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Abstract

Non-equilibrium microscopic processes can drive macroscopic shape changes in soft materials. Feedback arises when such shape changes alter the geometry constraining the microscopic dynamics. Although such feedback is common in living materials, which can actively change their chemical composition in response to environmental signals, the underlying theoretical principles, and the resulting dynamical phenomena are not well understood. Motivated by biological cells exchanging shape-dependent signals at physical contacts, I investigated incompressible droplets adjusting their interfacial tensions in response to contact-dependent signals. I derived a minimal set of equations governing the macroscopic droplet states controlled by two dimensionless feedback parameters. I discovered that the droplet’s adaptive wetting properties give rise to rich dynamical phenomena, including regimes of multistability, symmetry-breaking, excitability, and self-sustained shape oscillations. For some configurations, the topology of the arising phase-space structures is analogous to Hodgkin-Huxley type neuronal models, allowing me to identify parallels between adaptive wetting dynamics and signal processing in neurons. Applying these theoretical results to experimental shape measurements from imaging data of zebrafish embryos, I found that the critical point arising from a shape multistability promotes the formation of boundaries between different developing tissues. Moreover, using fully data-derived contact-networks, I predicted cellular differentiation patterns driven by contact-dependent signaling in mechanosensory epithelia of zebrafish larvae. Together, this thesis provides new paradigms for physical signal processing through shape adaptation in soft active materials, and uncovers novel modes of self-organisation in the collective dynamics of biological tissues.