Modeling mechanochemical pattern formation in elastic sheets of biological matter

Abstract

Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility inhibitor and depending on the threshold in the coupling, qualitatively different patterns occur. The second model is based on the stress--dependent activity of myosin motors, and demonstrates how the concentration distribution patterns of molecular motors are affected by the long-range deformations generated by them. Since the propagation of mechanical deformations is typically faster than chemical kinetics (of molecular motors or signaling agents that affect motors), we describe in detail and implement a numerical method based on separation of timescales to effectively simulate such systems. We show that mechanochemical coupling leads to long-range propagation of patterns in disparate systems through elastic instabilities even without the diffusive or advective transport of the chemicals.

References in corpus (7)

• Biopolymers: life's mechanical scaffolds
• Theory of mechano-chemical patterning in biphasic biological tissues
• Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity
• First-order patterning transitions on a sphere as a route to cell morphology
• Tunable corrugated patterns in an active gel sheet
• Theory of epithelial cell shape transitions induced by mechanoactive chemical gradients
• Wrinkle patterns in active viscoelastic thin sheets

Cited by in corpus (3)

• Hydra morphogenesis as phase-transition dynamics
• Shape Transitions in Network Model of Active Elastic Shells
• A full contraction-reaction-diffusion model for pattern formation in geometrically confined microtissues