Angle-dependent protrusion of cell membranes

Protrusion induced by cylindrical tubes against cell membranes plays essential roles in numerous biological processes, including filopodia growth, cellular packing or entry of one-dimensional nanomaterials, and indentation of cells by needle-like probes. Though the mechanical interaction between the cell membrane and a perpendicular tube has been widely investigated, little is known about how an inclined protruding tube interacts with the cell membrane. Here, we theoretically investigate the angle-dependent protrusion of cylindrical tubes against cell membranes. It is found that perpendicular protrusion is stabilized by the elastic deformation of cell membranes. Increasing the angle between the protrusion direction and perpendicular direction or increasing membrane tension leads to an increasing peak force for the membrane tubulation and increasing plateau resistive force for the maintenance of membrane tubules. Moreover, two fundamental protruding modes leading to the tip-roof and finial-roof system configurations are identified. Inclined protrusion retards the configurational transition from the tip-roof to the finialroof configuration, and causes possible bending and buckling of protruding tubes due to a large membrane resistive force. Our results offer fundamental insights into the interaction between cell membranes and one-dimensional nanomaterials, and contribute to the understanding and control of membrane protrusion in biological systems.