Membrane elastic fluctuations and the insertion and tilt of β-barrel proteins

Folding of porin-like beta-barrel outer membrane proteins can be achieved in the presence of phospholipid vesicles, and takes place concurrently with incorporation into the membrane. The pronounced dependence found for the insertion of the protein OmpA on membrane thickness (Kleinschmidt, J. H., and L. K. Tamm. 2002. J. Mol. Biol. 324: 319-330) is analyzed in terms of the effects of out-of-plane elastic fluctuations on the area dilation modulus ( Evans, E., and W. Rawicz. 1990. Phys. Rev. Lett. 64: 2094 - 2097). For unstrained large unilamellar vesicles, the elastic free energy for membrane insertion is predicted to depend on the fourth power of the membrane thickness. The influence of thermally induced bending fluctuations on the effective tilt of the OmpA beta-barrel in disaturated phosphatidylcholine membranes of different thicknesses (Ramakrishnan, M., J. Qu, C. L. Pocanschi, J. H. Kleinschmidt, and D. Marsh. 2005. Biochemistry. 44: 3515 - 3523) is also considered. A contribution to the orientational order parameter that scales as the inverse second power of the membrane thickness is predicted.