Does cell shape predict whether a tissue flows or holds?
In plain words
Computer models of tightly packed cells predict that a tissue switches from solid-like to fluid-like once cells become elongated beyond a critical shape. Experiments disagree on whether this shape rule works in real tissues.
Precise statement
The 2D vertex model with energy $E = \operatorname{sum}_i [K_A (A_i - A_0)^2 + K_P (P_i - P_0)^2]$ ($A_i, P_i$ = cell area and perimeter) has a rigidity transition at target shape index $p_0 = P_0/\sqrt{A_0} \sim 3.81$. Determine whether the observed shape index $q = \langle P/\sqrt{A}\rangle$ classifies fluid versus solid epithelia in vivo across tissues and species, or whether fluctuations, division and active tension remodeling set fluidity independently of q.
What would settle it
Simultaneous in vivo measurement of q and of tissue rheology (cell rearrangement rate, stress relaxation) across several tissues and perturbations.
Status in the literature
Unverified note
Support from airway epithelia (2015) contrasts with 2026 reports of shape-independent fluidity in epithelial monolayers (arXiv 2603.05548).