We define the dielectric constant (susceptibility) that should enter the Maxwell boundary value problem when applied to microscopic dielectric interfaces polarized by external fields. The dielectric constant (susceptibility) of the interface is defined by exact linear-response equations involving correlations of statistically fluctuating interface polarization and the Coulomb interaction energy of external charges with the dielectric. The theory is applied to the interface between water and spherical solutes of altering size studied by molecular dynamics (MD) simulations. The effective dielectric constant of interfacial water is found to be significantly lower than its bulk value, and it also depends on the solute size. For TIP3P water used in MD simulations, the interface dielectric constant changes from 9 to 4 when the solute radius is increased from ∼5 to 18 Å.

A model of low-temperature polar liquids is constructed that accounts for the configurational heat capacity, entropy, and the effect of a strong electric field on the glass transition. The model is based on the Padé-truncated perturbation expansions of the liquid state theory. Depending on parameters, it accommodates an ideal glass transition of vanishing configurational entropy and its avoidance, with a square-root divergent enumeration function at the point of its termination. A composite density-temperature parameter ρ^γ/T, often used to represent combined pressure and temperature data, follows from the model. The theory is in good agreement with the experimental data for excess (over the crystal state) thermodynamics of molecular glass formers. We suggest that the Kauzmann entropy crisis might be a signature of vanishing configurational entropy of a subset of degrees of freedom, multipolar rotations in our model. This scenario has observable consequences: (i) a dynamical crossover of the relaxation time and (ii) the fragility index defined by the ratio of the excess heat capacity and excess entropy at the glass transition. The Kauzmann temperature of vanishing configurational entropy and the corresponding glass transition temperature shift upward when the electric field is applied. The temperature shift scales quadratically with the field strength.

Complex I is a part of the respiration energy chain converting the redox energy into the cross-membrane proton gradient. The electron-transfer chain of iron-sulfur cofactors within the water-soluble peripheral part of the complex is responsible for the delivery of electrons to the proton pumping subunit. The protein is porous to water penetration and the hydration level of the cofactors changes when the electron is transferred along the chain. High reaction barriers and trapping of the electrons at the iron-sulfur cofactors are prevented by the combination of intense electrostatic noise produced by the protein-water interface with the high density of quantum states in the iron-sulfur clusters caused by spin interactions between paramagnetic iron atoms. The combination of these factors substantially lowers the activation barrier for electron transfer compared to the prediction of the Marcus theory, bringing the rate to the experimentally established range. The unique role of iron-sulfur clusters as electron-transfer cofactors is in merging protein-water fluctuations with quantum-state multiplicity to allow low activation barriers and robust operation. Water plays a vital role in electron transport energetics by electrowetting the cofactors in the chain upon arrival of the electron. A general property of a protein is to violate the fluctuation-dissipation relation through nonergodic sampling of its landscape. High functional efficiency of redox enzymes is a direct consequence of nonergodicity.

Enzymes in biology’s energy chains operate with low energy input distributed through multiple electron transfer steps between protein active sites. The general challenge of biological design is how to lower the activation barrier without sacrificing a large negative reaction free energy. We show that this goal is achieved through a large polarizability of the active site. It is polarized by allowing a large number of excited states, which are populated quantum mechanically by electrostatic fluctuations of the protein and hydration water shells. This perspective is achieved by extensive mixed quantum mechanical/molecular dynamics simulations of the half reaction of reduction of cytochrome c. The barrier for electron transfer is consistently lowered by increasing the number of excited states included in the Hamiltonian of the active site diagonalized along the classical trajectory. We suggest that molecular polarizability, in addition to much studied electrostatics of permanent charges, is a key parameter to consider in order to understand how enzymes work.