Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H₂O) _n ^- can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

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.

Electrostatic lock in the transport cycle of the multidrug resistance transporter EmrE

EmrE is a small, homodimeric membrane transporter that exploits the established electrochemical proton gradient across the Escherichia coli inner membrane to export toxic polyaromatic cations, prototypical of the wider small-multidrug resistance transporter family. While prior studies have established many fundamental aspects of the specificity and rate of substrate transport in EmrE, low resolution of available structures has hampered identification of the transport coupling mechanism. Here we present a complete, refined atomic structure of EmrE optimized against available cryo-electron microscopy (cryo-EM) data to delineate the critical interactions by which EmrE regulates its conformation during the transport process. With the model, we conduct molecular dynamics simulations of the transporter in explicit membranes to probe EmrE dynamics under different substrate loading and conformational states, representing different intermediates in the transport cycle. The refined model is stable under extended simulation. The water dynamics in simulation indicate that the hydrogen-bonding networks around a pair of solvent-exposed glutamate residues (E14) depend on the loading state of EmrE. One specific hydrogen bond from a tyrosine (Y60) on one monomer to a glutamate (E14) on the opposite monomer is especially critical, as it locks the protein conformation when the glutamate is deprotonated. The hydrogen bond provided by Y60 lowers the [Formula: see text] of one glutamate relative to the other, suggesting both glutamates should be protonated for the hydrogen bond to break and a substrate-free transition to take place. These findings establish the molecular mechanism for the coupling between proton transfer reactions and protein conformation in this proton-coupled secondary transporter.

Probing key elements of teixobactin-lipid II interactions in membranes

Two binding poses of the teixobactin–lipid II complex were captured with MD simulations at the membrane surface.

Teixobactin (Txb) is a recently discovered antibiotic against Gram-positive bacteria that induces no detectable resistance. The bactericidal mechanism is believed to be the inhibition of cell wall biosynthesis by Txb binding to lipid II and lipid III. Txb binding specificity likely arises from targeting of the shared lipid component, the pyrophosphate moiety. Despite synthesis and functional assessment of numerous chemical analogs of Txb, and consequent identification of the Txb pharmacophore, the detailed structural information of Txb–substrate binding is still lacking. Here, we use molecular modeling and microsecond-scale molecular dynamics simulations to capture the formation of Txb–lipid II complexes at a membrane surface. Two dominant binding conformations were observed, both showing characteristic lipid II phosphate binding by the Txb backbone amides near the C-terminal cyclodepsipeptide (d-Thr8–Ile11) ring. Additionally, binding by Txb also involved the side chain hydroxyl group of Ser7, as well as a secondary phosphate binding provided by the side chain of l-allo-enduracididine. Interestingly, those conformations differ by swapping two groups of hydrogen bond donors that coordinate the two phosphate moieties of lipid II, resulting in opposite orientations of lipid II binding. In addition, residues d-allo-Ile5 and Ile6 serve as the membrane anchors in both Txb conformations, regardless of the detailed phosphate binding interactions near the cyclodepsipeptide ring. The role of hydrophobic residues in Txb activity is primarily for its membrane insertion, and subsidiarily to provide non-polar interactions with the lipid II tail. Based on the Txb–lipid II interactions captured in their complexes, as well as their partitioning depths into the membrane, we propose that the bactericidal mechanism of Txb is to arrest cell wall synthesis by selectively inhibiting the transglycosylation of peptidoglycan, while possibly leaving the transpeptidation step unaffected. The observed “pyrophosphate caging” mechanism of lipid II inhibition appears to be similar to some lantibiotics, but different from that of vancomycin or bacitracin.

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). Copyright 2017, Electrochemical Society, INC.

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.

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.

Comparison of single-ion molecular dynamics in common solvents

Laying a basis for molecularly specific theory for the mobilities of ions in solutions of practical interest, we report a broad survey of velocity autocorrelation functions (VACFs) of Li⁺ and PF₆^- ions in water, ethylene carbonate, propylene carbonate, and acetonitrile solutions. We extract the memory function, γ(t), which characterizes the random forces governing the mobilities of ions. We provide comparisons controlling for the effects of electrolyte concentration and ion-pairing, van der Waals attractive interactions, and solvent molecular characteristics. For the heavier ion (PF₆^-), velocity relaxations are all similar: negative tail relaxations for the VACF and a clear second relaxation for γt, observed previously also for other molecular ions and with n-pentanol as the solvent. For the light Li⁺ ion, short time-scale oscillatory behavior masks simple, longer time-scale relaxation of γt. But the corresponding analysis of the solventberg Li⁺H₂O₄ does conform to the standard picture set by all the PF₆^- results.

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.

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.

Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations

The envelope (E) protein of Dengue virus rearranges to a trimeric hairpin to mediate fusion of the viral and target membranes, which is essential for infectivity. Insertion of E into the target membrane serves to anchor E and possibly also to disrupt local order within the membrane. Both aspects are likely to be affected by the depth of insertion, orientation of the trimer with respect to the membrane normal, and the interactions that form between trimer and membrane. In the present work, we resolved the depth of insertion, the tilt angle, and the fundamental interactions for the soluble portion of Dengue E trimers (sE) associated with planar lipid bilayer membranes of various combinations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-rac-glycerol (POPG), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and cholesterol (CHOL) by neutron reflectivity (NR) and by molecular dynamics (MD) simulations. The results show that the tip of E containing the fusion loop (FL) is located at the interface of the headgroups and acyl chains of the outer leaflet of the lipid bilayers, in good agreement with prior predictions. The results also indicate that E tilts with respect to the membrane normal upon insertion, promoted by either the anionic lipid POPG or CHOL. The simulations show that tilting of the protein correlates with hydrogen bond formation between lysines and arginines located on the sides of the trimer close to the tip (K246, K247, and R73) and nearby lipid headgroups. These hydrogen bonds provide a major contribution to the membrane anchoring and may help to destabilize the target membrane.

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials.

Polyelectrolyte layer-by-layer deposition on nanoporous supports for ion selective membranes

This work demonstrates that the ionic selectivity and ionic conductivity of nanoporous membranes can be controlled independently via layer-by-layer (LbL) deposition of polyelectrolytes and subsequent selective cross-linking of these polymer layers. LbL deposition offers a scalable, inexpensive method to tune the ion transport properties of nanoporous membranes by sequentially dip coating layers of cationic polyethyleneimine and anionic poly(acrylic acid) onto polycarbonate membranes. The cationic and anionic polymers are self-assembled through electrostatic and hydrogen bonding interactions and are chemically crosslinked to both change the charge distribution and improve the intermolecular integrity of the deposited films. Both the thickness of the deposited coating and the use of chemical cross-linking agents influence charge transport properties significantly. Increased polyelectrolyte thickness increases the selectivity for cationic transport through the membranes while adding polyelectrolyte films decreases the ionic conductivity compared to an uncoated membrane. Once the nanopores are filled, no additional decrease in conductivity is observed with increasing film thickness and, upon cross-linking, a portion of the lost conductivity is recovered. The cross-linking agent also influences the ionic selectivity of the resulting polyelectrolyte membranes. Increased selectivity for cationic transport occurs when using glutaraldehyde as the cross-linking agent, as expected due to the selective cross-linking of primary amines that decreases the net positive charge. Together, these results inform deposition of chemically robust, highly conductive, ion-selective membranes onto inexpensive porous supports for applications ranging from energy storage to water purification.

This work demonstrates that the ionic selectivity and ionic conductivity of nanoporous membranes can be controlled independently via layer-by-layer (LbL) deposition of polyelectrolytes and subsequent selective cross-linking of these polymer layers.

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.

Method for measuring the unbinding energy of strongly-bound membrane-associated proteins

We describe a new method to measure the activation energy for unbinding (enthalpy ΔH*_u and free energy ΔG*_u) of a strongly-bound membrane-associated protein from a lipid membrane. It is based on measuring the rate of release of a liposome-bound protein during centrifugation on a sucrose gradient as a function of time and temperature. The method is used to determine ΔH*_u and ΔG*_u for the soluble dengue virus envelope protein (sE) strongly bound to 80:20 POPC:POPG liposomes at pH5.5. ΔH*_u is determined from the Arrhenius equation whereas ΔG*_u is determined by fitting the data to a model based on mean first passage time for escape from a potential well. The binding free energy ΔG_b of sE was also measured at the same pH for the initial, predominantly reversible, phase of binding to a 70:30 PC:PG lipid bilayer. The unbinding free energy (20±3kcal/mol, 20% PG) was found to be roughly three times the binding energy per monomer, (7.8±0.3kcal/mol for 30% PG, or est. 7.0kcal/mol for 20% PG). This is consistent with data showing that free sE is a monomer at pH5.5, but assembles into trimers after associating with membranes. This new method to determine unbinding energies should be useful to understand better the complex interactions of integral monotopic proteins and strongly-bound peripheral membrane proteins with lipid membranes.

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.

Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration

A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.

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.