Electric field-controlled water permeation coupled to ion transport through a nanopore

We report molecular dynamics simulations of a generic hydrophobic nanopore connecting two reservoirs which are initially at different Na(+) concentrations, as in a biological cell. The nanopore is impermeable to water under equilibrium conditions, but the strong electric field caused by the ionic concentration gradient drives water molecules in. The density and structure of water in the pore are highly field dependent. In a typical simulation run, we observe a succession of cation passages through the pore, characterized by approximately bulk mobility. These ion passages reduce the electric field, until the pore empties of water and closes to further ion transport, thus providing a possible mechanism for biological ion channel gating.     

Not ions alone: barriers to ion permeation in nanopores and channels

A hydrophobic pore of subnanometer dimensions can appear impermeable to an ion even though its radius is still much wider than that of the ion. Pores of molecular dimensions can be found, for instance, in carbon nanotubes, zeolites, or ion channel proteins. We quantify this barrier to ion permeation by calculating the potential of mean force from umbrella-sampled molecular dynamics simulations and compare them to continuum-electrostatic Poisson-Boltzmann calculations. The latter fail to describe the ion barrier because they do not account for the properties of water in the pore. The barrier originates from the energetic cost to desolvate the ion. Even in wide pores, which could accommodate an ion and its hydration shell, a barrier of several kT remains because the liquid water phase is not stable in the hydrophobic pore. Thus, the properties of the solvent play a crucial role in determining permeation properties of ions in confinement at the molecular scale.     

Barriers to ion translocation in cationic and anionic receptors from the Cys-loop family

Understanding the mechanisms of gating and ion permeation in biological channels and receptors has been a long-standing challenge in biophysics. Recent advances in structural biology have revealed the architecture of a number of transmembrane channels and allowed detailed, molecular-level insight into these systems. Herein, we have examined the barriers to ion conductance and origins of ion selectivity in models of the cationic human alpha7 nicotinic acetylcholine receptor (nAChR) and the anionic alpha1 glycine receptor (GlyR), based on the structure of Torpedo nAChR. Molecular dynamics simulations were used to determine water density profiles along the channel length, and they established that both receptor pores were fully hydrated. The very low water density in the middle of the nAChR pore indicated the existence of a hydrophobic constriction. By contrast, the pore of GlyR was lined with hydrophilic residues and remained well-hydrated throughout. Adaptive biasing force simulations allowed us to reconstruct potentials of mean force (PMFs) for chloride and sodium ions in the two receptors. For the nicotinic receptor we observed barriers to ion translocation associated with rings of hydrophobic residues-Val13' and Leu9'-in the middle of the transmembrane domain. This finding further substantiates the hydrophobic gating hypothesis for nAChR. The PMF revealed no significant hydrophobic barrier for chloride translocation in GlyR. For both receptors nonpermeant ions displayed considerable barriers. Thus, the overall electrostatics and the presence of rings of charged residues at the entrance and exit of the channels were sufficient to explain the experimentally observed anion and cation selectivity.     

BROMOC-D: Brownian Dynamics/Monte-Carlo Program Suite to Study Ion and DNA Permeation in Nanopores

A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion-ion and ion-DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)(n) and ss-poly(dC)(n). The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.     

Transport of hydrated nitrate and nitrite ions through graphene nanopores in aqueous medium

Nitrate () and nitrite () ions are naturally occurring inorganic ions that are part of the nitrogen cycle. High doses of these ions in drinking water impose a potential risk to public health. In this work, molecular dynamics simulations are carried out to study the passage of nitrate and nitrite ions from water through graphene nanosheets (GNS) with hydrogen-functionalized narrow pores in presence of an external electric field. The passage of ions through the pores is investigated through calculations of ion flux, and the results are analyzed through calculations of various structural and thermodynamic properties such as the density of ions and water, ion–water radial distribution functions, two-dimensional density distribution functions, and the potentials of mean force of the ions. Current simulations show that the nitrite ions can pass more in numbers than the nitrate ions in a given time through GNS hydrogen-functionalized pore of different geometry. It is found that the nitrite ions can permeate faster than the nitrate ions despite the former having higher hydration energy in the bulk. This can be explained in terms of the competition between the number density of the ions along the pore axis and the free energy barrier calculated from the potential of mean force. Also, an externally applied electric field is found to be important for faster permeation of the nitrite over the nitrate ions. The current study suggests that graphene nanosheets with carefully created pores can be effective in achieving selective passage of ions from aqueous solutions.     

Effect of Protein Dimerization on Ion Conductivity of Gramicidin A Channel Studied Using Polarizable Force Field

In studies of ion channel systems, due to the huge computational cost of polarizable force fields, classical force fields remain the most widely used for a long time. In this work, we used the AMOEBA polarizable atomic multipole force field in enhanced sampling simulations of single-channel gramicidin A (gA) and double-channel gA systems and investigated its reliability in characterizing ion-transport properties of the gA ion channel under dimerization. The influence of gA dimerization on the permeation of potassium and sodium ions through the channel was described in terms of conductance, diffusion coefficient, and free energy profile. Results from the polarizable force field simulations show that the conductance of potassium and sodium ions passing through the single- and double-channel agrees well with experimental values. Further data analysis reveals that the molecular mechanism of protein dimerization affects the ion-transport properties of gA channels, i.e., protein dimerization accelerates the permeation of potassium and sodium ions passing through the double-channel by adjusting the environment around gA protein (the distribution of phospholipid head groups, ions outside the channel, and bulk water), rather than directly adjusting the conformation of gA protein.     

Pore formation coupled to ion transport through lipid membranes as induced by transmembrane ionic charge imbalance: atomistic molecular dynamics study

We have employed atomic-scale molecular dynamics simulations to address ion transport through transient water pores in phospholipid membranes. The formation of a water pore is induced by a transmembrane ionic charge imbalance, which gives rise to a significant potential difference across the membrane. The subsequent transport of ions through the pore discharges the transmembrane potential and makes the water pore metastable, leading eventually to its sealing. The findings highlight the importance of ionic charge fluctuations in spontaneous pore formation and their role in ion leakage through protein-free lipid membranes.     

Water between plates in the presence of an electric field in an open system

Molecular dynamics simulations of water at 298 K and 1 atm of pressure are used to investigate the electric-field dependence of the density and polarization density of water between two graphite-like plates of different sizes (9.8 x 9.2 and 17.7 x 17.2 A) in an open system for plate separations of 8.0, 9.5, and 16.4 A. The interactions with water were tuned to "hard-wall-like" and "normal" C-O hydrophobic potentials. Water between the larger plates at 16.4 A separation is layered but is metastable with respect to capillary evaporation at zero field (Bratko, D.; Curtis, R. A.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 2001, 115, 3873). Applying a field decreases the density of the water between the plates, in apparent contradiction to thermodynamic and integral equation theories of bulk fluid electrostriction that ignore surface effects, rendering them inapplicable to finite-sized films of water between hydrophobic plates. This suggests that the free energy barrier for evaporation is lowered by the applied field. Water, between "hard-wall-like" plates at narrower separations of 9.5 A and less, shows a spontaneous but incomplete evaporation at zero field within the time scale of our simulation. Evaporation is further enhanced by an electric field. No such evaporation occurs, on these time scales, for the smaller plates with the "hard-wall-like" potential at a separation of 8.0 A at zero field, signaling a crossover in behavior as the plate dimension decreases, but the water density still diminishes with increasing field strength. These observations could have implications for the behavior of thin films of water between surfaces in real physical and biological systems.     

Mean force potential of interaction between Na<Superscript>+</Superscript> and Cl<Superscript>−</Superscript> ions in planar nanopores in contact with water under pressure

The mean force potential (MFP) of interaction between counterions Na⁺ and Cl^? in a planar nanopore with structureless hydrophobic walls is calculated via computer simulation under the condition that the nanopore is in contact with water at an external pressure that exceeds the saturation pressure but remains insufficient to fill the nanopore with water. For a nanopore with a liquid phase, the MFP dependence on the interionic distance indicates the dissociation of an ion pair into two hydrated ions in a nanopore that is not completely filled with water. Fluctuations in the number of water molecules drawn into the interionic space decisively influence the dissociation. The attraction between counterions, averaged over thermal fluctuations, depends largely on the pore width and grows as the shielding of the ions’ electric field by water molecules in a narrow pore diminishes. The contributions from energy and entropy to the free energy of hydration are analyzed.     

Ion pairs in aqueous electrolyte microdrops under conditions of a flat nanopore

The molecular mechanisms of aqueous solvent penetration into a flat nanopore with hydrophobic structureless walls containing a Na⁺Cl^? ion pair with nonfixed distance between ions is studied by computer simulations. A detailed many-body polycenter model of intermolecular interactions calibrated with respect to experimental data for the free energy of attachment of water vapor molecules and quantum-chemical calculations in clusters is used. The ion pair hydration results in its decomposition. Drawing the molecules into the gap between ions makes easier penetration of solvent and filling of the nanopore with electrolyte. The ion-pair dissociation is accompanied by dramatic changes in the chemical potential of molecules and electric properties of the whole system. The thermodynamic characteristics of decomposition are stable as regards variations in the pore width. The post-decomposition electric polarizability demonstrates strong anisotropy associated with the nanopore flatness.     

Ion permeation dynamics in carbon nanotubes

Molecular dynamics simulations are carried out to investigate the permeation of ions and water in a membrane consisting of single wall carbon nanotubes possessing no surface charges connecting two reservoirs. Our simulations reveal that there are changes in the first hydration shell of the ions upon confinement in tubes of 0.82 or 0.90 nm effective internal diameter. Although the first minimum in the g(r) is barely changed in the nanotube compared to in the bulk solution, the hydration number of Na(+) ion is reduced by 1.0 (from 4.5 in bulk to 3.5 in the 0.90 nm tube) and the hydration number is reduced further in the 0.82 nm tube. The changes in the hydration shell of Cl(-) ion are negligible, within statistical errors. The water molecules of the first hydration shell of both ions exchange less frequently inside the tube than in the bulk solution. We compare ion trajectories for ions in the same tube under identical reservoir conditions but with different numbers of ions in the tubes. This permits investigation of changes in structure and dynamics which arise from multiple ion occupancy in a carbon nanotube possessing no surface charges. We also investigated the effects of tube flexibility. Ions enter the tubes so as to form a train of ion pairs. We find that the radial distribution profiles of Na(+) ions broaden significantly systematically with increasing number of ion pairs in the tube. The radial distribution profiles of Cl(-) ions change only slightly with increasing number of ions in the tube. Trajectories reveal that Na(+) ions do not pass each other in 0.90 nm tubes, while Cl(-) ions pass each other, as do ions of opposite charge. An ion entering the tube causes the like-charged ions preceding it in the tube to be displaced along the tube axis and positive or negative ions will exit the tube only when one or two other ions of the same charge are present in the tube. Thus, the permeation mechanism involves multiple ions and Coulomb repulsion among the ions plays an essential role.     

Surface tension of electrolytes: hydrophilic and hydrophobic ions near an interface

We calculate the ion distributions around an interface in fluid mixtures of highly polar and less polar fluids (water and oil) for two and three ion species. We take into account the solvation and image interactions between ions and solvent. We show that hydrophilic and hydrophobic ions tend to undergo a microphase separation at an interface, giving rise to an enlarged electric double layer. We also derive a general expression for the surface tension of electrolyte systems, which contains a negative electrostatic contribution proportional to the square root of the bulk salt density. The amplitude of this square-root term is small for hydrophilic ion pairs but is much increased for hydrophilic and hydrophobic ion pairs. For three ion species, including hydrophilic and hydrophobic ions, we calculate the ion distributions to explain those obtained by x-ray reflectivity measurements.     

Structural and electric field effects of ions in aqueous nanodrops

Ensemble infrared photodissociation (IRPD) spectra in the hydrogen stretch region (～2950-3800 cm(-1)) are reported for M(H(2)O)(35-37), with M = I(-), Cl(-), HCO(3)(-), OH(-), tetrabutyl-, tetrapropyl-, and tetramethylammonium, Cs(+), Na(+), Li(+), H(+), Ba(2+), Ca(2+), Co(2+), Mg(2+), La(3+), and Tm(3+), at 133 K. A single, broad feature is observed in the bonded-OH region of the spectra that indicates that the water network in these clusters is bulk-like and likely resembles liquid water more strongly than ice. The free-OH region for all of these clusters is dominated by peaks corresponding to water molecules that accept two and donate one hydrogen bond (AAD water molecules), indicating that AAD water molecules are more abundant at the surface of these ions than AD water molecules. A-only water molecules are present in significant abundance only for the trivalent metal cations. The frequency of the AAD free-OH stretch band shifts nearly linearly with the charge state of the ion, consistent with a Stark shift attributable to the ion's electric field. From these data, a frequency range of 3704.9-3709.7 cm(-1) is extrapolated for the free-OH of AAD water molecules at the (uncharged) bulk liquid water surface, consistent with sum-frequency generation spectroscopy experiments. Differences in both the bonded- and the free-OH regions of the spectra for these ions are attributable to ion-induced patterning of the water network that extends to the surface of the clusters, which includes water molecules in the third and fourth solvation shells; that is, these ions pattern water molecules at long distance to various extents. These spectra are simulated using two different electrostatic models previously used to calculate OH-stretch spectra of bulk water and aqueous solutions and parametrized for bonded-OH frequencies. These models qualitatively reproduce a number of features in the experimental spectra, although it is evident that more sophisticated treatment of water molecule and ion polarizability and vibrational coupling is necessary for more quantitative comparisons.     

Ion current rectification at nanopores in glass membranes

The origin of ion current rectification observed at conical-shaped nanopores in glass membranes immersed in KCl solutions has been investigated using finite-element simulations. The ion concentrations and fluxes (due to diffusion, migration, and electroosmotic convection) were determined by the simultaneous solution of the Nernst-Planck, Poisson, and Navier-Stokes equations for the two-ion (K+ and Cl-) system. Fixed surface charge on both the internal and external glass surfaces that define the pore structure was included to account for electric fields and nonuniform ion conductivity within the nanopores and electric fields in the external solution near the pore mouth. We demonstrate that previous observations of ion current rectification in conical-shaped glass nanopores are a consequence of the voltage-dependent solution conductivity in the vicinity of the pore mouth, both inside and outside of the pore. The simulations also demonstrate that current rectification is maximized at intermediate bulk ion concentrations, a combination of (i) the electrical screening of surface charge at high concentrations and (ii) a fixed number of charge-carrying ions in the pore at lower concentration, which are physical conditions where the voltage dependence of the conductivity disappears. In addition, we have quantitatively shown that electroosmotic flow gives rise to a significant but small contribution to current rectification.     

Phenomenon of the ousting of a monatomic ion from its hydration shell in flat nanopores

The structure and stability of hydrate shells of singly charged sodium and chlorine ions are studied by computer simulations under the conditions of nanoscopic flat pores with the use of the previously proposed detailed force field model containing polarization interactions, transferring charge effects as well as manybody interactions of covalent type. It is found that the effect of ousting a monatomic ion from its hydration shell, which has previously been observed by independent authors in bulk vapor, is also reproduced persistently in nanoscopic pores. Whereas the ousting of the ion from its hydration shell in bulk vapor is accompanied by the loss of thermodynamic stability of the system and at sufficiently high vapor pressure causes avalanche-like condensation, under the conditions of a nanoscopic pore the thermodynamic stability is retained. The obtained data show that the ousting of the ion from its hydration shell is a universal phenomenon covering the majority, if not all, of monatomic and, possibly, some of molecular ions.     

Hydration of alkali ions from first principles molecular dynamics revisited

Structural and dynamical properties of the hydration of Li(+), Na(+), and K(+) in liquid water at ambient conditions were studied by first principles molecular dynamics. Our simulations successfully captured the different hydration behavior shown by the three alkali ions as observed in experiments. The present analyses of the dependence of the self-diffusion coefficient and rotational correlation time of water on the ion concentration suggest that Li(+) (K(+)) is certainly categorized as a structure maker (breaker), whereas Na(+) acts as a weak structure breaker. An analysis of the relevant electronic structures, based on maximally localized Wannier functions, revealed that the dipole moment of H(2)O molecules in the first solvation shell of Na(+) and K(+) decreases by about 0.1 D compared to that in the bulk, due to a contraction of the oxygen lone pair orbital pointing toward the metal ion.     

Thermodynamics of water entry in hydrophobic channels of carbon nanotubes

Experiments and computer simulations demonstrate that water spontaneously fills the hydrophobic cavity of a carbon nanotube. To gain a quantitative thermodynamic understanding of this phenomenon, we use the recently developed two phase thermodynamics method to compute translational and rotational entropies of confined water molecules inside single-walled carbon nanotubes and show that the increase in energy of a water molecule inside the nanotube is compensated by the gain in its rotational entropy. The confined water is in equilibrium with the bulk water and the Helmholtz free energy per water molecule of confined water is the same as that in the bulk within the accuracy of the simulation results. A comparison of translational and rotational spectra of water molecules confined in carbon nanotubes with that of bulk water shows significant shifts in the positions of the spectral peaks that are directly related to the tube radius.     

Molecular-dynamics simulation of the effect of ions on a liquid-liquid interface for a partially miscible mixture

Molecular-dynamics simulations were performed to model the effect of added salt ions on the liquid-liquid interface in a partially miscible system. Simulations of the interface between saturated phases of a model 1-hexanol+water system show a bilayer structure of 1-hexanol molecules at the interface with -OH heads of the first layer directed into the water phase and the opposite orientation for the second layer. The alignment of the polar -OH groups at the interface stabilizes a charge separation of sodium and chloride ions when salt is introduced into the aqueous phase, producing an electrical double layer. Chloride ions aggregate nearer the interface and sodium ions move toward the bulk water phase, consistent with the explanation that the -OH alignment presents a region of partial positive charges to which the hydrated chloride atoms are attracted. Ions near the interface were found to be less solvated than those in the bulk phase. An electric field was also applied to drive ions through the interface. Ions crossing the interface tended to shed water molecules as they entered the hexanol bilayer, leaving a trail of water molecules. Stabilization and facilitated transport of the ion by interactions with the second layer of hexanol molecules appeared to be an important step in the mechanism of sodium ion transport.     

Role of water molecules in the KcsA protein channel by molecular dynamics calculations

Molecular dynamics simulations supported by electrostatic calculations have been conducted on the KcsA channel to determine the role of water molecules in the pore. Starting from the X-ray structure of the KcsA channel in its closed state at 2.0 angstroms resolution, the opening of the pore towards a conformation built on the basis of EPR results is studied. We show that water molecules act as a structural element for the K+ ions inside the filter and the hydrophobic cavity of the channel. In the filter, water tends to enhance the depth of the wells occupied by the K+ ions, while in the cavity there is a strong correlation between the water molecules and the cavity ion. As a consequence, the protein remains very stable in the presence of three K+ ions in the selectivity filter and one in the cavity. The analysis of the dynamics of water molecules in the cavity reveals preferred orientations of the dipoles along the pore axis, and a correlated behavior between this dipole orientation and the displacement of the K+ ion during the gating process.     

Ca ion permeation through liposome membranes with heat generation by square-wave electric field

Phospholipid liposomes that contain Ca ions in inside compartment were subjected to external alternating electric fields of square wave form at several frequencies: 10, 100 Hz, 1, 10, 100 kHz. The leakage of Ca ions from inside to bulk solution caused by the electric fields was detected by the fluorescence change due to Ca-Quin 2 (fluorescent dye) complex formation in the bulk aqueous solution. The temperature increments of the sample solution in the chamber were also measured. The amplitude of the electric field and time interval between application of the electric field were varied. The frequency dependency of both the leakage of Ca ion and the temperature increments was observed. It was observed that the efficiency of the leakage had a minimum at 1 kHz. The origin of the frequency dependency of the leakage is discussed, and it is concluded that the energy consumption on a microscopic scale in the liposome membrane zone can be the reason for membrane permeation in this experimental system.