Calculation of the dielectric permittivity profile for a nonuniform system: Application to a lipid bilayer simulation

How Molecular Orientation Affects the Static Permittivity Profile of the Polar and Nonpolar Liquid-Liquid Interface

The dielectric permittivity across the liquid-liquid interface presents an intrinsic response, with respect to the instantaneous interface reference. We hypothesize that dielectric responses across the nonpolar and polar liquid-liquid interfaces have different behaviors and underlying mechanisms. Molecular dynamics simulations were used to compare and contrast the dielectric response of a nonpolar (1,2-dichloroethane/water) and a polar (1-octanol/water) liquid-liquid interface system. We found that the enhanced dielectric permittivity at the nonpolar interface is attributed to the increased water dipole orientation and polarization density. In the case of the polar interface, strong association of the immiscible solvents inhibits the molecular dipole orientation, counteracting the effect from the enhanced surface water polarization density and resulting in a standard dielectric response. Detailed knowledge of the hydrogen bond networks and molecular dipole orientation with respect to the specific instantaneous interfacial and bulk regions reveals the effect of molecular proximity and the interaction with the opposing interfacial molecules on the mechanism of the dielectric permittivity response across the liquid-liquid interface phase boundary.

Uniaxial Symmetry Breaking in Bacteriorhodopsin at the Thermal Phase Transition of Lipids of Purple Membranes

The article correlates between symmetry breaking and phase transition. An analogy, extending from physics to biology, is known to exist between these two topics. Bacteriorhodopsin (bR) as a paradigm of membrane proteins has been used as a case study in the present work. The bR, as the sole protein embedded in what is called a purple membrane (PM), has attracted widespread interest in bionanotechnological applications. The lipids of PM have a crucial role in maintaining the crystal lattice of bR inside PM. For this reason, the present work has been concerned with elucidating the thermal phase transition properties of the PM lipids in orthogonal directions. The results indicated that the axial symmetry of bR exhibits considerable changes occurring at the thermal phase transition of lipids. These changes are brought by an anomaly observed in the time course of orthogonal electric responses during the application of thermal fields on PM. The observed anomaly may bear on symmetry breaking in bR occurring at the phase transition of lipids based on such analogy found between symmetry breaking and phase transition. Lipid-protein interactions may underlie the broken axial symmetry of bR at such lipid thermal transition of PM. Accordingly, thermally perturbed axial symmetry of bR may be of biological relevance relying on the essence of the crystal lattice of bR. Most importantly, a question has to be raised in the present study: Can bR, as a helical protein with broken axial symmetry, affect the symmetry breaking of helical light? This may be of potential technical applications based on a recent discovery that bR breaks the symmetry of helical light.

Generalized Helmholtz model describes capacitance profiles of ionic liquids and concentrated aqueous electrolytes

In this work, we propose and validate a generalization of the Helmholtz model that can account for both "bell-shaped" and "camel-shaped" differential capacitance profiles of concentrated electrolytes, the latter being characteristic of ionic liquids. The generalization is based on introducing voltage dependence of both the dielectric constant "ϵr(V)" and thickness "L(V)" of the inner Helmholtz layer, as validated by molecular dynamics (MD) simulations. We utilize MD simulations to study the capacitance profiles of three different electrochemical interfaces: (1) graphite/[BMIm+][BF4-] ionic liquid interface; (2) Au(100)/[BMIm+][BF4-] ionic liquid interface; (3) Au(100)/1M [Na+][Cl-] aqueous interface. We compute the voltage dependence of ϵr(V) and L(V) and demonstrate that the generalized Helmholtz model qualitatively describes both camel-shaped and bell-shaped differential capacitance profiles of ionic liquids and concentrated aqueous electrolytes (in lieu of specific ion adsorption). In particular, the camel-shaped capacitance profile that is characteristic of ionic liquid electrolytes arises simply from combination of the voltage-dependent trends of ϵr(V) and L(V). Furthermore, explicit analysis of the inner layer charge density for both concentrated aqueous and ionic liquid double layers reveal similarities, with these charge distributions typically exhibiting a dipolar region closest to the electrode followed by a monopolar peak at larger distances. It is appealing that a generalized Helmholtz model can provide a unified description of the inner layer structure and capacitance profile for seemingly disparate aqueous and ionic liquid electrolytes.

Molecular Simulations Reveal the Free Energy Landscape and Transition State of Membrane Electroporation

The formation of pores over lipid membranes by the application of electric fields, termed membrane electroporation, is widely used in biotechnology and medicine to deliver drugs, vaccines, or genes into living cells. Continuum models for describing the free energy landscape of membrane electroporation were proposed decades ago, but they have never been tested against spatially detailed atomistic models. Using molecular dynamics (MD) simulations with a recently proposed reaction coordinate, we computed potentials of mean force of pore nucleation and pore expansion in lipid membranes at various transmembrane potentials. Whereas the free energies of pore expansion are compatible with previous continuum models, the experimentally important free energy barrier of pore nucleation is at variance with established models. The discrepancy originates from different geometries of the transition state; previous continuum models assumed the presence of a membrane-spanning defect throughout the process, whereas, according to the MD simulations, the transition state of pore nucleation is typically passed before a transmembrane defect has formed. A modified continuum model is presented that qualitatively agrees with the MD simulations. Using kinetics of pore opening together with transition state theory, our free energies of pore nucleation are in excellent agreement with previous experimental data.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Negative Dielectric Constant of Water at a Metal Interface

Water polarizability at a metal interface plays an essential role in electrochemistry. We devise a classical molecular dynamics approach with an efficient description of metal polarization and a novel ac field method to measure the local dielectric response of interfacial water. Water adlayers next to the metal surface exhibit higher-than-bulk in-plane and negative out-of-plane dielectric constants, the latter corresponding physically to overscreening of the applied field. If we account for the gap region at the interface, the average out-of-plane dielectric constant is quite low (ε_{⊥}≈2), in agreement with reported measurements on confined thin films.

Finding Infinities in Nanoconfined Geothermal Electrolyte Static Dielectric Properties and Implications on Ion Adsorption/Pairing

Infinities should naturally occur in the dielectric responses of ionic solutions relevant to many geochemical, energy storage, and electrochemical applications at a strictly zero frequency. Using molecular dynamics simulations cross-referenced with coarse-grained Monte Carlo models, using nanoslit pore models at hydrothermal conditions, and treating confined mobile charges as polarization, we demonstrate the far reaching consequences. The dielectric permittivity profile perpendicular to the slit (ϵ⊥(z)) increases, not decreases, with ionic concentration, unlike in the more widely studied megahertz-to-gigahertz frequency range. In confined electrolytes, the divergences in ϵ⊥(z) correctly describe crossovers between bulk- and surface-dominated dielectric behavior. Nanoconfinement at low ionic concentrations changes monovalent ion energetics by 1-2 kJ/mol, but no dielectric property studied so far is universally correlated to ion adsorption or ion-ion interactions. We caution that infinities signal violation of the "electrical insulator" dielectric assumption.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Dielectric Properties of Nanoconfined Water from Ab Initio Thermopotentiostat Molecular Dynamics

We discuss how to include our recently proposed thermopotentiostat technique [Deissenbeck et al. Phys. Rev. Lett. 2021, 126, 136803] into any existing ab initio molecular dynamics (AIMD) package. Using thermopotentiostat AIMD simulations in the canonical NVTΦ ensemble at a constant electrode potential, we compute the polarization bound charge and dielectric response of interfacial water from first principles.

Does twist angle affect the properties of water confined inside twisted bilayer graphene?

Graphene nanoslit pores are used for nanofluidic devices, such as, in water desalination, ion-selective channels, ionic transistors, sensing, molecular sieving, blue energy harvesting, and protein sequencing. It is a strenuous task to prepare nanofluidic devices, because a small misalignment leads to a significant alteration in various properties of the devices. Here, we focus on the rotational misalignment between two parallel graphene sheets. Using molecular dynamics simulation, we probe the structure and dynamics of monolayer water confined inside graphene nanochannels for a range of commensurate twist angles. With SPC/E and TIP4P/2005 water models, our simulations reveal the independence of the equilibrium number density- n ∼ 13 nm^-2 for SPC/E and n ∼ 11.5 nm^-2 for TIP4P/2005- across twists. Based on the respective densities of the water models, the structure and dielectric constant are invariant of twist angles. The confined water structure at this density shows square ice ordering for SPC/E water only. TIP4P/2005 shows ordering at the vicinity of a critical density (n ∼ 12.5 nm^-2). The average perpendicular dielectric constant of the confined water remains anomalously low (∼2 for SPC/E and ∼6 for TIP4P/2005) for the studied twist angles. We find that the friction coefficient of confined water molecules varies for small twist angles, while becoming independent for twists greater than 5.1°. Our results indicate that a small, angular misalignment will not impair the dielectric properties of monolayer water within a graphene slit-pore, but can significantly influence its dynamics.

Dielectric dispersion characteristics of the phospholipid bilayer with subnanometer resolution from terahertz to mid-infrared

There is growing interest in whether the myelinated nerve fiber acts as a dielectric waveguide to propagate terahertz to mid-infrared electromagnetic waves, which are presumed stable signal carrier for neurotransmission. The myelin sheath is formed as a multilamellar biomembrane structure, hence insights into the dielectric properties of the phospholipid bilayer is essential for a complete understanding of the myelinated fiber functioning. In this work, by means of atomistic molecular dynamics simulations of the dimyristoylphosphatidylcholine (DMPC) bilayer in water and numerical calculations of carefully layered molecules along with calibration of optical dielectric constants, we for the first time demonstrate the spatially resolved (in sub-nm) dielectric spectrum of the phospholipid bilayer in a remarkably wide range from terahertz to mid-infrared. More specifically, the membrane head regions exhibit both larger real and imaginary permittivities than that of the tail counterparts in the majority of the 1–100 THz band. In addition, the spatial variation of dielectric properties suggests advantageous propagation characteristics of the phospholipid bilayer in a relatively wide band of 55–85 THz, where the electromagnetic waves are well confined within the head regions.

Effects of surface rigidity and metallicity on dielectric properties and ion interactions at aqueous hydrophobic interfaces

Using classical molecular dynamics simulations we investigate the dielectric properties at interfaces of water with graphene, graphite, hexane and water vapor. For graphite we compare metallic and non-metallic versions. At the vapor-liquid water and hexane-water interfaces the laterally averaged dielectric profiles are significantly broadened due to interfacial roughness and only slightly anisotropic. In contrast, at the rigid graphene surface the dielectric profiles are strongly anisotropic and the perpendicular dielectric profile exhibits pronounced oscillations and sign changes. The interfacial dielectric excess, characterized by the shift of the dielectric-dividing-surface with respect to the Gibbs-dividing-surface, is positive for all surfaces, showing that water has an enhanced dielectric response at hydrophobic surfaces. The dielectric-dividing-surface positions vary significantly among the different surfaces, which points to pronounced surface-specific dielectric behavior. The interfacial repulsion of a chloride ion is shown to be dominated by electrostatic interactions for the soft fluid-fluid interfaces and by non-electrostatic Lennard-Jones interactions for the rigid graphene-water interface. A linear tensorial dielectric model for the ion-interface interaction with sharp dielectric interfaces located on the dielectric-dividing-surface positions works well for graphene but fails for vapor and hexane, because these interfaces are smeared out. The repulsion of chloride from the metallic and non-metallic graphite versions differs very little, which reflects the almost identical interfacial water structure and can be understood based on linear continuum dielectric theory. Interface flexibility shows up mostly in the non-linear Coulomb part of the ion-interface interaction, which changes significantly close to the interfaces and signals the breakdown of linear dielectric continuum theory.

Measuring anion binding at biomembrane interfaces

The quantification of anion binding by molecular receptors within lipid bilayers remains challenging. Here we measure anion binding in lipid bilayers by creating a fluorescent macrocycle featuring a strong sulfate affinity. We find the determinants of anion binding in lipid bilayers to be different from those expected that govern anion binding in solution. Charge-dense anions H₂PO₄^- and Cl^- that prevail in dimethyl sulfoxide fail to bind to the macrocycle in lipids. In stark contrast, ClO₄^- and I^- that hardly bind in dimethyl sulfoxide show surprisingly significant affinities for the macrocycle in lipids. We reveal a lipid bilayer anion binding principle that depends on anion polarisability and bilayer penetration depth of complexes leading to unexpected advantages of charge-diffuse anions. These insights enhance our understanding of how biological systems select anions and guide the design of functional molecular systems operating at biomembrane interfaces.

The lung surfactant activity probed with molecular dynamics simulations

The surface of pulmonary alveolar subphase is covered with a mixture of lipids and proteins. This lung surfactant plays a crucial role in lung functioning. It shows a complex phase behavior which can be altered by the interaction with third molecules such as drugs or pollutants. For studying multicomponent biological systems, it is of interest to couple experimental approach with computational modelling yielding atomic-scale information. Simple two, three, or four-component model systems showed to be useful for getting more insight in the interaction between lipids, lipids and proteins or lipids and proteins with drugs and impurities. These systems were studied theoretically using molecular dynamic simulations and experimentally by means of the Langmuir technique. A better understanding of the structure and behavior of lung surfactants obtained from this research is relevant for developing new synthetic surfactants for efficient therapies, and may contribute to public health protection.

Dielectric Properties of Aqueous Electrolyte Solutions Confined in Silica Nanopore: Molecular Simulation vs. Continuum-Based Models

Dielectric behavior of electrolyte aqueous solutions with various concentrations in a cylindrical nanopore of MCM 41 silica has been investigated. The effect of confinement is investigated by using isothermal-isosurface-isobaric statistical ensemble, which has proved to be an effective alternative to the Grand Canonical Monte Carlo (GCMC) simulation method. Several single-salt solutions have been considered (e.g., NaCl, NaI, BaCl₂, MgCl₂) in order to investigate the effect of ion polarizability, ion size, and ion charge. The effect of salt concentration has also been addressed by considering NaCl solutions at different concentrations (i.e., 0.1 mol/L, 0.5 mol/L, and 1 mol/L). The motivation in performing this integrated set of simulations is to provide deep insight into the dielectric exclusion in NF theory that plays a significant role in separation processes. It was shown that the dielectric constant increased when ions were added to water inside the nanopore (with respect to the dielectric constant of confined pure water) unlike what was obtained in the bulk phase and this phenomenon was even more pronounced for electrolytes with divalent ions (MgCl₂ and BaCl₂). Therefore, our simulations indicate opposite effects of ions on the dielectric constant of free (bulk) and nanoconfined aqueous solutions.

The permeability of human red blood cell membranes to hydrogen peroxide is independent of aquaporins

Hydrogen peroxide (H₂O₂) not only is an oxidant but also is an important signaling molecule in vascular biology, mediating several physiological functions. Red blood cells (RBCs) have been proposed to be the primary sink of H₂O₂ in the vasculature because they are the main cellular component of blood with a robust antioxidant defense and a high membrane permeability. However, the exact permeability of human RBC to H₂O₂ is neither known nor is it known if the mechanism of permeation involves the lipid fraction or protein channels. To gain insight into the permeability process, we measured the partition constant of H₂O₂ between water and octanol or hexadecane using a novel double-partition method. Our results indicated that there is a large thermodynamic barrier to H₂O₂ permeation. The permeability coefficient of H₂O₂ through phospholipid membranes containing cholesterol with saturated or unsaturated acyl chains was determined to be 4 × 10⁻⁴ and 5 × 10⁻³ cm s⁻¹, respectively, at 37 °C. The permeability coefficient of human RBC membranes to H₂O₂ at 37 °C, on the other hand, was 1.6 × 10⁻³ cm s⁻¹. Different aquaporin-1 and aquaporin-3 inhibitors proved to have no effect on the permeation of H₂O₂. Moreover, human RBCs devoid of either aquaporin-1 or aquaporin-3 were equally permeable to H₂O₂ as normal human RBCs. Therefore, these results indicate that H₂O₂ does not diffuse into RBCs through aquaporins but rather through the lipid fraction or a still unidentified membrane protein.

Pressure-Biased Nanopores for Excluded Volume Metrology, Lipid Biomechanics, and Cell-Adhesion Rupturing

Nanopore sensing has been widely used in applications ranging from DNA sequencing to disease diagnosis. To improve these capabilities, pressure-biased nanopores have been explored in the past to-primarily-increase the residence time of the analyte inside the pore. Here, we studied the effect of pressure on the ability to accurately quantify the excluded volume which depends on the current drop magnitude produced by a single entity. Using the calibration standard, the inverse current drop (1/ΔI) decreases linearly with increasing pressure, while the dwell drop reduces exponentially. We therefore had to derive a pressure-corrected excluded volume equation to accurately assess the volume of translocating species under applied pressure. Moreover, a method to probe deformation in nanoliposomes and a single cell is developed as a result. We show that the soft nanoliposomes and even cells deform significantly under applied pressure which can be probed in terms of the shape factor which was introduced in the excluded volume equation. The proposed work has practical applications in mechanobiology, namely, assessing the stiffness and mechanical rigidity of liposomal drug carriers. Pressure-biased pores also enabled multiple observations of cell-cell aggregates as well as their subsequent rupture, potentially allowing for the study of microbial symbioses or pathogen recognition by the human immune system.

Dielectric Properties of Phosphatidylcholine Membranes and the Effect of Sugars

Simple carbohydrates are associated with the enhanced risk of cardiovascular disease and adverse changes in lipoproteins in the organism. Conversely, sugars are known to exert a stabilizing effect on biological membranes, and this effect is widely exploited in medicine and industry for cryopreservation of tissues and materials. In view of elucidating molecular mechanisms involved in the interaction of mono- and disaccharides with biomimetic lipid systems, we study the alteration of dielectric properties, the degree of hydration, and the rotational order parameter and dipole potential of lipid bilayers in the presence of sugars. Frequency-dependent deformation of cell-size unilamellar lipid vesicles in alternating electric fields and fast Fourier transform electrochemical impedance spectroscopy are applied to measure the specific capacitance of phosphatidylcholine lipid bilayers in sucrose, glucose and fructose aqueous solutions. Alteration of membrane specific capacitance is reported in sucrose solutions, while preservation of membrane dielectric properties is established in the presence of glucose and fructose. We address the effect of sugars on the hydration and the rotational order parameter for 1-palmitoyl-2-oleoyl-sn-glycero-3- phosphocholine (POPC) and 1-stearoyl-2-oleoyl-sn-glycero-3- phosphocholine (SOPC). An increased degree of lipid packing is reported in sucrose solutions. The obtained results provide evidence that some small carbohydrates are able to change membrane dielectric properties, structure, and order related to membrane homeostasis. The reported data are also relevant to future developments based on the response of lipid bilayers to external physical stimuli such as electric fields and temperature changes.

Diptool-A Novel Numerical Tool for Membrane Interactions Analysis, Applying to Antimicrobial Detergents and Drug Delivery Aids

The widespread problem of resistance development in bacteria has become a critical issue for modern medicine. To limit that phenomenon, many compounds have been extensively studied. Among them were derivatives of available drugs, but also alternative novel detergents such as Gemini surfactants. Over the last decade, they have been massively synthesized and studied to obtain the most effective antimicrobial agents, as well as the most selective aids for nanoparticles drug delivery. Various protocols and distinct bacterial strains used in Minimal Inhibitory Concentration experimental studies prevented performance benchmarking of different surfactant classes over these last years. Motivated by this limitation, we designed a theoretical methodology implemented in custom fast screening software to assess the surfactant activity on model lipid membranes. Experimentally based QSAR (quantitative structure-activity relationship) prediction delivered a set of parameters underlying the Diptool software engine for high-throughput agent-membrane interactions analysis. We validated our software by comparing score energy profiles with Gibbs free energy from the Adaptive Biasing Force approach on octenidine and chlorhexidine, popular antimicrobials. Results from Diptool can reflect the molecule behavior in the lipid membrane and correctly predict free energy of translocation much faster than classic molecular dynamics. This opens a new venue for searching novel classes of detergents with sharp biologic activity.

Ewald sum corrections in simulations of ion and dipole solvation and electron transfer

Periodic boundary conditions and Ewald sums used in standard simulation protocols require finite-size corrections when the total charge of the simulated system is nonzero. Corrections for ion solvation were introduced by Hummer, Pratt, and García, [J. Chem. Phys. 107, 9275 (1997)]. The latter approach is extended here to derive finite-size correction for the Stokes-shift and reorganization energy applied to electron-transfer reactions. The same correction term, scaling inversely with the box size, adds to the reorganization energy from the energy-gap variance but is subtracted from the reorganization energy calculated from the Stokes shift. Finite-size corrections thus widen the gap between these two quantities, which were recently found to diverge for protein electron transfer. Corrections to the free energy of dipole solvation and the variance of the electric field scale as m²/L³ with the solute dipole m and the box size L.

Dielectric Susceptibility of Water in the Interface

It has long been anticipated that dielectric constants of polar liquids are reduced in the interfacial layer. Recent experiments and computer simulations support these expectations. A strong reduction of the dielectric constant is found in the direction perpendicular to a planar substrate, while the parallel response is bulk-like. This Perspective highlights recent theoretical calculations and simulations with an eye on relating them to properties observable in the laboratory. The average interface dielectric constant computed from simulations connects to thin films experiments, but this cannot be extended to screening of charges. In contrast to dielectric theories where a single dielectric constant gauges both the polarization energy and screening, these two signatures of dielectric polarization diverge on the molecular scale. The reduction of the dielectric constant of water in thin films is currently viewed as a combined effect of geometric confinement imposed by the substrate and the reconstruction of water hydrogen bonds in the surface layer.

Dielectric Profile and Electromelting of a Monolayer of Water Confined in Graphene Slit Pore

A monolayer of water confined between two parallel graphene sheets exists in many different phases and exhibits fascinating dielectric properties that have been studied in experiments. In this work, we use molecular dynamics simulations to study how the dielectric properties of a confined monolayer of water is affected by its structure. We consider six of the popular nonpolarizable water models-SPC/E, SPC/Fw, TIP3P, TIP3P_M (modified), TIP4P-2005, and TIP4P-2005f-and find that the in-plane structure of the water molecules at ambient temperature and pressure is strongly dependent on the water model: all the 3-point water models considered here show square ice formation, whereas no such structural ordering is observed for the 4-point water models. This allows us to investigate the role of the in-plane structure of the water monolayer on its dielectric profile. Our simulations show an anomalous perpendicular dielectric constant compared to the bulk, and the models that do not exhibit ice formation show very different dielectric response along the channel width compared to models that exhibit square ice formation. We also demonstrate the occurrence of electromelting of the in-plane ordered water under the application of a perpendicular electric field and find that the critical field for electromelting strongly depends on the water model. Together, we have shown the dependence of confined water properties on the different water structures that it may take when sandwiched between bilayer graphene. These remarkable properties of confined water can be exploited in various nanofluidic devices, artificial ion channels, and molecular sieving.

Confinement-Controlled Aqueous Chemistry within Nanometric Slit Pores

In this Focus Review, we put the spotlight on very recent insights into the fascinating world of wet chemistry in the realm offered by nanoconfinement of water in mechanically rather rigid and chemically inert planar slit pores wherein only monolayer and bilayer water lamellae can be hosted. We review the effect of confinement on different aspects such as hydrogen bonding, ion diffusion, and charge defect migration of H⁺(aq) and OH^-(aq) in nanoconfined water depending on slit pore width. A particular focus is put on the strongly modulated local dielectric properties as quantified in terms of anisotropic polarization fluctuations across such extremely confined water films and their putative effects on chemical reactions therein. The stunning findings disclosed only recently extend wet chemistry in particular and solvation science in general toward extreme molecular confinement conditions.

Confined Water's Dielectric Constant Reduction Is Due to the Surrounding Low Dielectric Media and Not to Interfacial Molecular Ordering

Liquid water confined within nanometer-sized channels exhibits a surprisingly low dielectric constant along the direction orthogonal to the channel walls. This is typically assumed to result from a pronounced heterogeneity across the sample: the dielectric constant would be bulk-like everywhere except at the interface, where it would be dramatically reduced by strong restrictions on interfacial molecules. Here we study the dielectric properties of water confined within graphene slit channels via classical molecular dynamics simulations. We show that the permittivity reduction is not due to any important alignment of interfacial water molecules, but instead to the long-ranged anisotropic dipole correlations combined with an excluded-volume effect of the low-dielectric confining material. The bulk permittivity is gradually recovered only over several nanometers due to the impact of long-range electrostatics, rather than structural features. This has important consequences for the control of, e.g., ion transport and chemical reactivity in nanoscopic channels and droplets.

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.

Dielectric Properties of Nanoconfined Water: A Canonical Thermopotentiostat Approach

We introduce a novel approach to sample the canonical ensemble at constant temperature and applied electric potential. Our approach can be straightforwardly implemented into any density-functional theory code. Using thermopotentiostat molecular dynamics simulations allows us to compute the dielectric constant of nanoconfined water without any assumptions for the dielectric volume. Compared to the commonly used approach of calculating dielectric properties from polarization fluctuations, our thermopotentiostat technique reduces the required computational time by 2 orders of magnitude.

Dielectric Behavior near a Spherical Ion

The dielectric response of a polar solvent to an ion is analyzed in terms of the bound charge, the net charge that accumulates near the ion as a consequence of the inhomogeneous polarization of the surrounding solvent. We demonstrate that the total bound charge arising in a full molecular treatment is identical to the total bound charge from standard continuum theory. In continuum theory, the bound charge resides in an infinitely thin layer, while in a molecular description the bound charge is spread over a region of finite width. Near simple atomic ions, the width of the bound charge distribution is roughly 1.3 nm. By simulating a sequence of ion charges from 0.1 to 2 e, where e is the magnitude of the electron charge, we analyze the applicability of linear response theory, which has been used by several authors. With increasing charge, the nonlinear response extends to an increasing distance from the ion. However, outside the region containing bound charge, the response is linear and in accord with continuum theory. Previous attempts to assign a dielectric constant to a solvent in the interfacial region are analyzed.

Theory of cell membrane interaction with glass

There are three regimes of cell membrane interaction with glass: Tight and loose adhesion, separated by repulsion. Explicitly including hydration, this paper evaluates the pressure between the surfaces as functions of distance for ion correlation and ion-screened electrostatics and electromagnetic fluctuations. The results agree with data for tight adhesion energy (0.5-3 vs 0.4-4 mJ/m^{2}), detachment pressure (7.9 vs. 9 MPa), and peak repulsion (3.4-7.5 vs. 5-10 kPa), also matching the repulsion's distance dependence on renormalization by steric pressure mainly from undulations.

Molecular Dynamics Simulations Based on Polarizable Models Show that Ion Permeation Interconverts between Different Mechanisms as a Function of Membrane Thickness

Different mechanisms have been proposed to explain the permeation of charged compounds through lipid membranes. Overall, it is expected that an ion-induced defect permeation mechanism, where substantial membrane deformations accompany ion movement, should be dominant in thin membranes but that a solubility-diffusion mechanism, where ions partition into the membrane core with large associated dehydration energy costs, becomes dominant in thicker membranes. However, while this physical picture is intuitively reasonable, capturing the interconversion between these two permeation mechanisms in molecular dynamics (MD) simulations based on atomic models is challenging. In particular, simulations relying on nonpolarizable force fields are artificially unfavorable to the solubility-diffusion mechanism, as induced polarization of the nonpolar hydrocarbon is ignored, causing overestimated free energy costs for charged molecules to enter into this region of the membrane. In this study, all-atom MD simulations based on nonpolarizable and polarizable force fields are used to quantitatively characterize the permeation process for the arginine side chain analog methyl-guanidinium through bilayer membranes of mono-unsaturated phosphatidylcholine lipids with and without cholesterol, resulting in thicknesses spanning from ∼24 to ∼42 Å. With simulations based on a nonpolarizable force field, ion translocation can take place solely through an ion-induced defect mechanism, with free energy barriers increasing linearly from 14 to 40 kcal/mol, depending on the thickness. However, with simulations based on a polarizable force field, ion translocation is predominantly dominated by an ion-induced defect mechanism in thin membranes, which progressively converts to a solubility-diffusion mechanism as the membranes get thicker. The transition between the two mechanisms occurs at a thickness of ∼29 Å, with lipid tails of 22 or more carbon atoms. This situation appears to represent the upper limit for ion-induced defect permeation within the current polarizable models. Beyond this thickness, it becomes energetically preferable for the ion to dehydrate and partition into the membrane core-a phenomenon that cannot be captured using the nonpolarizable models. Induced electronic polarizability therefore leads not just to a shift in permeation energetics but to an interconversion between two strikingly different physical mechanisms. The result highlights the importance of induced polarizability in modeling lipid membranes.

Universal Reduction in Dielectric Response of Confined Fluids

Dielectric permittivity is central to many biological and physiochemical systems, as it affects the long-range electrostatic interactions. Similar to many fluid properties, confinement greatly alters the dielectric response of polar liquids. Many studies have focused on the reduction of the dielectric response of water under confinement. Here, using molecular dynamics simulations, statistical-mechanical theories, and multiscale methods, we study the out-of-plane (z-axis) dielectric response of protic and aprotic fluids confined inside slit-like graphene channels. We show that the reduction in perpendicular permittivity is universal for all the fluids and exhibits a Langevin-like behavior as a function of channel width. We show that this reduction is due to the favorable in-plane (x-y plane) dipole-dipole electrostatic interactions of the interfacial fluid layer. Furthermore, we observe an anomalously low dielectric response under an extreme confinement.

Reversible Switching of Charge Transfer at the Graphene-Mica Interface with Intercalating Molecules

Understanding and controlling charge transfer through molecular nanostructures at interfaces is of paramount importance, particularly for electronic devices but also for contact electrification or in bioelectronics. We investigate the influence of intercalation and exchange of molecularly thin layers of small molecules (water, ethanol, 2-propanol, and acetone) on charge transfer at the well-defined interface between an insulator (muscovite mica) and a conductor (graphene). Raman spectroscopy is used to probe the charge carriers in graphene. While a molecular layer of water blocks charge transfer between mica and graphene, a layer of the organic molecules allows for it. The exchange of molecular water layers with ethanol layers switches the charge transfer very efficiently from off to on and back. We propose a charge transfer model between occupied mica trap states and electronic states of graphene, offset by the electrostatic potentials produced by the molecular dipole layers, as supported by molecular dynamics simulations. Our work demonstrates how intercalation of molecules of volatile liquids can reversibly affect charge transfer at interfaces. This implies its strong impact on the function of hybrid inorganic-organic electronic devices in different ambients and potential applications, including sensors and actuators.

Accurate Estimation of Membrane Capacitance from Atomistic Molecular Dynamics Simulations of Zwitterionic Lipid Bilayers

Lipid membranes are indispensable to life, and they regulate countless cellular processes. To investigate the properties of membranes under controlled conditions, numerous reconstitution methods have been developed over the last few decades. Several of these methods result in the formation of lipid bilayers containing residual hydrophobic molecules between the two monolayers. These contaminants might alter membrane properties, including bilayer thickness, that is usually inferred from measurements of membrane capacitance assuming a simple slab model. However, recent measurements on solvent-free bilayers raised significant questions on the reliability of this approach. To reconcile the observed discrepancies, we developed a protocol to predict membrane capacitance from the dielectric profile of lipid bilayers computed from molecular dynamics simulations. Our methodology shows excellent agreement against available data on solvent-free noncharged bilayers, and it confirms that the uniform slab model is a reliable approximation from which to infer membrane capacitance. We find that the effective electrical thickness contributing to membrane capacitance is different from the hydrophobic thickness inferred from X-ray scattering form factors. We apply our model to estimate the concentration of residual solvent in reconstituted systems, and we propose that our protocol could be used to infer membrane properties in the presence of hydrophobic solvents.

Molecular dynamics simulation of proton-transfer coupled rotations in ATP synthase FO motor

The F_O motor in F_OF₁ ATP synthase rotates its rotor driven by the proton motive force. While earlier studies elucidated basic mechanisms therein, recent advances in high-resolution cryo-electron microscopy enabled to investigate proton-transfer coupled F_O rotary dynamics at structural details. Here, taking a hybrid Monte Carlo/molecular dynamics simulation method, we studied reversible dynamics of a yeast mitochondrial F_O. We obtained the 36°-stepwise rotations of F_O per one proton transfer in the ATP synthesis mode and the proton pumping in the ATP hydrolysis mode. In both modes, the most prominent path alternatively sampled states with two and three deprotonated glutamates in c-ring, by which the c-ring rotates one step. The free energy transduction efficiency in the model F_O motor reached ~ 90% in optimal conditions. Moreover, mutations in key glutamate and a highly conserved arginine increased proton leakage and markedly decreased the coupling, in harmony with previous experiments. This study provides a simple framework of simulations for chemical-reaction coupled molecular dynamics calling for further studies in ATP synthase and others.

Universal and Nonuniversal Aspects of Electrostatics in Aqueous Nanoconfinement

Dielectric water properties, which significantly change in confinement, determine electrostatic interactions and thereby influence all molecular forces and chemical reactions. We present comparative simulations of water between graphene sheets, decanol monolayers, and phospholipid and glycolipid bilayers. Generally, dielectric profiles strongly differ in perpendicular and parallel surface directions and for large surface separation decay to the bulk value 1-2 nm away from the surface. Polar surface groups enhance the local interfacial dielectric response and for phospholipid bilayers induce a giant parallel contribution. A mapping on a box model with asymptotically determined effective water layer widths demonstrates that the perpendicular effective dielectric constant for all systems decreases for confinement below a nanometer, while the parallel one stays rather constant. The confinement-dependent perpendicular effective dielectric constant for graphene is in agreement with experimental data only if the effective water layer width is suitably adjusted. The interactions between two charges at small separation depend on the product of parallel and perpendicular effective water dielectric components; for large separation the interactions depend on the confining medium. For metallic confining media the interactions at large separation decay exponentially with a decay length that depends on the ratio of the effective parallel and perpendicular water dielectric components.

Investigation of dielectric constants of water in a nano-confined pore

We report the dielectric properties of pure water confined in a silica hydrophilic nanopore determined from the computation of the density of liquid in the confined phase by the grand canonical Monte Carlo (GCMC) simulations. The silica cylindrical nanopore is divided into n concentric radial shells to get a better insight into the dielectric properties of nanoconfined water. We find that the average values of the dielectric constants are very close and almost independent of the number of concentric radial shells. The decrease in the dielectric constant of confined pure water is due to the strong orientation of water dipoles in the vicinity of the surface while water dipoles do not exhibit any preferential orientation in bulk phase.

Investigation of dielectric properties in a silica hydrophilic pore with two water reservoirs.

Quantifying anisotropic dielectric response properties of nanoconfined water within graphene slit pores

Water presents puzzling properties once it gets confined, in particular its dielectric response becomes highly anisotropic. Here, we analyze the dielectric response of water within graphene slit pores based on molecular dynamics simulations.

Dimerization energetics of the G-protein coupled bile acid receptor TGR5 from all-atom simulations

We describe the first extensive energetic evaluation of GPCR dimerization on the atomistic level by means of potential of mean force (PMF) computations and implicit solvent/implicit membrane end-point free energy calculations (MM-PBSA approach). Free energies of association computed from the PMFs show that the formation of both the 1/8 and 4/5 interface is energetically favorable for TGR5, the first GPCR known to be activated by hydrophobic bile acids and neurosteroids. Furthermore, formation of the 1/8 interface is favored over that of the 4/5 interface. Both results are in line with our previous FRET experiments in live cells. Differences in lipid-protein interactions are identified to contribute to the observed differences in free energies of association. A per-residue decomposition of the MM-PBSA effective binding energy reveals hot spot residues specific for both interfaces that form clusters. This knowledge may be used to guide the design of dimerization inhibitors or perform mutational studies to explore physiological consequences of distorted TGR5 association. Finally, we characterized the role of Y111, located in the conserved (D/E)RY motif, as a facilitator of TGR5 interactions. The types of computations performed here should be transferable to other transmembrane proteins that form dimers or higher oligomers as long as good structural models of the dimeric or oligomeric states are available. Such computations may help to overcome current restrictions due to an imperfect energetic representation of protein association at the coarse-grained level. © 2019 Wiley Periodicals, Inc.

Giant Axial Dielectric Response in Water-Filled Nanotubes and Effective Electrostatic Ion-Ion Interactions from a Tensorial Dielectric Model

Molecular dynamics simulations in conjunction with effective medium theory are used to investigate dielectric effects in water-filled nanotubes. The resulting effective axial dielectric constant shows a divergent increase for small nanotube radii that depends on the nanotube length, while the effective radial dielectric constant decreases significantly for thin nanotubes. By solving Poisson's equation for an anisotropic dielectric medium in cylindrical geometry, we show that the axial ion-ion interaction depends for small separations primarily on the radial dielectric constant, not on the axial one. This means that electrostatic ion-ion interactions in thin water-filled nanotubes are on the linear dielectric level significantly enhanced due to water confinement effects at small separations, while at large separations the outside medium dominates. If the outside medium is metallic, then the ion-ion interaction decays exponentially for large ion separation.

Adsorption and Conformation of Bovine Serum Albumin with Blue-Emitting Gold Nanoclusters at the Air/Water and Lipid/Water Interfaces

Protein-encapsulated nanoclusters (NCs) are emerging as a versatile platform for in-vivo imaging and other biomedical applications due to their ultrasmall size and excitation in the near-infrared region. Encapsulation may however affect protein structure, size, charge, and its interaction with lipid membranes. In this study, bulk characterization methods along with surface-sensitive vibrational sum-frequency generation (VSFG) spectroscopy were employed to study the secondary structure of bovine serum albumin (BSA) with blue-emitting Au₈NCs at the air/water and 1,2-dipalmitoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DPPG) lipid/water interfaces. With this approach, the difference in the adsorption behavior between native BSA and BSA with an increasing number of blue-emitting NCs was investigated under different pH conditions. At pH 7, at which both BSA and the lipid are negatively charged, protein molecules are found to associate with the DPPG monolayer via hydrophobic interactions with no preferential orientation across the lipid monolayer. At pH 3, adsorption of BSA at the DPPG monolayer occurs mainly due to electrostatic interactions between the negatively charged lipid headgroups and the positively charged protein, resulting in a uniform orientation of the protein across the lipid monolayer. Complimentary bulk studies by circular dichroism and particle size measurements show that the encapsulation of Au₈NCs is associated with the loss of BSA helicity, which makes BSA-encapsulated Au₈NCs prone to oligomerization, especially at a high content of Au₈NCs at one BSA protein. The results indicate that the hydrodynamic diameter of BSA with Au₈NCs strongly depends on the molar fraction of gold, the pH, and the storage time. A prolonged storage of Au₈NCs@BSA at pH 7 increases the rate of protein oligomerization.

Long-range electron-electron interaction and charge transfer in protein complexes: a numerical approach

With application to the nitrite reductase hexameric protein complex of Desulfovibrio vulgaris, NrfH2A4, we suggest a strategy to compute the energy landscape of electron transfer in large systems of biochemical interest. For small complexes, the energy of all electronic configurations can be scanned completely on the level of a numerical solution of the Poisson-Boltzmann equation. In contrast, larger systems have to be treated using a pair approximation, which is verified here. Effective Coulomb interactions between neighbouring sites of excess electron localization may become as large as 200 meV, and they depend in a nontrivial manner on the intersite distance. We discuss the implications of strong Coulomb interactions on the thermodynamics and kinetics of charging and decharging a protein complex. Finally, we turn to the effect of embedding the system into a biomembrane.

Structure and Function in Antimicrobial Piscidins: Histidine Position, Directionality of Membrane Insertion, and pH-Dependent Permeabilization

Piscidins are histidine-enriched antimicrobial peptides that interact with lipid bilayers as amphipathic α-helices. Their activity at acidic and basic pH in vivo makes them promising templates for biomedical applications. This study focuses on p1 and p3, both 22-residue-long piscidins with 68% sequence identity. They share three histidines (H3, H4, and H11), but p1, which is significantly more permeabilizing, has a fourth histidine (H17). This study investigates how variations in amphipathic character associated with histidines affect the permeabilization properties of p1 and p3. First, we show that the permeabilization ability of p3, but not p1, is strongly inhibited at pH 6.0 when the conserved histidines are partially charged and H17 is predominantly neutral. Second, our neutron diffraction measurements performed at low water content and neutral pH indicate that the average conformation of p1 is highly tilted, with its C-terminus extending into the opposite leaflet. In contrast, p3 is surface bound with its N-terminal end tilted toward the bilayer interior. The deeper membrane insertion of p1 correlates with its behavior at full hydration: an enhanced ability to tilt, bury its histidines and C-terminus, induce membrane thinning and defects, and alter membrane conductance and viscoelastic properties. Furthermore, its pH-resiliency relates to the neutral state favored by H17. Overall, these results provide mechanistic insights into how differences in the histidine content and amphipathicity of peptides can elicit different directionality of membrane insertion and pH-dependent permeabilization. This work features complementary methods, including dye leakage assays, NMR-monitored titrations, X-ray and neutron diffraction, oriented CD, molecular dynamics, electrochemical impedance spectroscopy, surface plasmon resonance, and quartz crystal microbalance with dissipation.

Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies

Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y₁₂R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.

Dielectric-Dependent Strength of Interlipid Hydrogen Bonding in Biomembranes: Model Case Study

Atomistic aspects of the structural organization, dynamics, and functioning of hydrated lipid bilayers-model cell membranes-are primarily governed by the fine balance of intermolecular interactions between all constituents of these systems. Besides the hydrophobic effect, which shapes the overall skeleton of lipid membranes, a very important contribution to their behavior is made by hydrogen bonds (H-bonds) between lipid head groups. The latter determine crucial phenomena in cell membranes, such as dynamic ultrananodomain organization, hydration, and fine-tuning of microscopic physicochemical properties that allow the membrane to adapt quickly when binding/insertion external agents (proteins, etc.). The characteristics of such H-bonds (strength, spatial localization, etc.) dramatically depend on the local polarity properties of the lipid-water environment. In this work, we calculated free energies of H-bonded complexes between typical donor (NH₃⁺, NH, OH) and acceptor (C═O, OH, COO^-, COOH) groups of lipids in vacuo and in a set of explicit solvents with dielectric constants (ε) from 1 to 78.3, which mimic membrane environment at different depths. This was done using Monte Carlo simulations and an assessment of the corresponding potential of mean force profiles. The strongest H-bonded complexes were observed in the nonpolar environment, and their strength increased sharply with decreasing ε below 17. When ε changed, the largest free energy gain (>10.8 kcal/mol) was observed for pairs of acceptors C═O and O(H) with donor NH₃⁺. The complexation of the same acceptors with NH donor in this range of ε values was rather less sensitive to the environmental polarity, by ∼1.5 kcal/mol. Dielectric-dependent interactions of polar lipid groups with water were evaluated as well. The results explain the delicate balance that determines the unique pattern of H-bonds for a particular lipid bilayer. Understanding the factors that regulate the propensity for H-bonding in lipid bilayers provides a fundamental basis for the rational design of new membrane nano objects with predefined properties.