Geometry of wave propagation on active deformable surfaces

TL;DR

This paper develops a theoretical framework coupling chemical and mechanical surface waves on deformable surfaces, validated with biological data, and demonstrates how geometry and signaling can enable autonomous wave-guided motion.

Contribution

It introduces a novel chemo-mechanical model for wave propagation on active surfaces, linking surface geometry with wave dynamics, validated with biological data, and exploring applications in soft robotics.

Findings

Good quantitative agreement with biological wave data

Geometry and symmetry can focus active surface waves

Spontaneous wave-induced locomotion demonstrated on elastic shells

Abstract

Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between surface geometry and contraction wave dynamics remains poorly understood, but will be essential for the future design of chemically-driven soft robots and active materials. Here, we couple prototypical chemical wave and reaction-diffusion models to non-Euclidean shell mechanics to identify and characterize generic features of chemo-mechanical wave propagation on active deformable surfaces. Our theoretical framework is validated against recent data from contractile wave measurements on ascidian and starfish oocytes, producing good quantitative agreement in both cases. The theory is then applied to illustrate how geometry and preexisting discrete symmetries can be utilized to focus active elastic surface waves. We highlight the practical potential of chemo-mechanical coupling by demonstrating spontaneous wave-induced locomotion of elastic shells of various geometries. Altogether, our results show how geometry, elasticity and chemical signaling can be harnessed to construct dynamically adaptable, autonomously moving mechanical surface wave guides.