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Normal mode analysis of protein dynamics in a non-Eckart frame.

Normal mode analysis, with the all-atom or coarse-grained elastic network model, represents the equilibrium fluctuation of protein molecule in the Eckart frame, where contributions from external motions (translation and rotation) of the entire protein molecule are eliminated. On the other hand, domain motion is frequently exhibited by the relative motion of one domain to the other. Such a representation of fluctuations in the non-Eckart frame cannot be achieved by conventional normal mode analysis. Here, we propose normal mode analysis in a non-Eckart frame, where the external degrees of freedom are fixed for any portion of the system. In this analysis, the covariance matrix in the Eckart frame is transformed into one in the non-Eckart frame. Using a molecular dynamics simulation, we have confirmed the validity of the transformation formula and discussed the physical implication of the formula.