Alex Mietke

Spontaneous shape transformations of active surfaces

Biological matter has the fascinating ability to autonomously generate material deformations via intrinsic active forces, where the latter are often present within effectively two-dimensional structures. The dynamics of such “active surfaces” inevitably entails a complex, self-organized interplay between the geometry of a surface and its mechanical interactions with the surrounding. In this talk, I will first discuss general numerical challenges in analyzing self-organizing active surfaces and the bifurcation structure of emergent shape spaces. I will then focus on active surfaces with broken up-down symmetry, of which the eukaryotic cell cortex and epithelial tissues are key biological examples. A natural interplay between active stress and curvature leads for such surfaces to a comprehensive library of spontaneous shape transformations that resemble stereotypical morphogenetic processes. These include cell-division-like invaginations and the autonomous formation of tubular surfaces of arbitrary length, both of which robustly overcome well-known shape instabilities that would arise in analogue passive systems.