Curved crease origami and topological singularities at a cellular scale enable hyper-extensibility of .

Eukaryotic cells undergo dramatic morphological changes during cell division, phagocytosis and motility. Fundamental limits of cellular morphodynamics such as how fast or how much cellular shapes can change without harm to a living cell remain poorly understood. Here we describe hyper-extensibility in the single-celled protist , a 40 m cell which is capable of reversible and repeatable extensions (neck-like protrusions) up to 1500 m in 30 seconds. We discover that a unique and intricate organization of cortical cytoskeleton and membrane enables these hyper-extensions that can be described as the first cellular scale curved crease origami. Furthermore, we show how these topological singularities including d-cones and twisted domain walls provide a geometrical control mechanism for the deployment of membrane and microtubule sheets as they repeatably spool thousands of time from the cell body. We lastly build physical origami models to understand how these topological singularities provide a mechanism for the cell to control the hyper-extensile deployable structure. This new geometrical motif where a cell employs curved crease origami to perform a physiological function has wide ranging implications in understanding cellular morphodynamics and direct applications in deployable micro-robotics.