalasin B or colchicine. The time course of the aspirated length into the pipette was measured after applying a stepwise increase in aspiration pressure. To analyze the data, a standard linear viscoelastic half-space model of the endothelial cell was used. The aspirated length was expressed as an exponential function of time. The actin microfilaments were found to be the major cytoskeletal component determining the viscoelastic response of endothelial cells grown in static culture.     

Influence of power-law rheology on cell injury during microbubble flows

The reopening of fluid-occluded pulmonary airways generates microbubble flows which impart complex hydrodynamic stresses to the epithelial cells lining airway walls. In this study we used boundary element solutions and finite element techniques to investigate how cell rheology influences the deformation and injury of cells during microbubble flows. An optimized Prony–Dirichlet series was used to model the cells’ power-law rheology (PLR) and results were compared with a Maxwell fluid model. Results indicate that membrane strain and the risk for cell injury decreases with increasing channel height and bubble speed. In addition, the Maxwell and PLR models both indicate that increased viscous damping results in less cellular deformation/injury. However, only the PLR model was consistent with the experimental observation that cell injury is not a function of stress exposure duration. Correlation of our models with experimental observations therefore highlights the importance of using PLR in computational models of cell mechanics/deformation. These computational models also indicate that altering the cell’s viscoelastic properties may be a clinically relevant way to mitigate microbubble-induced cell injury.     

Micropipette aspiration method for characterizing biological materials with surface energy

Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration method to measure the mechanical properties of soft tissues and cells with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is taken into account by the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decrease with increasing surface energy, and thus neglecting the surface energy would lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to determine the mechanical properties of soft biological tissues and organs, e.g., livers, tumors and embryos.     

Adhesivity and rigidity of erythrocyte membrane in relation to wheat germ agglutinin binding

Binding of the plant lectin wheat germ agglutinin (WGA) to erythrocyte membranes causes membrane rigidification. One of our objectives has been to directly measure the effects of WGA binding on membrane rigidity and to relate rigidification to the kinetics and levels of WGA binding. Our other objective has been to measure the strength of adhesion and mechanics of cell separation for erythrocytes bound together by WGA. The erythrocyte membrane rigidity was measured on single cells by micropipette aspiration. The slope of the suction pressure-length data for entry into the pipette provided the measure of the membrane extensional modulus. Data were collected for cells equilibrated with WGA solutions in the range of concentrations of 0.01- 10 micrograms/ml. Erythrocyte-erythrocyte adherence properties were studied by micropipette separation of two-cell aggregates. First, a "test" cell was selected from a WGA solution by aspiration into a small micropipette, then transferred to a separate chamber that contained erythrocytes in WGA-free buffer. Here, a second cell was aspirated with another pipette and maneuvered into close proximity of the test cell surface, and adhesive contact was produced. The flaccid cell was separated from the test cell surface in steps at which the force of attachment was derived from the pipette suction pressure and cell geometry. In addition, we measured the time-dependent binding and release of fluorescently labeled WGA to single erythrocytes with a laser microfluorometry system. The results showed that the stiffening of the erythrocyte membrane and binding of fluorescently labeled WGA to the membrane surface followed the same concentration and time dependencies. The threshold concentration for membrane stiffening was at approximately 0.1 microgram/ml where the time course to reach equilibrium was close to 1 h. The maximal stiffening (almost 30-fold over the normal membrane elastic modulus) occurred in concentrations greater than 2 micrograms/ml where the time to reach equilibrium took less than 1 min. The WGA binding also altered the normal elastic membrane behavior into an inelastic, plastic-like response which indicated that mechanical extension of the membrane caused an increase in cross-linking within the surface plane. Similar to the stiffening effect, we observed that the membrane adhesivity of cells equilibrated with WGA solutions greatly increased with concentration greater than 0.1 microgram/ml.(ABSTRACT TRUNCATED AT 400 WORDS)     

Optical evaluation of red blood cell geometry using micropipette aspiration.

Although red blood cell (RBC) geometry has been extensively studied by micropipette aspiration, the small size of RBC and pipettes vs. the optical resolution of light microscopy suggests the need to consider potential errors. The present study addressed such difficulties and investigated four specific problems: (1) use of exact equations to calculate RBC membrane area and volume; (2) calibration of the pipette internal diameter (PID); (3) correction for a noncylindrical pipette barrel; (4) diffraction distortion of the RBC image. The observed PID represents a cylinder lens enlargement that can be theoretically derived from the glass/buffer refractive index ratio (1.49/1.33 = 1.12). This enlargement was experimentally confirmed by: (1) studying pipettes bent to allow measurement through the barrel (horizontal) and at the orifice (vertical), with a resulting diameter ratio of 1.12 +/- 0.01; (2) and by replacing the surrounding buffer with immersion oil and hence abolishing the lens phenomenon (ratio = 1.12 +/- 0.02). In addition, use of aspirated oil droplets demonstrated a 3.2 +/- 0.2% error when the PID is focused at a sharp, maximum diameter. The average pipette cone angle was 1.49 +/- 0.09 degrees and varied considerably with pipette pulling procedures; calculated tongue geometry inside the pipette was affected by the noncylindrical pipette barrel. The RBC diffraction error, demonstrated by touching two aspirated cells held by opposing pipettes, was 0.091 +/- 0.002 microns. The PID, cone angle, and diffraction artifacts significantly (p < 0.001) affected calculated RBC geometry (average errors up to 5.4% for area and 9.6% for volume). Two new methods to calculate, rather than directly measure, the PID from images of a single RBC, during either osmotic or pressure manipulation, were evaluated; the osmotic method closely predicted the PID, whereas the pressure method markedly underestimated the PID. Our results thus confirm the need to consider the above-mentioned phenomena when determining RBC geometric parameters via micropipette aspiration.     

Estimating the sensitivity of mechanosensitive ion channels to membrane strain and tension

Bone adapts to its environment by a process in which osteoblasts and osteocytes sense applied mechanical strain. One possible pathway for the detection of strain involves mechanosensitive channels and we sought to determine their sensitivity to membrane strain and tension. We used a combination of experimental and computational modeling techniques to gain new insights into cell mechanics and the regulation of mechanosensitive channels. Using patch-clamp electrophysiology combined with video microscopy, we recorded simultaneously the evolution of membrane extensions into the micropipette, applied pressure, and membrane currents. Nonselective mechanosensitive cation channels with a conductance of 15 pS were observed. Bleb aspiration into the micropipette was simulated using finite element models incorporating the cytoplasm, the actin cortex, the plasma membrane, cellular stiffening in response to strain, and adhesion between the membrane and the micropipette. Using this model, we examine the relative importance of the different cellular components in resisting suction into the pipette and estimate the membrane strains and tensions needed to open mechanosensitive channels. Radial membrane strains of 800% and tensions of 5 10(-4) N.m(-1) were needed to open 50% of mechanosensitive channels. We discuss the relevance of these results in the understanding of cellular reactions to mechanical strain and bone physiology.     

Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis

No technology is presently available to provide real-time information on internal deformations and stresses in plantar soft tissues of individuals during evaluation of the gait pattern. Because internal deformations and stresses in the plantar pad are critical factors in foot injuries such as diabetic foot ulceration, this severely limits evaluation of patients. To allow such real-time subject-specific analysis, we developed a hierarchal modeling system which integrates a two-dimensional gross structural model of the foot (high-order model) with local finite element (FE) models of the plantar tissue padding the calcaneus and medial metatarsal heads (low-order models). The high-order whole-foot model provides real-time analytical evaluations of the time-dependent plantar fascia tensile forces during the stance phase. These force evaluations are transferred, together with foot-shoe local reaction forces, also measured in real time (under the calcaneus, medial metatarsals and hallux), to the low-order FE models of the plantar pad, where they serve as boundary conditions for analyses of local deformations and stresses in the plantar pad. After careful verification of our custom-made FE solver and of our foot model system with respect to previous literature and against experimental results from a synthetic foot phantom, we conducted human studies in which plantar tissue loading was evaluated in real time during treadmill gait in healthy individuals (N = 4). We concluded that internal deformations and stresses in the plantar pad during gait cannot be predicted from merely measuring the foot-shoe force reactions. Internal loading of the plantar pad is constituted by a complex interaction between the anatomical structure and mechanical behavior of the foot skeleton and soft tissues, the body characteristics, the gait pattern and footwear. Real-time FE monitoring of internal deformations and stresses in the plantar pad is therefore required to identify elevated deformation/stress exposures toward utilizing it in gait laboratories to protect feet that are susceptible to injury.     

Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy

We propose a model for membrane-cortex adhesion that couples membrane deformations, hydrodynamics, and kinetics of membrane-cortex ligands. In its simplest form, the model gives explicit predictions for the critical pressure for membrane detachment and for the value of adhesion energy. We show that these quantities exhibit a significant dependence on the active acto-myosin stresses. The model provides a simple framework to access quantitative information on cortical activity by means of micropipette experiments. We also extend the model to incorporate fluctuations and show that detailed information on the stability of membrane-cortex coupling can be obtained by a combination of micropipette aspiration and fluctuation spectroscopy measurements.     

Intracellular mechanics and mechanotransduction associated with chondrocyte deformation during pipette aspiration

The present study utilised pipette aspiration and simultaneous confocal microscopy to test the hypothesis that chondrocyte deformation is associated with distortion of intracellular organelles and activation of calcium signalling. Aspiration pressure was applied to isolated articular chondrocytes in increments of 2 cm of water every 60 seconds up to a maximum of 10 cm of water. At each pressure increment, confocal microscopy was used to visualise the mitochondria and nucleus labelled with JC-1 and Syto-16, respectively. To investigate intracellular calcium signalling, separate cells were labelled with Fluo 4, rapidly aspirated to 5 cm of water and then imaged for 5 minutes at a tare pressure of 0.1 cm of water. Partial cell aspiration was associated with distortion of the mitochondrial network, elongation of the nucleus and movement towards the pipette mouth. Treatment with cytochalasin D or nocodazole produced an increase in cell aspiration indicating that both the actin microfilaments and microtubules provide mechanical integrity to the cell. When the data was normalised to account for the increased cell deformation, both actin microfilaments and microtubules were shown to be necessary for strain transfer to the intracellular organelles. Mitochondria and nucleus deformation may both be involved in chondrocyte mechanotransduction as well as cellular and intracellular mechanics. In addition, pipette aspiration induced intracellular calcium signalling which may also form part of a mechanotransduction pathway. Alternatively calcium mobilisation may serve to modify actin polymerisation, thereby changing cell mechanics and membrane rigidity in order to facilitate localised cell deformation. These findings have important implications for our understanding of cell mechanics and mechanotransduction as well as interpretation and modelling of pipette aspiration data.