Rigidity
Compliance is a material property that is often used to describe the stiffness, rigidity, or elasticity of a substance. The use of these terms can be confusing, since stiffness and rigidity are the opposites of elasticity and compliance – something that is highly compliant or elastic tends to exhibit low stiffness and rigidity. The quantitative measure of these qualities is often the Elastic Modulus, which is a measure of the increase in stress when strain is applied to a material, or
E = σ/ε,Where E = Modulus, σ = stress, and ε = strain.There are several ways to measure the elastic modulus, including tensile testing, rheological measurements, and atomic force microscopy (AFM). AFM is convenient for doing measurements on a microscopic scale, when the subject is an individual cell or cell substrate.The study of matrix stiffness and its effects on cellular behavior has generated a great deal of interest among cell biologists and tissue engineers. The stiffness of a cell substrate can affect cell motility(1,2), phagocytosis(3), and differentiation(4). Moreover, different cell types react disparately to varying degrees of matrix stiffness(5). For example, fibroblasts have been shown to prefer stiffer substrates (2,6), while hepatocytes have been observed to maintain a differentiated phenotype only on soft materials (5,9). The table below depicts a sampling of the wide range of material compliances and cellular behaviors, including actual tissue compliances where available.
Table 1: Compliance Effects on Different Cell Types
|
Cell Type
|
Substrate Compliance
|
Cell Behavior
|
Native Tissue
|
Tissue Compliance
|
Ref
|
|
Fibroblasts
|
1 kPa
|
Diffuse, dynamic adhesion complex
|
Connective tissue, Extracellular matrix
|
Varies
|
7
|
|
Fibroblasts
|
30-100 kPa
|
Stable focal adhesions
|
Fibrous tissue
|
Varies
|
7
|
|
Muscle cells
|
8-11 kPa
|
Definitive actomyosin striations
|
Muscle
|
10 kPa (relaxed muscle bundles)
|
8
|
|
Muscle cells
|
1 kPa
|
No myosin striation
|
Muscle
|
10 kPa (relaxed muscle bundles)
|
8
|
|
Muscle cells
|
17 kPa
|
No myosin striation
|
Muscle
|
10 kPa (relaxed muscle bundles)
|
8
|
|
Hepatocytes
|
34 Pa
|
Round morphology and maintains differentiated phenotype
|
Liver
|
NA
|
9
|
|
Hepatocytes
|
180 Pa
|
More responsive to growth factor-induced aggregation
|
Liver
|
NA
|
9
|
|
Astrocytes
|
< 1 kPa
|
Small, round morphology with no stress fibers
|
Central Nervous System
|
330 Pa (Rat Brain)
|
10
|
|
Astrocytes
|
1-2 kPa
|
Begin to spread
|
Central Nervous System
|
330 Pa (Rat Brain)
|
10
|
|
Astrocytes
|
> 2 kPa
|
Well spread, good adhesion
|
Central Nervous System
|
330 Pa (Rat Brain)
|
10
|
|
Neurons
|
50-200 Pa
|
Cells can deform gel, increased branching than on harder substrates
|
Brain
|
330 Pa (Rat Brain)
|
10
|
References
- Lo, C. M., H. B. Wang, M. Dembo, and Y. L. Wang. Cell movement is guided by the rigidity of the substrate. Biophysics. J. 79: 144–152, 2000.
- Pelham, R. J. Jr., and Y. Wang. Cell locomotion and focal adhesions are regulated by substrate flexibility. Procedures of the National Academy of Science. USA. 94:13661–13665, 1997.
- Beningo, K. A., C. M. Lo, and Y. L. Wang. Flexible polyacrylamide substrata for the analysis of mechanical interactions at cell-substratum adhesions. Methods in Cellular Biology. 69:325–339, 2002.
- Cukierman, E., R. Pankov, D. R. Stevens, and K. M. Yamada. Taking cell-matrix adhesions to the third dimension. Science. 294: 1708–1712, 2001.
- Georges, P. C., and P. A. Janmey. Cell type-specific response to growth on soft materials. Journal of Applied Physiology. 98:1547–1553, 2005.
- Discher D, Jamney P and YL Wang. Tissue Cells Feel and Respond to the Stiffness of their Substrate. Science 310, 1139, 2005.
- (Fibroblasts and epithelial cells) R. J. Pelham, Y. Wang. Proc. Natl. Acad. Sci. U.S.A. 94, 13661 (1997) with Erratum 95, 12070a (1998).
- Engler AJ, Griffin MA, Sen S, Bonnemann CG, Sweeney HL, and DE Discher. Myotubes differentiate optimally on substrates with tissuelike stiffness: pathological implications for soft or stiff microenvironments. Journal of Cellular Biology. 166: 877–887, 2004.
- Semler EJ and PV Moghe. Engineering hepatocyte functional fate through growth factor dynamics: the role of cell morphologic priming. Biotechnology and Bioengineering. 75: 510–520, 2001.
- Penelope C. Georges, William J. Miller, David F. Meaney, Evelyn S. Sawyer, and Paul A. Janmey. Matrices with Compliance Comparable to that of Brain Tissue Select Neuronal over Glial Growth in Mixed Cortical Cultures. Biophysical Journal Vol 90, 3012–3018. April, 2001.
