Frustrated frustules: geometric frustration in diatom frustules

Diatoms are single-celled organisms with a remarkable cell wall made of silica called the frustule. The frustule is porous, with multi-scale nano- and micro-pores. While diatoms have fascinated scientists for centuries, it is still unknown how the cell wall structures are created. In our work we investigate the intricate arrangement of the microstructure pattern of the diatom C.granii and related species. Here, we used confocal fluorescence microscopy to obtain high-resolution 3-D images of fluorescently-labeled C.granii diatom, and precisely located the positions of their structural features. We find that the micro-pores are arranged in a radially aligned hexagonal lattice. Tiling a circular structure with a radially aligned hexagonal lattice requires insertion of lattice defects. We find that the micro-pore structure has geometrically necessary defects, reminiscent of a circular crochet pattern, where the number of defects increases linexarly with size.