Dynamical pattern formation and mode selection on a deformable biological surface

Self-organization of individual units into patterns arises in many biological systems across vast length scales. These ordered structures drive and regulate a plethora of vital biological functions from molecular to ecological level. The study of pattern formation has thus far been limited to surfaces with uniform curvature, even though most biological surfaces are highly non-uniform. Recent theoretical work has shown that by breaking symmetries in these systems, inhomogeneities in the curvature can select for certain patterns. Here, we use cortical Rho activity in starfish oocyte as a model system to explore such effects. In addition to being highly deformable, the oocyte cortex exhibits versatile dynamical chemical patterns that can be tuned. By mapping such patterns onto a two-dimensional sphere using spherical harmonics, we identify the spatio-temporal modes of the pattern, thus revealing the underlying features of the dynamics. By changing the curvature, we can correlate the dynamic features of the pattern with the local curvature perturbation. This framework will allow us to experimentally verify the important role of geometry in pattern formation in biological systems.