Thermal motion of whole protein molecules in protein solids

A preliminary analysis is presented of whether and to what extent thermal motion of protein molecules as rigid bodies contributes to the mobility found in X-ray and Mössbauer studies. A simple theory is advanced enabling the estimation of mean-square amplitudes of translational and librational motion of the protein molecules in crystals and amorphous glasses from the experimental data on the elastic properties of these solids. The values calculated and their dependence on the crystal packing, temperature and hydration level were found to be in good accord with the data of X-ray analysis and Mössbauer spectroscopy. The external modes were concluded to contribute significantly to the values of mean value of chi 2 measured by the last two methods meaning that the conventional amplitudes of internal motion in proteins were overestimated. The real average amplitude of thermal motion of atoms in the protein interior should be close to that in molecular crystals, in accordance with the crystal-like packing of atoms inside the protein globule and some other "crystal-like" physical characteristics such as Young's modulus, adiabatic compressibility and thermal expansion coefficient. Factors are discussed which determine the temperature dependence of the amplitudes of external and internal modes of protein motion.