Heterogeneous vesicles: an analytical approach to equilibrium shapes

Area of Science:

• Soft Matter Physics
• Biophysics
• Materials Science

Background:

• Heterogeneous vesicles and capsules exhibit complex equilibrium shapes.
• Understanding these shapes is crucial for biological and synthetic systems.
• Previous studies relied heavily on numerical simulations.

Purpose of the Study:

• To develop an analytical model for predicting equilibrium shapes of two-component heterogeneous vesicles.
• To investigate shape transitions between spherical and polyhedral states.
• To identify key parameters influencing vesicle morphology.

Main Methods:

• Utilized a free energy functional incorporating bending energies and line tension.
• Analyzed shape transitions across varying relative area fraction, bending modulus ratio, and line tension.
• Compared energies of regular, semiregular, and prismatic polyhedra.

Main Results:

• Identified a robust region favoring polyhedral shapes under weak line tension and large bending modulus ratio.
• Demonstrated fragmentation into two components at high line tension.
• Found that non-Platonic polyhedra (Archimedean, prismatic) can be energetically optimal.
• Determined that lowest energy polyhedra are three-fold coordinated.

Conclusions:

• The analytical model accurately predicts heterogeneous vesicle shapes.
• Provides a framework for estimating physical properties of vesicle components.
• Offers insights into the non-intuitive nature of optimal vesicle morphology.