Comment on "Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin" by O. Kontkanen, D. Biriukov and Z. Futera, Phys. Chem. Chem. Phys., 2023, 25, 12479.

Polarizability is a fundamental property of all molecular systems describing the deformation of the molecular electronic density in response to an applied electric field. The question of whether polarizability of the active site needs to be included in theories of enzymatic activity remains open. Hybrid quantum mechanical/molecular mechanical calculations are hampered by difficulties faced by many quantum-chemistry algorithms to provide sufficiently accurate estimates of the anisotropic second-rank tensor of molecular polarizability. In this Comment, we provide general theoretical arguments for the values of polarizability of the quantum region or a molecule which have to be reproduced by electronic structure calculations.

Theory of Protein Charge Transfer: Electron Transfer between Tryptophan Residue and Active Site of Azurin.

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 Q-model 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.

Enhanced Molecular Diffusivity through Destructive Interference between Electrostatic and Osmotic Forces.

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.

Driving Forces of Protein Diffusion.

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.

Effective Dielectric Constant of Water at the Interface with Charged C60 Fullerenes.

The 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 C60. Dielectric constants in the range 10-22, depending on temperature and solute charge, were found. These values are consistent with recent reports for biological and nanometer-scale interfaces. The hydration water undergoes a structural crossover as a function of the surface charge of the charged fullerene. 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 showing a Curie-type phenomenology. 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 with the electrostatic potential of the solvent inside the solute.

Interfacial structural crossover and hydration thermodynamics of charged C60 in water.

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.