A section of bilayer membrane is pulled into a long cylindrical tube of radius and length

PHYSICS · Subjective · 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

A section of bilayer membrane is pulled into a long cylindrical tube of radius R=100 nmR = 100\,\mathrm{nm} and length L=10 μmL = 10\,\mu\mathrm{m}. Its bending modulus is κb=20kBT\kappa_{\rm b} = 20k_BT at T=298 KT = 298\,\mathrm{K}, and its spontaneous curvature is zero. The Helfrich energy density is f=12κb(c1+c2)2+κˉbc1c2f = \tfrac12\kappa_{\rm b}(c_1+c_2)^2 + \bar\kappa_{\rm b}c_1c_2, where c1,c2c_1,c_2 are the principal curvatures. For a cylinder, one principal curvature is c1=1/Rc_1 = 1/R and the other is c2=0c_2 = 0, so the Gaussian term vanishes. Calculate the total Helfrich bending energy of the tube, in units of kBTk_BT and in joules.

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