Implementation of the Tangent Sphere and Cutting Plane Methods in the Quantitative Determination of Ligand Binding Site Burial Depths in Proteins Using FORTRAN 77/90 Language

Ligand burial depth is an indicator of protein flexibility, as the extent of receptor conformational change required to bind a ligand in general varies directly with its depth of burial. In a companion paper (Reyes, V.M. 2015a), we report on the Tangent Sphere (TS) and Cutting Plane (CP) methods -- complementary methods to quantify, independent of protein size, the degree of ligand burial in a protein receptor. In this report, we present results that demonstrate the effectiveness of a set of FORTRAN 77 and 90 source codes used in the implementation of the two related procedures, as well as the precise implementation of the procedures. Particularly, we show here that application of the TS and CP methods on a theoretical model protein in the form of a spherical grid of points accurately portrays the behavior of the TS and CP indices, the predictive parameters obtained from the two methods. We also show that results of the implementation of the TS and CP methods on six protein receptors (Laskowski et al. 1996) are inagreement with their findings regarding cavity sizes in these proteins. The six FORTRAN programs we present here are: find_molec_centr.f, tangent_sphere.f, find_CP_coeffs.f, CPM_Neg_Side.f, CPM_Pos_Side.f and CPM_Zero_Side.f. The first program calculates the x-, y- and z-coordinates of the molecular geometric centroid of the protein (global centroid, GC), the center of the TS. Its radius is the distance between the GC and the local centroid (LC), the centroid of the bound ligand or a portion of its binding site. The second program finds the number of protein atoms inside, outside and on the TS. The third determines the four coefficients A, B, C and D of the equation of the CP, Ax + By + Cz + D = 0. The CP is tangent to the TS at GC. The fourth, fifth and sixth programs determine the number of protein atoms lying on the negative side, positive side, and on the CP.