Effective viscosity and dynamics of spreading epithelia: a solvable model

Abstract

Collective cell migration in spreading epithelia in controlled environments has become a landmark in our current understanding of fundamental biophysical processes in development, regeneration, wound healing or cancer. Epithelial monolayers are treated as thin layers of a viscous fluid that exert active traction forces on the substrate. The model is exactly solvable and shows a broad range of applicabilities for the quantitative analysis and interpretation of force microscopy data of monolayers from a variety of experiments and cell lines. In addition, the proposed model provides physical insights into how the biological regulation of the tissue is encoded in a reduced set of time-dependent physical parameters. In particular the temporal evolution of the effective viscosity entails a mechanosensitive regulation of adhesion. Besides, the observation of an effective elastic tensile modulus can be interpreted as an emergent phenomenon in an active fluid.

Physical Models of Collective Cell Migration

“…In this case, for an unpolarized tissue (a > 0 in Eq. (11)), the polarity decays from the boundary with the characteristic length L c = K/a, which defines the width of the polarized boundary layer observed in experiments [28,149] ( Fig. 7a).…”

Emergence of epithelial cell density waves

“…In order to describe faithfully the experimental observations [8,10], the model needs to be extended to a 2D geometry, and to include a moving free boundary in the numerical simulations, close to which polar order may be confined within a band of finite extension [19]. The same epithelial monolayers exhibit topological defects of the cell shape tensor field characteristic of a nematic material [38].…”

“…As an example motivated by [23], we add to our minimal model the β a p 2 term in (19), and show in Fig. 6 the resulting bifurcation diagrams in the (γ a , β a ) plane, at constant δ a and in the (β a , δ a ) plane, at constant γ a (compare with Fig.…”

Active wetting of epithelial tissues

“…To understand how the wetting transition emerges from active cellular forces, we build upon a continuum mechanical model of epithelial spreading 26 . Given the long time scales of the wetting/dewetting processes, we neglect the elastic response of the tissue 21,[27][28][29] , assuming that it has a purely viscous behavior 26,[30][31][32][33][34][35] . Thus, taking a coarse-grained approach, the model describes the cell monolayer as a two-dimensional (2D) active polar fluid [36][37][38][39] , namely in terms of a polarity field p(r, t) and a velocity field v(r, t) (Supplementary Note).…”