Fig. 4: A model for tissue mechanics and actin nematodynamics recapitulates the response of endothelial tubes.
From: Interplay of actin nematodynamics and anisotropic tension controls endothelial mechanics
a, Schematic of cylindrical tube or radius R subjected to the pressure difference ΔP, balanced by the circumferential tension \({t}_{\theta }^{\theta }\) (i). The change in orientation of actin fibres from longitudinal to circumferential corresponds to a change in sign of the order parameter q (ii). b, Circumferential actin nematic order q as a function of the normalized tube radius R/R0. Dots: experimental data, corresponding to d(i),(ii). Grey lines: numerically computed contribution of deformation by the tissue shear, starting with six sample images at R/R0 = 1. Insets: actin fibres colour coded based on their orientation, before tube stretching (yellow), after 7 h of 650 Pa pressure application (red) and for an artificial deformation of the initial image by an amount corresponding to the observed deformation R/R0 at 7 h (blue). c, Schematic of tube expansion dynamics and nematic reorientation induced by tube expansion. A sudden increase in the luminal pressure from ΔP ≈ 150 Pa to ΔP ≈ 650 Pa results in an instantaneous deformation, followed by a reorientation of actin fibres and an increase in the tension generated in actin stress fibres, \({{t}^{{\rm{a}}}}_{\theta }^{\theta }\), that slows down tube expansion. d, Actin order parameter q (i) and normalized tube radius R/R0 (ii) as a function of time, comparing the experimental data (dots) and model prediction (solid lines), for a constant pressure ΔP ≈ 150 Pa (yellow) and with pressure increase ΔP ≈ 650 Pa (red); the experimental data is as in Fig. 2a (with radius normalized by R0 for each experiment) and Fig. 2c(iv). Model predictions without the elastic component of the actin tension (green line, Ka = 0) and without the tension-coupling-inducing actin reorientation (blue line, β = 0) are also shown. Normalized total circumferential tension \({t}_{\theta }^{\theta }/{\zeta }_{0}\) (solid red line) and total longitudinal tension \({t}_{z}^{z}/{\zeta }_{0}\) (solid blue line) as a function of time (iii). Normalized total circumferential tension \({t}_{\theta }^{\theta }/{\zeta }_{0}\) (solid red line), circumferential tension in the actin stress fibre network \({{t}^{{\rm{a}}}}_{\theta }^{\theta }/{\zeta }_{0}\) (dashed green line) and residual tension \({{t}^{{\rm{r}}}}_{\theta }^{\theta }/{\zeta }_{0}\) (dotted red line) (iv).
