Folding of colloidal membranes into complex topologies

Three-dimensional shaping of thin sheets is a ubiquitous feature of materials science and underlies diverse biological processes, ranging from large scale morphogenesis to molecular drug delivery. At the nanometer scale, cell membranes seamlessly transition between distinct topological structures during endo- and exo-cytosis. However, the timescales of cell membrane remodeling are too fast to permit real time observations. The model system of colloidal membranes which are micro-meter thick fluid-like monolayers of aligned rods are ideally suited to fill this gap. We show that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddles. Coalescence of  saddles drives formation of catenoids and other architectures of increasing complexity. Our results demonstrate a pathway based on tuning the elasticity of membranes to control their shape and topology.