Computing Potential of the Mean Force Profiles for Ion Permeation Through Channelrhodopsin Chimera, C1C2.

Umbrella sampling, coupled with a weighted histogram analysis method (US-WHAM), can be used to construct potentials of mean force (PMFs) for studying the complex ion permeation pathways of membrane transport proteins. Despite the widespread use of US-WHAM, obtaining a physically meaningful PMF can be challenging. Here, we provide a protocol to resolve that issue. Then, we apply that protocol to compute a meaningful PMF for sodium ion permeation through channelrhodopsin chimera, C1C2, for illustration.

Hydration Mimicry by Membrane Ion Channels.

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

Probing Translocation in Mutants of the Anthrax Channel: Atomically Detailed Simulations with Milestoning.

Anthrax toxin consists of a cation channel and two protein factors. Translocation of the anthrax protein factors from endosomal to the cytosolic compartment is a complex process which utilizes the cation channel. An atomically detailed understanding of the function of the anthrax translocation machinery is incomplete. We report atomically detailed simulations of the lethal factor and channel mutants. Kinetic and thermodynamic properties of early events in the translocation process are computed within the Milestoning theory and algorithm. Several mutants of the channel illustrate that long-range electrostatic interactions provide the dominant driving force for translocation. No external energy input is required because the lower pH in the endosome relative to the cytosol drives the initial translocation process forward. Channel mutants with variable sizes cause smaller effects on translocation events relative to charge manipulations. Comparison with available experimental data is provided.

Molecular Dynamics of Lithium Ion Transport in a Model Solid Electrolyte Interphase.

Li+ transport within a solid electrolyte interphase (SEI) in lithium ion batteries has challenged molecular dynamics (MD) studies due to limited compositional control of that layer. In recent years, experiments and ab initio simulations have identified dilithium ethylene dicarbonate (Li2EDC) as the dominant component of SEI layers. Here, we adopt a parameterized, non-polarizable MD force field for Li2EDC to study transport characteristics of Li+ in this model SEI layer at moderate temperatures over long times. The observed correlations are consistent with recent MD results using a polarizable force field, suggesting that this non-polarizable model is effective for our purposes of investigating Li+ dynamics. Mean-squared displacements distinguish three distinct Li+ transport regimes in EDC - ballistic, trapping, and diffusive. Compared to liquid ethylene carbonate (EC), the nanosecond trapping times in EDC are significantly longer and naturally decrease at higher temperatures. New materials developed for fast-charging Li-ion batteries should have a smaller trapping region. The analyses implemented in this paper can be used for testing transport of Li+ ion in novel battery materials. Non-Gaussian features of van Hove self -correlation functions for Li+ in EDC, along with the mean-squared displacements, are consistent in describing EDC as a glassy material compared with liquid EC. Vibrational modes of Li+ ion, identified by MD, characterize the trapping and are further validated by electronic structure calculations. Some of this work appeared in an extended abstract and has been reproduced with permission from ECS Transactions, 77, 1155-1162 (2017).

Strontium and barium in aqueous solution and a potassium channel binding site.

Ion hydration structure and free energy establish criteria for understanding selective ion binding in potassium (K+) ion channels and may be significant to understanding blocking mechanisms as well. Recently, we investigated the hydration properties of Ba2+, the most potent blocker of K+ channels among the simple metal ions. Here, we use a similar method of combining ab initio molecular dynamics simulations, statistical mechanical theory, and electronic structure calculations to probe the fundamental hydration properties of Sr2+, which does not block bacterial K+ channels. The radial distribution of water around Sr2+ suggests a stable 8-fold geometry in the local hydration environment, similar to Ba2+. While the predicted hydration free energy of -331.8 kcal/mol is comparable with the experimental result of -334 kcal/mol, the value is significantly more favorable than the -305 kcal/mol hydration free energy of Ba2+. When placed in the innermost K+ channel blocking site, the solvation free energies and lowest energy structures of both Sr2+ and Ba2+ are nearly unchanged compared with their respective hydration properties. This result suggests that the block is not attributable to ion trapping due to +2 charge, and differences in blocking behavior arise due to free energies associated with the exchange of water ligands for channel ligands instead of free energies of transfer from water to the binding site.

Role of Solute Attractive Forces in the Atomic-Scale Theory of Hydrophobic Effects.

The role that van der Waals (vdW) attractive forces play in the hydration and association of atomic hydrophobic solutes such as argon (Ar) in water is reanalyzed using the local molecular field (LMF) theory of those interactions. In this problem, solute vdW attractive forces can reduce or mask hydrophobic interactions as measured by contact peak heights of the ArAr correlation function compared to reference results for purely repulsive core solutes. Nevertheless, both systems exhibit a characteristic hydrophobic inverse temperature behavior in which hydrophobic association becomes stronger with increasing temperature through a moderate temperature range. The new theoretical approximation obtained here is remarkably simple and faithful to the statistical mechanical LMF assessment of the necessary force balance. Our results extend and significantly revise approximations made in a recent application of the LMF approach to this problem and, unexpectedly, support a theory of nearly 40 years ago.

Molecular Simulation Results on Charged Carbon Nanotube Forest-Based Supercapacitors.

Electrochemical double-layer capacitances of charged carbon nanotube (CNT) forests with tetraethyl ammonium tetrafluoro borate electrolyte in propylene carbonate are studied on the basis of molecular dynamics simulation. Direct molecular simulation of the filling of pore spaces of the forest is feasible even with realistic, small CNT spacings. The numerical solution of the Poisson equation based on the extracted average charge densities then yields a regular experimental dependence on the width of the pore spaces, in contrast to the anomalous pattern observed in experiments on other carbon materials and also in simulations on planar slot-like pores. The capacitances obtained have realistic magnitudes but are insensitive to electric potential differences between the electrodes in this model. This agrees with previous calculations on CNT forest supercapacitors, but not with experiments which have suggested electrochemical doping for these systems. Those phenomena remain for further theory/modeling work.

Nanoporous Hydrogels for the Observation of Anthrax Exotoxin Translocation Dynamics.

The ability to observe lethal anthrax exotoxins translocating through size-constricting nanopores in vitro, combined with detailed sequence and structural data, has aided in elucidated mechanisms of exotoxin cell entry and toxicity. However, due to limited observations of anthrax exotoxins translocating through protective antigen nanopores in vitro and the instability of protective antigen-functionalized suspended lipid bilayers, questions remain regarding the native mechanisms of cell entry. Nanoporous hydrogel membranes offer a robust tool for studying protein translocation with ensemble measurements that complement conventional single-molecule translocation measurements. Here, we utilize nanoporous hydrogel membranes to assess the translocation of full-length anthrax lethal and edema factors through nanopores similar in diameter to protective antigen translocons. We find that, relative to globular serum and other proteins that do not translocate natively through nanopores, anthrax exotoxins demonstrate significantly reduced barriers to pore entry. Computed free-energy barriers to the unfolding of proteins and the dissociation of macromolecular complexes are generally found to coincide with translocation. Finally, a nanopore-blocking strategy is developed that utilizes nonspecific synthetic peptide constructs and effectively prevents LF translocation within the nanoporous hydrogel.

Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions.

Progress in understanding liquid ethylene carbonate (EC) and propylene carbonate (PC) on the basis of molecular simulation, emphasizing simple models of interatomic forces, is reviewed. Results on the bulk liquids are examined from the perspective of anticipated applications to materials for electrical energy storage devices. Preliminary results on electrochemical double-layer capacitors based on carbon nanotube forests and on model solid-electrolyte interphase (SEI) layers of lithium ion batteries are considered as examples. The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions to Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li[Formula: see text] deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li[Formula: see text] ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and ab initio molecular dynamics simulations, and also experimental results on Li[Formula: see text] thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li[Formula: see text] transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited.

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

The Impact of Protonation on Early Translocation of Anthrax Lethal Factor: Kinetics from Molecular Dynamics Simulations and Milestoning Theory.

We report atomically detailed molecular dynamics simulations of the permeation of the lethal factor (LF) N-terminal segment through the anthrax channel. The N-terminal chain is unstructured and leads the permeation process for the LF protein. The simulations were conducted in explicit solvent with milestoning theory, making it possible to extract kinetic information from nanosecond to millisecond time scales. We illustrate that the initial event is strongly influenced by the protonation states of the permeating amino acids. While the N-terminal segment passes easily at high protonation state through the anthrax channel (and the ϕ clamp), the initial permeation represents a critical step, which can be irreversible and establishes a hook in the channel mouth.

Scaling Atomic Partial Charges of Carbonate Solvents for Lithium Ion Solvation and Diffusion.

Lithium-ion solvation and diffusion properties in ethylene carbonate (EC) and propylene carbonate (PC) were studied by molecular simulation, experiments, and electronic structure calculations. Studies carried out in water provide a reference for interpretation. Classical molecular dynamics simulation results are compared to ab initio molecular dynamics to assess nonpolarizable force field parameters for solvation structure of the carbonate solvents. Quasi-chemical theory (QCT) was adapted to take advantage of fourfold occupancy of the near-neighbor solvation structure observed in simulations and used to calculate solvation free energies. The computed free energy for transfer of Li+ to PC from water, based on electronic structure calculations with cluster-QCT, agrees with the experimental value. The simulation-based direct-QCT results with scaled partial charges agree with the electronic structure-based QCT values. The computed Li+/PF6- transference numbers of 0.35/0.65 (EC) and 0.31/0.69 (PC) agree well with NMR experimental values of 0.31/0.69 (EC) and 0.34/0.66 (PC) and similar values obtained here with impedance spectroscopy. These combined results demonstrate that solvent partial charges can be scaled in systems dominated by strong electrostatic interactions to achieve trends in ion solvation and transport properties that are comparable to ab initio and experimental results. Thus, the results support the use of scaled partial charges in simple, nonpolarizable force fields in future studies of these electrolyte solutions.

Statistical Analyses of Hydrophobic Interactions: A Mini-Review.

This review focuses on the striking recent progress in solving for hydrophobic interactions between small inert molecules. We discuss several new understandings. First, the inverse temperature phenomenology of hydrophobic interactions, i.e., strengthening of hydrophobic bonds with increasing temperature, is decisively exhibited by hydrophobic interactions between atomic-scale hard sphere solutes in water. Second, inclusion of attractive interactions associated with atomic-size hydrophobic reference cases leads to substantial, nontrivial corrections to reference results for purely repulsive solutes. Hydrophobic bonds are weakened by adding solute dispersion forces to treatment of reference cases. The classic statistical mechanical theory for those corrections is not accurate in this application, but molecular quasi-chemical theory shows promise. Finally, because of the masking roles of excluded volume and attractive interactions, comparisons that do not discriminate the different possibilities face an interpretive danger.

Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions.

The role of solute attractive forces on hydrophobic interactions is studied by coordinated development of theory and simulation results for Ar atoms in water. We present a concise derivation of the local molecular field (LMF) theory for the effects of solute attractive forces on hydrophobic interactions, a derivation that clarifies the close relation of LMF theory to the EXP approximation applied to this problem long ago. The simulation results show that change from purely repulsive atomic solute interactions to include realistic attractive interactions diminishes the strength of hydrophobic bonds. For the Ar-Ar rdfs considered pointwise, the numerical results for the effects of solute attractive forces on hydrophobic interactions are opposite in sign and larger in magnitude than predicted by LMF theory. That comparison is discussed from the point of view of quasichemical theory, and it is suggested that the first reason for this difference is the incomplete evaluation within LMF theory of the hydration energy of the Ar pair. With a recent suggestion for the system-size extrapolation of the required correlation function integrals, the Ar-Ar rdfs permit evaluation of osmotic second virial coefficients B2. Those B2's also show that incorporation of attractive interactions leads to more positive (repulsive) values. With attractive interactions in play, B2 can change from positive to negative values with increasing temperatures. This is consistent with the puzzling suggestions of decades ago that B2 ≈ 0 for intermediate cases of temperature or solute size. In all cases here, B2 becomes more attractive with increasing temperature.

Dielectric Relaxation of Ethylene Carbonate and Propylene Carbonate from Molecular Dynamics Simulations.

Ethylene carbonate (EC) and propylene carbonate (PC) are widely used solvents in lithium (Li)-ion batteries and supercapacitors. Ion dissolution and diffusion in those media are correlated with solvent dielectric responses. Here, we use all-atom molecular dynamics simulations of the pure solvents to calculate dielectric constants and relaxation times, and molecular mobilities. The computed results are compared with limited available experiments to assist more exhaustive studies of these important characteristics. The observed agreement is encouraging and provides guidance for further validation of force-field simulation models for EC and PC solvents.

Octa-Coordination and the Aqueous Ba(2+) Ion.

The hydration structure of Ba(2+) ion is important for understanding blocking mechanisms in potassium ion channels. Here, we combine statistical mechanical theory, ab initio molecular dynamics simulations, and electronic structure methods to calculate the hydration free energy and local hydration structure of Ba(2+)(aq). The predicted hydration free energy (-304 ± 1 kcal/mol) agrees with the experimental value (-303 kcal/mol) when a maximally occupied, unimodal inner solvation shell is treated. In the local environment defined by the first shell of hydrating waters, Ba(2+) is directly and stably coordinated by eight (8) waters. Octa-coordination resembles the crystal structure of Ba(2+) and K(+) bound in potassium ion channels, but differs from the local hydration structure of K(+)(aq) determined earlier.

Hydration of Kr(aq) in Dilute and Concentrated Solutions.

Molecular dynamics simulations of water with both multi-Kr and single Kr atomic solutes are carried out to implement quasi-chemical theory evaluation of the hydration free energy of Kr(aq). This approach obtains free energy differences reflecting Kr-Kr interactions at higher concentrations. Those differences are negative changes in hydration free energies with increasing concentrations at constant pressure. The changes are due to a slight reduction of packing contributions in the higher concentration case. The observed Kr-Kr distributions, analyzed with the extrapolation procedure of Krüger et al., yield a modestly attractive osmotic second virial coefficient, B2 ≈ -60 cm(3)/mol. The thermodynamic analysis interconnecting these two approaches shows that they are closely consistent with each other, providing support for both approaches.

Molecular-scale hydrophobic interactions between hard-sphere reference solutes are attractive and endothermic.

The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (ΔB2/ΔT < 0) in the temperature range 300 K ≤ T ≤ 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes.