Amphiphiles and self-assembly (Chapter 9) found that a flat bilayer disc has an…

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

Soft Matter at the Thermal Scale, Ch Membranes, fluctuations and soft matter in biology

Problem

Amphiphiles and self-assembly (Chapter 9) found that a flat bilayer disc has an exposed hydrophobic rim whose line tension, read from pores opened in real bilayers, is Λ≈10 pN\Lambda \approx 10\,\mathrm{pN} for a typical phospholipid. Take T=298 KT=298\,\mathrm{K}, kBT=4.11×10−21 Jk_BT = 4.11\times10^{-21}\,\mathrm{J}, and a bending modulus κb=15kBT\kappa_b = 15k_BT. ((a)) Find the disc radius R∗R^* at which closing into a vesicle becomes favourable if the Gaussian modulus is κˉb=0\bar\kappa_b = 0. ((b)) Find R∗R^* if instead κˉb=−κb\bar\kappa_b = -\kappa_b.

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