Pitch-balanced helical motifs in tightly packed lamellar structures

Many biological and manmade lamellar structures form minimal surfaces due to surface area or bending energy minimization (or both). Recently, the endoplasmic reticulum sheets were shown to contain both right and left-handed helical motifs at equal amounts. In this talk, I will show that the lamellar structures that house photosynthesis in some plants, the thylakoid, also display right and left-handed motifs. The oppositely handed motifs, unlike those of the endoplasmic reticulum, differ in pitch and diameter, yet the stoichiometry is such that pitch is balanced between the differently handed motifs. We argue that the optimal packing of helical motifs in lamellar structures requires global pitch balance. We support this by a new constructive recipe that allows us to generate exact minimal surfaces with any arrangement of helical motifs.