Molecular theory of hydrophobic mismatch between lipids and peptides

Effects of the mismatch between the hydrophobic length d, of transmembrane alpha helices of integral proteins and the hydrophobic thickness, Dh, of the membranes they span are studied theoretically utilizing a microscopic model of lipids. In particular, we examine the dependence of the period of a lamellar phase on the hydrophobic length and volume fraction of a rigid, integral, peptide. We find that the period decreases when a short peptide, such that d<Dh, is inserted. More surprising, we find that the period increases when a long peptide, such that d>Dh, is inserted. The effect is due to the replacement of extensible lipid tails by rigid peptide. As the peptide length is increased, the lamellar period continues to increase, but at a slower rate, and can eventually decrease. The amount of peptide which fails to incorporate and span the membrane increases with the magnitude of the hydrophobic mismatch |d−Dh|. We explicate these behaviors which are all in accord with experiment. Predictions are made for the dependence of the tilt of a single trans-membrane alpha helix on hydrophobic mismatch and helix density.