Normal modes of low-frequency vibrations are calculated for a small globular protein, bovine pancreatic trypsin inhibitor. In modes with frequencies below 120 cm-' the protein molecule behaves like a continuous elastic body. Most modes with frequencies above 50 cm-' are shown to behave harmonically within the range of thermal fluctuations at room temperature. Those with frequencies below 50 cm-' show some anharmonicity. Magnitudes of displacements of atoms are mainly determined by the modes with frequencies below 30 cm-'. These very-low-frequency modes contribute significantly to the entropy of the system. The dynamic structure of the globular protein is described as a superposition of harmonic high-frequency motions and coupled anharmonic lowfrequency motions of collective variables corresponding to the normal modes of vibration.

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SynopsisA powerful Monte Carlo method is described to simulate thermal conformational fluctuations in native proteins by using an empirical conformational energy function in which bond lengths and bond angles are kept fixed and only dihedral angles are independent variables. In this method, collective variables corresponding to eigenvectors of the secondderivative matrix of the energy function at its minimum point are scaled according to corresponding eigenvalues in such a way that the energy function in terms of the scaled collective variables is isotropic a t the minimum point. Simulation is carried out with an isotropic step size in the space of these scaled collective variables. This simulation method is applied to a small protein, bovine pancreatic trypsin inhibitor (BPTI), and its model harmonic system defined by a quadratic energy function with the same second-derivative matrix as that of BPTI at its minimum point. Efficiency of the simulation method with an isotropic step size in the space of the scaled collective variables is found to be about 5 W 50 times greater than the conventional method with with an isotropic step in the space of the usual nonscaled variables. One step of this new method generates conformational changes that occur in the real-time range of 0.05 ps. In a record of 5 X lo5 step simulation, the BPTI molecule is observed to migrate beyond a single minimum-energy region.

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