Vibrational dynamics of hydrogen in proteins

Biological macromolecules expand with increasing temperature and this dynamic expansion is associated with the onset of function. The expansion is typically characterized by the mean square vibrational displacement (MSD), of specific constituents such as hydrogen within the macromolecules. The increases with increasing temperature and the slope of versus temperature can increase significantly at a temperature T{D} identified as a dynamical transition. We illustrate that the observed expansion and change in slope of with temperature at T{D} can be reproduced within a simple model of the vibration, an atom in an anharmonic potential, V(u). Given V(u), only the temperature is varied in the model. A simple Gaussian potential or a potential containing a hard wall is particularly effective is reproducing the observed change in the slope of with temperature around T{D}.