Fundamental helical geometry consolidates the plant photosynthetic membrane.

Plant photosynthetic (thylakoid) membranes are organized into complex networks that are differentiated into 2 distinct morphological and functional domains called grana and stroma lamellae. How the 2 domains join to form a continuous lamellar system has been the subject of numerous studies since the mid-1950s. Using different electron tomography techniques, we found that the grana and stroma lamellae are connected by an array of pitch-balanced right- and left-handed helical membrane surfaces of different radii and pitch. Consistent with theoretical predictions, this arrangement is shown to minimize the surface and bending energies of the membranes. Related configurations were proposed to be present in the rough endoplasmic reticulum and in dense nuclear matter phases theorized to exist in neutron star crusts, where the right- and left-handed helical elements differ only in their handedness. Pitch-balanced helical elements of alternating handedness may thus constitute a fundamental geometry for the efficient packing of connected layers or sheets.