Reversible elastic phase field approach and application to cell monolayers
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Reversible elastic phase field approach and application to cell monolayers Robert Chojowski1,2 , Ulrich S. Schwarz1,2 , and Falko Ziebert1,2,a 1 2
Institute for Theoretical Physics, Heidelberg University, D-69120 Heidelberg, Germany BioQuant, Heidelberg University, D-69120 Heidelberg, Germany Received 21 July 2020 / Received in final form 15 September 2020 / Accepted 16 September 2020 Published online: 1 October 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com Abstract. Motion and generation of forces by single cells and cell collectives are essential elements of many biological processes, including development, wound healing and cancer cell migration. Quantitative wound healing assays have demonstrated that cell monolayers can be both dynamic and elastic at the same time. However, it is very challenging to model this combination with conventional approaches. Here we introduce an elastic phase field approach that allows us to predict the dynamics of elastic sheets under the action of active stresses and localized forces, e.g. from leader cells. Our method ensures elastic reversibility after release of forces. We demonstrate its potential by studying several paradigmatic situations and geometries relevant for single cells and cell monolayers, including elastic bars, contractile discs and expanding monolayers with leader cells.
1 Introduction Cell and tissue mechanics is an essential element of many physiological processes, including development, tissue homeostasis and wound healing [1,2]. Both single cells and cell collectives are highly dynamic. For animal cells, fluorescence-based experiments have shown that subcellular structures like the actomyosin cortex, lamellipodia and adhesion complexes turn over on the timescale of minutes, despite their function to provide mechanical stability to cells and tissues [3–5]. In most developing and even in some homeostatic tissues (notably skin and intestine), there exists a constant flow of cells [6]. Together, these observations suggest that biological systems should be viscous rather than elastic on large time scales, at least in the absence of extracellular matrix [7]. Surprisingly, recent experiments with epithelial monolayers did reveal elastic signatures despite the high cellular and subcellular dynamics. The standard setup in this context is the so-called wound healing assay. In these experiments, cell monolayers of well-defined geometry migrate into free space created by the removal of a straight barrier. This setup has been used to quantify cellular velocity fields, traction forces and intramonolayer tension [8–10]. Several new effects have been discovered, including plithotaxis [11] and collective durotaxis [12]. Very important in our context, it has been shown that one can extract a linear relation between stress and strain, thus defining an elastic modulus [13]. This agrees with the a
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results of experiments that stretch free-standing m
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