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doi: 10.1242/10.1242/jcs.00359

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Tensegrity I. Cell structure and hierarchical systems biology

Departments of Surgery and Pathology, Children's Hospital and Harvard Medical School, Enders 1007, 300 Longwood Avenue, Boston, MA 02115, USA

View larger version (97K): [in a new window]   Fig. 1. Tensegrity structures. (A) Triple crown, a tensegrity sculpture, by the artist Kenneth Snelson, that is composed of stainless steel bars and tension cables. Note that this structure is composed of multiple tensegrity modules that are interconnected by similar rules. (B) A tensegrity sphere composed of six wood struts and 24 white elastic strings, which mimics how a cell changes shape when it adheres to a substrate (Ingber, 1993b). (C) The same tensegrity configuration as in B constructed entirely from springs with different elasticities.

View larger version (65K): [in a new window]   Fig. 2. (A) A high magnification view of a Snelson sculpture with sample compression and tension elements labeled to visualize the tensegrity force balance based on local compression and continuous tension. (B) A schematic diagram of the complementary force balance between tensed microfilaments (MFs), intermediate filaments (IFs), compressed microtubules (MTs) and the ECM in a region of a cellular tensegrity array. Compressive forces borne by microtubules (top) are transferred to ECM adhesions when microtubules are disrupted (bottom), thereby increasing substrate traction.

View larger version (35K): [in a new window]   Fig. 3. Microtubules, microfilaments and intermediate filaments within the cytoskeleton of endothelial cells visualized with GFP-tubulin, rhodaminated-phalloidin and antibodies to vimentin, respectively. (A) Microtubules (green) span large regions of the cytoplasm and often appear curved in form. (B) Microfilaments (green-yellow) appear linear in form within long stress fibers and triangulated actin `geodomes'; blue staining indicates nuclei. (C) Intermediate filaments (red) appear within a spread cell as a reticulated network that extends from the nucleus to the cell periphery.

View larger version (58K): [in a new window]   Fig. 4. Tensegrity cell models composed of sticks-and-strings. (A) A model was suspended from above and loaded, from left to right, with 0, 20, 50, 100 or 200 g weights on a single strut at its lower end. Note that a local stress induces global structural arrangements. Reprinted (abstracted/excerpted) with permission from (Wang et al., 1993) American Association for the Advancement of Science. (B) A tensegrity model of a nucleated cell when adherent and spread on a rigid substrate (left) or detached and round (right). The cell model is composed of large metal struts and elastic cord; the nucleus contains sticks and elastic strings. In this cell model, the large struts conceptually represent microtubules; the elastic cords correspond to microfilaments and intermediate filaments that carry tensional forces in the cytoskeleton.

View larger version (56K): [in a new window]   Fig. 5. Force transfer through discrete molecular networks in living cells. Polarization optics (A,B,E,F), phase contrast (C,D) and fluorescence (G) views of cells whose integrin receptors were mechanically stressed using surface-bound glass micropipettes coated with fibronectin (A-F) or uncoated micropipettes with ECM-coated microbeads (G). (A) Cells exhibiting positively (white) and negatively (black) birefringent cytoskeletal bundles aligned horizontally and vertically, respectively, in the cytoplasm of adherent cells. (B) Birefringent cytoskeletal bundles that originally appeared white in A immediately changed to black (black arrow) as they turned 90° and realigned vertically along the axis of the applied tension field when integrins were pulled laterally (downward in this view). (C,E) An adherent cell immediately before a fibronectincoated micropipette was bound to integrin receptors on its surface and pulled laterally (downward in this view) using a micromanipulator as shown in D,F. (D) The black arrow indicates nuclear elongation and downward extension of the nuclear border along the applied tension field lines. (F) White arrows abut on white birefringent spots that indicate induction of molecular realignment within nucleoli in the center of the nucleus by applying mechanical stress to integrins microns away on the cell surface (see Maniotis et al., 1997a). (G) A cell containing EYFP-labeled mitochondria that was stressed by pulling on a surface-bound RGD-microbead using a micromanipulator. Vertical arrow, direction and extent of bead displacement; white circle, position of bead after stress application; green, position of mitochondria before stress application; red, their position approximately 3 seconds after stress was applied; Nuc, nucleus of the cell. Note that long distance transfer of mechanical force across integrins result in movement of mitochondria deep in the cytoplasm. Panel G reproduced with permission from the National Academy of Sciences (Wang et al., 2001).

View larger version (58K): [in a new window]   Fig. 6. Three sequential fluorescent images from a time-lapse recording of the same cell expressing GFP-tubulin showing buckling of a microtubule (arrowhead) as it polymerizes (from left to right) and impinges end-on on the cell cortex at the top of the view [reproduced with permission from the National Academy of Sciences (Wang et al., 2001)].

View larger version (55K): [in a new window]   Fig. 7. Multimodular tensegrities. (A) A side view of a tensegrity structure composed of four interconnected modules which each contain five struts. (B) A top view of the tensegrity structure shown in A, showing five-fold symmetry and a central pore. (C) A tensegrity lattice comprising seven similar tensegrity modules; a single three-strut module is shown in red.

View larger version (67K): [in a new window]   Fig. 8. Sequential images (left to right) from computer simulations of multimodular tensegrities (A,C) or from time-lapse video recording of living cells (B,D). (A) Structural rearrangements within a prestressed tensegrity lattice immediately following release of its anchors (at the top and bottom of the view). Note that the material simultaneously retracts throughout its entire depth. (B) When the ECM adhesions of a spread, adherent cell are dislodged using trypsin, the cell, cytoplasm and nucleus all simultaneously retract as the cell rounds (left to right). (C) A prestressed tensegrity fabric created from 36 interconnected tensegrity modules of the type shown in Fig. 1B that experiences a distending force at the top right corner; the other three corners are fixed. Notice that the entire material responds to the local force and that it exhibits undulating motion. (D) Undulating motion of a lamellipodium in a living cell.

View larger version (34K): [in a new window]   Fig. 9. Visualization of expansion and contraction behavior through use of a geodesically structured support network using the Hoberman Sphere created by the designer, Chuck Hoberman (Hoberman Toys, Inc.). This single structure, which is shown in three states of expansion in this figure, uses scissor-like struts that extend in a coordinated manner via a kinematic mechanism to provide large-scale shape changes in the entire structure without disrupting network integrity. In geodesic molecular networks, such as the submembranous cytoskeleton or viral capsids, extension is largely driven by molecular shape changes (e.g. elongation of individual spectrin molecules or viral proteins).

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