A giant unilamellar vesicle has area modulus and bending modulus at (use )

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

A giant unilamellar vesicle has area modulus

K_A = 0.22\,\mathrm{N\,m^{-1}}

and bending modulus

\kappa = 22k_BT

298\,\mathrm{K}

(use

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

). The bilayer ruptures at an area strain of

3\%

. ((a)) Find the lysis tension

\sigma_{\rm lys}

. ((b)) Treating the vesicle as a sphere with zero spontaneous curvature, find its Helfrich bending energy, in units of

k_BT

and in joules. ((c)) If the membrane tension were raised to

\sigma_{\rm lys}

, find the crossover wavelength

2\pi/q^*

of the undulation spectrum, where

q^* = \sqrt{\sigma/\kappa}

, and state whether undulations longer than this wavelength are bending- or tension-dominated.

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