Non-Gaussian statistics of the vibrational fluctuations of myoglobin

Experiments on the dynamics of vibrational fluctuations in myoglobin revealed an interesting behavioral cross-over occurring in the range 180-200 K. In this temperature range the mean square displacement of atomic positions versus temperature sharply increases its slope, indicating the dissociation of CO from the heme group. In this paper we develop a theoretical model that provides a framework for the quantitative description of this phenomenon. The basis of our calculations is an assumption of an effective potential with multiple local minima. In particular, we consider a quartic potential in place of the simple quadratic. We then use non-Gaussian statistics to obtain a relationship between the mean square displacement and model parameters. We compare our model to published experimental data and show that it can describe the data set using physically meaningful parameters which are fitted to the experimental data. In the process we verify the Gaussian approximation's applicability only to the low-temperature régime. In the high-temperature limit, however, deviations from the Gaussian approximation are due to the double-well nature of our effective potential. We find that the published datasets showing the thermal transition display the qualitative trends predicted by appropriate algebraic approximations to our predicted myoglobin behavior.