Stress normal to the boundary of an epithelial sheet can arise in constrained and unconstrained cell layers through pushing and pulling of surrounding tissue and wettability of the substrate, respectively. A continuum model describes the epithelium as a polarizable and chemo-mechanically interacting layer under the influence of such stresses. This model links the experimentally observed formation of finger-like protrusions at the edge of unconstrained spreading cell monolayers to substrate wettability [1]. Statistics of the velocity orientation shows a strong alignment in the fingers opposed to an isotropic distribution in the bulk, in agreement with measurements by Reffay et al [2]. The model further exhibits a stress accumulation within the tissue that proceeds in form of a mechanical wave, starting at the wound edge [3]. Additionally, four types of spreading and motility can identified, depending on the normal stress at the boundaries: Uniform deformation, non-uniform deformation, uniform gliding and peristaltic ("worm-like") progression. Analytical and numerical solutions are presented along with bifurcation diagrams using normal stress and active force as control parameters [4].

[1] Köpf, Pismen, Soft Matter 9 (2013) 3727-3734
[2] Reffay et al., Biophysical Journal 100 (2011) 2566-2575
[3] Serra-Picamal et al., Nature Physics 8 (2012) 628-634
[4] Köpf (2014) submitted