The Hidden Drag

The vertex model predicts tissue fluidity from cell shape. Cells with a shape index above a critical threshold — roughly 3.81 — are fluid; below it, they jam. The model works because adhesion sets the interfacial energy at cell-cell junctions, which determines the preferred geometry, which determines whether cells can rearrange. Reduce adhesion, cells become rounder, the shape index drops, and the tissue solidifies. The pathway runs through geometry.

Bera and colleagues blocked E-cadherin with antibodies and chelated calcium to weaken cell-cell adhesion in epithelial monolayers. Fluidity increased sixfold. Cell shape barely changed. The shape index stayed between 3.87 and 3.91 — well within the fluid regime before and after treatment. Cell density was constant. Substrate traction was constant. The vertex model predicted a 1.2-fold change. The experiment showed a sixfold change.

The missing factor was kinetic. Adhesion does two things: it sets the energy cost of separating two cells (thermodynamic), and it generates viscous drag when neighboring cells slide past each other (kinetic). The vertex model captured the first and ignored the second. When E-cadherin is blocked, the interfacial energy barely changes — the cells keep their shapes. But the drag coefficient drops by an order of magnitude. Cells that used to resist sliding now glide past each other freely.

The extended model adds an interfacial drag force proportional to relative cell velocity at the junction. This single term, independent of geometry, recovers the sixfold effect. It also opens a new axis in the rigidity phase diagram — tissue can fluidize without changing shape, something the original model declared impossible.

One word — adhesion — named two mechanisms. The model heard one.