RapidRMSD

We randomly generated flexible molecular docking poses for several molecules of a different size – on which we performed two clustering algorithms. Both algorithms use the same classification procedure but different ways to compute the RMSD: our approach is compared with the standard one.

Another application of our method is the generation of pseudo-random structural ensembles along a few lowest normal modes. These structural ensembles can be useful to mimic molecular fluctuations at a constant temperature, or be used in machine-learning applications to mimic non-native docking poses

Molecular flexibility is described with linear collective motions. Collective motions are a linear transformation of the original structure, more precisely a weighted sum of orthogonal vectors, computed with, e.g., PCA or NMA methods.

Using the rigid-body motion formalism extended with collective motions, we express the RMSD between two molecules according to the spatial transformation operators : rotation, translation and the amplitudes of the collective motion vectors set of vectors.

This allows for a reduced computational time:
The initialisation step computational cost is at worst linear with the number of atoms and  quadratic with the number of collective motion vectors. When one of the molecule is the rigid reference, it is linear with the number of atoms and linear with the number of collective motion vectors, whereas when the motion is purely flexible, this step costs nothing.
Then, each computation of RMSD takes at worst quadratic time with the number of collective motion vectors. When one of the molecule is the rigid reference or when the motions are purely flexible, it is linear with the number of collective motion vectors.