Lateral interactions among membrane proteins. Valid estimates based on freeze-fracture electron microscopy

We consider the lateral distribution of intrinsic membrane proteins from the viewpoint of the statistical-mechanical theory of liquids. We connect the information in freeze-fracture electron micrographs--positions of proteins but not lipids or aqueous species--to a well developed theory of liquid mixtures. An algorithm, based on the Born-Green-Yvon integral equation, is presented for deducing forces between proteins from correlations among protein positions that are observed in micrographs. The algorithm is tested on simulated micrographs, obtained by Monte-Carlo methods, where forces between proteins are known analytically. We conclude that valid estimates of such forces, both attractions and repulsions, can be obtained from the positions of a few thousand proteins.