Curved crease origami at cellular scales enables hyper-extensibility of Lacrymaria olor

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 Lacrymaria olor, a 40 μm cell which is capable of reversible and repeatable extensions (neck-like protrusions) up to 1500 μm in 20 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 dcones and twisted domain walls provide a geometrical control mechanism for the deployment of membrane and microtubule sheets as they repeatably spool thousands of times 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.