Erratum: Addition to "Carbonic Anhydrase Robustness for Use in Nanoscale CO2 Capture Technologies"

[This corrects the article DOI: 10.1021/acsomega.3c02630.].

Transport and Energetics of Carbon Dioxide in Ionic Liquids at Aqueous Interfaces

A major hurdle in utilizing carbon dioxide (CO2) lies in separating it from industrial flue gas mixtures and finding suitable storage methods that enable its application in various industries. To address this issue, we utilized a combination of molecular dynamics simulations and experiments to investigate the behavior of CO2 in common room-temperature ionic liquids (RTIL) when in contact with aqueous interfaces. Our investigation of RTILs, [EMIM][TFSI] and [OMIM][TFSI], and their interaction with a pure water layer mimics the environment of a previously developed ultrathin enzymatic liquid membrane for CO2 separation. We analyzed diffusion constants and viscosity, which reveals that CO2 molecules exhibit faster mobility within the selected ILs compared to what would be predicted solely based on the viscosity of the liquids using the standard Einstein-Stokes relation. Moreover, we calculated the free energy of translocation for various species across the aqueous-IL interface, including CO2 and HCO3-. Free energy profiles demonstrate that CO2 exhibits a more favorable partitioning behavior in the RTILs compared to that in pure water, while a significant barrier hinders the movement of HCO3- from the aqueous layer. Experimental measurement of the CO2 transport in the RTILs corroborates the model. These findings strongly suggest that hydrophobic RTILs could serve as a promising option for selectively transporting CO2 from aqueous media and concentrating it as a preliminary step toward storage.

Energetics of high temperature degradation of fentanyl into primary and secondary products

Fentanyl is a synthetic opioid used for managing chronic pain. Due to its higher potency (50-100×) than morphine, fentanyl is also an abused drug. A sensor that could detect illicit fentanyl by identifying its thermally degraded fragments would be helpful to law enforcement. While experimental studies have probed the thermal degradation of fentanyl, little theoretical work has been done to understand the mechanism. Here, we studied the thermal degradation pathways of fentanyl using extensive ab initio molecular dynamics simulations combined with enhanced sampling via multiple-walker metadynamics. We calculated the free energy profile for each bond suggested earlier as a potential degradation point to map the thermodynamic driving forces. We also estimated the forward attempt rate of each bond degradation reaction to gain information about degradation kinetics.

Carbonic Anhydrase Robustness for Use in Nanoscale CO2 Capture Technologies

Continued dependence on crude oil and natural gas resources for fossil fuels has caused global atmospheric carbon dioxide (CO2) emissions to increase to record-setting proportions. There is an urgent need for efficient and inexpensive carbon sequestration systems to mitigate large-scale emissions of CO2 from industrial flue gas. Carbonic anhydrase (CA) has shown high potential for enhanced CO2 capture applications compared to conventional absorption-based methods currently utilized in various industrial settings. This study aims to understand structural aspects that contribute to the stability of CA enzymes critical for their applications in industrial processes, which require the ability to withstand conditions different from those in their native environments. Here, we evaluated the thermostability and enzyme activity of mesophilic and thermophilic CA variants at different temperature conditions and in the presence of atmospheric gas pollutants like nitrogen oxides and sulfur oxides. Based on our enzyme activity assays and molecular dynamics simulations, we see increased conformational stability and CA activity levels in thermostable CA variants incubated week-long at different temperature conditions. The thermostable CA variants also retained high levels of CA activity despite changes in solution pH due to increasing NO and SO2 concentrations. A loss of CA activity was observed only at high concentrations of NO/SO2 that possibly can be minimized with the appropriate buffered solutions.

Molecular Cage Reports on Its Contents: Spectroscopic Signatures of Cryo-Cooled K+- and Ba2+-Benzocryptand Complexes

UV photofragment spectroscopy and IR-UV double resonance methods are used to determine the structure and spectroscopic responses of a three-dimensional [2.2.2]-benzocryptand cage to the incorporation of a single K⁺ or Ba²⁺ imbedded inside it (labeled as K⁺-BzCrypt, Ba²⁺-BzCrypt). We studied the isolated ion-cryptand complex under cryo-cooled conditions, brought into the gas phase by nano-electrospray ionization. Incorporation of a phenyl ring in place of the central ethyl group in one of the three N-CH₂-CH₂-O-CH₂-CH₂-O-CH₂-CH₂-N chains provides a UV chromophore whose S₀-S₁ transition we probe. K⁺-BzCrypt and Ba²⁺-BzCrypt have their S₀-S₁ origin transitions at 35,925 and 36,446 cm^-1, respectively, blue-shifted by 174 and 695 cm^-1 from that of 1,2-dimethoxybenzene. These origins are used to excite a single conformation of each complex selectively and record their IR spectra using IR-UV dip spectroscopy. The alkyl CH stretch region (2800-3000 cm^-1) is surprisingly sensitive to the presence and nature of the encapsulated ion. We carried out an exhaustive conformational search of cage conformations for K⁺-BzCrypt and Ba²⁺-BzCrypt, identifying two conformations (A and B) that lie below all others in energy. We extend our local mode anharmonic model of the CH stretch region to these strongly bound ion-cage complexes to predict conformation-specific alkyl CH stretch spectra, obtaining quantitative agreement with experiment for conformer A, the gas-phase global minimum. The large electrostatic effect of the charge on the O- and N-lone pairs affects the local mode frequencies of the CH₂ groups adjacent to these atoms. The localized CH₂ scissors modes are pushed up in frequency by the adjacent O/N-atoms so that their overtones have little effect on the alkyl CH stretch region. However, the localized CH₂ wags are nearly degenerate and strongly coupled to one another, producing an array of delocalized wag normal modes, whose highest frequency members reach up above 1400 cm^-1. As such, their overtones mix significantly with the CH stretch modes, most notably involving the CH₂ symmetric stretch fundamentals of the central ethyl groups in the all-alkyl chains and the CH stretches adjacent to the N-atoms and antiperiplanar to the nitrogen lone pair.

Control of the Structural Charge Distribution and Hydration State upon Intercalation of CO2 into Expansive Clay Interlayers

Numerous experimental investigations indicated that expansive clays such as montmorillonite can intercalate CO₂ preferentially into their interlayers and therefore potentially act as a material for CO₂ separation, capture, and storage. However, an understanding of the energy-structure relationship during the intercalation of CO₂ into clay interlayers remains elusive. Here, we use metadynamics molecular dynamics simulations to elucidate the energy landscape associated with CO₂ intercalation. Our free energy calculations indicate that CO₂ favorably partitions into nanoconfined water in clay interlayers from a gas phase, leading to an increase in the CO₂/H₂O ratio in clay interlayers as compared to that in bulk water. CO₂ molecules prefer to be located at the centers of charge-neutral hydrophobic siloxane rings, whereas interlayer spaces close to structural charges tend to avoid CO₂ intercalation. The structural charge distribution significantly affects the amount of CO₂ intercalated in the interlayers. These results provide a mechanistic understanding of CO₂ intercalation in clays for CO₂ separation, capture, and storage.

Development of AMOEBA Polarizable Force Field for Rare-Earth La3+ Interaction with Bioinspired Ligands

Rare-earth metals (REMs) are crucial for many important industries, such as power generation and storage, in addition to cancer treatment and medical imaging. One promising new REM refinement approach involves mimicking the highly selective and efficient binding of REMs observed in relatively recently discovered proteins. However, realizing any such bioinspired approach requires an understanding of the biological recognition mechanisms. Here, we developed a new classical polarizable force field based on the AMOEBA framework for modeling a lanthanum ion (La3+) interacting with water, acetate, and acetamide, which have been found to coordinate the ion in proteins. The parameters were derived by comparing to high-level ab initio quantum mechanical (QM) calculations that include relativistic effects. The AMOEBA model, with advanced atomic multipoles and electronic polarization, is successful in capturing both the QM distance-dependent La3+-ligand interaction energies and experimental hydration free energy. A new scheme for pairwise polarization damping (POLPAIR) was developed to describe the polarization energy in La3+ interactions with both charged and neutral ligands. Simulations of La3+ in water showed water coordination numbers and ion-water distances consistent with previous experimental and theoretical findings. Water residence time analysis revealed both fast and slow kinetics in water exchange around the ion. This new model will allow investigation of fully solvated lanthanum ion-protein systems using GPU-accelerated dynamics simulations to gain insights on binding selectivity, which may be applied to the design of synthetic analogues.

Hydrophobic Nanoconfinement Enhances CO2 Conversion to H2CO3

Understanding the formation of H₂CO₃ in water from CO₂ is important in environmental and industrial processes. Although numerous investigations have studied this reaction, the conversion of CO₂ to H₂CO₃ in nanopores, and how it differs from that in bulk water, has not been understood. We use ReaxFF metadynamics molecular simulations to demonstrate striking differences in the free energy of CO₂ conversion to H₂CO₃ in bulk and nanoconfined aqueous environments. We find that nanoconfinement not only reduces the energy barrier but also reverses the reaction from endothermic in bulk water to exothermic in nanoconfined water. Also, charged intermediates are observed more often under nanoconfinement than in bulk water. Stronger solvation and more favorable proton transfer with increasing nanoconfinement enhance the thermodynamics and kinetics of the reaction. Our results provide a detailed mechanistic understanding of an important step in the carbonation process, which depends intricately on confinement, surface chemistry, and CO₂ concentration.

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here, we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F^- over Cl^- in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory-experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

Enhancing Paraoxon Binding to Organophosphorus Hydrolase Active Site

Organophosphorus hydrolase (OPH) is a metalloenzyme that can hydrolyze organophosphorus agents resulting in products that are generally of reduced toxicity. The best OPH substrate found to date is diethyl p-nitrophenyl phosphate (paraoxon). Most structural and kinetic studies assume that the binding orientation of paraoxon is identical to that of diethyl 4-methylbenzylphosphonate, which is the only substrate analog co-crystallized with OPH. In the current work, we used a combined docking and molecular dynamics (MD) approach to predict the likely binding mode of paraoxon. Then, we used the predicted binding mode to run MD simulations on the wild type (WT) OPH complexed with paraoxon, and OPH mutants complexed with paraoxon. Additionally, we identified three hot-spot residues (D253, H254, and I255) involved in the stability of the OPH active site. We then experimentally assayed single and double mutants involving these residues for paraoxon binding affinity. The binding free energy calculations and the experimental kinetics of the reactions between each OPH mutant and paraoxon show that mutated forms D253E, D253E-H254R, and D253E-I255G exhibit enhanced substrate binding affinity over WT OPH. Interestingly, our experimental results show that the substrate binding affinity of the double mutant D253E-H254R increased by 19-fold compared to WT OPH.

Quantum Calculations of VX Ammonolysis and Hydrolysis Pathways via Hydrated Lithium Nitride

Recently, lithium nitride (Li₃N) has been proposed as a chemical warfare agent (CWA) neutralization reagent for its ability to produce nucleophilic ammonia molecules and hydroxide ions in aqueous solution. Quantum chemical calculations can provide insight into the Li₃N neutralization process that has been studied experimentally. Here, we calculate reaction-free energies associated with the Li₃N-based neutralization of the CWA VX using quantum chemical density functional theory and ab initio methods. We find that alkaline hydrolysis is more favorable to either ammonolysis or neutral hydrolysis for initial P-S and P-O bond cleavages. Reaction-free energies of subsequent reactions are calculated to determine the full reaction pathway. Notably, products predicted from favorable reactions have been identified in previous experiments.

Bio-inspired incorporation of phenylalanine enhances ionic selectivity in layer-by-layer deposited polyelectrolyte films

The addition of a common amino acid, phenylalanine, to a Layer-by-Layer (LbL) deposited polyelectrolyte (PE) film on a nanoporous membrane can increase its ionic selectivity over a PE film without the added amino acid. The addition of phenylalanine is inspired by detailed knowledge of the structure of the channelrhodopsins family of protein ion channels, where phenylalanine plays an instrumental role in facilitating sodium ion transport. The normally deposited and crosslinked PE films increase the cationic selectivity of a support membrane in a controllable manner where higher selectivity is achieved with thicker PE coatings, which in turn also increases the ionic resistance of the membrane. The increased ionic selectivity is desired while the increased resistance is not. We show that through incorporation of phenylalanine during the LbL deposition process, in solutions of NaCl with concentrations ranging from 0.1 to 100 mM, the ionic selectivity can be increased independently of the membrane resistance. Specifically, the addition is shown to increase the cationic transference of the PE films from 81.4% to 86.4%, an increase on par with PE films that are nearly triple the thickness while exhibiting much lower resistance compared to the thicker coatings, where the phenylalanine incorporated PE films display an area specific resistance of 1.81 Ω cm2 in 100 mM NaCl while much thicker PE membranes show a higher resistance of 2.75 Ω cm2 in the same 100 mM NaCl solution.

Thermodynamics of ion binding and occupancy in potassium channels

Potassium channels modulate various cellular functions through efficient and selective conduction of K⁺ ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K⁺ ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated by ab initio calculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations.

Polarization shapes the energy landscape of ion conduction in potassium channels.

Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F−, Cl−, Br−, and I− on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal (H2O)nX clusters, with X = Cl−, Br−, and I−, exhibit surface hydration structures. Computed free energies, based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (ab initio molecular dynamics) simulation stream. This rough-landscape procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect addressed. Nevertheless, this procedure can break down when n≳4, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of (H2O)nX clusters, including ramified structures natural in physical cluster theories. With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

Channelrhodopsin C1C2: Photocycle kinetics and interactions near the central gate

Channelrhodopsins (ChR) are light-sensitive cation channels used in optogenetics, a technique that applies light to control cells (e.g., neurons) that have been modified genetically to express those channels. Although mutations are known to affect pore kinetics, little is known about how mutations induce changes at the molecular scale. To address this issue, we first measured channel opening and closing rates of a ChR chimera (C1C2) and selected variants (N297D, N297V, and V125L). Then, we used atomistic simulations to correlate those rates with changes in pore structure, hydration, and chemical interactions among key gating residues of C1C2 in both closed and open states. Overall, the experimental results show that C1C2 and its mutants do not behave like ChR2 or its analogous variants, except V125L, making C1C2 a unique channel. Our atomistic simulations confirmed that opening of the channel and initial hydration of the gating regions between helices I, II, III, and VII of the channel occurs with 1) the presence of 13-cis retinal; 2) deprotonation of a glutamic acid gating residue, E129; and 3) subsequent weakening of the central gate hydrogen bond between the same glutamic acid E129 and asparagine N297 in the central region of the pore. Also, an aspartate (D292) is the unambiguous primary proton acceptor for the retinal Schiff base in the hydrated channel.

Evaluation of Electrodialysis Desalination Performance of Novel Bioinspired and Conventional Ion Exchange Membranes with Sodium Chloride Feed Solutions

Electrodialysis (ED) desalination performance of different conventional and laboratory-scale ion exchange membranes (IEMs) has been evaluated by many researchers, but most of these studies used their own sets of experimental parameters such as feed solution compositions and concentrations, superficial velocities of the process streams (diluate, concentrate, and electrode rinse), applied electrical voltages, and types of IEMs. Thus, direct comparison of ED desalination performance of different IEMs is virtually impossible. While the use of different conventional IEMs in ED has been reported, the use of bioinspired ion exchange membrane has not been reported yet. The goal of this study was to evaluate the ED desalination performance differences between novel laboratory‑scale bioinspired IEM and conventional IEMs by determining (i) limiting current density, (ii) current density, (iii) current efficiency, (iv) salinity reduction in diluate stream, (v) normalized specific energy consumption, and (vi) water flux by osmosis as a function of (a) initial concentration of NaCl feed solution (diluate and concentrate streams), (b) superficial velocity of feed solution, and (c) applied stack voltage per cell-pair of membranes. A laboratory‑scale single stage batch-recycle electrodialysis experimental apparatus was assembled with five cell‑pairs of IEMs with an active cross-sectional area of 7.84 cm2. In this study, seven combinations of IEMs (commercial and laboratory-made) were compared: (i) Neosepta AMX/CMX, (ii) PCA PCSA/PCSK, (iii) Fujifilm Type 1 AEM/CEM, (iv) SUEZ AR204SZRA/CR67HMR, (v) Ralex AMH-PES/CMH-PES, (vi) Neosepta AMX/Bare Polycarbonate membrane (Polycarb), and (vii) Neosepta AMX/Sandia novel bioinspired cation exchange membrane (SandiaCEM). ED desalination performance with the Sandia novel bioinspired cation exchange membrane (SandiaCEM) was found to be competitive with commercial Neosepta CMX cation exchange membrane.

Ab initio and force field molecular dynamics study of bulk organophosphorus and organochlorine liquid structures

We performed ab initio molecular dynamics (AIMD) simulations to benchmark bulk liquid structures and to evaluate results from all-atom force field molecular dynamics (FFMD) simulations with the generalized Amber force field (GAFF) for organophosphorus (OP) and organochlorine (OC) compounds. Our work also addresses the current and important topic of force field validation, applied here to a set of nonaqueous organic liquids. Our approach differs from standard treatments, which validate force fields based on thermodynamic data. Utilizing radial distribution functions (RDFs), our results show that GAFF reproduces the AIMD-predicted asymmetric liquid structures moderately well for OP compounds that contain bulky alkyl groups. Among the OCs, RDFs obtained from FFMD overlap well with AIMD results, with some offsets in position and peak structuring. However, re-parameterization of GAFF for some OCs is needed to reproduce fully the liquid structures predicted by AIMD. The offsets between AIMD and FFMD peak positions suggest inconsistencies in the developed force fields, but, in general, GAFF is able to capture short-ranged and long-ranged interactions of OPs and OCs observed in AIMD. Along with the local coordination structure, we also compared enthalpies of vaporization. Overall, calculated bulk properties from FFMD compared reasonably well with experimental values, suggesting that small improvements within the FF should focus on parameters that adjust the bulk liquid structures of these compounds.

Partitioning of Seven Different Classes of Antibiotics into LPS Monolayers Supports Three Different Permeation Mechanisms through the Outer Bacterial Membrane

The outer membrane (OM) of Gram-negative (G-) bacteria presents a barrier for many classes of antibacterial agents. Lipopolysaccharide (LPS), present in the outer leaflet of the OM, is stabilized by divalent cations and is considered to be the major impediment for antibacterial agent permeation. However, the actual affinities of major antibiotic classes toward LPS have not yet been determined. In the present work, we use Langmuir monolayers formed from E. coli Re and Rd types of LPS to record pressure-area isotherms in the presence of antimicrobial agents. Our observations suggest three general types of interactions. First, some antimicrobials demonstrated no measurable interactions with LPS. This lack of interaction in the case of cefsulodin, a third-generation cephalosporin antibiotic, correlates with its low efficacy against G- bacteria. Ampicillin and ciprofloxacin also show no interactions with LPS, but in contrast to cefsulodin, both exhibit good efficacy against G- bacteria, indicating permeation through common porins. Second, we observe substantial intercalation of the more hydrophobic antibiotics, novobiocin, rifampicin, azithromycin, and telithromycin, into relaxed LPS monolayers. These largely repartition back to the subphase with monolayer compression. We find that the hydrophobic area, charge, and dipole all show correlations with both the mole fraction of antibiotic retained in the monolayer at the monolayer-bilayer equivalence pressure and the efficacies of these antibiotics against G- bacteria. Third, amine-rich gentamicin and the cationic antimicrobial peptides polymyxin B and colistin show no hydrophobic insertion but are instead strongly driven into the polar LPS layer by electrostatic interactions in a pressure-independent manner. Their intercalation stably increases the area per molecule (by up to 20%), which indicates massive formation of defects in the LPS layer. These defects support a self-promoted permeation mechanism of these antibiotics through the OM, which explains the high efficacy and specificity of these antimicrobials against G- bacteria.

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.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.

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.

Machine Learning-Guided Approach for Studying Solvation Environments

Molecular-level understanding and characterization of solvation environments are often needed across chemistry, biology, and engineering. Toward practical modeling of local solvation effects of any solute in any solvent, we report a static and all-quantum mechanics-based cluster-continuum approach for calculating single-ion solvation free energies. This approach uses a global optimization procedure to identify low-energy molecular clusters with different numbers of explicit solvent molecules and then employs the smooth overlap for atomic positions learning kernel to quantify the similarity between different low-energy solute environments. From these data, we use sketch maps, a nonlinear dimensionality reduction algorithm, to obtain a two-dimensional visual representation of the similarity between solute environments in differently sized microsolvated clusters. After testing this approach on different ions having charges 2+, 1+, 1-, and 2-, we find that the solvation environment around each ion can be seen to usually become more similar in hand with its calculated single-ion solvation free energy. Without needing either dynamics simulations or an a priori knowledge of local solvation structure of the ions, this approach can be used to calculate solvation free energies within 5% of experimental measurements for most cases, and it should be transferable for the study of other systems where dynamics simulations are not easily carried out.

Glutaminase Activity of L-Asparaginase Contributes to Durable Preclinical Activity against Acute Lymphoblastic Leukemia

We and others have reported that the anticancer activity of L-asparaginase (ASNase) against asparagine synthetase (ASNS)-positive cell types requires ASNase glutaminase activity, whereas anticancer activity against ASNS-negative cell types does not. Here, we attempted to disentangle the relationship between asparagine metabolism, glutamine metabolism, and downstream pathways that modulate cell viability by testing the hypothesis that ASNase anticancer activity is based on asparagine depletion rather than glutamine depletion per se. We tested ASNase wild-type (ASNase^WT) and its glutaminase-deficient Q59L mutant (ASNase^Q59L) and found that ASNase glutaminase activity contributed to durable anticancer activity against xenografts of the ASNS-negative Sup-B15 leukemia cell line in NOD/SCID gamma mice, whereas asparaginase activity alone yielded a mere growth delay. Our findings suggest that ASNase glutaminase activity is necessary for durable, single-agent anticancer activity in vivo, even against ASNS-negative cancer types.

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.