Figure 4.

Physical model of epithelial closure. (A) Sketch of a closing circular wound, of initial radius R₀ = R(t = 0). Two border forces may drive closure: σ_p is the protrusive stress produced by lamellipodia and γ the line tension due to the contractile circumferential cable (see the stress boundary condition (Eq. S4)). (B–F) Model predictions. Plots of the closure time, t_c, as a function of the initial effective radius, R₀. (B) Effect of the variation of D while R_max = 110 μm is fixed, inviscid rheology without cable (Eqs. 1 and S27). (C) Effect of the variation of R_γ = γ/σ_p while D = 200 μm² h⁻¹ and R_max = 110 μm are fixed, inviscid rheology with a cable (Eq. S28). (D) Effect of the variation of $R_{\eta }=\sqrt{\eta /\xi }$ while D = 200 μm² h⁻¹, R_max = 110 μm, and R_γ = 10 μm are fixed, viscous rheology (Eq. S29). (E) Effect of the variation of μ/σ_p while D = 200 μm² h⁻¹, R_max = 110 μm, and R_γ = 100 μm are fixed, elastic rheology (Eq. S30). When μ/σ_p = 1, closure is complete and characterized by a finite closure time only below a value of R₀ above which elastic forces are strong enough to stop epithelization. To see this figure in color, go online.