Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Petr Popov (1) , Sergei Grudinin (1)

1 NANO-D - Algorithms for Modeling and Simulation of Nanosystems

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of 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. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high-throughput analysis of rigid body modeling and simulation results. We also introduce a constant-time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano-d.inrialpes.fr/software/RigidRMSD.

Mots clés: MSD calculation; rigid body motion; quaternion arithmetic; structure comparison; spatial transformations

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Modélisation et simulation

Petr Popov, Sergei Grudinin. Rapid determination of RMSDs corresponding to macromolecular rigid body motions. Journal of Computational Chemistry, 2014, 35 (12), pp.950-956. ⟨10.1002/jcc.23569⟩. ⟨hal-00952248⟩