Surface Patterns on Single Cells: A Consequence of a Phase Transition to Modulated Phases

Patterns are ubiquitous in the world around us, and we have only begun to scratch the surface of understanding their complexity and formation. In this thesis, we draw inspiration from rigid, extracellular surface patterns found on single living cells in many taxa and try to understand if there is a common thread in their pattern formation mechanisms that can be described by a single physical formalism. Pollen grains, butterfly wing scales, and deep-sea protists called phaeodarians all have beautifully ornate and varied hard surface structures that are likely patterned by the deposition of some soft organic matrix originating inside of the cell. We focus on pollen grain surfaces because of their remarkable geometric variety that is well documented. We find, through our own electron microscopy and careful histological techniques, that the patterns arise due to a phase separation of a transient polysaccharide material mechanically coupled to the underlying elastic cell membrane. We then show that the entire evolved diversity of patterns can be recapitulated by exploring both the equilibrium states and the dynamics of a modified Landau-Ginzburg model of phase transitions to modulated phases. We observe the surprising fact that only ~10% of extant species exhibit patterns that reach equilibrium. Furthermore, we find that although these patterns have evolved many times in seed plants, they are not, on average, selected for. The remaining 90% of pollen grain surfaces resemble arrested intermediate states of the phase transition process. We then document the pattern formation process in butterfly wing scales and show that a transient, spatially periodic surface material sits between the global surface features of the scales (the ridges). We postulate that the phase transition of this material may also contribute to the regular patterns on wing scale cells. We finally image the full three-dimensional features of geodesic phaeodarians tests using x-ray-computed tomography