Quasi‐harmonic method for studying very low frequency modes in proteins

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Abstract
A quasi‐harmonic approximation is described for studying very low frequency vibrations and flexible paths in proteins. The force constants of the empirical potential function are quadratic approximations to the potentials of mean force; they are evaluated from a molecular dynamics simulation of a protein based on a detailed anharmonic potential. The method is used to identify very low frequency (∼1 cm−1) normal modes for the protein pancreatic trypsin inhibitor. A simplified model for the protein is used, for which each residue is represented by a single interaction center. The quasi‐harmonic force constants of the virtual internal coordinates are evaluated and the normal‐mode frequencies and eigenvectors are obtained. Conformations corresponding to distortions along selected low‐frequency modes are analyzed.