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Molecular dynamics simulations of a small redox-active protein plastocyanin address two questions. (i) Do protein electrostatics equilibrate to the Gibbsian ensemble? (ii) Do the electrostatic potential and electric field inside proteins follow the Gaussian distribution? The statistics of electrostatic potential and electric field are probed by applying small charge and dipole perturbations to different sites within the protein. Nonergodic (non-Gibbsian) sampling is detectable through violations of exact statistical rules constraining the first and second statistical moments (fluctuation–dissipation relations) and the linear relation between free-energy surfaces of the collective coordinate representing the Hamiltonian electrostatic perturbation. We find weakly nonergodic statistics of the electrostatic potential (simulation time of 0.4–1.0 μs) and non-Gibbsian and non-Gaussian statistics of the electric field. A small dipolar perturbation of the protein results in structural instabilities of the protein–water interface and multi-modal distributions of the Hamiltonian energy gap. The variance of the electrostatic potential passes through a crossover at the glass transition temperature Ttr ≃ 170 K. The dipolar susceptibility, reflecting the variance of the electric field inside the protein, strongly increases, with lowering temperature, followed by a sharp drop at Ttr. The linear relation between free-energy surfaces can be directly tested by combining absorption and emission spectra of optical dyes. It was found that the statistics of the electrostatic potential perturbation are nearly Gibbsian/Gaussian, with little deviations from the prescribed statistical rules. On the contrary, the (nonergodic) statistics of dipolar perturbations are strongly non-Gibbsian/non-Gaussian due to structural instabilities of the protein hydration shell. 

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment’s non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced. 

The nonlinear dielectric response of proteins in solution far exceeds that of surrounding water. This high nonlinear contrast can be used to monitor protein conformational activity altering its dipole moment. 

Cofactors of biological energy chains are highly polarizable posing the question of the effect of polarizability on enzymatic activity. Hybrid quantum mechanical/molecular mechanical calculations should satisfy restrictions on polarizabilities of quantum sites. 

Interest in the phenomenon of dielectrophoresis has gained significant attention in recent years due to its potential for sorting, manipulation, and trapping of solutes, such as proteins, in aqueous solutions. For many decades, protein dielectrophoresis was considered impossible, as the predicted magnitude of the force arising from experimentally accessible field strengths could not out-compete thermal energy. This conclusion was drawn from the mainstay Clausius–Mossotti (CM) susceptibility applied to the dielectrophoretic force. However, dielectric interfacial polarization leading to the CM result does not account for a large protein dipole moment that is responsible for the dipolar mechanism of dielectrophoresis outcompeting the CM induction mechanism by three to four orders of magnitude in the case of proteins. Here, we propose an explicit geometry within which the dipolar susceptibility may be put to the test. The electric field and dielectrophoretic force are explicitly calculated, and the dependence of the trapping distance on the strength of the applied field is explored. A number of observable distinctions between the dipolar and induction mechanisms are identified.