Rigidity of Epithelial Tissues as a Double Optimization Problem

TL;DR

This paper explores how tissues can regulate their rigidity by tuning cell-level properties using a vertex model, revealing that certain degrees of freedom influence the rigidity transition and tissue behavior.

Contribution

It introduces a novel framework for tissue rigidity regulation by treating cell stiffness, shape, and area as tunable degrees of freedom within a vertex model.

Findings

Cell stiffness tuning does not affect rigidity transition.

Tuning preferred shapes or areas shifts the rigidity transition.

Tissues can coordinate cell properties to control large-scale behavior.

Abstract

How do cells tune emergent properties at the scale of tissues? One class of such emergent behaviors are rigidity transitions, in which a tissue changes from a solid-like to a fluid-like state or vice versa. Here, we introduce a new way for a tissue described by a vertex model to tune its rigidity, by using ``tunable degrees of freedom." We use the vertex model elastic energy as a cost function and the cell stiffnesses, target shapes, and target areas as different sets of degrees of freedom describing cell-cell interactions that can be tuned to minimize the cost function. We show that the rigidity transition is unaffected when cell stiffnesses are treated as tunable degrees of freedom. When preferred shapes or areas are treated as tunable degrees of freedom, however, induced spatial correlations in target cell shapes or areas shift the rigidity transition. These observations suggest that tissues can coordinate changes in cell-scale properties, treated here as tunable degrees of freedom, to achieve desired tissue-scale behaviors.