Ergodicity breaking of iron displacement in heme proteins

TL;DR

This paper models the dynamical transition in proteins, showing how ergodicity breaking occurs at specific crossover temperatures due to vibrational softening and water molecule dynamics, with implications for understanding protein flexibility.

Contribution

It introduces a model linking vibrational softening and ergodicity breaking to protein-water interactions, explaining experimental observations of atomic displacements.

Findings

Identification of two crossover temperatures related to water molecule dynamics.

Ergodicity breaking transitions depend on observation window durations.

Stretched exponential relaxation improves model fit to experimental data.

Abstract

We present a model of the dynamical transition of atomic displacements in proteins. Increased mean-square displacement at higher temperatures is caused by softening of the vibrational force constant by electrostatic and van der Waals forces from the protein-water thermal bath. Vibrational softening passes through a nonergodic dynamical transition when the relaxation time of the force-force correlation function enters, with increasing temperature, the instrumental observation window. Two crossover temperatures are identified. The lower crossover, presently connected to the glass transition, is related to the dynamical unfreezing of rotations of water molecules within nanodomains polarized by charged surface residues of the protein. The higher crossover temperature, usually assigned to the dynamical transition, marks the onset of water translations. All crossovers are ergodicity breaking transitions depending on the corresponding observation windows. Allowing stretched exponential relaxation of the protein-water thermal bath significantly improves the theory-experiment agreement when applied to solid protein samples studied by Moessbauer spectroscopy.