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, D_h, 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<D_h, is inserted. More surprising, we find that the period increases when a long peptide, such that d>D_h, 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-D_h|. 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.