Solid angle to the unit sphere with center P, which can be calculated as the surface integral: where formula_5 is the unit vector corresponding to formula_6, the position vector of an infinitesimal area of surface with respect to point P, and where formula_7 represents the unit normal vector to . Even if the projection on the unit sphere to the surface S is not isomorphic, the multiple folds are correctly considered according to the surface orientation described by the sign of the scalar product formula_8. Thus one can approximate the solid angle subtended by a small facet having flat surface area ,
Volume Area Dihedral Angle Reporter is calculated by dividing a given residue’s observed accessible surface areas by the calculated accessible surface areas for that residue in an extended Gly-Xaa-Gly tripeptide (where Xaa is the residue of interest). VADAR reports accessible surface are values both for the entire amino acid residue and for the amino acid side chains. The accessible surface areas is also calculated for charged atoms (N, O), polar (N, O, S) atoms and for non-polar atoms (C). This information can be used to calculate charged, polar and non-polar surface area. Accessible surface areas measurements/estimates are particularly useful in protein structure assessment, protein structure