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.

Since the seminal paper by Panagiotopoulos [Mol. Phys. 61, 813 (1997)], the Gibbs ensemble Monte Carlo (GEMC) method has been the most popular particle-based simulation approach for the computation of vapor-liquid phase equilibria. However, the validity of GEMC simulations in the near-critical region has been questioned because rigorous finite-size scaling approaches cannot be applied to simulations with fluctuating volume. Valleau [Mol. Simul. 29, 627 (2003)] has argued that GEMC simulations would lead to a spurious overestimation of the critical temperature. More recently, Patel et al. [J. Chem. Phys. 134, 024101 (2011)] opined that the use of analytical tail corrections would be problematic in the near-critical region. To address these issues, we perform extensive GEMC simulations for Lennard-Jones particles in the near-critical region varying the system size, the overall system density, and the cutoff distance. For a system with N = 5500 particles, potential truncation at 8σ and analytical tail corrections, an extrapolation of GEMC simulation data at temperatures in the range from 1.27 to 1.305 yields T(c) = 1.3128 ± 0.0016, ρ(c) = 0.316 ± 0.004, and p(c) = 0.1274 ± 0.0013 in excellent agreement with the thermodynamic limit determined by Potoff and Panagiotopoulos [J. Chem. Phys. 109, 10914 (1998)] using grand canonical Monte Carlo simulations and finite-size scaling. Critical properties estimated using GEMC simulations with different overall system densities (0.296 ≤ ρ(t) ≤ 0.336) agree to within the statistical uncertainties. For simulations with tail corrections, data obtained using r(cut) = 3.5σ yield T(c) and p(c) that are higher by 0.2% and 1.4% than simulations with r(cut) = 5 and 8σ but still with overlapping 95% confidence intervals. In contrast, GEMC simulations with a truncated and shifted potential show that r(cut) = 8σ is insufficient to obtain accurate results. Additional GEMC simulations for hard-core square-well particles with various ranges of the attractive well and for n-decane molecules represented by the TraPPE force field yield data that support the trends observed for Lennard-Jones particles. The finite-size dependence of the critical properties obtained from GEMC simulations is significantly smaller than those from grand-canonical ensemble simulations. Thus, when resources are not available for a rigorous finite-size scaling study, GEMC simulations provide a straightforward route to determine fairly accurate critical properties using relatively small system sizes.

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 effective solute radius is increased from ∼ 5 to 18 Å.

Coarse-graining (CG) procedures provide computationally efficient methods for investigating the corresponding long time- and length-scale processes. In the bottom-up approaches, the effective interactions between the CG sites are obtained using the information from the atomistic simulations, but reliable CG procedures are required to preserve the structure and thermodynamics. In this regard, the integral equation coarse-graining (IECG) method is a promising approach that uses the first-principles Ornstein-Zernike equation in liquid state theory to determine the effective potential between CG sites. In this work, we present the details of the IECG method while treating the density as an intrinsic property and active variable of the CG system. Performing extensive simulations of polymer melts, we show that the IECG theory/simulation and atomistic simulation results are consistent in structural properties such as the pair-correlation functions and form factors, and also thermodynamic properties such as pressure. The atomistic simulations of the liquids show that the structure is largely sensitive to the repulsive part of the potential. Similarly, the IECG simulations of polymeric liquids show that the structure can be determined by the relatively short-range CG repulsive interactions, but the pressure is only accurately determined once the long-range, weak CG attractive interactions are included. This is in agreement with the seminal work by Widom on the influence of the potential on the phase diagram of the liquid [Widom, B. Science 1967 , 157 , 375 - 382 ]. Other aspects of the IECG theory/simulations are also discussed.

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. Within dielectric continuum models, this separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom. The main qualitative prediction of Pekar's perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. Here, we study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. However, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).