ERMSD

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:

- 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 \( \theta \approx 60^{\circ} \).
- Calculate all pairwise distance vectors \( \vec{r}_{i,j} \) among base centers.
- Rescale distance vectors as \( \tilde{\vec{r}}_{i,j} = (r_x/a,r_y/a,r_z/b) \), where a=b=5 , c= 3 . This rescaling has the effect of weghting more deviations on the z-axis with respect to the x/y directions.
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 [13]

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).

- Warning
- 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
- Notice that ERMSD expect a single molecule and makes coordinate whole before anything else. As such, results might be unexpected for a multi molecular system.

- The atoms involved can be specified using

ATOMS | the list of atoms (use lcs). For more information on how to specify lists of atoms see Groups and Virtual Atoms |

- Compulsory keywords

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. |

- Options

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. |

- 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.

MOLINFO STRUCTURE=reference.pdb eRMSD1: ERMSD REFERENCE=reference.pdb ATOMS=@lcs-1,@lcs-2,@lcs-3,@lcs-4,@lcs-5,@lcs-6