Action: ERMSD

Module	colvar
Description	Usage
Calculate eRMSD with respect to a reference structure.
output value	type
the eRMSD between the instantaneous structure and the reference structure that was input	scalar

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Further details and examples

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:

1. Set up a local reference system in the center of the six-membered ring of each nucleobase in a molecule. The xy plane lies on the plane of the nucleobase, and it is oriented such that the Watson-Crick interaction is always at $\theta\approx 60^{\circ}$.

2. Calculate all pairwise distance vectors $\vec{r}_{i,j}$ among base centers.

3. Rescale distance vectors as $\tilde{\vec{r}}_{i,j}=(r_x/a,r_y/a,r_z/b)$, where a=b=5 Angstrom, c=3 Angstrom. This rescaling has the effect of weighting more deviations on the z-axis with respect to the x/y directions.

4. 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.

1. 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 the first paper in the bibliography below.

ERMSD is computed using the position of three atoms on the 6-membered ring of each involved nucleobase. The atoms should be: - C2,C4,C6 for pyrimdines - C2,C6,C4 for purines

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).

[!CAUTION] Notice that the ERMSD implemented here is not integrated with the other metrics in plumed. As a consequence, it is not (yet) possible to e.g. build path collective variables using ERMSD

[!CAUTION] Notice that ERMSD expect a single molecule and makes coordinates whole before anything else. As such, results might be unexpected for a multi molecular system.

Examples

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.

Click on the labels of the actions for more information on what each action computes

#SETTINGS MOLFILE=regtest/basic/rt-ermsd/ref.pdb
MOLINFOThis command is used to provide information on the molecules that are present in your system. More details STRUCTUREa file in pdb format containing a reference structure=
regtest/basic/rt-ermsd/ref.pdb
 Click here to see an extract from this file.
  
  ×  
FILE: regtest/basic/rt-ermsd/ref.pdb
    
REMARK    GENERATED BY TRJCONV
TITLE     add Villa in water t=   0.00000
REMARK    THIS IS A SIMULATION BOX
CRYST1   79.904   79.904   79.904  60.00  60.00  90.00 P 1           1
MODEL        1
...
ATOM   2255 2HO' RG3    71      23.000  58.930  29.250  1.00  0.00            
ATOM   2256  O3' RG3    71      21.250  59.670  32.300  1.00  0.00            
ATOM   2257  H3T RG3    71      21.130  59.570  31.350  1.00  0.00            
TER
ENDMDL
  
The MOLINFO action with label  calculates somethingeRMSD1The ERMSD action with label eRMSD1 calculates the following quantities:
 Quantity   
 Type   
 Description  
eRMSD1
scalar
the eRMSD between the instantaneous structure and the reference structure that was input: ERMSDCalculate eRMSD with respect to a reference structure. This action has hidden defaults. More details REFERENCEa file in pdb format containing the reference structure and the atoms involved in the CV=
regtest/basic/rt-ermsd/ref.pdb
 Click here to see an extract from this file.
  
  ×  
FILE: regtest/basic/rt-ermsd/ref.pdb
    
REMARK    GENERATED BY TRJCONV
TITLE     add Villa in water t=   0.00000
REMARK    THIS IS A SIMULATION BOX
CRYST1   79.904   79.904   79.904  60.00  60.00  90.00 P 1           1
MODEL        1
...
ATOM   2255 2HO' RG3    71      23.000  58.930  29.250  1.00  0.00            
ATOM   2256  O3' RG3    71      21.250  59.670  32.300  1.00  0.00            
ATOM   2257  H3T RG3    71      21.130  59.570  31.350  1.00  0.00            
TER
ENDMDL
  
 ATOMSthe list of atoms (use lcs)=@lcs-1an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 1. Click here for more information. ,@lcs-2an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 2. Click here for more information. ,@lcs-3an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 3. Click here for more information. ,@lcs-4an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 4. Click here for more information. ,@lcs-5an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 5. Click here for more information. ,@lcs-6an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 6. Click here for more information. 
eRMSD1: ERMSDCalculate eRMSD with respect to a reference structure. This action uses the defaults shown here. More details REFERENCEa file in pdb format containing the reference structure and the atoms involved in the CV=
regtest/basic/rt-ermsd/ref.pdb
 Click here to see an extract from this file.
  
  ×  
FILE: regtest/basic/rt-ermsd/ref.pdb
    
REMARK    GENERATED BY TRJCONV
TITLE     add Villa in water t=   0.00000
REMARK    THIS IS A SIMULATION BOX
CRYST1   79.904   79.904   79.904  60.00  60.00  90.00 P 1           1
MODEL        1
...
ATOM   2255 2HO' RG3    71      23.000  58.930  29.250  1.00  0.00            
ATOM   2256  O3' RG3    71      21.250  59.670  32.300  1.00  0.00            
ATOM   2257  H3T RG3    71      21.130  59.570  31.350  1.00  0.00            
TER
ENDMDL
  
 ATOMSthe list of atoms (use lcs)=@lcs-1an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 1. Click here for more information. ,@lcs-2an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 2. Click here for more information. ,@lcs-3an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 3. Click here for more information. ,@lcs-4an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 4. Click here for more information. ,@lcs-5an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 5. Click here for more information. ,@lcs-6an ordered triplet of atoms on the 6-membered ring of the nucleobase in residue 6. Click here for more information.   CUTOFF only pairs of atoms closer than CUTOFF are considered in the calculation=2.4

References

More information about how this action can be used is available in the following articles: - S. Bottaro, F. Di Palma, G. Bussi, The role of nucleobase interactions in RNA structure and dynamics. Nucleic Acids Research. 42, 13306–13314 (2014)

Syntax

The following table describes the keywords and options that can be used with this action