Abstract
When a cytoskeletal protein, tubulin, is enclosed inside a liposome and the tubulin molecules assemble to form microtubules, a spherical liposome transforms into a rugby-ball shape due to the mechanical force generated by the microtubule assembly. Tubular projections of membrane then grow from both ends of the rugby-ball liposome, and finally the liposome transforms into a characteristic shape consisting of a central ellipsoid and straight tubes. Here we investigate mechanical aspects of the shape transformation of liposomes caused by microtubule assembly. We calculate the liposome shape using a mathematical model based on the notion of the minimum bending energy of the liposome membrane. The force generated by the microtubule assembly is incorporated in the model by considering the local force balance of the membrane. Numerical analysis of the model gives a series of shapes which are similar to the shapes observed in experiments. The force-transformation relationship obtained in our model predicts the existence of a critical force for the formation of tubular projections. The force exerted by microtubules is calculated using experimental data.
