Geometry of wave propagation on active deformable surfaces

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.

arXiv commenttext changes abstract and intro, new results on self-propelled elastic shells added; 5 pages, 3 figures; videos available on request

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Cited by in corpus (14)

• Topology and morphology of self-deforming active shells
• Vesicle shape transformations driven by confined active filaments
• Pattern Propagation Driven by Surface Curvature
• Oscillating membranes: modeling and controlling autonomous shape-transforming sheets
• Morphoelasticity of Large Bending Deformations of Cell Sheets during Development
• Odd elasticity and topological waves in active surfaces
• Pinning of Diffusional Patterns by Non-Uniform Curvature
• Geometry-induced patterns through mechanochemical coupling
• A model for boundary-driven tissue morphogenesis
• Shape Transitions in Network Model of Active Elastic Shells
• Euler buckling on curved surfaces
• Oscillatory and chaotic pattern dynamics driven by surface curvature
• Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces
• Active elastocapillarity in soft solids with negative surface tension