General neck condition for the limit shape of budding vesicles.

Area of Science:

• Membrane biophysics
• Soft matter physics
• Cell biology

Background:

• Vesicle budding is a fundamental process in cell biology.
• Understanding the shape and dynamics of budding vesicles is crucial for cellular functions.
• Previous conjectures on neck conditions for vesicle shapes require further validation.

Purpose of the Study:

• To derive the shape equation and linking conditions for a two-phase domain vesicle.
• To refine and rigorously prove the general neck condition for the limit shape of budding vesicles.
• To extend the validity of the neck condition to asymmetric budding vesicles.

Main Methods:

• Derivation of the shape equation for a two-phase domain vesicle.
• Formulation of linking conditions for vesicle budding.
• Mathematical proof using derived equations to validate the general neck condition.

Main Results:

• The shape equation and linking conditions for a two-phase domain vesicle were successfully derived.
• The conjecture on the general neck condition for budding vesicles was refined and proven.
• The neck condition was shown to hold for both axisymmetric and asymmetric budding vesicles.

Conclusions:

• The general neck condition for the limit shape of budding vesicles is validated for both axisymmetric and asymmetric cases.
• Mean curvature of membrane segments adjacent to the neck satisfies the neck condition under specific length scale conditions.
• This work provides a robust theoretical framework for understanding vesicle morphology during budding.