Root-Mean-Square Deviation (RMSD)

One of the aspects evaluated in docking programs is the accuracy of the generated geometry (Jain, 2008). Docking programs attempt to reproduce the conformation of the ligand-receptor complex in a crystallographic structure. The metric root-mean-square deviation (RMSD) of atomic coordinates after the ideal superposition of rigid bodies of two structures is popular. Its popularity is because it allows the quantification of the differences between two structures, and these can be structures with the same and different amino acid sequences (Sargsyan et al., 2017). RMSD is widely used to evaluate the quality of a docking process performed by a program (Ding et al., 2016). The RMSD between two structures can be calculated according to the following equation (Sargsyan et al., 2017):

where d is the distance between atom i in the two structures and N is the total number of equivalent atoms. Since the calculation of RMSD requires the same number of atoms in both structures, it is often used in the calculation of only the heavy atoms or backbone of each amino acid residue.

Using the RMSD calculation, it is possible to evaluate if a program was able to reliably reproduce a known crystallographic conformation, as well as their respective intramolecular interactions. To verify if a given program can accomplish this task, ligand-targets complexes are subjected to a redocking process. After redocking, the overlap of the crystallographic ligand with the conformation of the ligand obtained with the docking program is then performed. Then, the RMSD calculation is used to check the average distance between the corresponding atoms (usually backbone atoms).

Generally, the RMSD threshold value is 2.0 Å (Jain, 2008; Meier et al., 2010; Gowthaman et al., 2015). However, for ligands with several dihedral angles, an RMSD value of 2.5 Å is considered acceptable (De Magalhães et al., 2004). In the case of binding a large ligand, some authors generally relax this criterion (Méndez et al., 2003; Verschueren et al., 2013). For a model generated by homology modeling, evaluating the RMSD value is important, although visual inspection of the generated model is also essential.

However, RMSD has some important limitations:

RMSD can only compare structures with the same number of atoms;

A small perturbation in just one part of the structure can create large RMSD values, suggesting that the two structures are very different, although they are not (Carugo, 2007);

It has also been observed that RMSD values depend on the resolution of structures that are compared (Carugo, 2003);

RMSD does not distinguish between a structure with some very rigid regions and some very flexible regions from a molecule in which all regions are semiflexible (Sargsyan et al., 2017);

Comparing the RMSD value of large structures may be significantly distorted from the commonly used 2Å threshold (Méndez et al., 2003). Despite these limitations, RMSD remains one of the most commonly used metrics to quantify differences between structures (Sargsyan et al., 2017).

Figure 7 shows the visualization of the FCP ligand superposed with its conformation after redocking to a protein (PDB ID: 1VZK, A Thiophene Based Diamidine Forms a “Super” AT Binding Minor Groove Agent). The RMSD between the crystallographic ligand and the same ligand after the redocking using DOCK6 is 0.97 Å. In the figure below, red represents the crystallographic ligand FCP and yellow represents FCP ligand after redocking using DOCK 6.

RMSD between the ligand FCP with a protein (PDB ID: 1VZK) after redocking using DOCK6.