Shape of the conformational energy surface near the global minimum and low-frequency vibrations in the native conformation of globular proteins

Based on the assumption that the conformational energy surface of a protein molecule can be approximated near the global minimum point by a multidimensional parabola, conformational fluctuations in the native state are discussed. In this approximation the conformational fluctuations can be viewed as excitations of coupled harmonic oscillations of dihedral angles. For the purpose of estimating the range of frequencies vibrations, globular proteins are assumed to made of homogeneous continuous elastic material. The number of vibrational modes in such an elastic body, with the wavelength no less than the characteristic length of an amino acid residue, are estimated roughly to be three times the number of amino acid residues in a protein, which is slightly less than the number of variable dihedral angles in a protein. Their frequencies, when converted to the wavenumber of corresponding light, are found to range from 1.8 × 10 cm^?1 to 2.1 × 10²cm^?1 for a protein with the diameter d = 40 Å, when Young's E = 10¹¹ dyne/cm² is assumed. A significant fraction of the coupled vibrations of dihedral angles in real globular proteins are collective ones, i.e., those involving the whole protein molecules. Based on these results, it concluded that the depth of the global minimum s at least 150 Kcal/mol.