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Spherical vesicles distorted by a grafted latex bead: an exact solution.

Jérôme Benoit¹, Avadh Saxena

¹Graduate Institute of Biophysics and Center for Complex Systems, National Central University, 300 Jhongda Road, Jhongli City, Taoyuan, Taiwan 320, Taiwan. jgmbenoit@mailsnare.net

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2007

Summary

We solved the global shape of a spherical vesicle with a grafted latex bead using advanced mathematical techniques. The study reveals that the bead causes the opposite side of the vesicle to flatten.

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Area of Science:

Biophysics
Theoretical Physics

Background:

Spherical vesicles are fundamental biological structures.
Understanding vesicle deformation is crucial for cell mechanics.

Purpose of the Study:

To provide an exact mathematical solution for the global shape of a spherical vesicle distorted by a grafted latex bead.
To analyze the effects of bending elasticity and elastic compatibility on vesicle morphology.

Main Methods:

Utilizing the (topological) Bogomol'nyi decomposition technique to handle nonlinear bending elasticity.
Applying elastic compatibility principles to derive the vesicle's shape.
Employing a variational principle and constraints to formulate the shape equation.

Main Results:

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An exact solution for the vesicle's global shape was obtained.
The "hat-model" approximation was recovered in the limit of a small latex bead.
It was found that the region antipodal to the grafted latex bead flattens.

Conclusions:

The study provides a rigorous mathematical framework for vesicle shape analysis.
The findings offer insights into the mechanical behavior of lipid bilayers under external stress.
This work contributes to the understanding of cell membrane dynamics and morphology.