||In a self-assembling
lipid bilayer the two monolayers will tend,
energetically, to have the same lipid composition, as
favored by the entropy of lipid distribution in the membrane.
The resulting bilayer will be completely symmetric
with respect to its mid plane, and, hence, there
will be no preferential direction for its curving. As a result,
the bilayer will acquire neither positive nor negative
curvature and adopt a flat shape. Moreover, this bilayer
will oppose curving by external forces with a resistance
quantified by a bending modulus k [Helfrich 1973 PMID 4273690 and Helfrich W: Elasticity and thermal undulations of fluid films of
amphiphiles. In Les Houches – 1988 – Liquids and Interfaces, vol.
48. Edited by Charvolin J, Joanny J-F, Zinn-Justin J. Elsevier
1990:212-237.]. The value of the
latter of about k ~10^-19 Joules sets the scale of energies
needed for bilayer bending.