Modelling the mechanical properties of single suspension-cultured tomato cells

BACKGROUND AND AIMS: The relationship between composition and structure of plant primary cell walls, and cell mechanical properties is not fully understood, partly because intrinsic properties of walls such as Young's modulus cannot be obtained readily. The aim of this work is to show that Young's modulus of walls of single suspension-cultured tomato cells can be determined by modelling force-deformation data. METHODS: The model simulates the compression of a cell between two flat surfaces, with the cell treated as a liquid-filled sphere with thin compressible walls. The cell wall and membrane were taken to be permeable, but the compression was so fast that water loss could be neglected in the simulations. Force-deformation data were obtained by compressing the cells in micromanipulation experiments. RESULTS:Good fits were obtained between the model and low-strain experimental data, using the modulus and initial inflation of the cell as adjustable parameters. The mean Young's modulus for 2-week-old cells was found to be 2.3 +/- 0.2 GPa at pH 5. This corresponds to an instantaneous bulk modulus of elasticity of approx. 7 MPa, similar to a value found by the pressure probe method. However, Young's modulus is a better parameter, as it should depend only on the composition and structure of the cell wall, not on bulk cell behaviour. This new method has been used to show that Young's modulus of cultured tomato cell walls is at its lowest at pH 4.5, the pH optimum for expansin activity. CONCLUSIONS:The linear elastic model is very suitable for estimating wall Young's modulus from micromanipulation experiments on single tomato cells. This is a powerful method for determining cell wall material properties.     

Determining the mechanical properties of yeast cell walls

The intrinsic cell wall mechanical properties of Baker's yeast (Saccharomyces cerevisiae) cells were determined. Force-deformation data from compression of individual cells up to failure were recorded, and these data were fitted by an analytical model to extract the elastic modulus of the cell wall and the initial stretch ratio of the cell. The cell wall was assumed to be homogeneous, isotropic, and incompressible. A linear elastic constitutive equation was assumed based on Hencky strains to accommodate the large stretches of the cell wall. Because of the high compression speed, water loss during compression could be assumed to be negligible. It was then possible to treat the initial stretch ratio and elastic modulus as adjustable parameters within the analytical model. As the experimental data fitted numerical simulations well up to the point of cell rupture, it was also possible to extract cell wall failure criteria. The mean cell wall properties for resuspended dried Baker's yeast were as follows: elastic modulus 185 ± 15 MPa, initial stretch ratio 1.039 ± 0.006, circumferential stress at failure 115 ± 5 MPa, circumferential strain at failure 0.46 ± 0.03, and strain energy per unit volume at failure 30 ± 3 MPa. Data on yeast cells obtained by this method and model should be useful in the design and optimization of cell disruption equipment for yeast cell processing.     

Microrheology of human lung epithelial cells measured by atomic force microscopy

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.     

Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells

Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young’s modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell’s cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell's shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.     

Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells

Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young’s modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell’s cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell''s shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.     

Nanoscale strain-hardening of keratin fibres

Mammalian appendages such as hair, quill and wool have a unique structure composed of a cuticle, a cortex and a medulla. The cortex, responsible for the mechanical properties of the fibers, is an assemblage of spindle-shaped keratinized cells bound together by a lipid/protein sandwich called the cell membrane complex. Each cell is itself an assembly of macrofibrils around 300 nm in diameter that are paracrystalline arrays of keratin intermediate filaments embedded in a sulfur-rich protein matrix. Each macrofibril is also attached to its neighbors by a cell membrane complex. In this study, we combined atomic force microscopy based nano-indentation with peak-force imaging to study the nanomechanical properties of macrofibrils perpendicular to their axis. For indentation depths in the 200 to 500 nm range we observed a decrease of the dynamic elastic modulus at 1 Hz with increasing depth. This yielded an estimate of 1.6GPa for the lateral modulus at 1 Hz of porcupine quill's macrofibrils. Using the same data we also estimated the dynamic elastic modulus at 1 Hz of the cell membrane complex surrounding each macrofibril, i.e., 13GPa. A similar estimate was obtained independently through elastic maps of the macrofibrils surface obtained in peak-force mode at 1 kHz. Furthermore, the macrofibrillar texture of the cortical cells was clearly identified on the elasticity maps, with the boundaries between macrofibrils being 40-50% stiffer than the macrofibrils themselves. Elasticity maps after indentation also revealed a local increase in dynamic elastic modulus over time indicative of a relaxation induced strain hardening that could be explained in term of a α-helix to β-sheet transition within the macrofibrils.     

The effect of the 540-kilodalton actin cross-linking protein, actin-binding protein, on the mechanical properties of F-actin

This study describes the effect of actin-binding protein derived from rabbit lung macrophages on the mechanical properties of F-actin. The dynamic storage modulus, G'(omega), and loss modulus, G"(omega) of F-actin, at concentrations from 1 to 4 mg/ml, in the absence or presence of actin-binding protein at molar ratios to actin of 1:1000 to 1:125, were measured at frequencies ranging from 3 X 10(-3) to 0.5 Hz. Actin-binding protein increased the dynamic moduli of F-actin, but this increase was much greater as either the actin-binding protein/actin ratio or the total protein concentration increased. Moreover, there was a convergence of the values of G' and G" at high frequencies for F-actin which became more prominent upon the addition of actin-binding protein. The value of the modulus obtained by an extrapolation of these data to actin concentrations similar to that found in the cell cortex was close to values which have been obtained by direct measurements. The addition of actin-binding protein to an F-actin solution enabled it to reach an equilibrium strain following the application of a stress, in contrast to pure F-actin. These data allow a more rigorous definition of the "sol" to "gel" transition and suggest that the cross-linking of actin filaments by actin-binding protein leads to the formation of a network structure whose underlying mechanism of mechanical behavior is short range intrafilament bending in contrast to the classical rubber network.     

Mechano-acoustic determination of Young's modulus of articular cartilage

The compressive stiffness of an elastic material is traditionally characterized by its Young's modulus. Young's modulus of articular cartilage can be directly measured using unconfined compression geometry by assuming the cartilage to be homogeneous and isotropic. In isotropic materials, Young's modulus can also be determined acoustically by the measurement of sound speed and density of the material. In the present study, acoustic and mechanical techniques, feasible for in vivo measurements, were investigated to quantify the static and dynamic compressive stiffness of bovine articular cartilage in situ. Ultrasound reflection from the cartilage surface, as well as the dynamic modulus were determined with the recently developed ultrasound indentation instrument and compared with the reference mechanical and ultrasound speed measurements in unconfined compression (n=72). In addition, the applicability of manual creep measurements with the ultrasound indentation instrument was evaluated both experimentally and numerically. Our experimental results indicated that the sound speed could predict 47% and 53% of the variation in the Young's modulus and dynamic modulus of cartilage, respectively. The dynamic modulus, as determined manually with the ultrasound indentation instrument, showed significant linear correlations with the reference Young's modulus (r(2)=0.445, p<0.01, n=70) and dynamic modulus (r(2)=0.779, p<0.01, n=70) of the cartilage. Numerical analyses indicated that the creep measurements, conducted manually with the ultrasound indentation instrument, were sensitive to changes in Young's modulus and permeability of the tissue, and were significantly influenced by the tissue thickness. We conclude that acoustic parameters, i.e. ultrasound speed and reflection, are indicative to the intrinsic mechanical properties of the articular cartilage. Ultrasound indentation instrument, when further developed, provides an applicable tool for the in vivo detection of cartilage mechano-acoustic properties. These techniques could promote the diagnostics of osteoarthrosis.     

Responses of the less sensitive acoustic sense cells in the tympanic organs of some noctuid and geometrid moths

The separate impulses contributed by the A1 and A2 acoustic sense cells in the tympanic organs of the noctuids, Autographa pseudogamma and Noctua c.-nigrum, and by the A1, A2, and A3 sense cells in the tympanic organ of the geometrid, Ennomos magnarius, were identified and counted from oscillograms grams made as the moths were exposed to ultrasonic pulses of different intensities. These data were used to construct curves relating the response/intensity characteristics of the less sensitive acoustic sense cells to that of the most sensitive unit, A1. The A2 sense cells of the noctuids were found to be from 20 to 30 dB less sensitive than A1 at sound frequencies to which these ears are most sensitive. In the geometrid it was found that the A2 sense cell was 15 dB less sensitive than A1 and 12 dB more sensitive than A3. Only traces of the response of the fourth geometrid acoustic sense cell (A4) could be identified at high sound intensities. In both noctuids and geometrids the acoustic sensitivity of A2 relative to A1 remained unchanged when tested at selected ultrasonic frequencies between 28 and 50 kHz. This confirms the conclusion that the ears of these moths are incapable of pitch discrimination over this frequency range. Each of the systems had a dynamic range of 40 to 45 dB, that of the geometrid showing greater range overlap of the four A cells and hence greater capacity for sound intensity discrimination.     

Defining the role of matrix compliance and proteolysis in three-dimensional cell spreading and remodeling

Recent studies have identified extracellular matrix (ECM) compliance as an influential factor in determining the fate of anchorage-dependent cells. We explore a method of examining the influence of ECM compliance on cell morphology and remodeling in three-dimensional culture. For this purpose, a biological ECM analog material was developed to pseudo-independently alter its biochemical and physical properties. A set of 18 material variants were prepared with shear modulus ranging from 10 to 700 Pa. Smooth muscle cells were encapsulated in these materials and time-lapse video microscopy was used to show a relationship between matrix modulus, proteolytic biodegradation, cell spreading, and cell compaction of the matrix. The proteolytic susceptibility of the matrix, the degree of matrix compaction, and the cell morphology were quantified for each of the material variants to correlate with the modulus data. The initial cell spreading into the hydrogel matrix was dependent on the proteolytic susceptibility of the materials, whereas the extent of cell compaction proved to be more correlated to the modulus of the material. Inhibition of matrix metalloproteinases profoundly affected initial cell spreading and remodeling even in the most compliant materials. We concluded that smooth muscle cells use proteolysis to form lamellipodia and tractional forces to contract and remodel their surrounding microenvironment. Matrix modulus can therefore be used to control the extent of cellular remodeling and compaction. This study further shows that the interconnection between matrix modulus and proteolytic resistance in the ECM may be partly uncoupled to provide insight into how cells interpret their physical three-dimensional microenvironment.     

Relationship between ultrasonic properties and structural changes in the mesophyll during leaf dehydration

The broad-band ultrasonic spectroscopy technique allows the determination of changes in the relative water content (RWC) of leaves with contrasting structural features. Specifically, the standardized frequency associated with the maximum transmittance (f/f(o)) is strongly related to the RWC. This relationship is characterized by the existence of two phases separated by an inflexion point (associated with the turgor loss point). To obtain a better understanding of the strong relationship found between RWC and f/f(o), this work has studied the structural changes experienced by Quercus muehlenbergii leaves during dehydration in terms of ultrasounds measurements, cell wall elasticity, leaf thickness, leaf density, and leaf structure. The results suggest that the decrease found in f/f(o) before the turgor loss point can be attributed to the occurrence of changes in the estimation of the macroscopic effective elastic constant of the leaf (c(33)), mainly associated with changes in the bulk modulus of elasticity of the cell wall (ε). These changes are overriding or compensating for the thickness decreases recorded during this phase. On the other hand, the high degree of cell shrinkage and stretching found in the mesophyll cells during the second phase seem to explain the changes in the acoustic properties of the leaf beyond the turgor loss point. The formation of large intercellular spaces, which increased the irregularity in the acoustic pathway, may explain the increase of the attenuation coefficient of ultrasounds once the turgor loss point threshold is exceeded. The direct measurement of c(33) from ultrasonic measurements would allow a better knowledge of the overall biomechanical properties of the leaf further than those derived from the P-V analysis.     

Rotating versus perfusion bioreactor for the culture of engineered vascular constructs based on hyaluronic acid

It is generally accepted that dynamic culture conditions are required for vascular tissue engineering. We compared the effects of two dynamic culture systems, a perfusion and a rotating bioreactor, using tubular constructs based on hyaluronic acid seeded with porcine aortic smooth muscle cells (SMC), that we recently showed to be adequate for the generation of vascular tissue. In perfused constructs mechanical stimulation importantly affected cell morphology, increased the incidence of cell proliferation and reduced apoptosis. However, extracellular matrix deposition, cytoskeletal organization and mechanical properties were poor. In rotated constructs cell proliferation was also higher and apoptosis lower than in static controls. Rotated constructs showed the highest ultimate stress and the lowest elastic modulus. Our data indicate that the rotating bioreactor is more efficient than the perfusion bioreactor and we then suggest that this method can be considered a valid alternative to complex bioreactor systems described in the literature.     

Retention and viability characteristics of mammalian cells in an acoustically driven polymer mesh

A processing approach for the collection and retention of mammalian cells within a high porosity polyester mesh having millimeter-sized pores has been studied. Cell retention occurs via energizing the mesh with a low intensity, resonant acoustic field. The resulting acoustic field induces the interaction of cells with elements of the mesh or with each other and effectively prevents the entrainment of cells in the effluent stream. Experiments involving aqueous suspensions of polystyrene particles were used to provide benchmark data on the performance of the acoustic retention cell. Experiments using mouse hybridoma cells showed that retention densities of over 1.5 x 10(8) cell/mL could be obtained. In addition, the acoustic field was shown to produce a negligible effect on cell viability for short-term exposure.     

Methylation patterns of the E-cadherin 5' CpG island are unstable and reflect the dynamic, heterogeneous loss of E-cadherin expression during metastatic progression

Metastatic progression of most common epithelial tumors involves a heterogeneous, transient loss of expression of the homotypic cell adhesion protein, E-cadherin, rather than the uniform loss of a functional protein resulting from coding region mutation. Indeed, whereas E-cadherin loss may promote invasion, reexpression may facilitate cell survival within metastatic deposits. The mechanisms underlying such plasticity are unclear. We now show that the heterogeneous loss of E-cadherin expression in primary human breast cancers reflects a heterogeneous pattern of promoter region methylation, which begins early prior to invasion. In cultured human tumor cells, such heterogeneous methylation is dynamic, varying from allele to allele and shifting in relation to the tumor microenvironment. Following invasion in vitro, which favors diminished E-cadherin expression, the density of promoter methylation markedly increased. When these cells were cultured as spheroids, which requires homotypic cell adhesion, promoter methylation decreased dramatically, and E-cadherin was reexpressed. These data show that the methylation associated with E-cadherin loss in human breast cancer is heterogeneous and unstable and suggest that such epigenetic plasticity may contribute to the dynamic, phenotypic heterogeneity that drives metastatic progression.     

Influence of preparative procedures on the membrane viscoelasticity of human red cell ghosts

The effects of systematic variations in the preparative procedures on the membrane viscoelastic properties of resealed human red blood cell ghosts have been investigated. Ghosts, prepared by hypotonic lysis at 0 degrees C and resealing at 37 degrees C, were subjected to: measurement of the time constant for extensional recovery (tc); measurement of the membrane shear elastic modulus (mu) via three separate techniques; determination of the membrane viscosity (eta m) via a cone-plate Rheoscope. Membrane viscosity was also determined as eta m = mu X tc. Compared to intact cells, ghosts had shorter tc, regardless of their residual hemoglobin concentration (up to 21.6 g/dl). However, prolonged exposure to hypotonic media did increase their recovery time toward the intact cell value. The shear elastic modulus, as judged by micropipette aspiration of membrane tongues (mu p), was similar for all ghosts and intact cells. This result, taken with the tc data, indicates that ghosts have reduced membrane viscosity. Rheoscopic analysis also showed that eta m was reduced for ghosts, with the degree of reduction (approx. 50%) agreeing well with that estimated by the product mu p X tc. However, flow channel and pipette elongation estimates indicated that the ghost membrane elastic modulus was somewhat elevated compared to intact cells. We conclude that: ghosts have reduced membrane viscosity; ghosts have membrane rigidities close to intact cells, except possibly when the membrane is subjected to very large strains; the reduction in eta m is not directly related to the loss of hemoglobin; prolonged exposure of ghosts to low-ionic strength media increases the membrane viscosity toward its initial cellular level. These data indicate that the mechanical characteristics of ghost membranes can be varied by changing the methods of preparation and thus have potential application to further studies of the structural determinants of red cell membrane viscoelasticity.     

Differential Effect of Curcumin on the Nanomechanics of Normal and Cancerous Mammalian Epithelial Cells

Though the pharmacological activity of curcumin inhibiting the proliferation of certain cancer cells in culture was demonstrated, its effect on early-stage modifications induced in cell mechanics influencing hereby cell growth and cell adhesion are still questionable. We investigate the morphology and the elastic properties of live cultured, non-malignant human mammalian epithelial cells (HMEC) and cancerous breast epithelial cells (MCF7) by atomic force microscopy. We describe the different behavior of the two similar cell lines under curcumin treatment and we use fluorescence microscopy to identify the microtubules as the cytoskeleton structures responding to curcumin. The first changes in the HMEC cell morphology are observed after already 2 h incubation with curcumin. A 6-h long treatment leaves the MCF7 cells morphology non-affected, but the microtubules of HMEC cells disassemble and form a ring-like organization circumscribing the nuclear area. The observed morphological changes were correlated to modifications in cell’s mechanics via elasticity force mapping measurements. Curcumin treatment modified elasticity of the HMEC cells increasing the cell’s average Young’s modulus two- to threefold, especially in the cytoplasmic area. Contrariwise, a slight decrease in the Young’s modulus was noticed for the MCF7 cells, as they become softer due to the action of curcumin. Chemotherapeutic drugs exert their effect via the perturbation of the dynamic instability of the microtubule, hence the cell-specific perturbation induced by curcumin can help in future understanding of drug induced events on the cell behavior.     

Three approaches for estimating the elastic modulus of the tympanic membrane

The function of the middle ear is to resolve the acoustic impedance mismatch between the air in the ear canal and the fluid of the inner ear. Without this impedance matching, very little acoustic energy would be absorbed into the cochlea. The first step in this process is the tympanic membrane (TM) converting sound in the ear canal into vibrations of the middle ear bones. Understanding how the TM manages its task so successfully over such a broad frequency range should lead to more satisfactory and less variable TM repairs (myringoplasty). In addition, understanding the mechanics of the TM is necessary to improve the coupling between ossicular prostheses and the TM. Mathematical models have played a central role in helping the research community understand the mechanics of the eardrum. However, all models require parameters as inputs. Unfortunately, most of the parameters needed for modeling the TM are not well known. In this work, several approaches for inferring the material properties of the TM are explored. First, constitutive modeling is used to estimate an elastic modulus based on the elastic modulus of collagen and experimentally observed fiber densities. Second, experimental tension and bending test results from the literature are re-interpreted using composite laminate theory. Lastly, dynamic measurements of the cat TM are used in conjunction with a composite shell model to bound the material parameters. Values from the literature, both measurement and modeling efforts, and from the present analysis are brought together to form a coherent picture of the TM's material properties. In the human, the data bound the elastic modulus between 0.1 and 0.3 GPa. In the cat, the data suggest a range of 0.1-0.4 GPa. These values are significantly higher than previous estimates.     

Cyclic cryopreservation affects the nanoscale material properties of trabecular bone

Tissues such as bone are often stored via freezing, or cryopreservation. During an experimental protocol, bone may be frozen and thawed a number of times. For whole bone, the mechanical properties (strength and modulus) do not significantly change throughout five freeze-thaw cycles. Material properties at the trabecular and lamellar scales are distinct from whole bone properties, thus the impact of freeze-thaw cycling at this scale is unknown. To address this, the effect of repeated freezing on viscoelastic material properties of trabecular bone was quantified via dynamic nanoindentation. Vertebrae from five cervine spines (1.5-year-old, male) were semi-randomly assigned, three-to-a-cycle, to 0–10 freeze-thaw cycles. After freeze-thaw cycling, the vertebrae were dissected, prepared and tested. ANOVA (factors cycle, frequency, and donor) on storage modulus, loss modulus, and loss tangent, were conducted. Results revealed significant changes between cycles for all material properties for most cycles, no significant difference across most of the dynamic range, and significant differences between some donors. Regression analysis showed a moderate positive correlation between cycles and material property for loss modulus and loss tangent, and weak negative correlation for storage modulus, all correlations were significant. These results indicate that not only is elasticity unpredictably altered, but also that damping and viscoelasticity tend to increase with additional freeze-thaw cycling.     

Evaluating the nucleus effect on the dynamic indentation behavior of cells

The effect of the nucleus on the cell mechanical behavior was investigated based on the dynamic indentation response of cells under a spherical tip. A “two-component” cell model (including cytoplasm and nucleus) is used, and the dynamic indentation behavior is studied by a semiempirical method, which is established based on fitting the numerical simulation results of the quasi-static indentation response of cells. We found that the “routine analysis” (based on the Hertz’s contact solution of homogeneous model) significantly overestimated the nucleus effect on the overall cell indentation response due to the effects of the Hertz contact radius and the substrate stiffening. These effects are significantly stronger in the “two-component” cell model than in the homogeneous model. The inaccuracy created by the “routine analysis” slightly increases with the modulus ratio of nucleus to cytoplasm and the volume fraction of nucleus. Finally, the error sensitivity to the geometrical parameters used in the model is discussed, which shows the indentation analysis is not very sensitive to these parameters, and the reasonable assumptions for these parameters are effective. This systematic analysis can provide a useful guideline to understanding the mechanical behavior of cells and nuclei.