Mechanochemical induction of wrinkling morphogenesis on elastic shells

TL;DR

This paper introduces a minimal mechanochemical model for tissue morphogenesis, demonstrating how diffusible biomolecules induce wrinkling patterns on elastic shells through coupled chemical and mechanical dynamics.

Contribution

The study presents a novel coupled mechanochemical model that explains tissue patterning and wrinkling morphogenesis via chemical-mechanical interactions and elastic instabilities.

Findings

Different patterns emerge depending on chemical concentration thresholds.

Mechanochemical coupling produces distinct patterns from purely mechanical or chemical models.

Scaling laws are derived to predict wrinkling morphologies.

Abstract

Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner -- and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.