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We describe two complementary methods to quantify the degree of burial ofligand and/or ligand binding site (LBS) in a protein-ligand complex, namely,the "cutting plane" (CP) and the "tangent sphere" (TS) methods. To constructthe CP and TS, two centroids are required: the protein molecular centroid(global centroid, GC), and the LBS centroid (local centroid, LC). The CP isdefined as the plane passing through the LBS centroid (LC) and normal to theline passing through the LC and the protein molecular centroid (GC). The"anterior side" of the CP is the side not containing the GC (which the"posterior" side does). The TS is defined as the sphere with center at GC andtangent to the CP at LC. The percentage of protein atoms (a.) inside the TS,and (b.) on the anterior side of the CP, are two complementary measures ofligand 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 atest 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 ofa cubic lattice grid of points in the overall shape of a sphere and in whichLBS of any depth can be specified. Results from both the CP and TS methodsagree very well with data reported by Laskowski et al., and results from thetheoretical case further confirm that that both methods are suitable measuresof ligand or LBS burial. Prior to this study, there were no such numericalmeasures of LBS burial available, and hence no way to directly and objectivelycompare LBS depths in different proteins. LBS burial depth is an importantparameter as it is usually directly related to the amount of conformationalchange a protein undergoes upon ligand binding, and ability to quantify itcould allow meaningful comparison of protein dynamics and flexibility.

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