A tensegrity structure composed of six slender struts interconnected with 24 linearly elastic cables is used as a model of cell deformability. Struts are allowed to buckle under compression and their post-buckling behavior is determined from an energy formulation of the classical pin-ended Euler column. At the reference state, the cables carry initial tension balanced by forces exerted by struts. The structure is stretched uniaxially and the stretching force versus axial extension relationships are obtained for different initial cable tensions by considering equilibrium at the joints. Structural stiffness is calculated as the ratio of stretching force to axial extension. Predicted dependences of structural stiffness on initial cable tension and on stretching force are consistent with behaviors observed in living cells. These predictions are both qualitatively and quantitatively superior to those obtained previously from the model in which the struts are viewed as rigid.

Issue Section:
Technical Papers
Topics:
Buckling, Cellular mechanics, Compression, Tensegrity structures, Cables, Stiffness, Tension, Biological cells, Equilibrium (Physics)
1.
Amos, L. A., and Amos, W. B., 1991, Molecules of the Cytoskeleton, Guilford Press, New York.
2.
Danowski
B. A.
,
1989
, “
Fibroblast contractility and actin organization are stimulated by microtubule inhibitors
,”
Journal of Cell Science
, Vol.
93
, pp.
255
–
266
.
3.
Dennerll
T. J.
,
Joshi
H. C.
,
Steel
V. L.
,
Buxbaum
R. E.
, and
Heidemann
S. R.
,
1988
, “
Tension and compression in the cytoskeleton of PC-12 neurites II: Quantitative measurements
,”
Journal of Cell Biology
, Vol.
107
, pp.
665
–
674
.
4.
Frise´n
M.
,
Ma¨gi
M.
,
Sonnerup
I.
, and
Viidik
A.
,
1969
, “
Rheological analysis of soft collagenous tissue—I
,”
Journal of Biomechanics
, Vol.
2
, pp.
13
–
20
.
5.
Fuller
B.
,
1961
, “
Tensegrity
,”
Portfolio Artnews Annual
, Vol.
4
, pp.
112
–
127
.
6.
Gittes
F.
,
Mickey
B.
,
Nettleton
J.
, and
Howard
J.
,
1993
, “
Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape
,”
Journal of Cell Biology
, Vol.
120
, pp.
923
–
934
.
7.
Hubmayr
R. D.
,
Shore
S. A.
,
Fredberg
J. J.
,
Planus
E.
,
Panettieri
R. A.
,
Moiler
W.
,
Heyder
J.
, and
Wang
N.
,
1996
, “
Pharmacological activation changes stiffness of cultured human airway smooth muscle cells
,”
American Journal of Physiology
, Vol.
271
(Cell Physiology, Vol. 40), pp.
C1660–C1668
C1660–C1668
.
8.
Ingber
D. E.
,
1993
, “
Cellular tensegrity: defining new rules of biological design that govern the cytoskeleton
,”
Journal of Cell Science
, Vol.
104
, pp.
613
–
627
.
9.
Ingber, D. E., and Jamieson, J. D., 1985, “Cells as tensegrity structures: Architectural regulation of hystodifferentiation by physical forces transduced over basement membrane,” Gene Expression During Normal and Malignant Differentiation, L. C. Anderson, C. G, Gahmberg, and P. Ekblom, eds., Academic Press, London, pp. 13–32.
10.
Kolodney
M. S.
, and
Wysolmerski
R. B.
,
1992
, “
Isometric contraction of fibroblasts and endothelial cells in tissue culture: A quantitative study
,”
Journal of Cell Biology
, Vol.
117
, pp.
73
–
82
.
11.
Mow
V. C.
,
Ratcliffe
A.
, and
Poole
A. R.
,
1992
, “
Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures
,”
Biomaterials
, Vol.
13
, pp.
67
–
97
.
12.
Pugh, A., 1976, Introduction to Tensegrity, University of California Press, Berkeley, CA.
13.
Sims
J. R.
,
Karp
S.
, and
Ingber
D. E.
,
1992
, “
Altering the cellular mechanical force balance results in integrated changes in cell, cytoskeletal and nuclear shape
,”
Journal of Cell Science
, Vol.
103
, pp.
1215
–
1222
.
14.
Stamenovic´
D.
,
Fredberg
J. J.
,
Wang
N.
,
Butler
J. P.
, and
Ingber
D. E.
,
1996
, “
A microstructural approach to cytoskeletal mechanics based on tensegrity
,”
Journal of Theoretical Biology
, Vol.
181
, pp.
125
–
136
.
15.
Thompson
J. M. T.
, and
Hunt
G. W.
,
1969
, “
Comparative perturbation studies of the elastica
,”
International Journal of Mechanical Sciences
, Vol.
11
, pp.
999
–
1014
.
16.
Thoumine
O.
,
Ziegler
T.
,
Girard
P. R.
, and
Nerem
R. M.
,
1995
, “
Elongation of confluent endothelial cells in culture: The importance of fields of force in the associated alterations of their cytoskeletal structure
,”
Experimental Cell Research
, Vol.
219
, pp.
427
–
441
.
17.
Wang
N.
, and
Ingber
D. E.
,
1994
, “
Control of cytoskeletal mechanics by extracellular matrix, cell shape, and mechanical tension
,”
Biophysical Journal
, Vol.
66
, pp.
2181
–
2189
.
18.
Wang
N.
,
Butler
J. P.
, and
Ingber
D. E.
,
1993
, “
Mechanotransduction across the cell surface and through the cytoskeleton
,”
Science
, Vol.
260
, pp.
1124
–
1127
.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.