A non-linear approach to the structure–mobility relationship in protein main chains

A correlation investigation was carried out on the series of atomic coordinates (MPV) and temperature factor (Tf), respectively for human hemoglobin and HIV-1 protease protein main chains. The MPV series revealed resemblances to the corresponding Tf series. Each minor or major peak in a series had a corresponding peak in the related series. This brings a qualitative evidence for the connection of the two parameters. The series were further subjected to spectral and detrended fluctuation analysis which all revealed long-range correlation properties. This combined analysis revealed that the data were controlled both by the correlation of stationary fluctuation and trends or non-stationary contribution to correlation. The correlation of all MPV series was found to be much less sensitive to ligand binding than the corresponding Tf series. Thus the long-range correlation properties of the protein main chain structure and mobility revealed two complementary properties of protein molecules. While structure imparts constancy to the system, the atomic mobility represents function yet they are intimately connected.