Evidence of α fluctuations in myoglobin's denaturation in the high temperature region: Average relaxation time from an Adam-Gibbs perspective

In this work, we derive an analytical expression for the relaxation time τ as a function of temperature T for myoglobin protein (Mb, PDB:1MBN) in the high temperature limit (T > Tg = 200 K). The method is based on a modified version of the Adam-Gibbs theory (AG theory) for the glass transition in supercooled liquids and an implementation of differential geometry techniques. This modified version of the AG theory takes into account that the entropic component in protein's denaturation has two major sources: a configurational contribution ΔSc due to the unfolding of the highly ordered native state N and a hydration contribution ΔShyd arising from the exposure of non-polar residues to direct contact with solvent polar molecules. Our results show that the configurational contribution ΔSc is temperature-independent and one order of magnitude smaller than its hydration counterpart ΔShyd in the temperature range considered. The profile obtained for log τ(T) from T = 200 K to T = 300 K exhibits a non-Arrhenius behavior characteristic of α relaxation mechanisms in hydrated proteins and glassy systems. This result is in agreement with recent dielectric spectroscopy data obtained for hydrated myoglobin, where at least two fast relaxation processes in the high temperature limit have been observed. The connection between the relaxation process calculated here and the experimental results is outlined.