Continuum description of confluent tissues with spatial heterogeneous activity

TL;DR

This paper develops a continuum model to describe the deformation of confluent tissues with spatially heterogeneous activity, accurately predicting tissue behavior and cellular shape variations under localized contractions.

Contribution

It introduces a novel continuum framework incorporating heterogeneous activity and validates it against vertex model simulations, capturing both average deformations and fluctuations.

Findings

Continuum model accurately predicts tissue deformation under localized activity.

Perimeter activity induces anisotropic stress aligned with tissue texture.

Medial activity causes isotropic pressure and increased shape fluctuations.

Abstract

A continuum description is built to characterize the stationary and transient deformations of confluent tissues subject to heterogeneous activities. By defining a coarse-grained texture matrix field to represent the shape and size of cells, we derive the coarse-grained stress tensor for the vertex model. Activity in the tissue takes the form of inhomogeneous apical contractions, which can be modeled as reductions of the vertex model reference areas or perimeters representing activity in the medial and perimeter regions of the cells, respectively. For medial activity, the extra stress is just an isotropic pressure, while for perimeter activity, it also has a deviatoric component, which is aligned with the texture matrix. The predictions of the continuum description are compared with the average spatiotemporal deformations obtained in simulations of the vertex model subject to localized apical contractions, showing an excellent agreement, even if the active patch is as small as one cell. The fluctuations around the average are more prominent when the activity is in the medial region due to the lack of negative active shape feedback, which, coupled with the confluent property, increases cellular shape and size variations.