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Filamentous Network Mechanics and Active Contractility Determine Cell and Tissue Shape

Ilka B. Bischofs ^* , Franziska Klein , Dirk Lehnert , Martin Bastmeyer  and Ulrich S. Schwarz ^* 

^* University of Heidelberg, Bioquant 0013, D-69120 Heidelberg, Germany; University of California at Berkeley, Department of Bioengineering, Berkeley, California 94710; Universität Karlsruhe (TH), Institute of Zoology, Cell- and Neurobiology, D-76131 Karlsruhe, Germany; and Universität Karlsruhe (TH), Institute of Zoology, Theoretical Biophysics, D-76131 Karlsruhe, Germany

Correspondence: Address reprint requests to Martin Bastmeyer, E-mail: bastmeyer{at}bio.uka.de; and Ulrich S. Schwarz, E-mail: Ulrich.Schwarz{at}bioquant.uni-heidelberg.de.

For both cells and tissues, shape is closely correlated with function presumably via geometry-dependent distribution of tension. In this study, we identify common shape determinants spanning cell and tissue scales. For cells whose sites of adhesion are restricted to small adhesive islands on a micropatterned substrate, shape resembles a sequence of inward-curved circular arcs. The same shape is observed for fibroblast-populated collagen gels that are pinned to a flat substrate. Quantitative image analysis reveals that, in both cases, arc radii increase with the spanning distance between the pinning points. Although the Laplace law for interfaces under tension predicts circular arcs, it cannot explain the observed dependence on the spanning distance. Computer simulations and theoretical modeling demonstrate that filamentous network mechanics and contractility give rise to a modified Laplace law that quantitatively explains our experimental findings on both cell and tissue scales. Our model in conjunction with actomyosin inhibition experiments further suggests that cell shape is regulated by two different control modes related to motor contractility and structural changes in the actin cytoskeleton.