Relaxation kinetics and the glassiness of proteins: the case of bovine pancreatic trypsin inhibitor

Folded proteins may be regarded as soft active matter under physiological conditions. The densely packed hydrophobic interior, the relatively molten hydrophilic exterior, and the spacer connecting these put together a large number of locally homogeneous regions. For the case of the bovine pancreatic trypsin inhibitor, with the aid of molecular dynamics simulations, we have demonstrated that the kinetics of the relaxation of the internal motions is highly concerted, manifesting the protein's heterogeneity, which may arise from variations in density, local packing, or the local energy landscape. This behavior is characterized in a stretched exponential decay described by an exponent of approximately 0.4 at physiological temperatures. Due to the trapped conformations, configurational entropy becomes smaller, and the associated stretch exponent drops to half of its value below the glass transition range. The temperature dependence of the inverse relaxation time closely follows the Vogel-Tamman-Fulcher expression when the protein is biologically active.