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Open Access Highly Accessed Technical Note

GPU-Q-J, a fast method for calculating root mean square deviation (RMSD) after optimal superposition

Ling-Hong Hung, Michal Guerquin and Ram Samudrala*

Author Affiliations

Department of Microbiology, University of Washington, Seattle WA USA

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BMC Research Notes 2011, 4:97  doi:10.1186/1756-0500-4-97

Published: 1 April 2011



Calculation of the root mean square deviation (RMSD) between the atomic coordinates of two optimally superposed structures is a basic component of structural comparison techniques. We describe a quaternion based method, GPU-Q-J, that is stable with single precision calculations and suitable for graphics processor units (GPUs). The application was implemented on an ATI 4770 graphics card in C/C++ and Brook+ in Linux where it was 260 to 760 times faster than existing unoptimized CPU methods. Source code is available from the Compbio website webcite or from the author LHH.


The Nutritious Rice for the World Project (NRW) on World Community Grid predicted de novo, the structures of over 62,000 small proteins and protein domains returning a total of 10 billion candidate structures. Clustering ensembles of structures on this scale requires calculation of large similarity matrices consisting of RMSDs between each pair of structures in the set. As a real-world test, we calculated the matrices for 6 different ensembles from NRW. The GPU method was 260 times faster that the fastest existing CPU based method and over 500 times faster than the method that had been previously used.


GPU-Q-J is a significant advance over previous CPU methods. It relieves a major bottleneck in the clustering of large numbers of structures for NRW. It also has applications in structure comparison methods that involve multiple superposition and RMSD determination steps, particularly when such methods are applied on a proteome and genome wide scale.