Two spherical lipid vesicles

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch The fluid membrane: bending, flicker and shape

Problem

Two spherical lipid vesicles, of radius

100\,\mathrm{nm}

and

500\,\mathrm{nm}

, are made from the same lipid with bending modulus

\kappa = 22\,k_BT

(

k_BT = 4.11\,\mathrm{pN\,nm}

298\,\mathrm{K}

) and zero spontaneous curvature. ((a)) Evaluate the Helfrich mean-curvature bending energy

E = 8\pi\kappa

of each vesicle, in

k_BT

and in joules. ((b)) Using Gauss-Bonnet, explain whether the Gaussian-curvature term

4\pi\kappa_G

contributes differently to the two vesicles' energies.

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