Spectral properties of conformational motion in proteins

The conformational dynamics of large fragments of protein structure within the framework of a generalized model of bounded diffusion (GMBD) have been considered. This model is a development of the known ordinary model of bounded diffusion (MBD). The latter model assumes that the driving force of motion, which is at the same time a source of friction, has negligibly small correlation time (white noise). In contrast to the MBD, the GMBD takes into account the finite character of friction correlation time, i.e. memory friction effects. Two different mechanisms of friction for the fragment are considered: (1) friction by rapid density fluctuations due to the harmonic vibrational motion of atoms and (2) friction by slow encounters with surrounding fragments of protein structure. The present theory shows that at high frequencies the power decay of the spectrum which takes place in the MBD is replaced by an exponential one. In the narrow intermediate frequency range the results of the GMBD coincide with those of the MBD. At low frequencies the results of the two models differ quantitatively, though their qualitative behaviour is similar.