E(z), a depth-dependent potential for assessing the energies of insertion of amino acid side-chains into membranes: derivation and applications to determining the orientation of transmembrane and interfacial helices.

We have developed an empirical residue-based potential (E(z) potential) for protein insertion in lipid membranes. Propensities for occurrence as a function of depth in the bilayer were calculated for the individual amino acid types from their distribution in known structures of helical membrane proteins. The propensities were then fit to continuous curves and converted to a potential using a reverse-Boltzman relationship. The E(z) potential demonstrated a good correlation with experimental data such as amino acid transfer free energy scales (water to membrane center and water to interface), and it incorporates transmembrane helices of varying composition in the membrane with trends similar to those obtained with translocon-mediated insertion experiments. The potential has a variety of applications in the analysis of natural membrane proteins as well as in the design of new ones. It can help in calculating the propensity of single helices to insert in the bilayer and estimate their tilt angle with respect to the bilayer normal. It can be utilized to discriminate amphiphilic helices that assume a parallel orientation at the membrane interface, such as those of membrane-active peptides. In membrane protein design applications, the potential allows an environment-dependent selection of amino acid identities.