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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. 

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. 

Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O–H bonds pointing toward the solute. In contrast to the well accepted structure–function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute–solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.