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Can Conformational Change Be Described by Only a Few Normal Modes?

Paula Petrone ^* and Vijay S. Pande ^* 

^* Departments of Biophysics and Chemistry, Stanford University, Stanford, California

Correspondence: Address reprint requests to Vijay S. Pande, Dept. of Biophysics, Stanford University, Stanford, CA 94305-5080. E-mail: pande{at}stanford.edu.

We suggest a simple method to assess how many normal modes are needed to map a conformational change. By projecting the conformational change onto a subspace of the normal-mode vectors and using root mean square deviation as a test of accuracy, we find that the first 20 modes only contribute 50% or less of the total conformational change in four test cases (myosin, calmodulin, NtrC, and hemoglobin). In some allosteric systems, like the molecular switch NtrC, the conformational change is localized to a limited number of residues. We find that many more modes are necessary to accurately map this collective displacement. In addition, the normal-mode "spectra" can provide useful information about the details of the conformational change, especially when comparing structures with different bound ligands, in this case, calmodulin. Indeed, this approach presents normal-mode analysis as a useful basis in which to capture the mechanism of conformational change, and shows that the number of normal modes needed to capture the essential collective motions of atoms should be chosen according to the required accuracy.

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