-The tensegrity hypothesis holds that the cytoskeleton is a structure whose shape is stabilized predominantly by the tensile stresses borne by filamentous structures. Accordingly, cell stiffness must increase in proportion with the level of the tensile stress, which is called the prestress. Here we have tested that prediction in adherent human airway smooth muscle (HASM) cells. Traction microscopy was used to measure the distribution of contractile stresses arising at the interface between each cell and its substrate; this distribution is called the traction field. Because the traction field must be balanced by tensile stresses within the cell body, the prestress could be computed. Cell stiffness (G) was measured by oscillatory magnetic twisting cytometry. As the contractile state of the cell was modulated with graded concentrations of relaxing or contracting agonists (isoproterenol or histamine, respectively), the mean prestress (p t) ranged from 350 to 1,900 Pa. Over that range, cell stiffness increased linearly with the prestress: G (Pa) ϭ 0.18p t ϩ 92. While this association does not necessarily preclude other interpretations, it is the hallmark of systems that secure shape stability mainly through the prestress. Regardless of mechanism, these data establish a strong association between stiffness of HASM cells and the level of tensile stress within the cytoskeleton. tensegrity; mechanical stress; traction; cytoskeleton; actin microfilaments CONTROVERSY SURROUNDS the tensegrity hypothesis (23, 28). As described below, some part of this controversy is perhaps attributable to insufficient precision in the use of associated terminology and some part to insufficient emphasis on underlying mechanisms on which tensegrity rests. The major part of the controversy, however, is surely attributable to the fact that tensegrity is a hypothesis that has been rich in opinions but poor in quantitative data. Few, if any, data have been available that could be used to put the hypothesis to a rigorous test.The purpose of this series of companion papers is to amplify findings that have appeared recently in a brief report (55) and, in doing so, to bring to this controversy precision in the concepts, clarity about putative mechanisms, and new data that bear directly on the question itself. These data offer evidence that the tensegrity hypothesis, framed as it currently stands, captures certain central features of cell mechanical behavior but may be cast too narrowly.We begin by addressing a somewhat broader question: by what central mechanism does the cytoskeleton of adherent cells develop mechanical stresses that oppose distortion of cell shape? The answer to this question is important in understanding many cellular functions, including spreading, migration, contraction, growth, and mechanotransduction (9, 13, 29). To answer this question, several models of cell mechanics have been advanced, including tensegrity (1, 11, 12, 15, 16, 22, 24, 25, 27, 28, 30, 39, 40, 42, 44-46, 48, 51, 56-59, 60). This universe of cell models divid...

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.cytoskeleton ͉ microtubules ͉ cell mechanics ͉ myosin light chain phosphorylation ͉ mechanotransduction M echanical stress-induced alterations in cell shape and structure are critical for control of many cell functions, including growth, motility, contraction, and mechanotransduction (1). These functional alterations are mediated through changes in the internal cytoskeleton (CSK), which is composed of an interconnected network of microfilaments, microtubules, and intermediate filaments that links the nucleus to surface adhesion receptors. Advances in cell biology have resulted in better understanding of the polymerization behavior and physical properties of individual CSK filaments as well as of gels composed of combinations of filaments. Yet, the material properties measured in vitro neither explain nor predict complex mechanical behaviors that are observed in living cells (2, 3). At the same time, engineers have approached the problem of how cells stabilize their shape by developing mechanical models, without considering molecular specificity. For example, the living cell is often modeled as a continuum that contains an elastic cortex that surrounds a viscous (4) or viscoelastic (5) fluid; a more complex variation includes an elastic nucleus within a viscous cytoplasm (6). These models provide reasonable empirical fits to measured elastic moduli and viscosity in cells under specific experimental conditions (4-6), but they cannot predict from mechanistic principles how these properties alter under different challenges to the cell. Continuum models also assume that the load-bearing elements are infinitesimally small relative to the size of the cell and thus, they...

This paper deals with a unifying hypothesis addressed at lung tissue resistance and its responses to neurohumoral and biophysical stimuli. The hypothesis holds that dissipative and elastic processes within lung tissue are coupled at the level of the stress-bearing element. Such a description leads naturally to consideration of a readily measured attribute of organ-level dissipative behavior called lung tissue hysteresivity, eta. On preliminary analysis this attribute is found to be nearly frequency independent and numerically conserved across species. To the degree that the numerical value of eta might be conserved during an intervention in which tissue dynamic elastance changes, such behavior would be consistent with the notion that elastic energy storage and dissipative energy loss reside within the very same stress-bearing element and, moreover, that those processes within the stress-bearing element bear an approximately fixed relationship. Tissue hysteresivity is closely related to the parameter K used by Bachofen and Hildebrandt (J. Appl. Physiol. 30: 493-497, 1971) to describe energy dissipation per cycle, and both lend themselves directly to interpretation based on processes ongoing at the levels of microstructure and molecule. Intraparenchymal connective tissues, surface film, and contractile elements appear to submit individually to this description and, in doing so, yield respective hysteresivities that are relatively well matched; this suggests that such hysteretic matching may be a necessary condition for synchronous expansion of the alveolar duct. The overriding simplicity with which this description organizes diverse observations implies that it may capture some unifying attribute of underlying mechanism.

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life — from individual molecules to whole living organisms — to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

The biomechanical properties of connective tissues play fundamental roles in how mechanical interactions of the body with its environment produce physical forces at the cellular level. It is now recognized that mechanical interactions between cells and the extracellular matrix (ECM) have major regulatory effects on cellular physiology and cell-cycle kinetics that can lead to the reorganization and remodeling of the ECM. The connective tissues are composed of cells and the ECM, which includes water and a variety of biological macromolecules. The macromolecules that are most important in determining the mechanical properties of these tissues are collagen, elastin, and proteoglycans. Among these macromolecules, the most abundant and perhaps most critical for structural integrity is collagen. In this review, we examine how mechanical forces affect the physiological functioning of the lung parenchyma, with special emphasis on the role of collagen. First, we overview the composition of the connective tissue of the lung and their complex structural organization. We then describe how mechanical properties of the parenchyma arise from its composition as well as from the architectural organization of the connective tissue. We argue that, because collagen is the most important load-bearing component of the parenchymal connective tissue, it is also critical in determining the homeostasis and cellular responses to injury. Finally, we overview the interactions between the parenchymal collagen network and cellular remodeling and speculate how mechanotransduction might contribute to disease propagation and the development of small- and large-scale heterogeneities with implications to impaired lung function in emphysema.

It has been shown previously that intermediate filament (IF) gels in vitro exhibit stiffening at high-applied stress, and it was suggested that this stiffening property of IFs might be important for maintaining cell integrity at large deformations (Janmey PA, Evtenever V, Traub P, and Schliwa M, J Cell Biol 113: 155-160, 1991). In this study, the contribution of IFs to cell mechanical behavior was investigated by measuring cell stiffness in response to applied stress in adherent wild-type and vimentin-deficient fibroblasts using magnetic twisting cytometry. It was found that vimentin-deficient cells were less stiff and exhibited less stiffening than wild-type cells, except at the lowest applied stress (10 dyn/cm(2)) where the difference in the stiffness was not significant. Similar results were obtained from measurements on wild-type fibroblasts and endothelial cells after vimentin IFs were disrupted by acrylamide. If, however, cells were plated over an extended period of time (16 h), they exhibited a significantly greater stiffness before than after acrylamide, even at the lowest applied stress. A possible reason could be that the initially slack IFs became fully extended due to a high degree of cell spreading and thus contributed to the transmission of mechanical stress across the cell. Taken together, these findings were consistent with the notion that IFs play important roles in the mechanical properties of the cell during large deformation. The experimental data also showed that depleting or disrupting IFs reduced, but did not entirely abolish, cell stiffening. This residual stiffening might be attributed to the effect of geometrical realignment of cytoskeletal filaments in the direction of applied load. It was also found that vimentin-deficient cells exhibited a slower rate of proliferation and DNA synthesis than wild-type cells. This could be a direct consequence of the absence of the intracellular IFs that may be necessary for efficient mediation of mechanical signals within the cell. Taken together, results of this study suggest that IFs play important roles in the mechanical properties of cells and in cell growth.

The tensegrity model hypothesizes that cytoskeleton-based microtubules (MTs) carry compression as they balance a portion of cell contractile stress. To test this hypothesis, we used traction force microscopy to measure traction at the interface of adhering human airway smooth muscle cells and a flexible polyacrylamide gel substrate. The prediction is that if MTs balance a portion of contractile stress, then, upon their disruption, the portion of stress balanced by MTs would shift to the substrate, thereby causing an increase in traction. Measurements were done first in maximally activated cells (10 microM histamine) and then again after MTs had been disrupted (1 microM colchicine). We found that after disruption of MTs, traction increased on average by approximately 13%. Because in activated cells colchicine induced neither an increase in intracellular Ca(2+) nor an increase in myosin light chain phosphorylation as shown previously, we concluded that the observed increase in traction was a result of load shift from MTs to the substrate. In addition, energy stored in the flexible substrate was calculated as work done by traction on the deformation of the substrate. This result was then utilized in an energetic analysis. We assumed that cytoskeleton-based MTs are slender elastic rods supported laterally by intermediate filaments and that MTs buckle as the cell contracts. Using the post-buckling equilibrium theory of Euler struts, we found that energy stored during buckling of MTs was quantitatively consistent with the measured increase in substrate energy after disruption of MTs. This is further evidence supporting the idea that MTs are intracellular compression-bearing elements.

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