AZ 85287-1504 a) Dipolar susceptibility of interfacial water and the corresponding interface dielectric constant were calculated from numerical molecular dynamics simulations for neutral and charged states of buckminsterfullerene C 60 . Dielectric constants in the range 10-22, depending on temperature and solute charge, were found. The hydration water undergoes a structural crossover as a function of the solute charge. Its main signatures include the release of dangling O-H bonds pointing toward the solute and the change in the preferential orientations of hydration water from those characterizing hydrophobic to charged substrates. The interface dielectric constant marks the structural transition with a spike. The computational formalism adopted here provides direct access to interface susceptibility from configurations produced by computer simulations. The required property is the cross-correlation between the radial projection of the dipole moment of the solvation shell and the electrostatic potential of the solvent inside the solute.

Diffusivity of a protein (a Brownian particle) is caused by random molecular collisions in the Stokes–Einstein picture. Alternatively, it can be viewed as driven by unbalanced stochastic forces acting from water on the protein. Molecular dynamics simulations of protein mutants carrying different charges are analyzed here in terms of the van der Waals (vdW) and electrostatic forces acting on the protein. They turn out to be remarkably strongly correlated and the total force is largely a compensation between vdW and electrostatic forces. Both vdW and electrostatic forces relax on the same time scale of 5–6 ns separated by 6 orders of magnitude from the relaxation time of the total force. Similar phenomenology applies to the dynamics and statistics of the fluctuating torque responsible for rotational diffusion. Standard linear theories of dielectric friction are grossly inapplicable to translational and rotational diffusion of proteins overestimating friction by many orders of magnitude.

Small values of the reorganization energy, 0.2–0.3 eV, were reported by electrochemical kinetic measurements for the half redox reaction of the redox-active protein azurin. This theoretical study explores possible mechanisms for the low activation barrier for electrochemical protein electron transfer: (1) electronic polarizability of the active site, (2) altering protonation states of far-away histidine residues not directly connected to the active site, and (3) a partial desolvation of the protein when attached to the electrode. The last mechanism provides the most robust explanation of the observations. Constraints imposed by the protein fold on its ability to sample the configuration space lead to the breakdown of the fluctuation–dissipation relation (FDR) and a strong separation of the Stokes-shift and variance reorganization energies. The resulting nonergodic kinetic reorganization energy observed experimentally is significantly lowered compared to predictions of standard models based on Gibbsian statistics and the FDR. The fast rate of protein electron transfer is directly related to the ability of the protein scaffold to maintain nonequilibrium statistics of electrostatic fluctuations projected on the electron-transfer reaction coordinate.

One reaction step in the conductivity relay of azurin, electron transfer between the Cu-based active site and the tryptophan residue, is studied theoretically and by classical molecular dynamics simulations. Oxidation of tryptophan results in electrowetting of this residue. This structural change makes the free energy surfaces of electron transfer nonparabolic as described by the Qmodel of electron transfer. We analyze the medium dynamical effect on protein electron transfer produced by coupled Stokes-shift dynamics and the dynamics of the donor−acceptor distance modulating electron tunneling. The equilibrium donor−acceptor distance falls in the plateau region of the rate constant, where it is determined by the protein−water dynamics, and the probability of electron tunneling does not affect the rate. The crossover distance found here puts most intraprotein electron-transfer reactions under the umbrella of dynamical control. The crossover between the medium-controlled and tunneling-controlled kinetics is combined with the effect of the protein−water medium on the activation barrier to formulate principles of tunability of protein-based charge-transfer chains. The main principle in optimizing the activation barrier is the departure from the Gaussian-Gibbsian statistics of fluctuations promoting activated transitions. This is achieved either by incomplete (nonergodic) sampling, breaking the link between the Stokes-shift and variance reorganization energies, or through wetting-induced structural changes of the enzyme's active site.

Molecular charge asymmetrically distributed in a diffusing tagged particle causes a nonzero electrostatic force balanced by an opposing van der Waals (vdW) force. Fluctuations of electrostatic and vdW forces are highly correlated, and they destructively interfere in the force variance. This phenomenology is caused by the formation of a structurally frozen hydration layer for a particle diffusing in water and is responsible for a substantial speedup of translational diffusion compared to traditional theories of dielectric friction. Diffusion of proteins is insensitive to charge mutations, while smaller particles with asymmetric charge distribution can show a strong dependence of translational and rotational diffusion on molecular charge. Dielectric calculations of the electrostatic force require low values of ≃5 for the effective dielectric constant of interfacial water to be consistent with simulations.