In a packed tissue, cells are either jammed or unjammed. Jammed cells hold their positions — the tissue is solid, maintaining its shape under stress. Unjammed cells rearrange freely — the tissue is fluid, flowing in response to forces. The transition between these states matters for embryonic development, wound healing, and cancer metastasis.
The prevailing theory identifies cell shape as the order parameter. The shape index — perimeter divided by the square root of area — measures how elongated a cell is. Below a critical value (around 3.81 in the vertex model), cells are compact and the tissue is solid. Above it, cells are elongated and the tissue flows. The framework is elegant: measure cell shapes in a micrograph, compute the index, predict whether the tissue is jammed or fluid.
Bera, Nguyen, McCord, Bi, and Notbohm showed experimentally that the prediction fails.
They reduced intercellular adhesion in epithelial monolayers and observed the tissue fluidize — cells rearranged, the material flowed. But the cell shapes did not change. Neither did cell density, traction forces, or line tension. Every geometric quantity the vertex model uses to predict the transition stayed constant. The tissue crossed from solid to fluid while the shape index said it shouldn't.
The mechanism they uncovered has two channels. Adhesion acts thermodynamically — it sets the interfacial energy at cell-cell junctions, which is what the vertex model captures. But adhesion also acts kinetically — it generates viscous drag as cells slide past each other. This friction is a rate-dependent property. It doesn't appear in the energy landscape. It appears in the dissipation.
The vertex model is an energy model. It computes equilibrium configurations — where cells want to be. Friction is not an energy. It is a resistance to motion — how hard it is to get there. When adhesion friction dominates the transition, the energy landscape (captured by shape) stays the same while the dissipation landscape (captured by sliding resistance) changes. The tissue fluidizes not because the shapes prefer to rearrange but because the cost of rearrangement drops.
This is why the shape index worked as a predictor in earlier experiments. Those experiments varied cortical tension and adhesion together — changing conditions that move both the thermodynamic and kinetic channels in the same direction. Shape correlated with fluidity because both tracked a common upstream variable. The correlation was real but the causation was incomplete. Bera et al. found a perturbation that moves the kinetic channel alone, breaking the correlation and revealing which variable was actually controlling the transition.
The structural lesson: an order parameter that predicts a transition under correlated perturbations may fail when the perturbation is uncorrelated. The right variable is the one that still predicts when the others don't.