Opposing views on tensegrity as a structural framework for understanding cell mechanics.

Abstract

CONTROVERSIES IN PHYSIOLOGYOpposing views on tensegrity as a structural framework for understanding cell mechanicsDonald E. Ingber, Steven R. Heidemann, Phillip Lamoureux, and Robert E. BuxbaumDonald E. Ingber, Steven R. Heidemann, Phillip Lamoureux, and Robert E. BuxbaumPublished Online:01 Oct 2000https://doi.org/10.1152/jappl.2000.89.4.1663MoreSectionsPDF (503 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat Donald E. Ingber: Important new theories in science often ignite heated debates. If they do not, they are probably of little significance. Thus a strong argument in support of the importance of the tensegrity model of cell and tissue architecture first proposed almost 20 years ago (23, 24) is the large number of public and private criticisms that have been mounted against this theory. Demonstration of the ability of the tensegrity model to explain complex mechanical behaviors in viruses, nuclei, cells, tissues, and organs in animals as well as in insects and plants (reviewed in Refs. 4, 5, 7, 10, 17, 20-24, 26, 30, 32,42) has led to a drastic reduction in the number of these confrontations. Nevertheless, some intransigent critics remain. However, their remaining objections are limited in scope and largely result, I believe, from an overly concrete definition of what tensegrity is and how it can be applied. My purpose here, at the request of the Editor and Associate Editors of this journal, is to present the argument in support of the tensegrity model and to respond to some of these remaining concerns.The tensegrity model states that cells, tissues, and other biological structures at smaller and larger size scales in the hierarchy of life gain their shape stability and their ability to exhibit integrated mechanical behavior through use of the structural principles of tensegrity architecture (5, 20, 22-24). The term, “tensegrity” (contraction of “tensional integrity”) was first created by the architect R. Buckminster Fuller, who first explored use of this form of structural stabilization as early as 1927 in his plan for the Wichita Dymaxion house, which minimized weight by separating compression members from tension members (31). To create this cylindrical building, Fuller proposed to set a central mast in the earth as a vertical compression strut and to suspend from it multiple circular floors (horizontal wheels) using tension cables. Tensile guy wires that linked the mast to surrounding anchors in the ground provided the balancing tension necessary to stabilize the entire structure. “Fuller called this special discontinuous-compression, continuous-tension system, the Tensegrity” (31) to emphasize how it differs from conventional architectural systems (e.g., brick-on-brick type of construction), which depend on continuous compression for their shape stability. Fuller's more formal definition in his treatise, Synergetics, is “Tensegrity describes a structural-relationship principle in which structural shape is guaranteed by the finitely closed, comprehensively continuous, tensional behaviors of the system and not by the discontinuous and exclusively local compressional member behaviors” (16). Note that there is no mention of rigid struts, elastic strings, tensile filaments, internal vs. external members, or specific molecular constituents in this definition. In fact, Fuller describes a balloon with noncompressible gas molecules pushing out against a tensed rubber membrane as analogous to one of his geodesic domes when viewed at the microstructural level (i.e., the balloon is a porous, tensed molecular network on the microscale) and explains that both structures are classic examples of shape stability through tensegrity. Fuller also described hierarchical tensegrity structures in which individual struts or tensile elements are themselves tensegrity structures on a smaller scale; key to this concept is that smaller tensegrity units require external anchors to other tensegrity units to maintain higher order stability. In fact, he argued that nature utilizes this universal system of tensile structuring at all size scales and that it provides a way to mechanically integrate part and whole (16), a view I recently explored in greater depth (22).In 1948, Fuller's student, Kenneth Snelson, constructed the first “stick-and-string” tensegrity sculpture, which thrilled Fuller because it visibly communicated the essence of this novel form of shape stability to those who could not “see” it in more complex structures (e.g., geodesic domes with rigid struts; see Fig. 5 in Ref.5). Snelson's sculptures contain isolated compression members that are suspended in midair by interconnections with a continuous tensile network. Some of these structures require anchorage to the ground to remain stable (e.g., large cantilevered structures); however, most are entirely self-stabilizing. Similar stick-and-string tensegrity models have been used to visualize tensegrity in cells and other biological structures for those who cannot easily visualize them (Figs.1 and2). The appearance of geodesic patterns in biological structures, including viruses, clathrin-coated vesicles, and actin geodomes in the cytoskeleton of mammalian cells, provides additional visual evidence of nature's use of this form of architecture (20, 22).Fig. 1.A hierarchical tensegrity model of a nucleated cell composed of sticks and elastic string when unanchored and round (top) vs. attached and spread on a rigid adhesive substrate (bottom). The independent nuclear tensegrity sphere is mechanically connected to the surface of the larger tensegrity unit by black elastic filaments that are not visible against the black background. This model predicts that rapid pulling on surface receptors that mechanically couple to linking filaments in the cytoplasm may promote immediate changes in nuclear structure, as confirmed experimentally (Ref. 30 and Wang et al., unpublished observations; also see Fig. 3 below).Download figureDownload PowerPoint Fig. 2.A multimodular tensegrity model of a portion of the internal cytoskeleton containing long microtubules (yellow) that interconnect and stabilize multiple smaller polygonal networks comprised of contractile microfilaments (blue). Microfilament contraction induces compressive buckling in the semiflexible microfilament struts (right vs. left). This model is consistent with the finding that drugs that stimulate cell contraction increase microtubule curvature, whereas compounds that suppress this response promote straightening (Ref. 45 and Wang et al., unpublished observations).Download figureDownload PowerPoint My own view of tensegrity has been refined over the years as a result of extensive reading, personal correspondence with Fuller, conversations with Fuller's close associates (including Snelson), collaboration with expert mechanical engineers, and many hours of thinking about how to best respond (experimentally) to some very intelligent critics. In simplest terms, tensegrity structures maintain shape stability within a tensed network of structural members by incorporating other support elements that resist compression. The stiffness of the stick-and-string tensegrity structures, and hence their ability to resist shape distortion, depends on the level of preexisting tension or “prestress” in the structure before application of an external load. The distinguishing microstructural feature accounting for this behavior is that, when placed under load, the discrete structural elements move, changing orientation and spacing relative to one another, until a new equilibrium configuration is attained. For this reason, a local stress can result in global structural rearrangements and “action at a distance.”To visualize tensegrity at work, think of the human body: it stabilizes its shape by interconnecting multiple compression-resistant bones with a continuous series of tensile muscles, tendons, and ligaments, and its stiffness can vary depending on the tone (prestress) in its muscles. If I want to fully extend my hand upward to touch the ceiling, I have to tense muscles down to my toes, thus producing global structural rearrangements throughout my body and, eventually, upward extension of my fingers. However, the body is also multimodular and hierarchical: if I accidentally sever my Achilles tendon, I lose form control in my ankle module, but I still maintain structural stability in the rest of my body. Furthermore, every time I breath in, causing the muscles of my neck and chest to pull out on my lattice of ribs, my lung expands, alveoli open, taught bands of elastin in the extracellular matrix (ECM) relax, buckled bundles of cross-linked (stiffened) collagen filaments straighten, basement membranes tighten, and the adherent cells and cytoskeletal filaments feel the pull; however, nothing breaks and the deformation is reversible. Tensegrity provides a structural basis to explain all these phenomena.In the cellular tensegrity model, the stabilizing prestress is generated actively by the cell's contractile apparatus and passively by distension through extracellular adhesions, by osmotic forces acting on the cell's surface membrane, and, on a smaller scale, by forces exerted by molecular filaments extending through chemical polymerization. The model assumes that the prestress is carried by tensile elements in the cytoskeleton, primarily actin microfilaments and intermediate filaments, and that the cell is both a hierarchical and multimodular structure (5, 20-23) (Figs. 1 and2). This prestress is balanced by interconnected structural elements that resist being compressed at different size scales, including the cell's external adhesions to the relatively inflexible ECM and internal cytoskeletal filaments, specifically microtubules that stretch across large regions of the cytoplasm and cross-linked bundles of cytoskeletal filaments that stabilize specialized microdomains of the cell surface (e.g., actin microfilaments in filopodia; microtubules in cilia). In this model, the internal cytoskeleton is surrounded by an elastic submembranous cytoskeleton (e.g., actin-ankyrin-spectrin network) and its associated lipid bilayer, which may or may not mechanically couple to the internal, tensed microfilament-microtubule-intermediate filament lattice depending on the type of adhesion complex that forms. The entire cytoskeleton is permeated by the viscous cytosol. Most importantly, this micromechanical model leads to specific predictions relating to the mechanical role of distinct cellular and molecular elements in cell shape control.In contrast, a conventional model of cell structure (12), which is espoused by my esteemed counterparts in this article (18), depicts the cell as an elastic cortex that surrounds a viscous cytoplasm with an elastic nucleus in its center. In engineering terms, this is a “continuum” model, and, by definition, it assumes that the load-bearing elements are infinitesimally small relative to the size of the cell. It is essentially the balloon model considered by Fuller, but in this case all microstructure is ignored. Because they ignore microstructural features, continuum models cannot provide specific predictions that relate to the functional contribution of distinct cytoskeletal filaments to cell mechanics. Furthermore, although these models can provide empirical fits to measured mechanical properties in cells under specific experimental conditions, they cannot predict how these properties alter under new challenges to the cell.Future advancement of our understanding of the relation between cell mechanics, molecular structure, and biological function requires a more unified cell model. This model must build on our existing knowledge of cell microstructure and take into account experimental observations that reveal that the cytoskeleton is organized as a porous molecular network composed of discrete structural elements that physically interconnect with external support networks in the ECM and in neighboring cells (14). I would argue that tensegrity provides this model. In fact, we and others (including my counterparts in this article) have shown that both buildable tensegrity structures (17, 20, 23, 26, 42) and a theoretical tensegrity model developed from first principles (9, 38, 39, 46) are robust in terms of their ability to predict complex cell behaviors in various experimental systems and across many different size scales. Then why the continued criticisms? Let's explore this in greater detail.One of the most important features of the tensegrity model, as opposed to the viscous cytosol model, is that it predicts that applied mechanical forces will not be transmitted into the cell equally at all points on the cell surface. In the tensegrity model, the submembranous cytoskeleton (cortical actin-ankyrin-spectrin lattice) is viewed as an independent tensegrity structure, which is itself stabilized by the presence of a prestress within its discrete porous (and geodesic) molecular network, as recently demonstrated in the purest form of this structure, the red blood cell membrane (11). Depending on the molecular composition of the attachment substrate (e.g., ECM, surface of another cell) to which a cell anchors, this highly elastic cortex may or may not mechanically couple to the internal microfilament-microtubule-intermediate filament lattice, which, in turn, distributes loads throughout the cell and to the nucleus. A simple example of how the tensegrity model has contributed to the advancement of science is that it has led to the proposal that adhesion receptors, such as integrins, which form a transmembrane molecular bridge between the ECM and the internal cytoskeleton, provide a preferred path for transmembrane mechanical signal transfer and, hence, play a central role in cellular mechanotransduction. On the basis of subsequent experimental confirmation (8, 30, 35, 42), this role for integrins is now well established (7, 21).The point here is that, if cells use tensegrity, then long-distance force transfer should be observed in living cells. However, this action at a distance will only be observed if the correct series of molecular couplings are formed between the surface receptor and the internal cytoskeletal lattice; externally applied stresses would dissipate at the cell surface under other conditions. In contrast, the elastic cortex-viscous cytosol model (12, 18) would predict that living cells will never exhibit directed action at a distance inside the cell. Importantly, when we applied mechanical stresses directly to transmembrane integrin receptors using surface-bound micropipettes that were precoated with the ECM molecule fibronectin, we observed immediate repositioning of cytoskeletal filaments and elongation of nuclei along the applied tension field lines as well as molecular realignment within nucleoli deep in the center of the nucleus within living cells (30) (Fig.3). In contrast, no changes in intracellular structure were observed when tension was applied to other transmembrane receptors on the cell surface that only couple to the submembranous actin cytoskeleton. More recently, similar studies were carried out using pipettes to pull on ECM-coated microbeads bound to cell surface integrin receptors on cells that were transfected with enhanced yellow fluorescent protein (EYFP)-cytochromec to make mitochondria fluorescent throughout the entire cell. Real-time fluorescence microscopic analyses of these living cells revealed coordinated movement of mitochondria during the entire course of the pull and realignment of these natural fiducial markers; this was observed as far as 20 μm into the depth of the cell (N. Wang, K. Naruse, D. Stamenovic, J. J. Fredberg, S. M. Mijailovich, G. Maksym, T. Polte, and D. E. Ingber, unpublished observation). Again, pulling on other transmembrane receptors that do not couple to the internal cytoskeletal lattice (but do couple to the cortical actin cytoskeleton) did not result in long-distance force transfer as predicted by the tensegrity model. Because mitochondria directly associate with microtubules, these results indicate that forces transmitted to microfilaments via integrins can result in displacement of microtubules at distant sites and that these different filament networks are mechanically connected inside living cells.Fig. 3.Phase-contrast (left) and polarization optic (right) views of an adherent endothelial cell immediately before (top) and after (bottom) a fibronectin-coated micropipette (visible in bottom) was bound to integrin receptors on its surface and pulled laterally (downward in this view) using a micromanipulator. Arrow in bottom left indicates downward extension of the nuclear border along the applied tension field lines. Arrowheads in bottom rightpoint to white birefringent spots, which indicate induction of molecular realignment within nucleoli in the center of the nucleus by applying mechanical stress to integrins micrometers away on the cell surface. These results directly demonstrate that action at a distance can occur in living cells if external forces are applied via the correct set of transmembrane molecular linkages (e.g., integrins that form intact focal adhesion complexes), as predicted by the nucleated tensegrity model shown in Fig. 1 (see Ref. 30 for more details).Download figureDownload PowerPoint The main reason for Dr. Heidemann's change of heart regarding tensegrity (he was one of the first proponents of this model) is described in his recent publication (18) in which the action at a distance he expected to see was not observed when he pulled on cell surface receptors using ECM-coated micropipettes. However, the ECM protein laminin, which was used in that study, binds to classes of integrin receptors different from fibronectin and focal adhesion formation was not demonstrated in that study. In fact, his results are not new or surprising: we and others have experimentally observed similar local responses and high cell membrane deformability when cells were probed with beads coated with antibodies to certain integrin subtypes (44) and even with fibronectin when analyzed during the first few seconds after binding (i.e., before focal adhesion formation) (35) or when dragged over short distances in the plane of the membrane (i.e., when the submembranous cytoskeleton is the primary load-bearing element) (1). Thus, consistent with the tensegrity model, the cell may appear to behave like an elastic cortex surrounding a viscous cytosol, if the submembranous cytoskeletal network is probed independently of the internal cytoskeleton (microfilament-microtubule-intermediate filament lattice). In contrast, action at a distance can be observed when other receptors that provide deeper linkages (e.g., integrin α5β1) are ligated, although the specific molecular species involved will vary depending on cell type.The cellular tensegrity model also differs from other models of cell mechanics in that it predicts that cytoskeletal prestress is a critical determinant of cell shape stability. This has been demonstrated directly in studies in which cytoskeletal prestress was altered by modulating actomyosin-based contractility using drugs (19), transfecting cells with constitutively active myosin light chain (MLC) kinase (3), varying transmembrane osmotic forces (3) or quickly distending the flexible ECM substrate on which the cell is adherent (34), resulting in immediate changes in the cellular shear modulus (a quantitative measure of stiffness or shape stability). One may argue (and some have) that it may be prestress in the cortical cytoskeleton (the elastic cortex in the continuum models, which view the cell as an inflated balloon or rubber ball) that is responsible for these effects. However, when cell mechanics was measured by twisting on two differently sized magnetic beads bound to the same type of cell surface integrin receptor using cell magnetometry, cell stiffness scaled directly with bead size for a given applied stress (cells appeared to be less stiff using the smaller beads) (43); this result is the opposite of what would be predicted by a prestressed membrane cortex model. Furthermore, when cell mechanics was measured through cell surface integrins that connect to the internal cytoskeletal lattice, cell stiffness was found to be increased in spread vs. round cells (43) and in cells expressing constitutively active MLC kinase (3), whereas no significant difference in stiffness was measured when the same cells were probed through transmembrane receptors that only connect to the cortical cytoskeleton in those studies. Thus differences in shape stability due to altered prestress in these cells cannot be explained solely by changes in the cell cortex.The reality is that transmission of tension across molecular connections within the cytoskeletal network influences shape stability throughout the entire cell. For example, the shape and stiffness of the cell, internal cytoskeleton, and nucleus can be altered by using drugs (30, 42) or genetic techniques (e.g., vimentin knock-out mice; Ref. 13) to disrupt the intermediate filament lattice, which is known to extend throughout the depth of the cytoplasm. Coordinated retraction and rounding of the entire cell, cytoskeleton, and nucleus also were observed in membrane-permeabilized cells when ATP was added under conditions that supported microfilament contraction but not when a synthetic peptide that specifically blocks actomyosin filament sliding was present (37). Quantitation of changes in cell stiffness in these permeabilized cells confirmed that tension within the internal cytoskeleton directly determined cell and nuclear shape stability, independently of transmembrane osmotic forces (43), clearly demonstrating the inappropriateness of the “water balloon” or “inflated rubber ball”-type models of the cell. Finally, Dr. Heidemann's own elegant studies on neurites show that the elastic cortex-viscous cytosol model alone is not sufficient to explain how nerve cells produce highly extended processes such as neurites (17, 26). These cells also must be able to shift mechanical forces between tensile microfilaments in the cortex, central microtubule compression struts, and external ECM tethers to extend these specialized projections. In short, continuous transmission of tension through the depth of the cytoskeleton and between the cytoskeleton and ECM tethers is critical for cell shape stability.Probably the most common concern raised over the years has been, Where are the compression elements? The answer depends on the size scale and hierarchical level that one examines. If we ask how the whole cell controls its shape in living tissues (the ultimate question), then we have to take into account the contribution of the cell's adhesions to ECM and to other cells as well as internal support elements. The reality is that most cells cannot stabilize their shape in the absence of these adhesions: cells with highly specialized forms retract and round when detached from their anchoring substrate in vivo as well as in vitro. The reason that an adhesive substrate must be stiff (relative to the cell) to promote cell spreading is that isolated regions of the substrate located between the two integrin-containing focal adhesions that form at the opposite ends of each contractile stress fiber must resist local compression produced by the contraction and shortening of each fiber. The finding that cells can spread over multiple focal adhesion-sized ECM dots that are separated by nonadhesive regions many micrometers in length (6) clearly demonstrates this point.However, if the ECM were the only compression element, then all cells would be flat and smooth as a fried egg. The reality is that cells also use many different types of internal compression struts to further refine their shape, both in microdomains and at the whole cell level. Internal microtubule struts are used to stabilize local regions of the cytoplasm (25, 41), to stiffen the mitotic spindle (32), and, when oriented vertically, to maintain a cylindrical cell form (2). Bundles of cross-linked (and, hence, further stiffened) microtubules help to create specialized membrane extensions, such as cilia, and long cell processes, as in neurites (26). Stiffened bundles of cross-linked actin filaments similarly stabilize the shape of exploratory projections (filopodia) that extend from the cell surface at the leading edge of migratory cells (36). These locally rigidified structural elements are interconnected by a continuous cytoskeletal lattice that is otherwise under tension; severing the cell in any location results in spontaneous cell retraction (34). Again, we see local compression balanced by continuous tension, the defining features of Fuller's tensegrity systems.What is the evidence that these structures actually bear compression in living cells? Cilia and filopodia, which are rigid enough to resist distortion when probed by micropipettes (36), clearly must act locally to resist the inwardly directed compression caused by the tensed cortical membrane to maintain shape stability, regardless of the theoretical model one favors. Microtubules have also been directly shown to resist compression in the mitotic spindles of living cells: when an ultraviolet microbeam was used to sever one microtubule, the remaining microtubules buckled as expected if the same total compressive load was now distributed among a decreased number of semi-flexible compression struts (32). This is an example of tensegrity at a lower hierarchical level. Importantly, studies with green fluorescent protein (GFP)-labeled microtubules also revealed local buckling in the cytoplasm when polymerizing microtubules impinge end-on onto surrounding cellular structures and thus become compressed (Ref. 27 and Wang et al., unpublished observations) (Fig.4). My counterparts in this editorial have argued that this form of microtubule buckling involves very small compressive loads; hence, it could result from fluid flow in the surrounding cytosol (18). However, analysis of time-lapse video recordings of cells expressing GFP-microtubules reveals no evidence of flow; rather, individual buckled microtubules can be seen to immediately straighten when they slip by an obstacle and then only buckle again when they hit end-on on a second obstacle (Ref. 27 and Wang et al., unpublished observations). Furthermore, when cells containing EYFP-mitochondria or GFP-microtubules were repeatedly extended and compressed, with the extension sometimes held for more than 2 min before release, no evidence of intracellular cytoskeletal flow could be observed (Wang et al., unpublished observations). In addition, the curvature of GFP-microtubules (a visual read-out of compressive buckling) decreases when drugs are used to inhibit tension generation in the surrounding actin cytoskeleton, whereas buckling increases when constrictors are added (Ref. 45 and Wang et al., unpublished observations). Disruption of microtubules also significantly reduces the shear modulus (stiffness) of the cell and induces retraction of long processes in various cell types (26,41, 42), thus confirming the structural importance of their compression-bearing role.Fig. 4.Two sequential time-lapse immunofluorescence views of the same endothelial cell expressing GFP-tubulin showing a straight microtubule that extends through a large region of the cytoplasm (left), which then buckles locally due to compression (indicated by arrowhead) when it elongates through polymerization and impinges end-on on the stiffened cell cortex (right).Download figureDownload PowerPoint If microtubules are compression elements that maintain cell shape stability by supporting a substantial part of the tensile prestress, then their disruption should cause the prestress (or a significant portion of it) to be transferred to the ECM, thereby increasing the traction at the cell-ECM interface. In contrast, if microtubules were tension elements, then their disruption would inhibit transfer of traction to the ECM. In fact, many cell types increase tractional forces on their ECM substrate when treated with microtubule depolymerizing agents (10, 20, 29), whereas disruption of tensile microfilaments dissipates stress (29). However, part of the effect of microtubule disruption has been attributed by some to increases in MLC phosphorylation in response to release of free tubulin monomers after microtubule depolymerization rather than to a tensegrity-based force balance (28). Importantly, similar transfer of prestress from microtubules to the ECM was recently demonstrated in cells that were pretreated with chemical constrictors to optimally stimulate MLC phosphorylation before microtubule disruption (Wang et al., unpublished observations) and we have found that MLC phosphorylation does not increase when tubulin monomers are released in cells in which cytoskeletal tension is decreased using relaxant drugs before microtubule disruption (Polte and Ingber, unpublished observations). In other words, the increase in MLC phosphorylation observed after microtubule disruption (28) does not result from release of tubulin monomers; rather, it appears to be a compensatory mechanism that is activated in response to transfer of mechanical stress from microtubules to the ECM and the remaining cytoskeleton in these cells. This is yet another example of a complex behavior that can be explained by tensegrity and not by the other cell models.Some of those who accept that microtubules bear compression locally within an otherwise tensed cytoskeleton, a clear example of cellular tensegrity, then argue whether this contributes significantly to cell mechanics. To explore this idea in greater detail, studies were recently carried out in pulmonary airway smooth muscle cells cultured on