Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations

Abstract

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model.

Shape equilibria of vesicles with rigid planar inclusions

“…Applying this result to the shape equation, eqn (6), in the hinge region, we expect that P ( 2 SH s max ð Þ since H(s max ) E k hinge c H(0) C 1/R, suggesting that mechanically equilibrium in the hinge results from a balance of tension and bending terms, that is…”

“…The apparent separation of scales between the highcurvature ''hinge'' at the planar edge and the nearly spherical ''bulb'' that describes the bulk shape of the fluid phase suggest the following asymptotic analysis of shape equilibrium in the nearly isoperimetric limit. First, consideration of the shape equation, eqn (6), in the nearly uniform spherical bulb implies the standard equilibrium condition, P À 2SH(s = 0) E 0, effectively the Young-Laplace condition…”

“…4,5 Recent work shows that these distinct equilibria exhibit vastly different responses to shape perturbation upon localized forcing. 6 The possibilities for symmetry breaking are far more complex for inhomogeneous vesicles. 7 This includes fluid-fluid phase-separated vesicles, where mechanical properties (e.g.…”