Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations

This talk focuses on the numerical analysis of stationary shapes of giant vesicles motivated by the rich mechanical response of biomembranes to membrane activity. Vesicle shapes are determined by minimizing the membrane elastic energy under constraints of constant area and constant volume, where classical results for freely suspended vesicles are expanded to a broader set of axisymmetric shapes revealing the action of point forces at the poles. Examples encompass, but are not limited to, spindle-like and tether-like configurations. The governing shape equation is solved numerically using a pseudo-spectral method to yield stationary shapes. Results of vesicle contours, bending energies, and stresses are presented as a function of the vesicle reduced volume and are organized in a bending energy diagram where solution paths originate from the classical prolate branch. Higher-energy shapes are driven by pressure and tension modulations as analogs to the mechanical response of biomembranes to external forces. We show that spindle-like contours occur for reduce volumes close to unity, and that multi-lobed contours are determined by the non-trivial balance between global stresses and localized forces. We further present a qualitative agreement between numerical results and recent experimental results conducted in our group using giant unilamellar vesicles in uniform electric fields.