Prediction of mechanical damage to animal cells in turbulence

In previous work a model was proposed for estimation of disruption of animal cells in turbulent capillary flows using information about the hydrodynamics, and cell mechanical properties determined by micromanipulation. The model assumed that the capillary flow consists of a laminar sublayer and a homogeneous turbulent region, and within the latter eddies of sizes similar to or smaller than the cells interact with those cells, causing local surface deformations. The proposed mechanism of cell damage was that such deformations result in an increase in membrane tension and surface energy, and that a cell disrupts when its bursting membrane tension and bursting surface energy are exceeded. The surface energy of the cells was estimated from the kinetic energy of appropriate sized eddies. To test the model, cells were disrupted in turbulent flows in capillaries at mean energy dissipation rates ranging from 800 to 2×10⁴ Wkg^–1. The model assumed that the specific lysis rate is almost independent of the number of passes, which was verified by the experimental data. The implication was that despite the damage the cell mechanical properties did not change markedly during multiple recirculations through the capillaries. On average the model underestimated the cell disruption by about 15%. Although the model gave reasonably good predictions, it lacks proper explanation of the independence of the specific lysis rate on the number of passes. In this paper it is shown that this problem can be resolved in principle by consideration of the localisation of the energy dissipation in turbulent capillary flows. The necessity of further modelling of cell-turbulence interactions is demonstrated.     

Mechanical and failure properties of single attached cells under compression

Eukaryotic cells are continuously subjected to mechanical forces under normal physiological conditions. These forces and associated cellular deformations induce a variety of biological processes. The degree of deformation depends on the mechanical properties of the cell. As most cells are anchorage dependent for normal functioning, it is important to study the mechanical properties of cells in their attached configuration. The goal of the present study was to obtain the mechanical and failure properties of attached cells. Individual, attached C2C12 mouse myoblasts were subjected to unconfined compression experiments using a recently developed loading device. The device allows global compression of the cell until cell rupture and simultaneously measures the associated forces. Cell bursting was characterized by a typical reduction in the force, referred to as the bursting force. Mean bursting forces were calculated as 8.7+/-2.5 microN at an axial strain of 72+/-4%. Visualization of the cell using confocal microscopy revealed that cell bursting was preceded by the formation of bulges at the cell membrane, which eventually led to rupturing of the cell membrane. Finite element calculations were performed to simulate the obtained force-deformation curves. A finite element mesh was built for each cell to account for its specific geometrical features. Using an axisymmetric approximation of the cell geometry, and a Neo-Hookean constitutive model, excellent agreement between predicted and measured force-deformation curves was obtained, yielding an average Young's modulus of 1.14+/-0.32 kPa.     

Micromanipulation measurements of biological materials

Micromanipulation enables the mechanical properties of microscopic biological particles to be measured in particular cells. It is capable of measurements at high deformations, including up to cell bursting. Particles as small as 1 m, with breaking forces as low as 1 N, can be characterised. The method can be enhanced by mechanical modelling to allow intrinsic mechanical properties such as the cell wall elastic modulus to be estimated. Present and potential applications include studying yeast and bacterial cell disruption, mechanical damage to animal cells in suspension cultures and filamentous microorganisms in submerged fermentations, plant cell behaviour in food processing, and flocculation processes.     

A micromanipulation method to measure the mechanical properties of single tomato suspension cells

A micromanipulation method has been developed to measure the force required to burst single tomato cells (Lycopersicon esculentum vf36) taken from suspension cultures. The method works by compressing a cell between parallel surfaces whilst measuring the force being imposed on the cell, and its deformation. The mean bursting force for two-week-old cells was 3.6 mN (standard error 0.1 mN), at a compression speed of 23 m s^–1. Usually force-deformation curves showed a single bursting event, but sometimes multiple bursts were observed, implying cells could reseal after failure. If cells were deformed without bursting, and then held, they showed a relaxation of the force. This was attributed to water loss, although wall relaxation was also a possibility. The half time of this relaxation was between 1–10 s. Tests on protoplasts gave bursting forces 1000 fold lower than intact cells, and cells treated with Triton to disrupt the membranes and destroy turgor collapsed with no bursting. As expected, both turgor and the presence of a wall were essential to maintaining cell strength.     

Modelling the effect of osmolality on the bursting strength of yeast cells.

When yeast cells are resuspended in buffer prior to homogenisation, the diluent osmotic pressure can have a significant effect on cell mechanical strength. In this paper a model is proposed which describes the relationship between the cell bursting force and the osmotic pressure of the diluent, using chemical potential and force balance analyses. Yeast cells were exposed for 1 h to diluents with osmolalities varying from almost 0 to 700 mmol kg-1 before their bursting strengths were measured by micromanipulation. The experimental data were compared with the predictions made from the model and in general they were in good agreement. It is expected that this model might be used to understand cell disruption behaviour in downstream processing equipment such as homogenisers.     

Effect of Pluronic F-68 on the mechanical properties of mammalian cells

The mechanical properties of TB/C3 hybridoma cells taken from a continuous culture were measured by micromanipulation. The culture conditions were constant except for the presence or absence of Pluronic F-68 in the medium. It was found that the mean bursting membrane tension and the mean elastic area compressibility modulus of the cells were significantly greater (60% and 120%, respectively) in a medium with 0.05% (w/u) Pluronic F-68 compared to that without Pluronic. Pluronic F-68 therefore affected the strength of the membranes when the cells were exposed to it for a long period of time, i.e., in culture. The short-term effect of Pluronic F-68 on cell strength was also tested by its addition at various levels up to 0.2% (w/v) immediately before the mechanical property measurements. The resulting cell strength depended on the Pluronic concentration, but a significant short-term effect could only be detected above a threshold of 0.1% (w/v). Previous reports on the effect of Pluronic F-68 on animal cell culture are evaluated in the light of these observations.     

Comparison of the fragilities of several animal cell lines

Summary The mean bursting membrane tension, elastic area compressibility modulus, and cell diameter of PQX1/2 murine hybridomas, NS1 myelomas and SF9 insect cells were measured during batch cultures. The fragilities of the cells were characterised by these mechanical properties. In general, the bursting membrane tension and elastic area compressibility modulus rose during rapid growth phase and fell during the death phase. Among the three cell lines, NS1 myelomas seemed to be weakest, but all were weaker than TB/C3 murine hybridomas studied previously.     

Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells

A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated β-cells and coupled collections (islets) of β-cells. This work was supported by the National Science Foundation Grant DMS-97-04-966.     

Mixed mode oscillations as a mechanism for pseudo-plateau bursting

We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called “pseudo-plateau bursting”. Unlike standard bursting, the subsystem of fast variables does not possess a stable branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically excitable pituitary cells and isolated pancreatic β-cells.     

Cell wall mechanical properties as measured with bacterial thread made from Bacillus subtilis.

Engineering approaches used in the study of textile fibers have been applied to the measurement of mechanical properties of bacterial cell walls by using the Bacillus subtilis bacterial thread system. Improved methods have been developed for the production of thread and for measuring its mechanical properties. The best specimens of thread produced from cultures of strain FJ7 grown in TB medium at 20 degrees C varied in diameter by a factor of 1.09 over a 30-mm thread length. The stress-strain behavior of cell walls was determined over the range of relative humidities between 11 and 98%. Measurements of over 125 specimens indicated that cell wall behaved like other viscoelastic polymers, both natural and man-made, exhibiting relaxation under constant elongation and recovery upon load removal. This kinetic behavior and also the cell wall strength depended greatly on humidity. The recovery from extension observed after loading even up to a substantial fraction of the breaking load indicated that the properties measured were those of cell wall material rather than of behavior of the thread assemblage. Control experiments showed that neither drying of thread nor the length of time it remained dry before testing influenced the mechanical properties of the cell walls. Specimens drawn from TB medium and then washed in water and redrawn were found to be stiffer and stronger than controls not washed. However, tensile properties were not changed by exposure of cells to lysozyme before thread production. This suggests that glycan backbones are not arranged along the length of the cell cylinder. The strength of the cell wall in vivo was estimated by extrapolation to 100% relative humidity to be about 3 N/mm2. Walls of this strength would be able to bear a turgor pressure of 6 atm (ca. 607.8 kPa), but if the increase in strength of water-washed threads was appropriate, the figure could be 24 atm (ca. 2,431.2 kPa).     

Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling

Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as “fold/limit cycle” type of bursting, then anti-phase continuous spiking, followed by the “fold/torus” type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate “fold/Hopf” bursting via “fold/fold” hysteresis loop; whereas, the chemically coupled cells generate “fold/subHopf” bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast–slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.     

Effects of cell-seeding methods of human osteoblast culture on biomechanical properties of porous bioceramic scaffold

Many studies have been performed to accelerate osteoinduction and osteoconduction into porous ceramic scaffolds by seeding them with cells. In this study, we compared available cell-seeding methods on a porous β-tricalcium phosphate (β-TCP) scaffold and evaluated the effects of cell-seeding on the mechanical properties of the porous β-TCP scaffold. Three types of porous bioceramic scaffolds were used: dry scaffold, scaffold wetted with media, and scaffold cultivated with normal human osteoblasts (NHOs). Cell-seeding into the porous β-TCP scaffolds was performed by conventional, centrifuge, high-density, and vacuum methods. After confirming cell proliferation with MTT assay and cell staining, a compressive test was performed after 2 and 4 weeks of cell culture. The vacuum method based on the high-density cell culture inserted effectively NHOs into the β-TCP scaffolds. The compressive elastic modulus of wetted β-TCP scaffolds decreased significantly (p < 0.05) about 20∼30% after 2 and 4 weeks of incubation in comparison with that of the dry scaffold. However, the compressive strength of the scaffolds cultivated with NHOs for 3 weeks was significantly (p < 0.05) higher than that of scaffolds without NHOs. The vacuum with the high-density of cell-seeding seems to be a suitable method for seeding cells into complex porous ceramic scaffolds. Cell proliferation and uniform distribution in the scaffolds can change the initial mechanical properties of porous ceramic scaffolds.     

Focal adhesion kinase stabilizes the cytoskeleton

Focal adhesion kinase (FAK) is a central focal adhesion protein that promotes focal adhesion turnover, but the role of FAK for cell mechanical stability is unknown. We measured the mechanical properties of wild-type (FAKwt), FAK-deficient (FAK−/−), FAK-silenced (siFAK), and siControl mouse embryonic fibroblasts by magnetic tweezer, atomic force microscopy, traction microscopy, and nanoscale particle tracking microrheology. FAK-deficient cells showed lower cell stiffness, reduced adhesion strength, and increased cytoskeletal dynamics compared to wild-type cells. These observations imply a reduced stability of the cytoskeleton in FAK-deficient cells. We attribute the reduced cytoskeletal stability to rho-kinase activation in FAK-deficient cells that suppresses the formation of ordered stress fiber bundles, enhances cortical actin distribution, and reduces cell spreading. In agreement with this interpretation is that cell stiffness and cytoskeletal stability in FAK−/− cells is partially restored to wild-type level after rho-kinase inhibition with Y27632.     

Effects of glucanase treatment on the structure and mechanical properties of cell walls in the giant‐celled xanthophycean alga Vaucheria frigida

The cell wall of the tip‐growing cells of the giant‐cellular xanthophycean alga Vaucheria frigida is mainly composed of cellulose microfibrils (CMFs) arranged in random directions and the major matrix component into which the CMFs are embedded throughout the cell. The mechanical properties of a cell‐wall fragment isolated from the tip‐growing region, which was inflated by artificially applied pressure, were measured after enzymatic removal of the matrix component by using a protease; the results showed that the matrix component is involved in the maintenance of cell wall strength. Since glucose and uronic acid are present in the matrix component of Vaucheria cell walls, we measured the mechanical properties of the cell wall after treatment with endo‐1,3‐ß‐glucanase and observed the fine structures of its surfaces by atomic force microscopy. The major matrix component was partially removed from the cell wall by glucanase, and the enzyme treatment significantly weakened the cell wall strength without affecting the pH dependence of cell wall extensibility. The enzymatic removal of the major matrix component by using a protease released polysaccharide containing glucose and glucuronic acid. This suggests that the major matrix component of the algal cell walls contains both proteins (or polypeptides) and polysaccharides consisting of glucose and glucuronic acid as the main constituents.     

Fracture mechanics of the cell wall of Chara corallina

Previous mechanical studies using algae have concentrated on cell extension and growth using creep-type experiments, but there appears to be no published study of their failure properties. The mechanical strength of single large internode cell walls (up to 2 mm diameter and 100 mm in length) of the charophyte (giant alga) Chara corallina was determined by dissecting cells to give sheets of cell wall, which were then notched and fractured under tension. Tensile tests, using a range of notch sizes, were conducted on cell walls of varying age and maturity to establish their notch sensitivity and to investigate the propagation of cracks in plant cell walls. The thickness and stiffness of the walls increased with age whereas their strength was little affected. The strength of unnotched walls was estimated as 47 ± 13 MPa, comparable to that of some grasses but an order of magnitude higher than that published for model bacterial cellulose composite walls. The strength was notch-sensitive and the critical stress intensity factor K _1c was estimated to be 0.63 ± 0.19 MNm^−3/2, comparable to published values for grasses. Received: 4 April 2000 / Accepted: 21 July 2000     

pH and expansin action on single suspension-cultured tomato (Lycopersicon esculentum) cells

The aim of this study was to measure key material properties of the cell walls of single suspension-cultured plant cells and relate these to cell-wall biochemistry. To this end, micromanipulation was used to compress single tomato cells between two flat surfaces until they ruptured, and force-deformation data were obtained. In addition to measuring the bursting force, we also determined the elastic (Young’s) modulus of the cell walls by matching low strain (≤20% deformation) experimental data with a cell compression model, assuming linear elastic cell walls. The walls were most elastic at pH 4.5, the pH optimum for expansin activity, with an elastic modulus of 2.0 ± 0.1 GPa. Following the addition of exogenous expansins, cell walls became more elastic at all pH values. Western blot analysis of proteins from walls of cultured cells revealed the presence of expansin epitopes, suggesting that the inherent pH dependence of elasticity and other compression phenomena is related to the presence of endogenous expansin proteins and their wall-loosening ability. Although strict application of the linear-elastic model could not be applied to large deformations—for example, up to cell bursting—because of irreversible behaviour, the deviation of the data from the model was generally small enough to allow estimation of the strain in the cell wall at failure. This strain was greater at pH 4.5 and when expansins were added to the suspension. The changes in elasticity are consistent with suggestions about the mode of expansin action. The estimated strains at failure are compatible with data on the failure of Acetobacter-derived cellulose–xyloglucan composites and proposed mechanisms of such failure. Through the measurement of cell-wall material properties using micromanipulation, it may be possible to understand more fully how cell-wall composition, structure and biochemistry lead to cell mechanical behaviour.     

Micromanipulation measurement of the mechanical properties of baker's yeast cells

The mechanical properties of a sample of baker's yeast cells were measured by micromanipulation. The relationship between the force required to burst a single cell and its corresponding diameter was established. For stationary phase cells, the compressive force required to burst a cell varied between 55 and 175N, with a mean value of 101 ± 2N. This is a substantial force compared to that required to burst a single mammalian cell (1.5–4.5N), which presumably reflects the lack of a cell wall of the latter. From measurements on 120 cells, there was no significant dependence of bursting force on yeast cell size. The micromanipulation method will be valuable for studying the dependence of mechanical properties of yeast cells on fermentation conditions, and the consequential effects of their behaviour in process disruption operations. © Rapid Science Ltd. 1998     

Estimation of disruption of animal cells by turbulent capillary flow

Disruption of animal cells in turbulent capillary flows has been predicted from a model of cell-hydrodynamic interactions using cell mechanical properties determined by micromanipulation. Eddies of sizes similar to or smaller than the cells are presumed to interact with those cells, causing local surface deformations. The proposed mechanism of cell damage is that such deformations result in an increase in membrane tension and surface energy and that a cell disrupts when its bursting membrane tension and bursting surface energy are exceeded. The surface energy of the cells is estimated from the kinetic energy of appropriately sized eddies. To test the model, cells were disrupted in turbulent flows in capillaries at mean energy dissipation rates up to 2 x 10(4) m(2)/s(3). In all cases the model underestimated the cell disruption by about 15%. Such good agreement implies that the approach of the model to the complicated phenomena of cell turbulence interactions is reasonable. (c) 1993 John Wiley & Sons, Inc.     

Changing excitation and inhibition in simulated neural networks: effects on induced bursting behavior

 The development of synchronous bursting in neuronal ensembles represents an important change in network behavior. To determine the influences on development of such synchronous bursting behavior we study the dynamics of small networks of sparsely connected excitatory and inhibitory neurons using numerical simulations. The synchronized bursting activities in networks evoked by background spikes are investigated. Specifically, patterns of bursting activity are examined when the balance between excitation and inhibition on neuronal inputs is varied and the fraction of inhibitory neurons in the network is changed. For quantitative comparison of bursting activities in networks, measures of the degree of synchrony are used. We demonstrate how changes in the strength of excitation on inputs of neurons can be compensated by changes in the strength of inhibition without changing the degree of synchrony in the network. The effects of changing several network parameters on the network activity are analyzed and discussed. These changes may underlie the transition of network activity from normal to potentially pathologic (e.g., epileptic) states. Received: 21 May 2002 / Accepted in revised form: 3 December 2002 / Published online: 7 March 2003 Correspondence to: P. Kudela (e-mail: pkudela@jhmi.edu) Acknowledgements. This research was supported by NIH grant NS 38958.     

Does acclimation in cavitation resistance due to mechanical perturbation support the pit area or conduit reinforcement hypotheses in Phaseolus vulgaris?

Two Phaseolus vulgaris L. cultivars were exposed to reduced water and stem mechanical perturbation treatments (flexing) to determine if acclimation to these treatments induced hydraulic changes, altered cavitation resistance and changed stem mechanical properties. Additionally, this study sought to determine if changes in cavitation resistance would support the pit area or conduit reinforcement hypotheses. Flexing reduced biomass, leaf area, xylem vessel area and hydraulic conductivity. One cultivar had greater measures of stem strength and cavitation resistance. Flexing increased cavitation resistance (P₅₀) but did not increase Young's modulus, rigidity or flexural strength on dried stems. Stem rigidity and basal diameter were correlated with leaf mass. The ratio of conduit wall thickness to span [(t/b)_h²] increased under high water and flexing treatments while rigidity decreased for one cultivar exposed to both flexing and lower water suggesting an inability to compensate for two simultaneous stresses. Although P₅₀ was not correlated with measures of mechanical strength, P₅₀ was correlated with vessel diameter, consistent with the pit area hypothesis. This study confirmed that mechanical perturbation can impact xylem structural properties and result in altered plant water flow characteristics and cavitation resistance. Long‐term hydraulic acclimation in these herbaceous annuals was constrained by similar tradeoffs that constrain hydraulic properties across species.