Prof. Ulrich Schwarz "Material laws for cells and tissues"

Cells and tissues have unusual material properties which result from active processes like growth and contractility. In this talk, we will discuss how active contractility of cells and tissues can be modeled using concepts from soft condensed matter and statistical physics. Recently we have found that the shape of contractile model tissue pinned at discrete sites can be described neither by tension-based Laplace laws nor by traditional elasticity theory [1]. Rather a satisfying theoretical explanation of tissue shape as a function of pinning geometry could be achieved only by combining elements of tension and elasticity in the theoretical framework of actively contracting cable networks [1,2]. In contrast to spring networks, which correspond to material laws often used in approaches based on the finite element method (FEM), cable networks do not propagate compression. Under active contraction, they do not have a reference shape and therefore are only stable in combination with adhesion sites. Actively contracting cable networks are well suited for multi-scale modeling in the biological context, because their locally defined structural properties can be easily coupled to additional degrees of freedom. In contrast, FEM-models are especially suited if global systems properties are of interest. Here contractility can be modeled by including a negative pressure into the elastic equations (like for thermal cooling). We demonstrate the application of this approach by predicting the experimentally observed localization of stresses and strains to the periphery of epithelial monolayers [3].

References

[1] I. B. Bischofs et al., Biophys. J. 95, 3488-3496 (2008)
[2] P. Guthardt Torres et al., Phys. Rev. E 85, 011913 (2012)
[3] C. M. Edwards and U. S. Schwarz, Phys. Rev. Lett. 107, 128101 (2011)