DRMSD

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:

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

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.

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

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