Bulk-solvent and hydration-shell fluctuations, similar to alpha- and beta-fluctuations in glasses, control protein motions and functions

Abstract

The concept that proteins exist in numerous different conformations or conformational substates, described by an energy landscape, is now accepted, but the dynamics is incompletely explored. We have previously shown that large-scale protein motions, such as the exit of a ligand from the protein interior, follow the dielectric fluctuations in the bulk solvent. Here, we demonstrate, by using mean-square displacements (msd) from Mossbauer and neutron-scattering experiments, that fluctuations in the hydration shell control fast fluctuations in the protein. We call the first type solvent-slaved or alpha-fluctuations and the second type hydration-shell-coupled or beta-fluctuations. Solvent-slaved motions are similar to the alpha-fluctuations in glasses. Their temperature dependence can be approximated by a Vogel-Tammann-Fulcher relation and they are absent in a solid environment. Hydration-shell-coupled fluctuations are similar to the beta-relaxation in glasses. They can be approximated by a Ferry or an Arrhenius relation, are much reduced or absent in dehydrated proteins, and occur in hydrated proteins even if embedded in a solid. They can be responsible for internal processes such as the migration of ligands within myoglobin. The existence of two functionally important fluctuations in proteins, one slaved to bulk motions and the other coupled to hydration-shell fluctuations, implies that the environment can control protein functions through different avenues and that no real protein transition occurs at approximately 200 K. The large number of conformational substates is essential; proteins cannot function without this reservoir of entropy, which resides mainly in the hydration shell.

Fig. 1.

A stylized look into Mb displays the parts of the protein that are involved in protein dynamics and function. The lower half of the structure shows three α-helices, part of the protein backbone, with one side chain as an example. The upper half provides a space-filling view. Between the two halves is a heme group (in red). Hydration waters are shown as red-and-white spheres. Two cavities that can hold ligands are also depicted. The hydration shell and the bulk solvent envelop the protein and dominate protein dynamics.

Fig. 2.

Mössbauer scattering compared with hydration shell dielectric beta process. (A) The msd of ⁵⁷Fe in a Mb crystal, measured by Mössbauer spectroscopy [according to Parak et al. (9)]. The dashed line, denoted by V, is the vibrational contribution to 〈x²(T)〉; it is also plotted in B. (B) The rectangles (right y axis) give the rate coefficient k_β(T) for the dielectric relaxation of the hydration water in a metmyoglobin crystal (27). The circles (left y axis) are 〈x²(T)〉_c for ⁵⁷Fe in a deoxymyoglobin crystal (9). The solid square at 300 K gives the 〈x²(T)〉_c as measured by x-ray diffraction (28-30). The dotted line is the extrapolation of the x-ray value to low temperatures.

Fig. 3.

Hydration shell fluctuation is essential for protein β relaxation. (Left) The observables are plotted linearly versus temperature. (Right) The logarithms of the conformational components of the observables are redrawn vs. 1,000 K/T. (A and B) Mean-square displacement, 〈x²(T)〉, of the hydrogens in bacteriorhodopsin at 2 wt% hydration (open squares) and 35 wt% hydration (circles), as measured by neutron scattering with log(k_m/s^-1) ≈ 10. [according to Ferrand et al. (33)]. (C and D) msd for lysozyme in various solvents (70% lysozyme/30% water; 50% glycerol/50% lysozyme; 80% glycerol/20% lysozyme and dry lysozyme), measured by neutron scattering, with log(k_m/s^-1) ≈ 9 [from Tsai et al. (34)]. (E and F) Pure dephasing rate versus T in IR vibrational echo experiments with Mb in three different solvents (trehalose, 95% glycerol/5% water, 50% ethylene glycol/50% water. [From Rector et al. (35).]

Fig. 4.

Temperature dependence of rate coefficients for fluctuations and processes in Mb. Solvent: 3:1 glycerol/water, except for k_β(T), which was measured in a metMb crystal. Solid lines indicate measured values, dashed lines are extrapolations. α denotes the rate coefficient k_α(T) for the solvent dielectric relaxation; β denotes the rate coefficient k_β(T). Exit is the rate coefficient for the exit of CO from Mb. DA denotes the rate coefficient k_DA for the passage of CO from the Xe1 cavity to the bound state at the heme iron. k_exit is parallel to k_α(T). DA parallels β.

Fig. 5.

The EL of Mb. (Left) A projection of the very-high-dimensional EL onto one conformational coordinate. (Right) A projection onto two conformational coordinates. We call the CS0 taxonomic substates, because they can be distinguished and characterized in detail. In each CS0 reside a large number of CS1α substates. In each CS1α a large number of CS1β substates reside. The numbers of substates in CS1α and CS1β is so large that their properties must be described by distributions. We call them statistical substates. The substates below CS1 likely involve local regions of the protein.