Statistical criteria for the identification of protein active sites using Theoretical Microscopic Titration Curves

Theoretical Microscopic Titration Curves (THEMATICS) may be used to identify chemically important residues in active sites of enzymes by characteristic deviations from the normal, sigmoidal Henderson-Hasselbalch titration behavior. Clusters of such deviant residues in physical proximity constitute reliable predictors of the location of the active site. Originally the residues with deviant predicted behavior were identified by human observation of the computed titration curves. However, it is preferable to select the unusual residues by mathematically well-defined criteria, in order to reduce the chance of error, eliminate any possible biases, and substantially speed up the selection process. Here we present some simple statistical tests that constitute such selection criteria. The first derivatives of the predicted titration curves resemble distribution functions and are normalized. The moments of these first derivative functions are computed. It is shown that the third and fourth moments, measures of asymmetry and kurtosis, respectively, are good measures of the deviations from normal behavior. Results are presented for 44 different enzymes. Detailed results are given for 4 enzymes with 4 different types of chemistry: arginine kinase from Limulus polyphemus (horseshoe crab); beta-lactamase from Escherichia coli; glutamate racemase from Aquifex pyrophilus; and 3-isopropylmalate dehydrogenase from Thiobacillus ferrooxidans. The relationship between the statistical measures of nonsigmoidal behavior in the predicted titration curves and the catalytic activity of the residue is discussed.