Two Complementary Methods for Relative Quantification of Ligand Binding Site Burial Depth in Proteins: The"Cutting Plane"and"Tangent Sphere"Methods

We describe two complementary methods to quantify the degree of burial of ligand and/or ligand binding site (LBS) in a protein-ligand complex, namely, the ‘cutting plane’ (CP) and the ‘tangent sphere’ (TS) methods. To construct the CP and TS, two centroids are required: the protein molecular centroid (global centroid, GC), and the LBS centroid (local centroid, LC). The CP is defined as the plane passing through the LBS centroid (LC) and normal to the line passing through the LC and the protein molecular centroid (GC). The “exterior side” of the CP is the side opposite GC. The TS is defined as the sphere with center at GC and tangent to the CP at LC. The percentage of protein atoms (a.) inside the TS, and (b.) on the exterior side of the CP, are two complementary measures of ligand or LBS burial depth since the latter is directly proportional to (b.) and inversely proportional to (a.). We tested the CP and TS methods using a test set of 67 well characterized protein-ligand structures (Laskowski et al., 1996), as well as the theoretical case of an artificial protein in the form of a cubic lattice grid of points in the overall shape of a sphere and in which LBS of any depth can be specified. Results from both the CP and TS methods agree very well with data reported by Laskowski et al., and results from the theoretical case further confirm that that both methods are suitable measures of ligand or LBS burial. Prior to this study, there were no such numerical measures of LBS burial available, and hence no way to directly and objectively compare LBS depths in different proteins. LBS burial depth is an important parameter as it is usually directly related to the amount of conformational change a protein undergoes upon ligand binding, and ability to quantify it could allow meaningful comparison of protein dynamics and flexibility. Abbreviations: CP, cutting plane; TS, tangent sphere; CPM, cutting plane method; TSM, tangent sphere method; CPi, CP or CPM index; TSi, TS or TSM index; LBS, ligand binding site; GC, global or molecular centroid; LC, local or LBS centroid; lig, ligand; res, residue; sdc, sidechain; PPI, proteinprotein-interaction/s; PLI, protein-ligand interaction/s; PLC, protein-ligand complex