Tensegrity, cellular biophysics, and the mechanics of living systems

Abstract

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.

Fig. 1. Physical Tensegrity Models

A) A 3-strut tensegrity model composed of wood sticks and nylon strjngs. Note that the struts do not come in direct contact, but rather are suspended open and stabilized through connection with the continuous series of tension elements. B) A 6-strut tensegrity composed entirely of metal springs. C) A large 6-strut tensegrity model composed of metal struts and elastic cables assembled in the same form as the spring structure shown in B, but also connected to a smaller stick and string spherical tensegrity at its center by black elastic strings that are not visible due to the black background. This hierarchical tensegrity model has been used to model shape alterations in nuclear cells as when a subset of the elements of the model are attached to a rigid substrate to model cell adhesion, the cell flattens, and the cell and nucleus spread in a coordinated manner, as shown in D. Living cells display the same behavior when the attach and spread on ECM or culture substrates.

Fig. 2. Incision of actin stress fibers in living cells using a laser nanoscissor

A) Severing of a single stress fiber bundle in an endothelial cell expressing EYFP-actin. Note that the severed ends splay apart (inset) as the stress fiber retracts over a period of 15 s (arrowhead indicates the position of the laser spot; bar, 10 µm). B) Strain relaxation of a single stress fiber bundle after a 300-nm hole was punched in the fiber using the laser nanoscissor. Note the hole becomes elliptical as it distended along the tension field line, indicating the presence of a prestress. Bar, 2 µm. (Reprinted with permission from Kumar et al 2006).

Fig. 3. Periodic microtubule buckling induced by contractile beating in cultured heart cells

A) A time sequence showing a microtubule buckling and unbuckling successively three times in a beating cardiac myocyte. B) A similar time sequence showing one microtubule buckling and unbuckling at a single location, while neighboring microtubules remain straight. C) A Fourier mode analysis of the microtubule shown in B demonstrating that the amplitude of the bending on wavelengths of 3 µm shows periodic spikes induced by periodic buckling of the microtubule under successive contractile beats. There is some decrease in amplitude of the periodic buckling over time as the intensity of the contractile force decreases due to partial photodamage. Bar, 3 µm. (Reprinted with permission from Brangwynne et al 2006).

Fig. 4. Prestress dictates cell shear modulus

Cell prestress was increased or decreased from baseline (normal cells at resting state, ~1000 Pa) by treatment with contractile agonist histamine (0.1–10 µM for 1 min) or relaxation reagent isoproterenol (0.01–10 µM for 10 min) in living human airway smooth muscle cells. Cell prestress was calculated by measuring cell tractions and estimating cell cross-sectional areas. Cell shear modulus was measured with magnetic twisting cytometry. Cell spreading areas were constant before, during, and after drug treatments. Data are presented as means ± S.E.M. (Reprinted with permission from Wang et al 2002)

Fig. 5. Six-strut tensegrity model in the round (A) and spread (B) configurations

The model is anchored to the substrate (gray grid) via nodes A₁, A₂ and A₃ (round) and A₁, A₂, A₃, B₁, B₂ and B₃ (spread) indicated by black triangles. The black arrow at node D₁ indicates the vector of applied force F. Increasing the number of anchored nodes results in a greater distension of the structure causing an increase in the structural stiffness, enhanced stiffening, and an increase in the average prestress in the cable elements. This behavior is consistent with the mechanical behavior observed in spread vs round cells (Ingber and Wang 1994). (Reprinted with permission from Coughlin and Stamenović 1998.).

Fig. 6. Prestress dictates force propagation in the living cell

A) and B): A normal smooth muscle cell displacement (A) and stress (B) maps, exhibiting long-distance force propagation behavior (inset in (A), YFP (yellow fluorescent protein)-actin image of the cell). C) and D): Long-distance force propagation disappears (loss of displacements and stress concentration spots away from the loading site, the magnetic bead) after inhibition of prestress by overexpressing caldesmon. Displacement and stress fields of a cell whose prestress was inhibited by being infected with a low level of green fluorescent protein (GFP)-caldesmon. E) and F): Long-distance force propagation resumes after caldesmon is inhibited. Displacement and stress maps of the same cell in (C) and (D) after treatment with calcium ionophore A-23187 (5 µg/ml for 10 min), an inhibitor of caldesmon. The pink arrow, bead direction and displacement magnitude. Note that when prestress is downregulated (inset in C) or is resumed (inset in E), there are no apparent changes in patterns of stress fibers compared with those in a normal cell (inset in A). Insets in C, and E are fluorescent images of the corresponding cell. Green ellipses represent the position of the nuclei. (Reprinted with permission from Hu et al 2003).