In order to measure the alignment accuracy, we define a scoring function, PC-score, as follows:
PC-score = ∑Nali(0.45 / (1 + (di/d0)2) + 0.1 / (1 + (Δmi/Δm0)2) + 0.45 * BWJSi) / N
where Nali, di, Δmi, and BWJSi are the atom number of the aligned pairs, the distance between the i-th pair of the aligned pairs, the mass difference between the i-th pair of the aligned pairs, and the weighted Jaccard score of the bond stes of the i-th pair of the aligned pair. d0 and Δm0 are two corresponding scale to normalize the corresponding match difference. d0 = 0.55 * (min(Nq, Nt)-9)1/3 + 0.15. N can be the atom number of query ligand (Nq) or the atom number of template ligand (Nt). In LS-align, we will search the maximum of PC-score for each ligand pair.
Detail of PC-score in the manuscript : PDF (Coming soon).
Let Nq, Nt, and Nali be the atom numbers of query ligand, template ligand, and the aligned pairs, respectively. The equation of Jaccard Ratio as follows:
Jaccard Ratio = Nali / (Nq + Nt - Nali).
See also : Jaccard Index.
The classical RMSD can give a quantitative measure of similarity between two conformations of the same ligand. However, it could not normally work to evaluate the similarity between two different type ligands, whose atom numbers and types are different. Here, inspired by the definition of rmsd/lb in AutoDock vina, RMSDLS is provided to measure the similarity between two different type ligands. The definitions of rmsd/lb and RMSDLS are separately shown as follows:
rmsd/lb is defined as follows:
rmsd/lb(c1, c2) = max(rmsd'(c1, c2), rmsd'(c2, c1))
rmsd' is a function which matches each atom in one conformation with the closest atom of the same element type in the other conformation. Notice that
rmsd/lb is also proposed to measure of similarity between two conformations of the same ligand in AutoDock vina.
RMSDLS is defined as follows:
RMSDLS(lig1, lig2) = max(RMSD'(lig1, lig2), RMSD'(lig2, lig1))
RMSD' is a function which matches each atom in one ligand with the closest atom in the other ligand.
'Query Atom Index' means the heavy atom indexes of query ligand after removing all the hydrogen atoms and re-indexing the remaining heavy atoms.
'Templ Atom Index' means the heavy atom indexes of template ligand after removing all the hydrogen atoms and re-indexing the remaining heavy atoms.