Section: New Results

FastRMS: rapid determination of RMSDs corresponding to macromolecular rigid body motions, adding flexibility via collective motions

Participants : Sergei Grudinin, Petr Popov, Emilie Neveu.

Computing the root mean sum of squared deviations (RMSDs) between two sets of coordinates each describing a different conformation of a macromolecule is a necessary step in many structural bioinformatics and molecular modelling technics to assess structural predictions [43] , identify biding sites [49] or structurally classify proteins. A straightforward and universally-used method determines the RMSD with a computational complexity proportional to the number of atoms in the molecule. We recently presented RigidRMSD, a fast algorithm that determines RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule [57] . Here, we extend it to proteins with flexibility modelled with collective motion such as an elastic network model combined with normal mode analysis.

With these new assumptions, the complexity of the algorithm depends linearly or quadratically with the number of collective motion vectors selected to approximate the flexibility. The typical number of vectors needed to have accurate flexible movements being much lower than the number of atoms composing the molecules, we prove our algorithm is still faster than the common method. Our algorithm is particularly useful for rigid body modelling applications such as rigid body docking procedures allowing for flexibility via collective motions: clustering, high-throughput analysis and simulation results [49] , [26] , [59] . A C++ implementation of our algorithm will be soon available at http://nano-d.inrialpes.fr/software/RigidRMSD.