Protein dynamics is essential for specific biological functions. This paper reviews a large number of experiments and theoretical methods which have been applied in order to get a reliable physical picture. Many examples given here deal with myoglobin (Mb) which has been extensively investigated by several groups. It serves as a kind of `model protein'. The comparison of experiments at unphysiologically low temperatures with those at physiological temperatures proved to be of great help to separate the general dynamics of solids and modes of motion, which are essential for the biological function and become activated only above a characteristic temperature which is often called the dynamical transition temperature. By normal mode analysis a good insight into the molecular vibrations has been obtained. Recently, the Mössbauer effect with synchrotron radiation has been used to determine a density spectrum of phonons coupling to the heme iron in Mb. From this spectrum the mean square displacements at the position of the iron were calculated. The results are compared with those from incoherent neutron scattering. A normal mode refinement of x-ray structures of Mb in the temperature range from 40 to 300 K is discussed, which was used to determine the zero point structural distributions of protein molecules. Protein specific motions above a characteristic temperature have been investigated by Mössbauer absorption spectroscopy and incoherent neutron scattering. Different models to analyse the experiments are discussed, in particular two `state models' are compared. In the simplest case, atoms or groups of atoms jump between two positions which may be inequivalent in energy. At both positions they perform the same harmonic motions. In a more realistic assumption there are two types of states with different backdriving forces. At low temperatures the molecules are trapped in `rigid' states which are often called `conformational substates' in the literature. At increasing temperatures, the probability increases to reach states which allow more flexibility. In the model of a Brownian oscillator the motion in the flexible state is assumed to be stochastic and overdamped. Besides structural distributions and fluctuations, this review discusses conformational relaxation occurring as a consequence of changes at the active centre of a protein. X-ray structure analysis has been able to characterize intermediates between different conformations. It becomes obvious that protein-specific motions within one conformation are the essential prerequisite for a conformational relaxation.
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