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Title: Does cell shape predict whether a tissue flows or holds?
Plain: 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: 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.
Settled by: Simultaneous in vivo measurement of q and of tissue rheology (cell rearrangement rate, stress relaxation) across several tissues and perturbations.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: contested
Status note: Support from airway epithelia (2015) contrasts with 2026 reports of shape-independent fluidity in epithelial monolayers (arXiv 2603.05548).
Posed since: 2015