Role of methyl-induced polarization in ion binding

Insight into the K channel's selectivity from binding of K+, Na+ and water to N-methylacetamide

In potassium channels that conduct K+ selectively over Na+, which sites are occupied by K+ or water and the mechanism of selectivity are unresolved questions. The combination of the energetics and the constraints imposed by the protein structure yield the selective permeation and occupancy. To gain insight into the combination of structure and energetics, we performed density functional theory (DFT) calculations of multiple N-methyl acetamide (NMA) ligands binding to K+ and Na+, relative to hydrated K+ and Na+. NMA is an analogue of the amino acid backbone and provides the carbonyl binding to the ions that occurs in most binding sites of the K+ channel. Unconstrained optimal structures are obtained through geometry optimization calculations of the NMA ligand binding. The complexes formed by 8 NMA binding to the cations have the O atoms positioned in nearly identical locations as the O atoms in the selectivity filter. The transfer free energies between bulk water and K+ or Na+ bound to 8 NMA are almost identical, implying there is no selectivity by a single site. For water optimized with 8 NMA, binding is weak and O atoms are not positioned as in the K+ channel selectivity filter, suggesting that the ions are much more favored than water. Optimal structures of 8 NMA binding with two cations (K+ or Na+) are stable and have lower binding free energy than the optimal structures with just one cation. However, in the Na+ case, the optimal structure deforms and does not match the K+ channel; that is, two bound Na+ are destabilizing. In contrast, the two K+ structure is stabilized and the selectivity free energy favors K+. Overall, this study shows that binding site occupancy and the mechanism for K+ selectivity involves multiple K+ binding in multiple neighboring layers or sites of the K+ channel selectivity filter.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Effects of glutamine, glutamate, and aspartate on intestinal barrier integrity and amino acid pool of the small intestine in piglets with normal or low energy diet

Aspartate (asp), glutamate (glu), and glutamine (gln) are the major energy fuels for the small intestine, and it had been indicated in our previous study that the mix of these three amino acid supplementations could maintain intestinal energy homeostasis. This study aimed to further investigate whether the treatment of gln, glu, and asp in low energy diet affects the intestinal barrier integrity and amino acid pool in weaning piglets. A total of 198 weaned piglets were assigned to 3 treatments: control (basal diet + 1.59% L-Ala); T1 (basal diet + 1% L-Gln + 0.5% L-Glu + 0.1% L-Asp); and T2 (low energy diet + 1% L-Gln + 0.5% L-Glu + 0.1% L-Asp). The blood, jejunum, and ileum were obtained on day 5 or on day 21 post-weaning, respectively. Our results showed that T1 and T2 treatments increased the abundances of occludin, claudin-1, and claudin-3 in the small intestine while decreasing the serum diamine oxidase (DAO) and D-lactate levels in weaning piglets. Meanwhile, T1 and T2 treatments significantly increased the positive rate of proliferating cell nuclear antigen (PCNA) of the small intestine, promoting intestinal cell proliferation. We also found that supplementation with glu, gln, and asp improved the serum amino acid pool and promoted ileal amino acid transporter gene expression of slc3a2, slc6a14, and slc7a11 in weaned piglets. Additionally, on day 21 post-weaning, T1 and T2 treatments stimulated the phosphorylation of the mTOR-S6K1-4EBP1 signaling pathway in the small intestine, which may implicate the enhanced protein synthesis rate. In summary, dietary supplementation of gln, glu, and asp was beneficial to the intestinal barrier function and amino acid pool regulation, while the benefits of gln, glu, and asp treatment might be diminished by the low-energy diet. The results demonstrated that the supplementation of gln, glu, and asp under low energy levels was preferentially supplied as the energy fuel to restore the gut barrier function in piglets on day 5 post-weaning. With the increase in age and intestinal maturation (on day 21 post-weaning), gln, glu, and asp supplementation could also show an effect on the regulation of the amino acid pool and protein synthesis.

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.

Inclusion of High-Field Target Data in AMOEBA's Calibration Improves Predictions of Protein-Ion Interactions

The reliability of molecular mechanics simulations to predict effects of ion binding to proteins depends on their ability to simultaneously describe ion-protein, ion-water, and protein-water interactions. Force fields (FFs) to describe protein-water and ion-water interactions have been constructed carefully and have also been refined routinely to improve accuracy. Descriptions for ion-protein interactions have also been refined, although in an a posteriori manner through the use of "nonbonded-fix (NB-fix)" approaches in which parameters from default Lennard-Jones mixing rules are replaced with those optimized against some reference data. However, even after NB-fix corrections, there remains a significant need for improvement. This is also true for polarizable FFs that include self-consistent inducible moments. Our recent studies on the polarizable AMOEBA FF suggested that the problem associated with modeling ion-protein interactions could be alleviated by recalibrating polarization models of cation-coordinating functional groups so that they respond better to the high electric fields present near ions. Here, we present such a recalibration of carbonyls, carboxylates, and hydroxyls in the AMOEBA protein FF and report that it does improve predictions substantially─mean absolute errors in Na⁺-protein and K⁺-protein interaction energies decrease from 8.7 to 5.3 and 9.6 to 6.3 kcal/mol, respectively. Errors are computed with respect to estimates from van der Waals-inclusive density functional theory benchmarked against high-level quantum mechanical calculations and experiments. While recalibration does improve ion-protein interaction energies, they still remain underestimated, suggesting that further improvements can be made in a systematic manner through modifications in classical formalism. Nevertheless, we show that by applying our many-body NB-fix correction to Lennard-Jones components, these errors are further reduced to 2.7 and 2.6 kcal/mol, respectively, for Na⁺ and K⁺ ions. Finally, we show that the recalibrated AMOEBA protein FF retains its intrinsic reliability in predicting protein structure and dynamics in the condensed phase.

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.

Methyl-Induced Polarization Destabilizes the Noncovalent Interactions of N-Methylated Lysines

Lysine methylation can modify noncovalent interactions by altering lysine's hydrophobicity as well as its electronic structure. Although the ramifications of the former are documented, the effects of the latter remain largely unknown. Understanding the electronic structure is important for determining how biological methylation modulates protein-protein binding, and the impact of artificial methylation experiments in which methylated lysines are used as spectroscopic probes and protein crystallization facilitators. The benchmarked first-principles calculations undertaken here reveal that methyl-induced polarization weakens the electrostatic attraction of amines with protein functional groups - salt bridges, hydrogen bonds and cation-π interactions weaken by as much as 10.3, 7.9 and 3.5 kT, respectively. Multipole analysis shows that weakened electrostatics is due to the altered inductive effects, which overcome increased attraction from methyl-enhanced polarizability and dispersion. Due to their fundamental nature, these effects are expected to be present in many cases. A survey of methylated lysines in protein structures reveals several cases in which methyl-induced polarization is the primary driver of altered noncovalent interactions; in these cases, destabilizations are found to be in the 0.6-4.7 kT range. The clearest case of where methyl-induced polarization plays a dominant role in regulating biological function is that of the PHD1-PHD2 domain, which recognizes lysine-methylated states on histones. These results broaden our understanding of how methylation modulates noncovalent interactions.

In Vitro Screening of 21 Bisphenol A Replacement Alternatives: Compared with Bisphenol A, the Majority of Alternatives Are More Cytotoxic and Dysregulate More Genes in Avian Hepatocytes

An avian in vitro screening approach was used to determine the effects of 21 bisphenol A (BPA) alternatives. Cytotoxicity and dysregulation of genes associated with estrogen response and other toxicologically relevant pathways evoked by these alternatives were compared with BPA. Most of the BPA alternatives (15/21) were equally or more cytotoxic than BPA in chicken embryonic hepatocytes; variability in cell viability was associated with chemical structure and the log octanol-water partition coefficient (logP) values. A negative linear relationship (r ²  = 0.745; p = 0.49^-07 ; n = 18) was observed between logP and the log median lethal concentration (logLC50) values. The least cytotoxic BPA alternatives elicited the greatest gene dysregulation and, overall, most of the alternatives altered more genes than BPA (measured with a custom polymerase chain reaction array). This overall approach shows promise for use as a screen for hazard-based prioritization of BPA replacement alternatives and to ideally identify those that may be less harmful and/or require additional toxicity testing. Environ Toxicol Chem 2021;40:2026-2033. © 2021 Her Majesty the Queen in Right of Canada Environmental Toxicology and Chemistry © 2021 SETAC. Reproduced with the permission of the Minister of Environment and Climate Change Canada.

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.

Progress and challenges in ab initio simulations of quantum nuclei in weakly bonded systems

Atomistic simulations based on the first-principles of quantum mechanics are reaching unprecedented length scales. This progress is due to the growth in computational power allied with the development of new methodologies that allow the treatment of electrons and nuclei as quantum particles. In the realm of materials science, where the quest for desirable emergent properties relies increasingly on soft weakly bonded materials, such methods have become indispensable. In this Perspective, an overview of simulation methods that are applicable for large system sizes and that can capture the quantum nature of electrons and nuclei in the adiabatic approximation is given. In addition, the remaining challenges are discussed, especially regarding the inclusion of nuclear quantum effects (NQEs) beyond a harmonic or perturbative treatment, the impact of NQEs on electronic properties of weakly bonded systems, and how different first-principles potential energy surfaces can change the impact of NQEs on the atomic structure and dynamics of weakly bonded systems.

Pore-forming transmembrane domains control ion selectivity and selectivity filter conformation in the KirBac1.1 potassium channel

Potassium (K⁺) channels are membrane proteins with the remarkable ability to very selectively conduct K⁺ ions across the membrane. High-resolution structures have revealed that dehydrated K⁺ ions permeate through the narrowest region of the pore, formed by the backbone carbonyls of the signature selectivity filter (SF) sequence TxGYG. However, the existence of nonselective channels with similar SF sequences, as well as effects of mutations in other regions on selectivity, suggest that the SF is not the sole determinant of selectivity. We changed the selectivity of the KirBac1.1 channel by introducing mutations at residue I131 in transmembrane helix 2 (TM2). These mutations increase Na⁺ flux in the absence of K⁺ and introduce significant proton conductance. Consistent with K⁺ channel crystal structures, single-molecule FRET experiments show that the SF is conformationally constrained and stable in high-K⁺ conditions but undergoes transitions to dilated low-FRET states in high-Na⁺/low-K⁺ conditions. Relative to wild-type channels, I131M mutants exhibit marked shifts in the K⁺ and Na⁺ dependence of SF dynamics to higher K⁺ and lower Na⁺ concentrations. These results illuminate the role of I131, and potentially other structural elements outside the SF, in controlling ion selectivity, by suggesting that the physical interaction of these elements with the SF contributes to the relative stability of the constrained K⁺-induced SF configuration versus nonselective dilated conformations.

Preparation and characterization of iron-chelating peptides from whey protein: An alternative approach for chemical iron fortification

Iron fortification of staple food is a strategy utilized worldwide to address the concern of dietary iron deficiency. However, traditional salt-based fortification methods have limitations with gastrointestinal stability and bioavailability. Iron chelating peptides from easily available and scalable proteins such as whey protein have been proposed as promising candidates to circumvent the above mentioned limitations by enhancing iron absorption and bioavailability. In this study, we report methods to produce whey protein derived iron-chelating peptides and describe their physicochemical characteristics. Peptides derived from whey proteins prepared by ultrafiltration of whey followed by hydrolysation were iron chelated to produce peptide-iron complexes. These complexes had a size of 422.9 ± 3.41 nm, chelated iron content of 36.42 µg/ mg protein, and a low zeta potential (-10.80 mV) compared to whey peptides. Spectra analysis using ultraviolet-visible absorption and Fourier transform infrared spectroscopy showed structural transformation indicating iron chelation. Mass spectrometric analysis using LC-MS/MS confirmed the presence of both hydrophilic and hydrophobic peptides in the complexes with sizes ranging from 275 Da to 1916 Da. Furthermore, reduction in the antioxidant property of peptides following iron complexing indicates iron chelation. Our results suggest that whey protein derived peptide-iron complexes can be used as a potential alternative for chemical iron fortificants for food products and also as iron supplements.

Predictive QM/MM Modeling of Modulations in Protein-Protein Binding by Lysine Methylation

Lysine methylation is a key regulator of protein-protein binding. The amine group of lysine can accept up to three methyl groups, and experiments show that protein-protein binding free energies are sensitive to the extent of methylation. These sensitivities have been rationalized in terms of chemical and structural features present in the binding pockets of methyllysine binding domains. However, understanding their specific roles requires an energetic analysis. Here we propose a theoretical framework to combine quantum and molecular mechanics methods, and compute the effect of methylation on protein-protein binding free energies. The advantages of this approach are that it derives contributions from all local non-trivial effects of methylation on induction, polarizability and dispersion directly from self-consistent electron densities, and at the same time determines contributions from well-characterized hydration effects using a computationally efficient classical mean field method. Limitations of the approach are discussed, and we note that predicted free energies of fourteen out of the sixteen cases agree with experiment. Critical assessment of these cases leads to the following overarching principles that drive methylation-state recognition by protein domains. Methylation typically reduces the pairwise interaction between proteins. This biases binding toward lower methylated states. Simultaneously, however, methylation also makes it easier to partially dehydrate proteins and place them in protein-protein complexes. This latter effect biases binding in favor of higher methylated states. The overall effect of methylation on protein-protein binding depends ultimately on the balance between these two effects, which is observed to be tuned via several combinations of local features.

Peptide-Mineral Complexes: Understanding Their Chemical Interactions, Bioavailability, and Potential Application in Mitigating Micronutrient Deficiency

Iron, zinc, and calcium are essential micronutrients that play vital biological roles to maintain human health. Thus, their deficiencies are a public health concern worldwide. Mitigation of these deficiencies involves micronutrient fortification of staple foods, a strategy that can alter the physical and sensory properties of foods. Peptide-mineral complexes have been identified as promising alternatives for mineral-fortified functional foods or mineral supplements. This review outlines some of the methods used in the determination of the mineral chelating activities of food protein-derived peptides and the approaches for the preparation, purification and identification of mineral-binding peptides. The structure-activity relationship of mineral-binding peptides and the potential use of peptide-mineral complexes as functional food ingredients to mitigate micronutrient deficiency are discussed in relation to their chemical interactions, solubility, gastrointestinal digestion, absorption, and bioavailability. Finally, insights on the current challenges and future research directions in this area are provided.

Transferable interactions of Li+ and Mg2+ ions in polarizable models

Therapeutic implications of Li⁺, in many cases, stem from its ability to inhibit certain Mg²⁺-dependent enzymes, where it interacts with or substitutes for Mg²⁺. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li⁺ and Mg²⁺ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

Improved description of ligand polarization enhances transferability of ion-ligand interactions

The reliability of molecular mechanics (MM) simulations in describing biomolecular ion-driven processes depends on their ability to accurately model interactions of ions simultaneously with water and other biochemical groups. In these models, ion descriptors are calibrated against reference data on ion-water interactions, and it is then assumed that these descriptors will also satisfactorily describe interactions of ions with other biochemical ligands. The comparison against the experiment and high-level quantum mechanical data show that this transferability assumption can break down severely. One approach to improve transferability is to assign cross terms or separate sets of non-bonded descriptors for every distinct pair of ion type and its coordinating ligand. Here, we propose an alternative solution that targets an error-source directly and corrects misrepresented physics. In standard model development, ligand descriptors are never calibrated or benchmarked in the high electric fields present near ions. We demonstrate for a representative MM model that when the polarization descriptors of its ligands are improved to respond to both low and high fields, ligand interactions with ions also improve, and transferability errors reduce substantially. In our case, the overall transferability error reduces from 3.3 kcal/mol to 1.8 kcal/mol. These improvements are observed without compromising on the accuracy of low-field interactions of ligands in gas and condensed phases. Reference data for calibration and performance evaluation are taken from the experiment and also obtained systematically from "gold-standard" CCSD(T) in the complete basis set limit, followed by benchmarked vdW-inclusive density functional theory.

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.

Ion-Hydroxyl Interactions: From High-Level Quantum Benchmarks to Transferable Polarizable Force Fields

Ion descriptors in molecular mechanics models are calibrated against reference data on ion-water interactions. It is then typically assumed that these descriptors will also satisfactorily describe interactions of ions with other functional groups, such as those present in biomolecules. However, several studies now demonstrate that this transferability assumption produces, in many different cases, large errors. Here we address this issue in a representative polarizable model and focus on transferability of cationic interactions from water to a series of alcohols. Both water and alcohols use hydroxyls for ion-coordination, and, therefore, this set of molecules constitutes the simplest possible case of transferability. We obtain gas phase reference data systematically from "gold-standard" quantum Monte Carlo and CCSD(T) methods, followed by benchmarked vdW-corrected DFT. We learn that the original polarizable model yields large gas phase water → alcohol transferability errors - the RMS and maximum errors are 2.3 and 5.1 kcal/mol, respectively. These errors are, nevertheless, systematic in that ion-alcohol interactions are overstabilized, and systematic errors typically imply that some essential physics is either missing or misrepresented. A comprehensive analysis shows that when both low- and high-field responses of ligand dipole polarization are described accurately, then transferability improves significantly - the RMS and maximum errors in the gas phase reduce, respectively, to 0.9 and 2.5 kcal/mol. Additionally, predictions of condensed phase transfer free energies also improve. Nevertheless, within the limits of the extrathermodynamic assumptions necessary to separate experimental estimates of salt dissolution into constituent cationic and anionic contributions, we note that the error in the condensed phase is systematic, which we attribute, at least, partially to the parametrization in long-range electrostatics. Overall, this work demonstrates a rational approach to boosting transferability of ionic interactions that will be applicable broadly to improving other polarizable and nonpolarizable models.

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.

Tailoring van der Waals dispersion interactions with external electric charges

van der Waals (vdW) dispersion interactions strongly impact the properties of molecules and materials. Often, the description of vdW interactions should account for the coupling with pervasive electric fields, stemming from membranes, ionic channels, liquids, or nearby charged functional groups. However, this quantum-mechanical effect has been omitted in atomistic simulations, even in widely employed electronic-structure methods. Here, we develop a model and study the effects of an external charge on long-range vdW correlations. We show that a positive external charge stabilizes dispersion interactions, whereas a negative charge has an opposite effect. Our analytical results are benchmarked on a series of (bio)molecular dimers and supported by calculations with high-level correlated quantum-chemical methods, which estimate the induced dispersion to reach up to 35% of intermolecular binding energy (4 kT for amino-acid dimers at room temperature). Our analysis bridges electrostatic and electrodynamic descriptions of intermolecular interactions and may have implications for non-covalent reactions, exfoliation, dissolution, and permeation through biological membranes.

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.

The exceptionally high reactivity of Cys 621 is critical for electrophilic activation of the sensory nerve ion channel TRPA1

Electrophiles produced during oxidative stress trigger pain responses by reacting with TRPA1 ion channels on sensory nerves. Bahia et al. show that residue C621 on TRPA1 has remarkable reactivity with electrophiles—more than cellular antioxidants—and is crucial for this sensory response.

Activation of the sensory nerve ion channel TRPA1 by electrophiles is the key mechanism that initiates nociceptive signaling, and leads to defensive reflexes and avoidance behaviors, during oxidative stress in mammals. TRPA1 is rapidly activated by subtoxic levels of electrophiles, but it is unclear how TRPA1 outcompetes cellular antioxidants that protect cytosolic proteins from electrophiles. Here, using physiologically relevant exposures, we demonstrate that electrophiles react with cysteine residues on mammalian TRPA1 at rates that exceed the reactivity of typical cysteines by 6,000-fold and that also exceed the reactivity of antioxidant enzymes. We show that TRPA1 possesses a complex reactive cysteine profile in which C621 is necessary for electrophile-induced binding and activation. Modeling of deprotonation energies suggests that K620 contributes to C621 reactivity and mutation of K620 alone greatly reduces the effect of electrophiles on TRPA1. Nevertheless, binding of electrophiles to C621 is not sufficient for activation, which also depends on the function of another reactive cysteine (C665). Together, our results demonstrate that TRPA1 acts as an effective electrophilic sensor because of the exceptionally high reactivity of C621.

Stimulation of Nipah Fusion: Small Intradomain Changes Trigger Extensive Interdomain Rearrangements

Nipah is an emerging paramyxovirus that is of serious concern to human health. It invades host cells using two of its membrane proteins-G and F. G binds to host ephrins and this stimulates G to activate F. Upon activation, F mediates virus-host membrane fusion. Here we focus on mechanisms that underlie the stimulation of G by ephrins. Experiments show that G interacts with ephrin and F through separate sites located on two different domains, the receptor binding domain (RBD) and the F activation domain (FAD). No models explain this allosteric coupling. In fact, the analogous mechanisms in other paramyxoviruses also remain undetermined. The structural organization of G is such that allosteric coupling must involve at least one of the two interfaces-the RBD-FAD interface and/or the RBD-RBD interface. Here we examine using molecular dynamics the effect of ephrin binding on the RBD-RBD interface. We find that despite inducing small changes in individual RBDs, ephrin reorients the RBD-RBD interface extensively, and in a manner that will enhance solvent exposure of the FAD. While this finding supports a proposed model of G stimulation, we also find from additional simulations that ephrin induces a similar RBD-RBD reorientation in a stimulation-deficient G mutant, V₂₀₉ VG → AAA. Together, our simulations suggest that while inter-RBD reorientation may be important, it is not, by itself, a sufficient condition for G stimulation. Additionally, we find that the mutation affects the conformational ensemble of RBD globally, including the RBD-FAD interface, suggesting the latter's role in G stimulation. Because ephrin induces small changes in individual RBDs, a proper analysis of conformational ensembles required that they are compared directly-we employ a method we developed recently, which we now release at SimTK, and show that it also performs excellently for non-Gaussian distributions.

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in nature and influence the structure, stability, dynamics, and function of molecules and materials throughout chemistry, biology, physics, and materials science. These forces are quantum mechanical in origin and arise from electrostatic interactions between fluctuations in the electronic charge density. Here, we explore the conceptual and mathematical ingredients required for an exact treatment of vdW interactions, and present a systematic and unified framework for classifying the current first-principles vdW methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem (namely the Rutgers-Chalmers vdW-DF, Vydrov-Van Voorhis (VV), exchange-hole dipole moment (XDM), Tkatchenko-Scheffler (TS), many-body dispersion (MBD), and random-phase approximation (RPA) approaches). Particular attention is paid to the intriguing nature of many-body vdW interactions, whose fundamental relevance has recently been highlighted in several landmark experiments. The performance of these models in predicting binding energetics as well as structural, electronic, and thermodynamic properties is connected with the theoretical concepts and provides a numerical summary of the state-of-the-art in the field. We conclude with a roadmap of the conceptual, methodological, practical, and numerical challenges that remain in obtaining a universally applicable and truly predictive vdW method for realistic molecular systems and materials.

Ion-Specific Effects in Carboxylate Binding Sites

Specific ion binding by carboxylates (-COO^-) is a broadly important topic because -COO^- is one of the most common functional groups coordinated to metal ions in metalloproteins and synthetic polymers. We apply quantum chemical methods and the quasi-chemical free-energy theory to investigate how variations in the number of -COO^- ligands in a binding site determine ion-binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) and divalent (Zn²⁺, Ca²⁺) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation and ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion-binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy in ion association between molecular ligands in aqueous solutions and ionomers, and their chemical analogues in ion-channel binding sites.

POPC Bilayers Supported on Nanoporous Substrates: Specific Effects of Silica-Type Surface Hydroxylation and Charge Density

Recent advances in nanotechnology bring to the forefront a new class of extrinsic constraints for remodeling lipid bilayers. In this next-generation technology, membranes are supported over nanoporous substrates. The nanometer-sized pores in the substrate are too small for bilayers to follow the substrate topology; consequently, the bilayers hang over the pores. Experiments demonstrate that nanoporous substrates remodel lipid bilayers differently from continuous substrates. The underlying molecular mechanisms, however, remain largely undetermined. Here we use molecular dynamics (MD) simulations to probe the effects of silica-type hydroxylation and charge densities on adsorbed palmitoyl-oleoylphosphatidylcholine (POPC) bilayers. We find that a 50% porous substrate decorated with a surface density of 4.6 hydroxyls/nm(2) adsorbs a POPC bilayer at a distance of 4.5 Å, a result consistent with neutron reflectivity experiments conducted on topologically similar silica constructs under highly acidic conditions. Although such an adsorption distance suggests that the interaction between the bilayer and the substrate will be buffered by water molecules, we find that the substrate does interact directly with the bilayer. The substrate modifies several properties of the bilayer-it dampens transverse lipid fluctuations, reduces lipid diffusion rates, and modifies transverse charge densities significantly. Additionally, it affects lipid properties differently in the two leaflets. Compared to substrates functionalized with sparser surface hydroxylation densities, this substrate adheres to bilayers at smaller distances and also remodels POPC more extensively, suggesting a direct correspondence between substrate hydrophilicity and membrane properties. A partial deprotonation of surface hydroxyls, as expected of a silica substrate under mildly acidic conditions, however, produces an inverse effect: it increases the substrate-bilayer distance, which we attribute to the formation of an electric double layer over the negatively charged substrate, and restores, at least partially, leaflet asymmetry and headgroup orientations. Overall, this study highlights the intrinsic complexity of lipid-substrate interactions and suggests the prospect of making two surface attributes-dipole densities and charge densities-work antagonistically toward remodeling lipid bilayer properties.

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.

The role of an ancestral hyperpolarization-activated cyclic nucleotide-gated K+ channel in branchial acid-base regulation in the green crab, Carcinus maenas

Numerous electrophysiological studies on branchial K(+) transport in brachyuran crabs have established an important role for potassium channels in osmoregulatory ion uptake and ammonia excretion in the gill epithelium of decapod crustaceans. However, hardly anything is known of the actual nature of these channels in crustaceans. In the present study, the identification of a hyperpolarization-activated cyclic nucleotide-gated potassium channel (HCN) in the transcriptome of the green crab Carcinus maenas and subsequent performance of quantitative real-time PCR revealed the ubiquitous expression of this channel in this species. Even though mRNA expression levels in the cerebral ganglion were found to be approximately 10 times higher compared with all other tissues, posterior gills still expressed significant levels of HCN, indicating an important role for this transporter in branchial ion regulation. The relatively unspecific K(+)-channel inhibitor Ba(2+), as well as the HCN-specific blocker ZD7288, as applied in gill perfusion experiments and electrophysiological studies employing the split gill lamellae revealed the presence of at least two different K(+)/NH4(+)-transporting structures in the branchial epithelium of C. maenas. Furthermore, HCN mRNA levels in posterior gill 7 decreased significantly in response to the respiratory or metabolic acidosis that was induced by acclimation of green crabs to high environmental PCO2 and ammonia, respectively. Consequently, the present study provides first evidence that HCN-promoted NH4(+) epithelial transport is involved in both branchial acid-base and ammonia regulation in an invertebrate.

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

Cation Selectivity in Biological Cation Channels Using Experimental Structural Information and Statistical Mechanical Simulation

Cation selective channels constitute the gate for ion currents through the cell membrane. Here we present an improved statistical mechanical model based on atomistic structural information, cation hydration state and without tuned parameters that reproduces the selectivity of biological Na+ and Ca2+ ion channels. The importance of the inclusion of step-wise cation hydration in these results confirms the essential role partial dehydration plays in the bacterial Na+ channels. The model, proven reliable against experimental data, could be straightforwardly used for designing Na+ and Ca2+ selective nanopores.

Effect of intrinsic and extrinsic factors on the simulated D-band length of type I collagen

A signature feature of collagen is its axial periodicity visible in TEM as alternating dark and light bands. In mature, type I collagen, this repeating unit, D, is 67 nm long. This periodicity reflects an underlying packing of constituent triple-helix polypeptide monomers wherein the dark bands represent gaps between axially adjacent monomers. This organization is visible distinctly in the microfibrillar model of collagen obtained from fiber diffraction. However, to date, no atomistic simulations of this diffraction model under zero-stress conditions have reported a preservation of this structural feature. Such a demonstration is important as it provides the baseline to infer response functions of physiological stimuli. In contrast, simulations predict a considerable shrinkage of the D-band (11-19%). Here we evaluate systemically the effect of several factors on D-band shrinkage. Using force fields employed in previous studies we find that irrespective of the temperature/pressure coupling algorithms, assumed salt concentration or hydration level, and whether or not the monomers are cross-linked, the D-band shrinks considerably. This shrinkage is associated with the bending and widening of individual monomers, but employing a force field whose backbone dihedral energy landscape matches more closely with our computed CCSD(T) values produces a small D-band shrinkage of < 3%. Since this force field also performs better against other experimental data, it appears that the large shrinkage observed in earlier simulations is a force-field artifact. The residual shrinkage could be due to the absence of certain atomic-level details, such as glycosylation sites, for which we do not yet have suitable data.

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.

Hydrogen bonds as molecular timers for slow inactivation in voltage-gated potassium channels

Voltage-gated potassium (Kv) channels enable potassium efflux and membrane repolarization in excitable tissues. Many Kv channels undergo a progressive loss of ion conductance in the presence of a prolonged voltage stimulus, termed slow inactivation, but the atomic determinants that regulate the kinetics of this process remain obscure. Using a combination of synthetic amino acid analogs and concatenated channel subunits we establish two H-bonds near the extracellular surface of the channel that endow Kv channels with a mechanism to time the entry into slow inactivation: an intra-subunit H-bond between Asp447 and Trp434 and an inter-subunit H-bond connecting Tyr445 to Thr439. Breaking of either interaction triggers slow inactivation by means of a local disruption in the selectivity filter, while severing the Tyr445–Thr439 H-bond is likely to communicate this conformational change to the adjacent subunit(s).

DOI:http://dx.doi.org/10.7554/eLife.01289.001

Proteins are made from long chains of smaller molecules, called amino acids. These chains twist and bend into complex three-dimensional shapes, and sometimes two or more chains, or ‘subunits’, are packed into a protein. These shapes are often held together by hydrogen bonds between some of the amino acids. Moreover, since the shape of a protein defines its function, some proteins must be able to switch between different shapes to function properly.

Ion channels are proteins that form pores through cell membranes, allowing ions to flow in and out of the cell. Potassium ion channels, which are found in neurons and heart muscle cells, have four subunits that move to open or close the central pore in response to various signals.

The closing of the channels can be ‘fast’ or ‘slow’. When the channels are closed quickly (called fast inactivation), a small part of the protein ‘plugs’ the pore from the inside of the cell. However, the mechanism behind slow inactivation remained obscure. It was thought to involve hydrogen bonds between some of the bulky amino acids that are found at the edge the pore. However, testing this hypothesis—by replacing these amino acids with alternatives that cannot form hydrogen bonds—was tricky because none of the 20 naturally occurring amino acids were alike enough to be suitable replacements.

Now, Pless et al. have overcome this limitation by using synthetic amino acids that form hydrogen bonds that are stronger or weaker than those formed by the amino acids they are replacing. The results suggest that two types of hydrogen bond keep the pore open: one is a bond between two amino acids in the same subunit, and the other is an inter-subunit bond between amino acids in neighbouring subunits. Pless et al. suggest that opening the channel causes small movements that gradually weaken, and eventually break, these bonds in one of the four subunits. Specific amino acids within the pore are then free to twist and—via a cascade of similar movements in the other three subunits—block the pore and halt the flow of ions. As such, these networks of hydrogen bonds act as pre-set breaking points allowing channels to close, even in response to continued stimulation.

Since regulated potassium channel activity underpins healthy neurons and heart muscles; understanding what controls their inactivation rate may lead to new approaches to tune their activity and treatments for important diseases.

DOI:http://dx.doi.org/10.7554/eLife.01289.002