DRMSD

This is part of the colvar module |

Calculate the distance RMSD with respect to a reference structure.

To calculate the root-mean-square deviation between the atoms in two configurations you must first superimpose the two structures in some ways. Obviously, it is the internal vibrational motions of the structure - i.e. not the translations and rotations - that are interesting. However, aligning two structures by removing the translational and rotational motions is not easy. Furthermore, in some cases there can be alignment issues caused by so-called frame-fitting problems. It is thus often cheaper and easier to calculate the distances between all the pairs of atoms. The distance between the two structures, \(\mathbf{X}^a\) and \(\mathbf{X}^b\) can then be measured as:

\[ d(\mathbf{X}^A, \mathbf{X}^B) = \sqrt{\frac{1}{N(N-1)} \sum_{i \ne j} [ d(\mathbf{x}_i^a,\mathbf{x}_j^a) - d(\mathbf{x}_i^b,\mathbf{x}_j^b) ]^2} \]

where \(N\) is the number of atoms and \(d(\mathbf{x}_i,\mathbf{x}_j)\) represents the distance between atoms \(i\) and \(j\). Clearly, this representation of the configuration is invariant to translation and rotation. However, it can become expensive to calculate when the number of atoms is large. This can be resolved within the DRMSD colvar by setting LOWER_CUTOFF and UPPER_CUTOFF. These keywords ensure that only pairs of atoms that are within a certain range are incorporated into the above sum.

In PDB files the atomic coordinates and box lengths should be in Angstroms unless you are working with natural units. If you are working with natural units then the coordinates should be in your natural length unit. For more details on the PDB file format visit http://www.wwpdb.org/docs.html

- Compulsory keywords

REFERENCE | a file in pdb format containing the reference structure and the atoms involved in the CV. |

LOWER_CUTOFF | only pairs of atoms further than LOWER_CUTOFF are considered in the calculation. |

UPPER_CUTOFF | only pairs of atoms closer than UPPER_CUTOFF are considered in the calculation. |

TYPE | ( default=DRMSD ) what kind of DRMSD would you like to calculate. You can use either the normal DRMSD involving all the distances between the atoms in your molecule. Alternatively, if you have multiple molecules you can use the type INTER-DRMSD to compute DRMSD values involving only those distances between the atoms at least two molecules or the type INTRA-DRMSD to compute DRMSD values involving only those distances between atoms in the same molecule |

- Options

NUMERICAL_DERIVATIVES | ( default=off ) calculate the derivatives for these quantities numerically |

NOPBC | ( default=off ) ignore the periodic boundary conditions when calculating distances |

- Examples

The following tells plumed to calculate the distance RMSD between the positions of the atoms in the reference file and their instantaneous position. Only pairs of atoms whose distance in the reference structure is within 0.1 and 0.8 nm are considered.

DRMSD REFERENCE=file.pdb LOWER_CUTOFF=0.1 UPPER_CUTOFF=0.8

The following tells plumed to calculate a DRMSD value for a pair of molecules.

DRMSD REFERENCE=file.pdb LOWER_CUTOFF=0.1 UPPER_CUTOFF=0.8 TYPE=INTER-DRMSD

In the input reference file (file.pdb) the atoms in each of the two molecules are separated by a TER command as shown below.

ATOM 8 HT3 ALA 2 -1.480 -1.560 1.212 1.00 1.00 DIA H ATOM 9 CAY ALA 2 -0.096 2.144 -0.669 1.00 1.00 DIA C ATOM 10 HY1 ALA 2 0.871 2.385 -0.588 1.00 1.00 DIA H TER ATOM 12 HY3 ALA 2 -0.520 2.679 -1.400 1.00 1.00 DIA H ATOM 14 OY ALA 2 -1.139 0.931 -0.973 1.00 1.00 DIA O END

In this example the INTER-DRMSD type ensures that the set of distances from which the final quantity is computed involve one atom from each of the two molecules. If this is replaced by INTRA-DRMSD then only those distances involving pairs of atoms that are both in the same molecule are computed.