Viscoelastic influence on wall and baroreceptors of rabbit carotid sinus.

This study examined multifiber baroreceptor nerve activity (BNA) as a function of carotid sinus wall distension in 19 rabbits. Analysis estimated mechanical or viscoelastic properties of the sinus wall and their influence on BNA. In six sinuses, properties were altered by treatment with the enzyme protease to remove the endothelium and with nifedipine to passively relax smooth muscle. Properties were estimated from dynamic and steady state wall response to a 45 mm Hg step increase and decrease in intrasinus pressure (ISP) of 20 min. Control wall response had fast and slow (creep) portions with a viscosity increase from 1,370 N(s)/m to 17,864 N(s)/m during step-up in ISP. Wall elasticity averaged 77 N/m; which estimated the relationship of force and change in steady state response. Control BNA response also had fast and slow (resetting) portions. A BNA and wall response relationship (BNA/m) was defined as transduction-gain (T-G) with proportional and dynamic components. In the subgroup, wall creep and baroreceptor resetting were abolished by protease treatment, suggesting an endothelial mediator which influenced sinus smooth muscle. Histology data indicated enzyme damage was limited to tunica intima tissues, and nifedipine did not block Ca2+ channels on neural structures. By comparison of responses before and after treatments the proportional component of T-G was equated to an elastic influence (1/E), with E = 7.5 x 10(-6) m/BNA, while the dynamic component was equated to a viscous influence (1/V), with V = 1.53 x 10(-4) m(s)/BNA. A simple but fundamental relationship for baroreceptor-tissue linkages was estimated by BNA/m = 1/(Vs + E), a first-order transfer function.     

Thickness and elasticity of gram-negative murein sacculi measured by atomic force microscopy

Atomic force microscopy was used to measure the thickness of air-dried, collapsed murein sacculi from Escherichia coli K-12 and Pseudomonas aeruginosa PAO1. Air-dried sacculi from E. coli had a thickness of 3.0 nm, whereas those from P. aeruginosa were 1.5 nm thick. When rehydrated, the sacculi of both bacteria swelled to double their anhydrous thickness. Computer simulation of a section of a model single-layer peptidoglycan network in an aqueous solution with a Debye shielding length of 0.3 nm gave a mass distribution full width at half height of 2.4 nm, in essential agreement with these results. When E. coli sacculi were suspended over a narrow groove that had been etched into a silicon surface and the tip of the atomic force microscope used to depress and stretch the peptidoglycan, an elastic modulus of 2.5 x 10(7) N/m(2) was determined for hydrated sacculi; they were perfectly elastic, springing back to their original position when the tip was removed. Dried sacculi were more rigid with a modulus of 3 x 10(8) to 4 x 10(8) N/m(2) and at times could be broken by the atomic force microscope tip. Sacculi aligned over the groove with their long axis at right angles to the channel axis were more deformable than those with their long axis parallel to the groove axis, as would be expected if the peptidoglycan strands in the sacculus were oriented at right angles to the long cell axis of this gram-negative rod. Polar caps were not found to be more rigid structures but collapsed to the same thickness as the cylindrical portions of the sacculi. The elasticity of intact E. coli sacculi is such that, if the peptidoglycan strands are aligned in unison, the interstrand spacing should increase by 12% with every 1 atm increase in (turgor) pressure. Assuming an unstressed hydrated interstrand spacing of 1.3 nm (R. E. Burge, A. G. Fowler, and D. A. Reaveley, J. Mol. Biol. 117:927-953, 1977) and an internal turgor pressure of 3 to 5 atm (or 304 to 507 kPa) (A. L. Koch, Adv. Microbial Physiol. 24:301-366, 1983), the natural interstrand spacing in cells would be 1.6 to 2.0 nm. Clearly, if large macromolecules of a diameter greater than these spacings are secreted through this layer, the local ordering of the peptidoglycan must somehow be disrupted.     

On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields.

We present a new method to measure the shear elastic moduli and viscosities of erythrocyte membranes which is based on the fixation and transient deformation of cells in a high-frequency electric field. A frequency domain of constant force (arising by Maxwell Wagner polarization) is selected to minimize dissipative effects. The electric force is thus calculated by electrostatic principles by considering the cell as a conducting body in a dielectric fluid and neglecting membrane polarization effects. The elongation A of the cells perpendicular to their rotational axis exhibits a linear regime (A proportional to Maxwell tension or to square of the electric field E2) at small, and a nonlinear regime (A proportional to square root of Maxwell tension or to the electric field E) at large extensions with a cross-over at A approximately 0.5 micron. The nonlinearity leads to amplitude-dependent response times and to differences of the viscoelastic response and relaxation functions. The cells exhibit pronounced yet completely reversible tip formations at large extensions. Absolute values of the shear elastic modulus, mu, and membrane viscosity, eta, are determined by assuming that field-induced stretching of the biconcave cell may be approximately described in terms of a sphere to ellipsoid deformation. The (nonlinear) elongation-vs.-force relationship calculated by the elastic theory of shells agress well with the experimentally observed curves and the values of mu = 6.1 x 10(-6) N/m and eta = 3.4 x 10(-7) Ns/m are in good agreement with the micropipette results of Evans and co-workers. The effect of physical, biochemical, and disease-induced structural changes on the viscoelastic parameters is studied. The variability of mu and eta of a cell population of a healthy donor is +/- 45%, which is mainly due to differences in the cell age. The average mu value of cells of different healthy donors scatters by +/- 18%. Osmotic deflation of the cells leads to a fivefold increase of mu and 10-fold increase of eta at 500 mosm. The shear modulus mu increases with temperature showing that the cytoskeleton does not behave as a network of entropy elastic springs. Elliptic cells of patients suffering from elliptocytosis of the Leach phenotype exhibit a threefold larger value of mu than normal discocytes of control donors. Cross-linking of the spectrin by the divalent S-H agents diamide (1 mM, 15 min incubation) leads to an eightfold increase of mu whereas eta is essentially constant. The effect of diamide is reversed after treatment with S-S bond splitting agents.     

Mechanical properties of the lateral cortex of mammalian auditory outer hair cells.

Mammalian auditory outer hair cells generate high-frequency mechanical forces that enhance sound-induced displacements of the basilar membrane within the inner ear. It has been proposed that the resulting cell deformation is directed along the longitudinal axis of the cell by the cortical cytoskeleton. We have tested this proposal by making direct mechanical measurements on outer hair cells. The resultant stiffness modulus along the axis of whole dissociated cells was 3 x 10(-3) N/m, consistent with previously published values. The resultant axial and circumferential stiffness moduli for the cortical lattice were 5 x 10(-4) N/m and 3 x 10(-3) N/m, respectively. Thus the cortical lattice is a highly orthotropic structure. Its axial stiffness is small compared with that of the intact cell, but its circumferential stiffness is within the same order of magnitude. These measurements support the theory that the cortical cytoskeleton directs electrically driven length changes along the longitudinal axis of the cell. The Young's modulus of the circumferential filamentous components of the lattice were calculated to be 1 x 10(7) N/m2. The axial cross-links, believed to be a form of spectrin, were calculated to have a Young's modulus of 3 x 10(6) N/m2. Based on the measured values for the lattice and intact cell cortex, an estimate for the resultant stiffness modulus of the plasma membrane was estimated to be on the order of 10(-3) N/m. Thus, the plasma membrane appears to be relatively stiff and may be the dominant contributor to the axial stiffness of the intact cell.     

Turgor Pressure Regulation in Valonia utricularis: Effect of Cell Wall Elasticity and Auxin

The electrical membrane resistance rho(0) of the marine alga Valonia utricularis shows a marked maximum in dependence on the turgor pressure. The critical pressure, P(c), at which the maximum occurs, as well as its absolute value, rho(0) (max), are strongly volume-dependent. Both P(c) and rho(0) (max), increase with decreasing cell volume. It seems likely, that these relationships reflect the elastic properties of the cell wall, because the volumetric elastic modulus, epsilon, is also volume-dependent, increasing hyperbolically with cell volume. Both P(c) and rho(0) (max) can be affected by external application of indole-3-acetic acid at concentrations of 2.10(-7)m to 2 .10(-5)m. The critical pressure is shifted by 1.2 to 6 bars toward higher pressures and the maximum membrane resistance increased up to 5.6-fold. During the course of the experiments (up to 4 hours), however, IAA had no effect on the volumetric elastic modulus, epsilon.The maximum in membrane resistance is discussed in terms of a pressure-dependent change of potassium fluxes. The volume dependence of P(c) and rho(0) (max) suggests that not only turgor pressure but also epsilon must be considered as a regulating parameter during turgor pressure regulation. On this basis a hypothesis is presented for the transformation of both, a pressure signal and of changes in the elastic properties of the cell wall into alterations of ion fluxes. It is assumed that the combined effects of tension and compression of the membranes as well as the interaction between membrane and cell wall opposingly change the number of transport sites for K(+) providing a turgor-sensing mechanism that regulates ion fluxes. The IAA effects demonstrated are consistent with this view, suggesting that the basic mechanisms for turgor pressure regulation and growth regulation are similar.Any relation connecting growth rate with turgor pressure should be governed by two parameters, i.e. by a yielding pressure, at which cell growth starts, and by the critical pressure, at which it ceases again.     

Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.     

Unconfined creep compression of chondrocytes

The study of single cell mechanics offers a valuable tool for understanding cellular milieus. Specific knowledge of chondrocyte biomechanics could lead to elucidation of disease etiologies and the biomechanical factors most critical to stimulating regenerative processes in articular cartilage. Recent studies in our laboratory have suggested that it may be acceptable to approximate the shape of a single chondrocyte as a disc. This geometry is easily utilized for generating models of unconfined compression. In this study, three continuum mechanics models of increasing complexity were formulated and used to fit unconfined compression creep data. Creep curves were obtained from middle/deep zone chondrocytes (n = 15) and separately fit using the three continuum models. The linear elastic solid model yielded a Young's modulus of 2.55+/-0.85 kPa. The viscoelastic model (adapted from the Kelvin model) generated an instantaneous modulus of 2.47+/-0.85 kPa, a relaxed modulus of 1.48+/-0.35 kPa, and an apparent viscosity of 1.92+/-1.80 kPa-s. Finally, a linear biphasic model produced an aggregate modulus of 2.58+/-0.87 kPa, a permeability of 2.57 x 10(-12)+/-3.09 m(4)/N-s, and a Poisson's ratio of 0.069+/-0.021. The results of this study demonstrate that similar values for the cell modulus can be obtained from three models of increasing complexity. The elastic model provides an easy method for determining the cell modulus, however, the viscoelastic and biphasic models generate additional material properties that are important for characterizing the transient response of compressed chondrocytes.     

Osmotic relations of nerve fiber

Summary The volumetric elastic modulus of the sheath and the osmotic swelling pressure of the axoplasmic polymer network of the giant axon ofLoligo vulgaris were measured. Evidence was obtained that (1) the elastic modulus of the sheath, (2) the swelling pressure of axoplasm, and (3) theeffective osmotic pressure difference due to mobile solutes determine axonal volume. The contributions of the sheath and the axoplasm were significant because theeffective osmotic pressure due to mobile solutes was a small fraction of thetheoretical bulk osmotic pressure due to these solutes. The giant axon was converted from an imperfect to a near perfect osmometer by minimizing the contribution of the sheath and the axoplasmic gel.The early experiments were undertaken in the Stazione Zoologica, Naples, and the Democritus Nuclear Research Center, Athens, Greece; the more recent experiments were undertaken in facilities provided by Prof. N. Nikolaou, Aegina, Greece.     

MECHANICAL BEHAVIOR OF PLANT TISSUES AS INFERRED FROM THE THEORY OF PRESSURIZED CELLULAR SOLIDS

The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete “cell” walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive (“cell wall”) material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of “cell walls” and the magnitude of internal “cell” pressure. Analyses indicate that two “stiffening” agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or “densifying” material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.     

Computer simulation of a model network for the erythrocyte cytoskeleton.

The geometry and mechanical properties of the human erythrocyte membrane cytoskeleton are investigated by a computer simulation in which the cytoskeleton is represented by a network of polymer chains. Four elastic moduli as well as the area and thickness are predicted for the chain network as a function of temperature and the number of segments in each chain. Comparisons are made with mean field arguments to examine the importance of steric interactions in determining network properties. Applied to the red blood cell, the simulation predicts that in the bilayer plane the membrane cytoskeleton has a shear modulus of 10 +/- 2 x 10(-6) J/m2 and an areal compression modulus of 17 +/- 2 x 10(-6) J/m2. The volume compression modulus and the transverse Young's modulus of the cytoskeleton are predicted to be 1.2 +/- 0.1 x 10(3) J/m3 and 2.0 +/- 0.1 x 10(3) J/m3, respectively. Elements of the cytoskeleton are predicted to have a mean displacement from the bilayer plane of 15 nm. The simulation agrees with some, but not all, of the shear modulus measurements. The other predicted moduli have not been measured.     

A Conewise Linear Elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage

A biphasic mixture model is developed that can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J. Elasticity, 37, 1-38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H-A = 0.64 +/- 0.22 MPa, k2 = 3.62 +/- 0.97 x 10(-16) m4/N.s, r2 = 0.95 +/- 0.03), the tensile modulus, compressive Poisson ratio, and radial permeability were obtained from unconfined compression (E+Y = 12.75 +/- 1.56 MPa, v- = 0.03 +/- 0.01, kr = 6.06 +/- 2.10 x 10(-16) m4/N.s, r2 = 0.99 +/- 0.00), and the shear modulus was obtained from torsional shear (mu = 0.17 +/- 0.06 MPa). The model was also employed to predict the interstitial fluid pressure successfully at the center of the cartilage plug in unconfined compression (r2 = 0.98 +/- 0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage that can successfully curve-fit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.     

Contribution of the nucleus to the mechanical properties of endothelial cells.

The cell nucleus plays a central role in the response of the endothelium to mechanical forces, possibly by deforming during cellular adaptation. The goal of this work was to precisely quantify the mechanical properties of the nucleus. Individual endothelial cells were subjected to compression between glass microplates. This technique allows measurement of the uniaxial force applied to the cell and the resulting deformation. Measurements were made on round and spread cells to rule out the influence of cell morphology on the nucleus mechanical properties. Tests were also carried out with nuclei isolated from cell cultures by a chemical treatment. The non-linear force-deformation curves indicate that round cells deform at lower forces than spread cells and nuclei. Finite-element models were also built with geometries adapted to actual morphometric measurements of round cells, spread cells and isolated nuclei. The nucleus and the cytoplasm were modeled as separate homogeneous hyperelastic materials. The models simulate the compression and yield the force-deformation curve for a given set of elastic moduli. These parameters are varied to obtain a best fit between the theoretical and experimental data. The elastic modulus of the cytoplasm is found to be on the order of 500N/m(2) for spread and round cells. The elastic modulus of the endothelial nucleus is on the order of 5000N/m(2) for nuclei in the cell and on the order of 8000N/m(2) for isolated nuclei. These results represent an unambiguous measurement of the nucleus mechanical properties and will be important in understanding how cells perceive mechanical forces and respond to them.     

Confined compression experiments on bovine nucleus pulposus and annulus fibrosus: sensitivity of the experiment in the determination of compressive modulus and hydraulic permeability

The biphasic material properties for nucleus pulposus tissue in confined compression have not been reported previously, and are required for a better understanding of intervertebral disc function and to provide material properties for use in finite-element models. The aims of this study were to determine linear and non-linear material properties for nucleus pulposus and annulus fibrosus tissues in confined compression, to define the influence of swelling conditions on these properties, and to determine the changes in the compressive modulus and hydraulic permeability induced by the repetition of the stress-relaxation experiment after a return to swelling pressure equilibrium. Specimens from caudal bovine nucleus and annulus were tested in confined compression stress-relaxation experiments and analyzed to quantify the compressive modulus and hydraulic permeability using linear and non-linear biphasic models. Our results suggested the use of confined swelling pre-test condition and non-linear biphasic model, which provided the material parameters with lowest relative variance and water content most representative of physiological conditions. Smaller compressive modulus and higher hydraulic permeability were obtained for the nucleus (H(A0)=0.31+/-0.04 MPa, k(0)=0.67+/-0.09 x 10(-15)m(4)/Ns) than for the annulus (H(A0)=0.74+/-0.13 MPa, k(0)=0.23+/-0.19 x 10(-15)m(4)/Ns), with relatively weak non-linearities. Strains up to 20% resulted in material properties that were significantly altered upon retesting. These altered material properties are an effort to quantify non-recoverable damage that occurs in disc tissue and suggest that in vivo exposure of disc tissues to low strain-rate and high-deformation loading conditions which outpace biological repair may result in altered mechanical behaviors.     

Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry.

A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.     

Mechanical stimulation of tendon tissue engineered constructs: effects on construct stiffness, repair biomechanics, and their correlation

The objective of this study was to determine how in vitro mechanical stimulation of tissue engineered constructs affects their stiffness and modulus in culture and tendon repair biomechanics 12 weeks after surgical implantation. Using six female adult New Zealand White rabbits, autogenous tissue engineered constructs were created by seeding mesenchymal stem cells (0.1 x 10(6) cells/ml) in collagen gel (2.6 mg/ml) and combining both with a collagen sponge. Employing a novel experimental design strategy, four constructs from each animal were mechanically stimulated (one 1 Hz cycle every 5 min to 2.4% peak strain for 8 h/day for 2 weeks) while the other four remained unstretched during the 2 week culture period. At the end of incubation, three of the mechanically stimulated (S) and three of the nonstimulated (NS) constructs from each animal were assigned for in vitro mechanical testing while the other two autogenous constructs were implanted into bilateral full-thickness, full-length defects created in the central third of rabbit patellar tendons (PTs). No significant differences were found in the in vitro linear stiffnesses between the S (0.15+/-0.1 N/mm) and NS constructs (0.08+/-0.02 N/mm; mean+/-SD). However, in vitro mechanical stimulation significantly increased the structural and material properties of the repair tissue, including a 14% increase in maximum force (p=0.01), a 50% increase in linear stiffness (p=0.001), and 23-41% increases in maximum stress and modulus (p=0.01). The S repairs achieved 65%, 80%, 60%, and 40% of normal central PT maximum force, linear stiffness, maximum stress, and linear modulus, respectively. The results for the S constructs exceed values obtained previously by our group using the same animal and defect model, and to our knowledge, this is the first study to show the benefits of in vitro mechanical stimulation on tendon repair biomechanics. In addition, the linear stiffnesses for the construct and repair were positively correlated (r=0.56) as were their linear moduli (r=0.68). Such in vitro predictors of in vivo outcome hold the potential to speed the development of tissue engineered products by reducing the time and costs of in vivo studies.     

Elastic properties of the cell wall of Aspergillus nidulans studied with atomic force microscopy

Currently, little is known about the mechanical properties of filamentous fungal hyphae. To study this topic, atomic force microscopy (AFM) was used to measure cell wall mechanical properties of the model fungus Aspergillus nidulans. Wild type and a mutant strain (deltacsmA), lacking one of the chitin synthase genes, were grown in shake flasks. Hyphae were immobilized on polylysine-coated coverslips and AFM force--displacement curves were collected. When grown in complete medium, wild-type hyphae had a cell wall spring constant of 0.29 +/- 0.02 N/m. When wild-type and mutant hyphae were grown in the same medium with added KCl (0.6 M), hyphae were significantly less rigid with spring constants of 0.17 +/- 0.01 and 0.18 +/- 0.02 N/m, respectively. Electron microscopy was used to measure the cell wall thickness and hyphal radius. By use of finite element analysis (FEMLAB v 3.0, Burlington, MA) to simulate AFM indentation, the elastic modulus of wild-type hyphae grown in complete medium was determined to be 110 +/- 10 MPa. This decreased to 64 +/- 4 MPa for hyphae grown in 0.6 M KCl, implying growth medium osmotic conditions have significant effects on cell wall elasticity. Mutant hyphae grown in KCl-supplemented medium were found to have an elastic modulus of 67 +/- 6 MPa. These values are comparable with other microbial systems (e.g., yeast and bacteria). It was also found that under these growth conditions axial variation in elastic modulus along fungal hyphae was small. To determine the relationship between composition and mechanical properties, cell wall composition was measured by anion-exchange liquid chromatography and pulsed electrochemical detection. Results show similar composition between wild-type and mutant strains. Together, these data imply differences in mechanical properties may be dependent on varying molecular structure of hyphal cell walls as opposed to wall composition.     

Theoretical and experimental exclusion of errors in the determination of the elasticity and water transport parameters of plant cells by the pressure probe technique

The volumetric elastic modulus of the cell wall and the hydraulic conductivity of the cell membranes were measured on ligatured compartments of different sizes of Chara corallina internodes using the pressure probe technique. The ratio between intact cell surface area and the area of puncture in the cell wall and membrane introduced by the microcapillary of the pressure probe was varied over a large range by inserting microcapillaries of widely varying diameters in different sized compartments. The relationship of the elastic modulus and the hydraulic conductivity to turgor pressure was independent of the ratio of intact cell surface area to the area of injury. The increase in the hydraulic conductivity below 2 bar turgor pressure and the volume dependence of the elastic modulus were shown to be the same as those observed in intact nonligatured cells. Theoretical considerations of the possible influence of injury of the cell wall and cell membrane around the inserted microcapillary on the measurement of the water transport and cell wall parameters do not explain the experimental findings. Thus, mechanical artifacts, if at all present, are too small to account for the observed dependence of the hydraulic conductivity and the elastic modulus on turgor pressure. The pressure probe technique thus represents an accurate method for measuring water transport parameters in both giant algal cells and in tissue cells of higher plants.     

Onset of neonatal locomotor behavior and the mechanical development of Achilles and tail tendons

Tendon tissue engineering approaches are challenged by a limited understanding of the role mechanical loading plays in normal tendon development. We propose that the increased loading that developing postnatal tendons experience with the onset of locomotor behavior impacts tendon formation. The objective of this study was to assess the onset of spontaneous weight-bearing locomotion in postnatal day (P) 1, 5, and 10 rats, and characterize the relationship between locomotion and the mechanical development of weight-bearing and non-weight-bearing tendons. Movement was video recorded and scored to determine non-weight-bearing, partial weight-bearing, and full weight-bearing locomotor behavior at P1, P5, and P10. Achilles tendons, as weight-bearing tendons, and tail tendons, as non-weight-bearing tendons, were mechanically evaluated. We observed a significant increase in locomotor behavior in P10 rats, compared to P1 and P5. We also found corresponding significant differences in the maximum force, stiffness, displacement at maximum force, and cross-sectional area in Achilles tendons, as a function of postnatal age. However, the maximum stress, strain at maximum stress, and elastic modulus remained constant. Tail tendons of P10 rats had significantly higher maximum force, maximum stress, elastic modulus, and stiffness compared to P5. Our results suggest that the onset of locomotor behavior may be providing the mechanical cues regulating postnatal tendon growth, and their mechanical development may proceed differently in weight-bearing and non-weight-bearing tendons. Further analysis of how this loading affects developing tendons in vivo may inform future engineering approaches aiming to apply such mechanical cues to regulate engineered tendon formation in vitro.     

Affinity of red blood cell membrane for particle surfaces measured by the extent of particle encapsulation.

An experimental technique and a simple analysis are presented that can be used to quantitate the affinity of red blood cell membrane for surfaces of small beads or microsomal particles up to 3 micrometers Diam. The technique is demonstrated with an example of dextran-mediated adhesion of small spherical red cell fragments to normal red blood cells. Cells and particles are positioned for contact by manipulation with glass micropipets. The mechanical equilibrium of the adhesive contact is represented by the variational expression that the decrease in interfacial free energy due to a virtual increase in contact area is balanced by the increase in elastic energy of the membrane due to virtual deformation. The surface affinity is the reduction in free energy per unit area of the interface associated with the formation of adhesive contact. From numerical computations of equilibrium configurations, the surface affinity is derived as a function of the fractional extent of particle encapsulation. The range of surface affinities for which the results are applicable is increased over previous techniques to several times the value of the elastic shear modulus. It is shown that bending rigidity of the membrane has little effect on the analytical results for particles 1--3 micrometers Diam and that results are essentially the same for both cup- and disk-shaped red cells. A simple analytical model is shown to give a good approximation for surface affinity (normalized by the elastic shear modulus) as a function of the fractional extent of particle encapsulation. The model predicts that a particle would be almost completely vacuolized for surface affinities greater than or equal to 10 times the elastic shear modulus. Based on an elastic shear modulus of 6.6 x 10(-3) dyn/cm, the range for the red cell-particle surface affinity as measured by this technique is from approximately 7 x 10(-4) to 7 x 10(-2) erg/cm2. Also, an approximate relation is derived for the level of surface affinity necessary to produce particle vacuolization by a phospholipid bilayer surface which possesses bending rigidity and a fixed tension.     

Stiffness and heterogeneity of the pulmonary endothelial glycocalyx measured by atomic force microscopy

The mechanical properties of endothelial glycocalyx were studied using atomic force microscopy with a silica bead (diameter ～18 μm) serving as an indenter. Even at indentations of several hundred nanometers, the bead exerted very low compressive pressures on the bovine lung microvascular endothelial cell (BLMVEC) glycocalyx and allowed for an averaging of stiffness in the bead-cell contact area. The elastic modulus of BLMVEC glycocalyx was determined as a pointwise function of the indentation depth before and after enzymatic degradation of specific glycocalyx components. The modulus-indentation depth profiles showed the cells becoming progressively stiffer with increased indentation. Three different enzymes were used: heparinases III and I and hyaluronidase. The main effects of heparinase III and hyaluronidase enzymes were that the elastic modulus in the cell junction regions increased more rapidly with the indentation than in BLMVEC controls, and that the effective thickness of glycocalyx was reduced. Cytochalasin D abolished the modulus increase with the indentation. The confocal profiling of heparan sulfate and hyaluronan with atomic force microscopy indentation data demonstrated marked heterogeneity of the glycocalyx composition between cell junctions and nuclear regions.