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/Σ, Where E = Modulus, σ = stress, and Σ = 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 motility1,2, phagocytosis3, and differentiation4. Moreover, different cell types react disparately to varying degrees of matrix stiffness5. For example, fibroblasts have been shown to prefer stiffer substrates2,6, while hepatocytes have been observed to maintain a differentiated phenotype only on soft materials5,9. The table below depicts a sampling of the wide range of material compliances and cellular behaviors, including actual tissue compliances where available.

Table.Compliance Effects on Different Cell Types

References

1.
Lo C, Wang H, Dembo M, Wang Y. 2000. Cell Movement Is Guided by the Rigidity of the Substrate. Biophysical Journal. 79(1):144-152. http://dx.doi.org/10.1016/s0006-3495(00)76279-5
2.
Pelham RJ, Wang Y. 1997. Cell locomotion and focal adhesions are regulated by substrate flexibility. Proceedings of the National Academy of Sciences. 94(25):13661-13665. http://dx.doi.org/10.1073/pnas.94.25.13661
3.
Beningo KA, Lo C, Wang Y. 2002. Flexible polyacrylamide substrata for the analysis of mechanical interactions at cell-substratum adhesions.325-339. http://dx.doi.org/10.1016/s0091-679x(02)69021-1
4.
Cukierman E. 2001. Taking Cell-Matrix Adhesions to the Third Dimension. 294(5547):1708-1712. http://dx.doi.org/10.1126/science.1064829
5.
2005. Cell type-specific response to growth on soft materials. Journal of Applied Physiology. 98(4):1547-1553. http://dx.doi.org/10.1152/japplphysiol.01121.2004
6.
Discher DE. 2005. Tissue Cells Feel and Respond to the Stiffness of Their Substrate. Science. 310(5751):1139-1143. http://dx.doi.org/10.1126/science.1116995
7.
Pelham RJ. Proc. Natl. Acad.Sci. U.S.A.94, 13661 (1997) with Erratum 95, 12070a (1998). . (Fibroblasts and epithelial cells).
8.
Engler AJ, Griffin MA, Sen S, Bo?nnemann CG, Sweeney HL, Discher DE. 2004. Myotubes differentiate optimally on substrates with tissue-like stiffness. 166(6):877-887. http://dx.doi.org/10.1083/jcb.200405004
9.
Semler EJ, Moghe PV. 2001. Engineering hepatocyte functional fate through growth factor dynamics: The role of cell morphologic priming. Biotechnol. Bioeng.. 75(5):510-520. http://dx.doi.org/10.1002/bit.10113
10.
Georges PC, Miller WJ, Meaney DF, Sawyer ES, Janmey PA. 2006. Matrices with Compliance Comparable to that of Brain Tissue Select Neuronal over Glial Growth in Mixed Cortical Cultures. Biophysical Journal. 90(8):3012-3018. http://dx.doi.org/10.1529/biophysj.105.073114