Transforming tubular packings to bicontinuous surfaces

The link between bicontinuous architectures in biological membranes and triply periodic minimal surfaces (TPMS) is a well-established example of stunning geometric form in nature. The prolamellar body (PLB) in early plant plastid development is a classic example, forming the Diamond TPMS in a lipid-protein-pigment membrane. However, the early development of such spectacular geometric structures is poorly understood. Inspired by the presence of tubules in the micrographs of early plastid membrane formation, we explore here geometric modelling of transformations of packings of cylinders that coalesce together to form bicontinuous structures. Using computational modelling, we find that specific tubular packings transform into highly symmetric TPMS, which provide a geometric foundation for further investigation into the PLB, as well as other occurrences of bicontinuous membranes.