Ion transport through membrane-spanning nanopores studied by molecular dynamics simulations and continuum electrostatics calculations

Influence of CTAB Reverse Micellar Confinement on the Tetrahedral Structure of Liquid Water

The effect of confinement on the tetrahedral ordering of liquid water plays a vital role in controlling their microscopic structure and dynamics as well as their spectroscopic properties. In this article, we have performed the classical molecular dynamics simulations of four different CTAB/water/chloroform reverse micelles with varied water content to study how the tetrahedral ordering of nanoscale water inside reverse micellar confinement influences the microscopic dynamics and the structural relaxation of water···water hydrogen bonds and its impact on the low-frequency intermolecular vibrational bands. We have noticed from the results obtained from simulated trajectories the lowering trends of tetrahedral ordering of water pools in reverse micellar confinements as we move from bulk to confined and strictly confined environments. We have observed that the order of confinements significantly altered the relaxation pattern of water···water hydrogen bonds present in the nanoscale water pool of reverse micelles. The recrossing related to hydrogen bond dynamics can effectively explain the relaxation pattern of C HB WW ( t ) under confinement. The Br-1···water hydrogen bond depicts a much slower relaxation compared to the water···water hydrogen bonds inside reverse micelles. We have also explored the correlation between the tetrahedral ordering of nanoscale water pools and the relaxation of water···water hydrogen bonds with the 50 cm-1 band for water inside reverse micelles. The computations reported that compared to bulk water, the band appearing at 50 cm-1 for O···O···O triplet bending is nonuniformly blue-shifted by 18-45 cm-1 for the nanoscale water pool inside reverse micelles, and the intensity of the band drops from bulk to confined and strictly confined environments, which indicates the reduced tendency of such triplet formation. It is observed that a significant intensity variation at the 200 cm-1 band correlates with the effect of confinement on the tetrahedral ordering of the water pool inside reverse micelles. So, our observations support the influence of strictly confined environments on the tetrahedral water structure to adopt the quasi-two-dimensional water network and experience restricted longitudinal translations. It is further noticed that the 500 cm-1 librational band is also found to be blue-shifted by 71-112 cm-1 for the water pool in reverse micelles, and the extent of the shift being more noticeable for strictly confined environments correlates excellently with the sluggish relaxation of water···water hydrogen bonds in such environments.

Nonpreferential Solvent Transport through an Intrinsic Cyclodextrin Pore in a Polyester Film

We performed equilibrium molecular dynamics simulations to study the transport of water and hexane solvents through cyclodextrin(CD)-based membranes (α-/β-/γ-CD/TMC). Although it is known that water and hexane can permeate through the macrocyclic cavity, surprisingly, when it is present in the CD-based membrane (α-/β-/γ-CD/TMC), these solvents are not permeating through the CD cavity. Interactions between membrane functional group atoms with the water and hexane suggest that these solvents primarily permeate through the polar aggregate pores formed via ester-linkage rather than the CD cavity. Our observation reveals that both solvents can permeate through the membrane; however, the hexane flux was one order of magnitude lower than water flux. Our study suggests that further work is needed to confirm the functional significance of the macrocyclic cavity in solvent permeation and the existence of Janus pathways.

Molecular transport enhancement in pure metallic carbon nanotube porins

Nanofluidic channels impose extreme confinement on water and ions, giving rise to unusual transport phenomena strongly dependent on the interactions at the channel-wall interface. Yet how the electronic properties of the nanofluidic channels influence transport efficiency remains largely unexplored. Here we measure transport through the inner pores of sub-1 nm metallic and semiconducting carbon nanotube porins. We find that water and proton transport are enhanced in metallic nanotubes over semiconducting nanotubes, whereas ion transport is largely insensitive to the nanotube bandgap value. Molecular simulations using polarizable force fields highlight the contributions of the anisotropic polarizability tensor of the carbon nanotubes to the ion-nanotube interactions and the water friction coefficient. We also describe the origin of the proton transport enhancement in metallic nanotubes using deep neural network molecular dynamics simulations. These results emphasize the complex role of the electronic properties of nanofluidic channels in modulating transport under extreme nanoscale confinement.

Selective ion transport in large-area graphene oxide membrane filters driven by the ionic radius and electrostatic interactions

Filters made of graphene oxide (GO) are promising for purification of water and selective sieving of specific ions; while some results indicate the ionic radius as the discriminating factor in the sieving efficiency, the exact mechanism of sieving is still under debate. Furthermore, most of the reported GO filters are planar coatings with a simple geometry and an area much smaller than commercial water filters. Here, we show selective transport of different ions across GO coatings deposited on standard hollow fiber filters with an area >10 times larger than typical filters reported. Thanks to the fabrication procedure, we obtained a uniform coating on such complex geometry with no cracks or holes. Monovalent ions like Na+ and K+ can be transported through these filters by applying a low electric voltage, while divalent ions are blocked. By combining transport and adsorption measurements with molecular dynamics simulations and spectroscopic characterization, we unravel the ion sieving mechanism and demonstrate that it is mainly due to the interactions of the ions with the carboxylate groups present on the GO surface at neutral pH.

High-resolution discrimination of homologous and isomeric proteinogenic amino acids in nanopore sensors with ultrashort single-walled carbon nanotubes

The hollow and tubular structure of single-walled carbon nanotubes (SWCNTs) makes them ideal candidates for making nanopores. However, the heterogeneity of SWCNTs hinders the fabrication of robust and reproducible carbon-based nanopore sensors. Here we develop a modified density gradient ultracentrifugation approach to separate ultrashort (≈5-10 nm) SWCNTs with a narrow conductance range and construct high-resolution nanopore sensors with those tubes inserted in lipid bilayers. By conducting ionic current recordings and fluorescent imaging of Ca2+ flux through different nanopores, we prove that the ion mobilities in SWCNT nanopores are 3-5 times higher than the bulk mobility. Furthermore, we employ SWCNT nanopores to discriminate homologue or isomeric proteinogenic amino acids, which are challenging tasks for other nanopore sensors. These successes, coupled with the building of SWCNT nanopore arrays, may constitute a crucial part of the recently burgeoning protein sequencing technologies.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Different effects of two Poloxamers (L61 and F68) on the conductance of bilayer lipid membranes

The integral conductance of planar lipid bilayer membranes in the presence of two Poloxamers (Pluronics) L61 and F68 with the same lengths of hydrophobic poly(propylene oxide) blocks and the different lengths of hydrophilic poly(ethylene oxide) blocks increases with an increase in the concentration of both Pluronics; however, the shape of the conductance-concentration curves is super linear for L61 and sublinear for F68. In the presence of both Pluronics, rare discrete current jumps are observed against the background of continuous current. At high concentrations, the I-V curves of membranes with both L61 and F68 became nonlinear at sufficiently low voltages but differed significantly. At voltages greater than 50 mV, the conductance of membranes with L61 increased sharply and quantized jumps were observed toward higher conductance, which could be interpreted as the appearance of additional pores. On the contrary, the conductance of membranes with F68 decreased and quantized jumps to lower conductance were observed, which could be interpreted as blocking of already existing pores. We attributed the differences in the conductance-concentration and I-V curves of these two Pluronics to their different effects on the dynamics of membrane hydration and, accordingly, on the probability of formation of conducting pores.

Modulation of the IKS channel by PIP2 requires two binding sites per monomer

The phosphatidyl-inositol-4,5-bisphosphate (PIP₂) lipid has been shown to be crucial for the coupling between the voltage sensor and the pore of the potassium voltage-gated K_V7 channel family, especially the K_V7.1 channel. Expressed in the myocardium membrane, K_V7.1 forms a complex with KCNE1 auxiliary subunits to generate the I_KS current. Here we present molecular models of the transmembrane region of this complex in its three known states, namely the Resting/Closed (RC), the Intermediate/Closed (IC), and the Activated/Open (AO), robustness of which is assessed by agreement with a range of biophysical data. Molecular Dynamics (MD) simulations of these models embedded in a lipid bilayer including phosphatidyl-inositol-4,5-bisphosphate (PIP₂) lipids show that in presence of KCNE1, two PIP₂ lipids are necessary to stabilize each state. The simulations also show that KCNE1 interacts with both PIP₂ binding sites, forming a tourniquet around the pore and preventing its opening. The present investigation provides therefore key molecular elements that govern the role of PIP₂ in KCNE1 modulation of I_KS channels, possibly a common mechanism by which auxiliary KCNE subunits might modulate a variety of other ion channels.

Molecular modeling of thin-film nanocomposite membranes for reverse osmosis water desalination

The scarcity of freshwater resources is a major global challenge causedby population and economic growth. Water desalination using a reverse osmosis (RO) membrane is a promising technology to supply potable water from seawater and brackish water. The advancement of RO desalination highly depends on new membrane materials. Currently, the RO technology mainly relies on polyamide thin-film composite (TFC) membranes, which suffer from several drawbacks (e.g., low water permeability, permeability-selectivity tradeoff, and low fouling resistance) that hamper their real-world applications. Nanoscale fillers with specific characteristics can be used to improve the properties of TFC membranes. Embedding nanofillers into TFC membranes using interfacial polymerization allows the creation of thin-film nanocomposite (TFNC) membranes, and has become an emerging strategy in the fabrication of high-performance membranes for advanced RO water desalination. To achieve optimal design, it is indispensable to search for reliable methods that can provide fast and accurate predictions of the structural and transport properties of the TFNC membranes. However, molecular understanding of permeability-selectivity characteristics of nanofillers remains limited, partially due to the challenges in experimentally exploring microscopic behaviors of water and salt ions in confinement. Molecular modeling and simulations can fill this gap by generating molecular-level insights into the effects of nanofillers' characteristics (e.g., shape, size, surface chemistry, and density) on water permeability and ion selectivity. In this review, we summarize molecular simulations of a diverse range of nanofillers including nanotubes (carbon nanotubes, boron nitride nanotubes, and aquaporin-mimicking nanochannels) and nanosheets (graphene, graphene oxide, boron nitride sheets, molybdenum disulfide, metal and covalent organic frameworks) for water desalination applications. These simulations reveal that water permeability and salt rejection, as the major factors determining the desalination performance of TFNC membranes, significantly depend on the size, topology, density, and chemical modifications of the nanofillers. Identifying their influences and the physicochemical processes behind, via molecular modeling, is expected to yield important insights for the fabrication and optimization of the next generation high-performance TFNC membranes for RO water desalination.

Roles of Anion-Cation Coupling Transport and Dehydration-Induced Ion-Membrane Interaction in Precise Separation of Ions by Nanofiltration Membranes

Nanofiltration (NF) membranes are playing increasingly crucial roles in addressing emerging environmental challenges by precise separation, yet understanding of the selective transport mechanism is still limited. In this work, the underlying mechanisms governing precise selectivity of the polyamide NF membrane were elucidated using a series of monovalent cations with minor hydrated radius difference. The observed selectivity of a single cation was neither correlated with the hydrated radius nor hydration energy, which could not be explained by the widely accepted NF model or ion dehydration theory. Herein, we employed an Arrhenius approach combined with Monte Carlo simulation to unravel that the transmembrane process of the cation would be dominated by its pairing anion, if the anion has a greater transmembrane energy barrier, due to the constraint of anion-cation coupling transport. Molecular dynamics simulations further revealed that the distinct hydration structure was the primary origin of the energy barrier difference of cations. The cation having a larger incompressible structure after partial dehydration through subnanopores would induce a more significant ion-membrane interaction and consequently a higher energy barrier. Moreover, to validate our proposed mechanisms, a membrane grafting modification toward enlarging the energy barrier difference of dominant ions achieved a 3-fold enhancement in ion separation efficiency. Our work provides insights into the precise separation of ionic species by NF membranes.

Desalination Potential of Aquaporin-Inspired Functionalization of Carbon Nanotubes: Bridging Between Simulation and Experiment

Outstanding water/ion selectivity of aquaporins paves the way for bioinspired desalination membranes. Since the amino acid asparagine (Asn) plays a critical role in the fast water conduction of aquaporins through hydrogen bonding interactions, we adapted this feature by functionalizing carbon nanotubes (CNTs) with Asn. We also studied a nonpolar amino acid and carboxylate functional groups for comparison. Computation of the ideal performance of individual CNTs at atomistic scale is a powerful tool for probing the effect of tip-functionalized CNTs on water and ion transport mechanism. Molecular simulation study suggests that steric effects required for ion rejection compromise fast water conductivity; however, an Asn functional group having polarity and hydrogen bonding capability can be used to balance this trade-off to some extent. To test our hypothesis, we incorporated functionalized CNTs (f-CNTs) into the in situ polymerized selective polyamide (PA) layer of thin film nanocomposite membranes and compared their experimental RO desalination performance. The f-CNTs were found to change the separation environment through modification of cross-linking density, thickness, and hydrophilicity of the PA layer. Asn functionalization led to more cross-linked and thinner PA layer while hydrophilicity is improved compared to other functional groups. Accordingly, water permeance is increased by 25% relative to neat PA with a salt rejection above 98%. Starting from the nanomaterial itself and benefiting from molecular simulation, it is possible to design superior membranes suited for practical applications.

Comparison Study on Single Nucleotide Transport Phenomena in Carbon Nanotubes

To be considered as a promising candidate for mimicking biological nanochannels, carbon nanotubes (CNTs) have been used to explore the mass transport phenomena in recent years. In this study, the single nucleotide transport phenomena are comparatively studied using individual CNTs with a length of ∼15 μm and diameters ranging from 1.5 to 2.5 nm. In the case of CNTs with a diameter of 1.57-1.98 nm, the current traces of nucleotide transport are independent with the metallicity of CNTs and consist of single peak current pulses, whereas extraordinary stepwise current signals are observed in CNT with a diameter of 2.33 nm. It suggests that there is only one molecule in the nanochannel at a time until the diameter of CNT increases to 2.33 nm. Furthermore, it also demonstrates that the single nucleotides can be identified statistically according to their current pulses, indicating the potential application of CNT-based sensors for nucleotides identification.

Ion Selectivity and Permeation Mechanism in a Cyclodextrin-Based Channel

Synthetic ion channels are a promising technology in the medical and materials sciences because of their ability to conduct ions. Channels based on cyclodextrin, a cyclic oligomer of glucose, are of particular interest because of their nontoxicity and biocompatibility. Using molecular dynamics-based free energy calculations, this study identifies cyclodextrin channel types that are best suited to serve as synthetic ion channels. Free energy profiles show that the connectivity in the channel determines whether the channel is cation-selective or anion-selective. Furthermore, the energy barrier for ion transport is governed by the number of glucose molecules making up the cyclodextrin units of the channel. A detailed mechanism is proposed for ion transport through these channels. Findings from this study will aid in designing cyclodextrin-based channels that could be either cation-selective or anion-selective, by modifying the linkages of the channel or the number of glucose molecules in the cyclodextrin rings.

Simulations on Simple Models of Connexin Hemichannels Indicate That Ca2+ Blocking Is Not a Pure Electrostatic Effect

Connexin hemichannels allow the unspecific but regulated interchange of molecules from ions to second messenger and ATP, between the eukariotic cell and its extracellular space. The transport of ions and water through hemichannels is important for physiological functions and also in the progression of several pathological conditions. Extracellular Ca2+ concentration is one of the regulators that drives the channel to a closed state. However the relation between their functional and structural states is far for being totally understood. In this work, we modelled connexin hemichannels using simple systems based on a fixed array of carbon atoms and assess the Ca2+ regulation using molecular dynamics simulations. The two proposed mechanism described so far for calcium action were studied combined, e.g., an electrostatic effect and a pore stretching. Our results show that the addition of positive charge density inside the channel cannot stop the flow of potassium, chloride nor water. Only a pore stretching at the center of the pore can explain the channel blocking.

Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations

We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current–voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current–voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions.

Ionic Transport and Sieving Properties of Sub-nanoporous Polymer Membranes with Tunable Channel Size

Bioinspired nanoporous membranes show great potential in ionic separation and water filtration by offering high selectivity with less permeation resistance. However, complex processes always limit their applications. Here, we report a convenient approach to introduce ionic selective channels in a micron-thick polycarbonate membrane through swift heavy ion irradiation accompanied by UV sensitization and pulsed-electrical etching. The characteristic dimension of channels was tuned through regulating energy loss of the incident ion and UV sensitization time of the membrane, resulting in the sub-nanoporous membranes with mean channel diameter ranging from <2.4 to 9.7 Å. These membranes showed the voltage-activated ionic transport properties associated with the dehydration effect, and the corresponding I-V characteristics were related to ionic strength, solution pH, ionic type, and channel diameter. It was found that the transmembrane conduction of multivalent ions was severely suppressed compared to monovalent ions, until the size of the membrane channel was comparable to the hydrated diameter of multivalent ions. Ionic sieving experiments also demonstrated the excellent ionic valence selectivity of the membrane. Even for the membrane with a channel diameter close to 1 nm, the Li⁺/Mg²⁺ separation ratio was still as high as 40, and an even higher separation ratio was found for Li⁺/La³⁺ (>3000).

Advantages, limitations, and future suggestions in studying graphene-based desalination membranes

The potential of novel 2D carbon materials such as nanoporous single-layer graphene and multilayer graphene oxide membranes is based on their possible advantages such as high water permeability, high selectivity capable of rejecting monovalent ions, with high salt rejection, reduced fouling, and high chemical and physical stability. Here we review how the field has advanced in the study of their performances in various desalination approaches such as reverse osmosis, forward osmosis, nanofiltration, membrane distillation, and solar water purification. The research on making high-performance graphene membranes which started with reverse osmosis applications is seemingly evolving towards other directions.

Ion Selectivity of Water Molecules in Subnanoporous Liquid-Crystalline Water-Treatment Membranes: A Structural Study of Hydrogen Bonding

We demonstrate hydrogen-bonded structures of water in self-organized subnanoporous water treatment membranes obtained using synchrotron-based high-resolution soft X-ray emission spectroscopy. The ion selectivity of these water treatment membranes is usually understood by the size compatibility of nanochannels in the membrane with the Stokes radius of hydrated ions, or by electrostatic interaction between charges inside the nanochannels and such ions. However, based on a comparison between the hydrogen-bonded structures of water molecules in the nanochannels of the water treatment membrane and those surrounding the ions, we propose a definite contribution of structural consistency among the associated hydrogen-bonded water molecules to the ion selectivity. Our observation delivers a novel concept to the design of water treatment membranes where water molecules in the nanochannel can be regarded as a part of the material that controls the ion selectivity.

Water in Nanopores and Biological Channels: A Molecular Simulation Perspective

This Review explores the dynamic behavior of water within nanopores and biological channels in lipid bilayer membranes. We focus on molecular simulation studies, alongside selected structural and other experimental investigations. Structures of biological nanopores and channels are reviewed, emphasizing those high-resolution crystal structures, which reveal water molecules within the transmembrane pores, which can be used to aid the interpretation of simulation studies. Different levels of molecular simulations of water within nanopores are described, with a focus on molecular dynamics (MD). In particular, models of water for MD simulations are discussed in detail to provide an evaluation of their use in simulations of water in nanopores. Simulation studies of the behavior of water in idealized models of nanopores have revealed aspects of the organization and dynamics of nanoconfined water, including wetting/dewetting in narrow hydrophobic nanopores. A survey of simulation studies in a range of nonbiological nanopores is presented, including carbon nanotubes, synthetic nanopores, model peptide nanopores, track-etched nanopores in polymer membranes, and hydroxylated and functionalized nanoporous silica. These reveal a complex relationship between pore size/geometry, the nature of the pore lining, and rates of water transport. Wider nanopores with hydrophobic linings favor water flow whereas narrower hydrophobic pores may show dewetting. Simulation studies over the past decade of the behavior of water in a range of biological nanopores are described, including porins and β-barrel protein nanopores, aquaporins and related polar solute pores, and a number of different classes of ion channels. Water is shown to play a key role in proton transport in biological channels and in hydrophobic gating of ion channels. An overall picture emerges, whereby the behavior of water in a nanopore may be predicted as a function of its hydrophobicity and radius. This informs our understanding of the functions of diverse channel structures and will aid the design of novel nanopores. Thus, our current level of understanding allows for the design of a nanopore which promotes wetting over dewetting or vice versa. However, to design a novel nanopore, which enables fast, selective, and gated flow of water de novo would remain challenging, suggesting a need for further detailed simulations alongside experimental evaluation of more complex nanopore systems.

Integral Representation of Electrostatic Interactions inside a Lipid Membrane

Interactions between charges and dipoles inside a lipid membrane are partially screened. The screening arises both from the polarization of water and from the structure of the electric double layer formed by the salt ions outside the membrane. Assuming that the membrane can be represented as a dielectric slab of low dielectric constant sandwiched by an aqueous solution containing mobile ions, a theoretical model is developed to quantify the strength of electrostatic interactions inside a lipid membrane that is valid in the linear limit of Poisson-Boltzmann theory. We determine the electrostatic potential produced by a single point charge that resides inside the slab and from that calculate charge-charge and dipole-dipole interactions as a function of separation. Our approach yields integral representations for these interactions that can easily be evaluated numerically for any choice of parameters and be further simplified in limiting cases.

Cytotoxicity effects and ionic diffusion of single-wall carbon nanotubes in cell membrane

While carbon nanotubes have been put into massive practical industrial, environmental and biomedicine applications, the cytotoxicity effects or the effect to the ionic channels they bring into the living cells need to be thoroughly investigated. In this work, molecular dynamic simulations have been carried out to investigate the ionic diffusion through the single wall armchair carbon nanotube embedded right inside the cell membrane. By modeling a two-membrane system, we build a virtual cytoplasm environment including a cell chamber and an extracellular space, in which a certain amount of solute is dissolved. The system is first brought to its equilibrium by deployment of minimization and then simulated. The results suggested that carbon nanotubes (CNTs) with size less than (12, 12) shall be less cytotoxic since it does not bring any ionic diffusion through the CNT channel, so as to maintain active cytoplasm environment. Another phenomenon we observed is a notable shifting angle of the carbon nanotube which was normal to the surface of cell membrane initially. In general, the inclination angle of the carbon nanotube increases with its radius.

Charge Scaling Manifesto: A Way of Reconciling the Inherently Macroscopic and Microscopic Natures of Molecular Simulations

Electronic polarization effects play an important role in the interactions of charged species in biologically relevant aqueous solutions, such as those involving salt ions, proteins, nucleic acids, or phospholipid membranes. Explicit inclusion of electronic polarization in molecular modeling is tedious both from the point of view of force field parametrization and actual performance of the simulations. Therefore, the vast majority of biomolecular simulations is performed using nonpolarizable force fields, which can lead to artifacts such as dramatically overestimated ion pairing, particularly when polyvalent ions are involved. Here, we show that many of these issues can be remedied without extra computational costs by including electronic polarization in a mean field way via charge rescaling. We also lay the solid physical foundations of this approach and reconcile from this perspective the microscopic versus macroscopic natures of nonpolarizable force fields.

Computational Nanoscopy of Tight Junctions at the Blood-Brain Barrier Interface

The selectivity of the blood-brain barrier (BBB) is primarily maintained by tight junctions (TJs), which act as gatekeepers of the paracellular space by blocking blood-borne toxins, drugs, and pathogens from entering the brain. The BBB presents a significant challenge in designing neurotherapeutics, so a comprehensive understanding of the TJ architecture can aid in the design of novel therapeutics. Unraveling the intricacies of TJs with conventional experimental techniques alone is challenging, but recently developed computational tools can provide a valuable molecular-level understanding of TJ architecture. We employed the computational methods toolkit to investigate claudin-5, a highly expressed TJ protein at the BBB interface. Our approach started with the prediction of claudin-5 structure, evaluation of stable dimer conformations and nanoscale assemblies, followed by the impact of lipid environments, and posttranslational modifications on these claudin-5 assemblies. These led to the study of TJ pores and barriers and finally understanding of ion and small molecule transport through the TJs. Some of these in silico, molecular-level findings, will need to be corroborated by future experiments. The resulting understanding can be advantageous towards the eventual goal of drug delivery across the BBB. This review provides key insights gleaned from a series of state-of-the-art nanoscale simulations (or computational nanoscopy studies) performed on the TJ architecture.

Fabrication and characterization of zeolitic imidazolate framework-embedded cellulose acetate membranes for osmotically driven membrane process

Zeolitic imidazolate framework-302 (ZIF-302)-embedded cellulose acetate (CA) membranes for osmotic driven membrane process (ODMPs) were fabricated using the phase inversion method. We investigated the effects of different fractions of ZIF-302 in the CA membrane to understand their influence on ODMPs performance. Osmotic water transport was evaluated using different draw solution concentrations to investigate the effects of ZIF-302 contents on the performance parameters. CA/ZIF-302 membranes showed fouling resistance to sodium alginate by a decreased water flux decline and increased recovery ratio in the pressure retarded osmosis (PRO) mode. Results show that the hydrothermally stable ZIF-302-embedded CA/ZIF-302 composite membrane is expected to be durable in water and alginate-fouling conditions.

Calculating Single-Channel Permeability and Conductance from Transition Paths

Permeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.

Oriented chiral water wires in artificial transmembrane channels

Aquaporins (AQPs) feature highly selective water transport through cell membranes, where the dipolar orientation of structured water wires spanning the AQP pore is of considerable importance for the selective translocation of water over ions. We recently discovered that water permeability through artificial water channels formed by stacked imidazole I-quartet superstructures increases when the channel water molecules are highly organized. Correlating water structure with molecular transport is essential for understanding the underlying mechanisms of (fast) water translocation and channel selectivity. Chirality adds another factor enabling unique dipolar oriented water structures. We show that water molecules exhibit a dipolar oriented wire structure within chiral I-quartet water channels both in the solid state and embedded in supported lipid bilayer membranes (SLBs). X-ray single-crystal structures show that crystallographic water wires exhibit dipolar orientation, which is unique for chiral I-quartets. The integration of I-quartets into SLBs was monitored with a quartz crystal microbalance with dissipation, quantizing the amount of channel water molecules. Nonlinear sum-frequency generation vibrational spectroscopy demonstrates the first experimental observation of dipolar oriented water structures within artificial water channels inserted in bilayer membranes. Confirmation of the ordered confined water is obtained via molecular simulations, which provide quantitative measures of hydrogen bond strength, connectivity, and the stability of their dipolar alignment in a membrane environment. Together, uncovering the interplay between the dipolar aligned water structure and water transport through the self-assembled I-quartets is critical to understanding the behavior of natural membrane channels and will accelerate the systematic discovery for developing artificial water channels for water desalting.

Molecular dynamics simulations of carbon nanotube porins in lipid bilayers

Carbon nanotube porins embedded in lipid membranes are studied by molecular dynamics simulations.

Voltage-activated transport of ions through single-walled carbon nanotubes

Ionic transport through single-walled carbon nanotubes (SWCNTs) is promising for many applications but remains both experimentally challenging and highly debated. Here we report ionic current measurements through microfluidic devices containing one or several SWCNTs of diameter of 1.2 to 2 nm unexpectedly showing a linear or a voltage-activated I-V dependence. Transition from an activated to a linear behavior, and stochastic fluctuations between different current levels were notably observed. For linear devices, the high conductance confirmed with different chloride salts indicates that the nanotube/water interface exhibits both a high surface charge density and flow slippage, in agreement with previous reports. In addition, the sublinear dependence of the conductance on the salt concentration points toward a charge-regulation mechanism. Theoretical modelling and computer simulations show that the voltage-activated behavior can be accounted for by the presence of local energy barriers along or at the ends of the nanotube. Raman spectroscopy reveals strain fluctuations along the tubes induced by the polymer matrix but displays insufficient doping or variations of doping to account for the apparent surface charge density and energy barriers revealed by ion transport measurements. Finally, experimental evidence points toward environment-sensitive chemical moieties at the nanotube mouths as being responsible for the energy barriers causing the activated transport of ions through SWCNTs within this diameter range.

Multiscale modeling of a rectifying bipolar nanopore: explicit-water versus implicit-water simulations

In a multiscale modeling approach, we present computer simulation results for a rectifying bipolar nanopore at two modeling levels. In an all-atom model, we use explicit water to simulate ion transport directly with the molecular dynamics technique. In a reduced model, we use implicit water and apply the Local Equilibrium Monte Carlo method together with the Nernst-Planck transport equation. This hybrid method makes the fast calculation of ion transport possible at the price of lost details. We show that the implicit-water model is an appropriate representation of the explicit-water model when we look at the system at the device (i.e., input vs. output) level. The two models produce qualitatively similar behavior of the electrical current for different voltages and model parameters. Looking at the details of concentration and potential profiles, we find profound differences between the two models. These differences, however, do not influence the basic behavior of the model as a device because they do not influence the z-dependence of the concentration profiles which are the main determinants of current. These results then address an old paradox: how do reduced models, whose assumptions should break down in a nanoscale device, predict experimental data? Our simulations show that reduced models can still capture the overall device physics correctly, even though they get some important aspects of the molecular-scale physics quite wrong; reduced models work because they include the physics that is necessary from the point of view of device function. Therefore, reduced models can suffice for general device understanding and device design, but more detailed models might be needed for molecular level understanding.

Stability and dynamics of membrane-spanning DNA nanopores

Recently developed DNA-based analogues of membrane proteins have advanced synthetic biology. A fundamental question is how hydrophilic nanostructures reside in the hydrophobic environment of the membrane. Here, we use multiscale molecular dynamics (MD) simulations to explore the structure, stability and dynamics of an archetypical DNA nanotube inserted via a ring of membrane anchors into a phospholipid bilayer. Coarse-grained MD reveals that the lipids reorganize locally to interact closely with the membrane-spanning section of the DNA tube. Steered simulations along the bilayer normal establish the metastable nature of the inserted pore, yielding a force profile with barriers for membrane exit due to the membrane anchors. Atomistic, equilibrium simulations at two salt concentrations confirm the close packing of lipid around of the stably inserted DNA pore and its cation selectivity, while revealing localized structural fluctuations. The wide-ranging and detailed insight informs the design of next-generation DNA pores for synthetic biology or biomedicine.

Although DNA nanopores are widely explored as synthetic membrane proteins, it is still unclear how the anionic DNA assemblies stably reside within the hydrophobic core of a lipid bilayer. Here, the authors use molecular dynamics simulations to reveal the key dynamic interactions and energetics stabilizing the nanopore-membrane interaction.

Molecular Origin of Electric Double-Layer Capacitance at Multilayer Graphene Edges

Multilayer graphenes have been widely used as active materials for electric double-layer capacitors (EDLCs), where their numerous edges are demonstrated to play a crucial role in charge storage. In this work, the interfacial structure and capacitive behaviors of multilayer graphene edges with representative interlayer spacing are studied via molecular dynamics (MD) simulations. Compared with planar graphite surfaces, edges can achieve a 2-fold increase in the specific capacitance at a wider interlayer spacing of ∼5.0 Å. Unusually, the molecular origins for achieved charge storage are predominantly attributed to the structural evolutions of solvents occurring in the double layer, going beyond the traditional views of regulating the capacitance by ion adsorption/separation. Specifically, diverse ionic distributions exhibit similar screening ability and EDLC thickness, while water molecules can counterbalance the interfacial electric fields more effectively at edge site. The as-obtained findings will be instructive in designing graphene-based EDLCs for advanced capacitive performances.

Validity of the Electrodiffusion Model for Calculating Conductance of Simple Ion Channels

We examine the validity and utility of the electrodiffusion (ED) equation, i.e., the generalized Nernst-Planck equation, to characterize, in combination with molecular dynamics, the electrophysiological behavior of simple ion channels. As models, we consider three systems-two naturally occurring channels formed by α-helical bundles of peptaibols, trichotoxin, and alamethicin, and a synthetic, hexameric channel, formed by a peptide that contains only leucine and serine. All these channels mediate transport of potassium and chloride ions. Starting with equilibrium properties, such as the potential of mean force experienced by an ion traversing the channel and diffusivity, obtained from molecular dynamics simulations, the ED equation can be used to determine the full current-voltage dependence with modest or no additional effort. The potential of mean force can be obtained not only from equilibrium simulations, but also, with comparable accuracy, from nonequilibrium simulations at a single voltage. The main assumptions underlying the ED equation appear to hold well for the channels and voltages studied here. To expand the utility of the ED equation, we examine what are the necessary and sufficient conditions for Ohmic and nonrectifying behavior and relate deviations from this behavior to the shape of the ionic potential of mean force.

Functional Annotation of Ion Channel Structures by Molecular Simulation

Ion channels play key roles in cell membranes, and recent advances are yielding an increasing number of structures. However, their functional relevance is often unclear and better tools are required for their functional annotation. In sub-nanometer pores such as ion channels, hydrophobic gating has been shown to promote dewetting to produce a functionally closed (i.e., non-conductive) state. Using the serotonin receptor (5-HT₃R) structure as an example, we demonstrate the use of molecular dynamics to aid the functional annotation of channel structures via simulation of the behavior of water within the pore. Three increasingly complex simulation analyses are described: water equilibrium densities; single-ion free-energy profiles; and computational electrophysiology. All three approaches correctly predict the 5-HT₃R crystal structure to represent a functionally closed (i.e., non-conductive) state. We also illustrate the application of water equilibrium density simulations to annotate different conformational states of a glycine receptor.

Pore size matters for potassium channel conductance

Ion channels are membrane proteins that mediate efficient ion transport across the hydrophobic core of cell membranes, an unlikely process in their absence. K⁺ channels discriminate K⁺ over cations with similar radii with extraordinary selectivity and display a wide diversity of ion transport rates, covering differences of two orders of magnitude in unitary conductance. The pore domains of large- and small-conductance K⁺ channels share a general architectural design comprising a conserved narrow selectivity filter, which forms intimate interactions with permeant ions, flanked by two wider vestibules toward the internal and external openings. In large-conductance K⁺ channels, the inner vestibule is wide, whereas in small-conductance channels it is narrow. Here we raise the idea that the physical dimensions of the hydrophobic internal vestibule limit ion transport in K⁺ channels, accounting for their diversity in unitary conductance.

A computational assessment of the permeability and salt rejection of carbon nanotube membranes and their application to water desalination

Membranes made from nanomaterials such as nanotubes and graphene have been suggested to have a range of applications in water filtration and desalination, but determining their suitability for these purposes requires an accurate assessment of the properties of these novel materials. In this study, we use molecular dynamics simulations to determine the permeability and salt rejection capabilities for membranes incorporating carbon nanotubes (CNTs) at a range of pore sizes, pressures and concentrations. We include the influence of osmotic gradients and concentration build up and simulate at realistic pressures to improve the reliability of estimated membrane transport properties. We find that salt rejection is highly dependent on the applied hydrostatic pressure, meaning high rejection can be achieved with wider tubes than previously thought; while membrane permeability depends on salt concentration. The ideal size of the CNTs for desalination applications yielding high permeability and high salt rejection is found to be around 1.1 nm diameter. While there are limited energy gains to be achieved in using ultra-permeable CNT membranes in desalination by reverse osmosis, such membranes may allow for smaller plants to be built as is required when size or weight must be minimized. There are diminishing returns in further increasing membrane permeability, so efforts should focus on the fabrication of membranes containing narrow or functionalized CNTs that yield the desired rejection or selection properties rather than trying to optimize pore densities.

DNA translocation through single-layer boron nitride nanopores

Ultra-thin nanopores have become promising biological sensors because of their outstanding signal-to-noise ratio and spatial resolution. Here, we show that boron nitride (BN), which is a new two-dimensional (2D) material similar to graphene, could be utilized for making a nanopore with an atomic thickness. Using an all-atom molecular dynamics simulation, we investigated the dynamics of DNA translocation through the BN nanopore. The results of our simulations demonstrated that it is possible to detect different double-stranded DNA (dsDNA) sequences from the recording of ionic currents through the pore during the DNA translocation. Surprisingly, opposite to results for a graphene nanopore, we found the calculated blockage current for poly(A-T)40 in a BN nanopore to be less than that for poly(G-C)40. Also in contrast with the case of graphene nanopores, dsDNA models moved smoothly and in an unimpeded manner through the BN nanopores in the simulations, suggesting a potential advantage for using BN nanopores to design stall-free sequencing devices. BN nanopores, which display several properties (such as being hydrophilic and non-metallic) that are superior to those of graphene, are thus expected to find applications in the next generation of high-speed and low-cost biological sensors.

Sensitive Detection of a Modified Base in Single-Stranded DNA by a Single-Walled Carbon Nanotube

In this work, we use molecular dynamics simulations to study the responses of the configuration of single-strand DNA (ssDNA) within a carbon nanotube (CNT) and the concomitant ion flow to a single modified base, i.e., benzoimidazole (Bzim)-modified 5-hydroxymethyl cytosine (5hmC). Our simulation results show the Bzim-modified 5hmC can considerably increase the ion flow through a single-walled carbon nanotube (SWCNT), despite its larger size, which is consistent with prior experimental results. This phenomenon is attributed to enhanced adsorption of DNA to the interior wall of the CNT driven by the Bzim-modified 5hmC, leading to a reduced steric effect on ion transport through the CNT. As revealed in this work, the distribution of ssDNA can be affected by limited change in the interactions with the CNT surface. Such behavior of ssDNA within small-sized CNTs can be exploited to further improve the sensitivity of nanopore detection.

Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation

Fundamental understanding of ionic transport at the nanoscale is essential for developing biosensors based on nanopore technology and new generation high-performance nanofiltration membranes for separation and purification applications. We study here ionic transport through single putatively neutral hydrophobic nanopores with high aspect ratio (of length L = 6 μm with diameters ranging from 1 to 10 nm) and with a well controlled cylindrical geometry. We develop a detailed hybrid mesoscopic theoretical approach for the electrolyte conductivity inside nanopores, which considers explicitly ion advection by electro-osmotic flow and possible flow slip at the pore surface. By fitting the experimental conductance data we show that for nanopore diameters greater than 4 nm a constant weak surface charge density of about 10⁻² C m⁻² needs to be incorporated in the model to account for conductance plateaus of a few pico-siemens at low salt concentrations. For tighter nanopores, our analysis leads to a higher surface charge density, which can be attributed to a modification of ion solvation structure close to the pore surface, as observed in the molecular dynamics simulations we performed.