Charge Density in Enzyme Active Site as a Descriptor of Electrostatic Preorganization

Large protein macromolecules in enzymatic catalysis have been shown to exert a specific electric field that reduces the reorganization energy upon barrier crossing and thus reduces the reaction free energy barrier. In this work we suggest that the charge density in the active site of an enzyme investigated using formalisms embodied by the quantum theory of atoms in molecules (QTAIM) provides a sensitive and quantum mechanically rigorous probe of electrostatic preorganization. We focus on the active site of ketosteroid isomerase, a well-studied enzyme for which electrostatic preorganization has been modeled theoretically and studied experimentally. We study the charge density in the active site and the reaction mechanism in the presence of small external electric fields of various directions and magnitudes. We show that the geometry of the full charge density is a sensitive reporter on the external field experienced by the active site. Changes are observed in the relative positions of critical points and amount of charge at critical points as a function of the field. At the same time, a subset of these features correlates linearly with the barrier of the first reaction step in catalysis. Small changes in the barrier, within 1-2 kcal/mol, are reflected in the charge density, suggesting the existence of a field - reactant state charge density - reaction barrier correlation. Hence, QTAIM can be used for the analysis of electric field in enzyme active sites, and further investigations and exploitations of the found correlations may prove useful in enzyme design where preorganization is optimized.