The dynamical transition in proteins and non-Gaussian behavior of low frequency modes in Self Consistent Normal Mode Analysis

Abstract: Self Consistent Normal Mode Analysis (SCNMA) is applied to heme c type cytochrome f to study temperature dependent protein motion. Classical Normal Mode Analysis (NMA) assumes harmonic behavior and the protein Mean Square Displacement (MSD) has a linear dependence on temperature. This is only consistent with low temperature experimental results. To connect the protein vibrational motions between low temperature and physiological temperature, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, Quantum Harmonic Oscillator (QHO) theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests it may be the cause of the non-Gaussian behavior of the protein motions probed by Elastic Incoherent Neutron Scattering (EINS). The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low frequency regime (< 50cm-1or < 6meVor > 0.6ps). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.