Prediction of recursive convex hull class assignments for protein residues

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We introduce a new method for designating the location of residues in folded protein structures based on the recursive convex hull (RCH) of a point set of atomic coordinates. The RCH can be calculated with an efficient and parameterless algorithm. We show that residue RCH class contains information complementary to widely studied measures such as solvent accessibility (SA), residue depth (RD) and to the distance of residues from the centroid of the chain, the residues' exposure (Exp). RCH is more conserved for related structures across folds and correlates better with changes in thermal stability of mutants than the other measures. Further, we assess the predictability of these measures using three types of machine-learning technique: decision trees (C4.5), Naive Bayes and Learning Classifier Systems (LCS) showing that RCH is more easily predicted than the other measures. As an exemplar application of predicted RCH class (in combination with other measures), we show that RCH is potentially helpful in improving prediction of residue contact numbers (CN).