Turing Foams and Active Foams

Non-equilibrium protein pattern formation and the self-organization of motor-filament mixtures, driven by NTPase cycles, are crucial mechanisms for cellular processes like division and polarization. Despite their distinct physical origins, both systems can form remarkably similar structures. Protein diffusion-reaction dynamics lead to foam-like patterns, we termed "Turing foams," that follow non-equilibrium interface laws similar to equilibrium foams[1]. Motor-filament mixtures similarly self-organize into supramolecular structures including micelles, bilayers, and foams, driven by instabilities [2]. This talk will discuss the shared non-equilibrium principles governing these systems, focusing on interface laws linked to thermodynamic-like relations, and their applications in designing specific pattern morphologies for synthetic life-like systems.

[1] Deciphering the Interface Laws of Turing Mixtures and Foams, Henrik Weyer, Tobias A. Roth, and Erwin Frey, [arXiv:2409.20070].

[2] Supramolecular assemblies in active motor-filament systems: micelles, bilayers, and foams, Filippo De Luca, Ivan Maryshev, and Erwin Frey, Physical Review X 14, 031031 (2024).