Abstract
Cell membranes may fold up into three-dimensional nanoperiodic cubic structures in biological systems. Similar geometries are well studied in other disciplines such as mathematics, physics and polymer chemistry. The fundamental function of cubic membranes in biological systems has not been uncovered yet; however, their appearance in specialized cell types indicates a role as structural templates or perhaps direct physical entities with specialized biophysical properties. The mitochondria located at the inner segment of the retinal cones of tree shrew (Tupaia glis and Tupaia belangeri) contain unique patterns of concentric cristae with a highly ordered membrane arrangement in three dimensions similar to the photonic nanostructures observed in butterfly wing scales. Using a direct template matching method, we show that the inner mitochondrial membrane folds into multi-layered (8 to 12 layers) gyroid cubic membrane arrangements in the photoreceptor cells. Three-dimensional simulation data demonstrate that such multi-layer gyroid membrane arrangements in the retinal cones of a tree shrew's eye can potentially function as: (i) multi-focal lens; (ii) angle-independent interference filters to block UV light; and (iii) a waveguide photonic crystal. These theoretical results highlight for the first time the significance of multi-layer cubic membrane arrangements to achieve near-quasi-photonic crystal properties through the simple and reversible biological process of continuous membrane folding.