A quantitative model of cellular elasticity based on tensegrity.

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.

The role of prestress and architecture of the cytoskeleton and deformability of cytoskeletal filaments in mechanics of adherent cells: a quantitative analysis.

Mechanical properties of adherent cells were investigated using methods of engineering mechanics. The cytoskeleton (CSK) was modeled as a filamentous network and key mechanisms and corresponding molecular structures which determine cell elastic behavior were identified. Three models of the CSK were considered: open-cell foam networks, prestressed cable nets, and a tensegrity model as a special case of the latter. For each model, the modulus of elasticity (i.e. an index of resistance to small deformation) was given as a function of mechanical and geometrical properties of CSK filaments whose values were determined from the data in the literature. Quantitative predictions for the elastic modulus were compared with data obtained previously from mechanical tests on adherent cells. The open-cell foam model yielded the elastic modulus (10(3)-10(4)Pa) which was consistent with measurements which apply a large compressive stress to the cell. This suggests that bending of CSK filaments is the key mechanism for resisting large compression. The prestressed cable net and tensegrity model yielded much lower elastic moduli (10(1)-10(2)Pa) which were consistent with values determined from equilibrium measurements at low applied stress. This suggests that CSK prestress and architecture are the primary determinants of the cell elastic response. The tensegrity model revealed the possibility that buckling of microtubules of the CSK also contributed to cell elasticity.

Degradation of azo dyes containing aminonaphthol by Sphingomonas sp strain 1CX.

Sphingomonas sp strain 1CX was isolated from a wastewater treatment plant and is capable of aerobically degrading a suite of azo dyes, using them as a sole source of carbon and nitrogen. All azo dyes known to be decolorized by strain 1CX (Orange II, Acid Orange 8, Acid Orange 10, Acid Red 4, and Acid Red 88) have in their structure either 1-amino-2-naphthol or 2-amino-1-naphthol. In addition, an analysis of the structures of the dyes degraded suggests that there are certain positions and types of substituents on the azo dye which determine if degradation will occur. Growth and dye decolorization occurs only aerobically and does not occur under fermentative or denitrification conditions. The mechanism by which 1CX decolorizes azo dyes appears to be through reductive cleavage of the azo bond. In the case of Orange II, the initial degradation products were sulfanilic acid and 1-amino-2-naphthol. Sulfanilic acid, however, was not used by 1CX as a growth substrate. The addition of glucose or inorganic nitrogen inhibited growth and decoloration of azo dyes by 1CX. Attempts to grow the organism on chemically defined media containing several different amino acids and sugars as sources of nitrogen and carbon were not successful. Phylogenetic analysis of Sphingomonas sp strain 1CX shows it to be related to, but distinct from, other azo dye-decolorizing Sphingomonas spp strains isolated previously from the same wastewater treatment facility.

Mathematical modeling of the first inflation of degassed lungs.

The pressure-volume (P-V) relationship of degassed lungs during the first inflation is different from that in consecutive inflations. We developed a mathematical model of the P-V curve of the first inflation by assuming that (1) central airways are open leading to many subtrees of n generations that are initially closed; (2) an airway opens when inflation pressure reaches the opening threshold pressure of that segment; and (3) the opening threshold pressures do not depend on airway generation. In this model, airway opening occurs in cascades or avalanches. To test the model which contains only two parameters, n and a pressure, P(low), at which at least one subtree completely opens, we measured the first inflation P-V curves of 15 excised and degassed rabbit lungs. By fitting these data, we found that n=17+/-5, P(low)=23+/-4 cmH2O, and that there is a wide distribution of threshold pressures for airways with diameters <2 mm. Analysis of the P-V curve in a lung which was lavaged with a liquid of constant surface tension and in which airways are presumably open demonstrated that the distribution of threshold pressures is narrow, and hence no avalanches occur during inflation. We conclude that in normal lungs the first inflation is dominated by avalanche behavior of airway opening providing information on the global distribution of threshold pressures and the average site of airway closure.

A tensegrity model of the cytoskeleton in spread and round cells.

Measurements on adherent cells have shown that spreading affects their mechanics. Highly spread cells are stiffer than less spread cells. The stiffness increases approximately linearly with increasing applied stress and more so in highly spread cells than in less spread cells. In this study, a six-strut tensegrity model of the cytoskeleton is used to analyze the effect of spreading on cellular mechanics. Two configurations are considered: a "round" configuration where a spherically shaped model is anchored to a flat rigid surface at three joints, and a "spread" configuration, where three additional joints of the model are attached to the surface. In both configurations a pulling force is applied at a free joint, distal from the anchoring surface, and the corresponding deformation is determined from equations of equilibrium. The model stiffness is obtained as the ratio of applied force to deformation. It is found that the stiffness changes with spreading consistently with the observations in cells. These findings suggest the possibility that the spreading-induced changes of the mechanical properties of the cell are the result of the concomitant changes in force distribution and microstructural geometry of the cytoskeleton.

Dynamic behavior of lung parenchyma in shear.

Dynamic shear properties of excised rabbit lungs were studied by measuring creep deformation after application of a step indentation force to the pleural surfaces by a rigid cylindrical punch. The punch diameter was 9.5 mm, and punch forces were 2,4, and 6 g. Measurements were made at lung volumes of 40, 60, and 90% of the total lung capacity before and after lavage with 3-dimethyl siloxane, which provided a constant surface tension of 16 dyn/cm at the alveolar surfaces. A power-law model was fitted to creep data and then transformed into the frequency (f) domain by using Laplace transforms. The optimum model parameters were used to calculate shear elastance (E mu), shear resistance (R mu), and shear hysteresivity (2 pi fR mu/E mu) between 0.01 and 2.0 Hz. It was found that E mu slightly increased and R mu decreased nearly hyperbolically with increasing f, both decreased with increasing indentation force, and both increased with increasing mean lung volume. Shear hysteresivity decreased sharply from 0.01 to 0.25 Hz and then assumed a nearly steady value that was an order of magnitude lower than the value reported previously for uniformly oscillated lungs. Changes in E mu and R mu after lavage were correlated with changes in transpulmonary pressure and not with changes in surface film properties. These results suggest that in the breathing range of frequencies 1) the energy loss of lung parenchyma is a much smaller fraction of the stored elastic energy in shear than in uniformly oscillated lungs and 2) transpulmonary pressure, not dynamic properties of surface film, is the primary determinant of lung dynamic properties in shear.