Figure 3. Endothelial monolayer modeled as a tensed, disordered assembly of cohesive particles far from equilibrium.

a. We construct a minimalist model of the monolayer as an assembly of particles, poly-disperse in size, joined by an attractive inter-particle interaction potential. The pair potential has components that act along the inter-particle contact radius and also tangential to it, to mimic the mechanics of actual cell-cell junctions. b. To mimic the action of contractile agonists such as thrombin, the model is strained by a symmetric, bi-axial expansion. The imposed external strain is balanced by a build-up of internal tensions. c. Load curve for the model monolayer subjected to biaxial strain. At slow rates of expansion, G, the stress-strain relationship is relatively linear (inset) and terminates with abrupt fracture. As G is increased the relationship changes, indicating the onset of plastic deformation and yielding rather than abrupt fracture. At the same time, the peak internal tension generated prior to failure is increased (solid and dashed lines). d. Spatial autocorrelation function of the model monolayer at different points on the load curves. The onset of plastic behavior is associated with the emergence of long-range correlations. e. Number of gaps (rescaled by the total number of particles N). f. Average gap area as a function of strain. In the yielding regime, permeability increases primarily by growth of existing gaps. Close to the maximum of the load curve, a few gaps of relatively small size are present. Further increasing the strain beyond the yielding threshold causes a rapid increase in gap area with a less dramatic increase in gap number. This is in contrast to the small and fairly constant average gap area measured in the linear regime, where the number of gaps rapidly increases.