Interplay of geometry and mechanics in epithelial wound healing

Wound healing is a complex biological process critical for maintaining an organisms structural integrity and tissue repair following an infection or injury. Recent studies have unveiled the mechanisms involving the coordination of biochemical and mechanical responses in the tissue in wound healing. In this article, we focus on the healing property of an epithelial tissue as a material while the effects of biological mechanisms such as cell crawling and tissue proliferation is minimal. We present a mathematical framework that predicts the fate of a wounded tissue based on the wounds geometrical features and the tissues mechanical properties. Precisely, adapting the vertex model of tissue mechanics, we predict whether a wound of a specific size in an epithelial monolayer characterized by certain levels of acto-myosin contractility and cell-cell adhesion will heal (i.e., close), shrink in size, or rupture the tissue further. Moreover, we show how tissue-mediated mechanisms such as purse-string tension at the wound boundary facilitate wound healing. Finally, we validate the predictions of our model by designing an experimental setup that enables us to create wounds of specific sizes in MDCK monolayers. Altogether, this work sets up a basis for interpreting the interplay of mechanical and geometrical features of a tissue in the process of wound healing.