Elastic energy of polyhedral bilayer vesicles

Area of Science:

• Soft Matter Physics
• Materials Science
• Biophysics

Background:

• Recent experiments observed spontaneous formation of hollow bilayer vesicles with polyhedral symmetry.
• The prevailing hypothesis suggests vesicle formation is driven by the minimization of elastic bending energy.

Purpose of the Study:

• To investigate the elastic bending energy of polyhedral bilayer vesicles.
• To determine the energetic favorability of polyhedral versus spherical bilayer vesicles.
• To elucidate the role of molecular segregation and pore formation in vesicle stability.

Main Methods:

• Theoretical analysis of elastic bending energy in polyhedral bilayer vesicles.
• Comparison of bending energies for various polyhedral shapes (icosahedron, snub cube, snub dodecahedron).
• Consideration of amphiphile properties like spontaneous curvature and molecular segregation.

Main Results:

• Polyhedral bilayer vesicles are energetically favorable over spherical ones when excess amphiphiles with spontaneous curvature are present.
• Pore formation can locally reduce bending energy at vertices, consistent with experimental findings.
• Stabilization relies on molecular segregation along ridges, not vertices.
• The icosahedron does not minimize bending energy for all sizes; snub cube and snub dodecahedron are more favorable for large polyhedra.

Conclusions:

• Elastic bending energy minimization is a key factor in the formation and stability of polyhedral bilayer vesicles.
• Molecular segregation at ridges is crucial for stabilizing polyhedral shapes.
• Specific polyhedral geometries, like the snub cube and snub dodecahedron, offer lower bending energies than the icosahedron for large vesicles.