This is part of the colvar module |
Calculate eRMSD with respect to a reference structure.
eRMSD is a metric developed for measuring distances between three-dimensional RNA structures. The standard RMSD measure is highly inaccurate when measuring distances among three-dimensional structures of nucleic acids. It is not unusual, for example, that two RNA structures with low RMSD (i.e. less than 0.4nm) display a completely different network of base-base interactions.
eRMSD measures the distance between structures by considering only the relative positions and orientations of nucleobases. The eRMSD can be considered as a vectorial version of contact maps and it is calculated as follows:
Calculate the G vectors
\[ \vec{G}(\tilde{\vec{r}}) = (\sin(\gamma \tilde{r}) \tilde{r}_x/\tilde{r},\sin(\gamma \tilde{r}) \tilde{r}_y/\tilde{r},\sin(\gamma \tilde{r}) \tilde{r}_z/\tilde{r}, 1+\cos(\gamma \tilde{r})) \times \frac{\Theta(\tilde{r}_{cutoff}-\tilde{r})}{\gamma} \]
Here, \( \gamma = \pi/\tilde{r}_{cutoff}\) and \( \Theta \) is the Heaviside step function. The default cutoff is set to 2.4.
The eRMSD between two structures \( \alpha \) and \( \beta \) reads
\[ eRMSD = \sqrt{\frac{1}{N} \sum_{j,k} \vert \vec{G}(\tilde{\vec{r}}_{jk}^{\alpha}) - \vec{G}(\tilde{\vec{r}}_{jk}^{\beta}) \vert^2 } \]
Using the default cutoff, two structures with eRMSD of 0.7 or lower can be considered as significantly similar. A full description of the eRMSD can be found in [22]
ERMSD is computed using the position of three atoms on the 6-membered ring of each involved nucleobase. The atoms should be:
The different order for purines and pyrimidines is fundamental and allows you to compute ERMSD between structures with different sequences as well! Notice that the simplest way to avoid mistakes in choosing these atoms is to use the @lcs-#
strings as shown in the examples (see also MOLINFO).
Calculate the eRMSD from reference structure reference.pdb using the default cutoff (2.4). The list of residues involved in the calculation has to be specified. In this example, the eRMSD is calculated considering residues 1,2,3,4,5,6.
#SETTINGS MOLFILE=regtest/basic/rt-ermsd/ref.pdb MOLINFOSTRUCTURE=reference.pdb eRMSD1: ERMSDcompulsory keyword a file in pdb format containing a reference structure.REFERENCE=reference.pdbcompulsory keyword a file in pdb format containing the reference structure and the atoms involved in the CV.ATOMS=@lcs-1,@lcs-2,@lcs-3,@lcs-4,@lcs-5,@lcs-6the list of atoms (use lcs).
ATOMS | the list of atoms (use lcs). For more information on how to specify lists of atoms see Groups and Virtual Atoms |
REFERENCE | a file in pdb format containing the reference structure and the atoms involved in the CV. |
CUTOFF | ( default=2.4 ) only pairs of atoms closer than CUTOFF are considered in the calculation. |
NUMERICAL_DERIVATIVES | ( default=off ) calculate the derivatives for these quantities numerically |
NOPBC | ( default=off ) ignore the periodic boundary conditions when calculating distances |
PAIRS | List of pairs considered. All pairs are considered if this value is not specified. |