Interstrand pairing patterns in $\beta$-barrel membrane proteins: the positive-outside rule, aromatic rescue, and strand registration prediction
$\beta$-barrel membrane proteins are found in the outer membrane of gram-negative bacteria, mitochondria, and chloroplasts. We have developed probabilistic models to quantify propensities of residues for different spatial locations and for interstrand pairwise contact interactions involving strong H-bonds, side-chain interactions, and weak H-bonds. The propensity values and p-values measuring statistical significance are calculated exactly by analytical formulae we have developed. Contrary to the ``positive-inside'' rule for helical membrane proteins, $\beta$-barrel membrane proteins follow a significant albeit weaker ``positive-outside'' rule, in that the basic residues Arg and Lys are disproportionately favored in the extracellular cap region and disfavored in the periplasmic cap region. Different residue pairs prefer strong backbone H-bonded interstrand pairings (e.g. Gly-Aromatic) or non-H-bonded pairings (e.g. Aromatic-Aromatic). In addition, Tyr and Phe participate in aromatic rescue by shielding Gly from polar environments. These propensities can be used to predict the registration of strand pairs, an important task for the structure prediction of $\beta$-barrel membrane proteins. Our accuracy of 44% is considerably better than random (7%) and other studies. Our results imply several experiments that can help to elucidate the mechanisms of in vitro and in vivo folding of $\beta$-barrel membrane proteins. See supplementary material after the bibliography for detailed techniques.