Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Robotics Research
Matrix computations (3rd ed.)
Estimating 3-D rigid body transformations: a comparison of four major algorithms
Machine Vision and Applications - Special issue on performance evaluation
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
Protein conformational flexibility analysis with noisy data
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
A Spectral Approach to Protein Structure Alignment
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Analysis of conformational changes is one of the keys to the understanding of protein functions and interactions. For the analysis, we often compare two protein structures, taking flexible regions like hinge regions into consideration. The Root Mean Square Deviation (RMSD) is the most popular measure for comparing two protein structures, but it is only for rigid structures without hinge regions. In this paper, we propose a new measure called RMSD considering hinges (RMSDh) and its variant {\rm RMSDh}^{(k)} for comparing two flexible proteins with hinge regions. We also propose novel efficient algorithms for computing them, which can detect the hinge positions at the same time. The RMSDh is suitable for cases where there is one small hinge region in each of the two target structures. The new algorithm for computing the RMSDh runs in linear time, which is the same as the time complexity for computing the RMSD and is faster than any of previous algorithms for hinge detection. The {\rm RMSDh}^{(k)} is designed for comparing structures with more than one hinge region. The {\rm RMSDh}^{(k)} measure considers at most k small hinge region, i.e., the {\rm RMSDh}^{(k)} value should be small if the two structures are similar except for at most k hinge regions. To compute the value, we propose an O(kn^{2})-time and O(n)-space algorithm based on a new dynamic programming technique. With the same computational time and space, we can enumerate the predicted hinge positions. We also test our algorithms against actual flexible protein structures, and show that the hinge positions can be correctly detected by our algorithms.