  Pollen grains are known for their impressive variety of species-specific,
microscale surface patterning. Despite having similar biological developmental
steps, pollen grain surface features are remarkably geometrically varied.
Previous work suggests that a physical process may drive this pattern formation
and that the observed diversity of patterns can be explained by viewing pollen
pattern development as a phase transition to a spatially modulated phase.
Several studies have shown that the polysaccharide material of plant cell walls
undergoes phase separation in the absence of cross-linking stabilizers of the
mixed phase. Here we show experimental evidence of a change in density of the
extracellular polysaccharide material (primexine) during pollen cell
development leads to a spatially modulated phase. The spatial pattern of this
phase-separated primexine is also mechanically coupled to the undulation of the
pollen cell membrane. The resulting patterned pools of denser primexine form
the negative template of the ultimate sites of sporopollenin deposition,
leading to the final micropattern observed in the mature pollen. We then
present a general physical model of pattern formation via modulated phases.
Using analytical and numerical techniques, we find that most of the pollen
micropatterns observed in biological evolution could result from a physical
process of modulated phases. However, an analysis of the relative rates of
transitions from states that are equilibrated to or from states that are not
equilibrated suggests that while equilibrium states of this process have
occurred throughout evolutionary history, there has been no particular
evolutionary selection for distinctly patterned equilibrated states.
