Nanosecond Stokes shift dynamics, dynamical transition, and gigantic reorganization energy of hydrated heme proteins

We report numerical simulations of three hydrated heme proteins, myoglobin, cytochrome c, and cytochrome B562. The properties of interest are the dynamics and statistics of the electric field and electrostatic potential at heme's iron, as well as their separation into the protein and water components. We find that the electric field produced by both the protein and the hydration water relaxes on the time scale of 3-6 ns, and the relaxation time of the electrostatic potential is close to 1 ns. The slow dynamics of the electrostatic observables is accompanied by their large variances. For the electrostatic potential, a large amplitude of its fluctuations leads to a gigantic reorganization energy of a half redox reaction changing the redox state of the protein. Both a large magnitude and a slow relaxation time of the electric field fluctuations are required to explain the onset of large mean-square displacements of iron at the point of protein's dynamical transition. These requirements are met by the simulations which are used to explain the temperature dependence of heme iron displacements measured by Mössbauer spectroscopy. All three phenomena, (i) nanosecond dynamics, (ii) protein dynamical transition and a large high-temperature excess of atomic mean-square displacements, and (iii) the gigantic reorganization energy, are explained here by one physical mechanism. This mechanism involves two components: nanosecond motions of the protein surface residues and polarization of the interfacial water by the protein charges. Global nanosecond conformations of the protein move the surface water. Since water is polarized, these movements create large-amplitude electrostatic fluctuations, sufficient to modify displacements of groups inside the protein and yield reorganization energies of protein electron transfer far exceeding those found for small molecules. Water follows adiabatically the protein motions. Therefore, the relaxation times of the protein and its hydration layer are close, leading to matching temperatures of the dynamical transition for the two components.