The effect of hydrophobic and hydrophilic channel walls on the structure and diffusion of water and ions

Biosensors Based on Acetylcholinesterase Immobilized on Clay-Gold Nanocomposites for the Discrimination of Chlorpyrifos and Carbaryl

This work aims at evaluating a utilization of diverse clay mineral/gold nanoparticles/acetylcholinesterase (clay/AuNPs/AChE) biosensors by using principal component analysis (PCA) for the discrimination of pesticide types and their concentration levels both in the synthetic and real samples. Applications of simple and low-cost clay/AuNP composites of different characteristics as modified-electrode materials are highlighted. Four types of clay minerals, namely, platelike kaolinite (Kaol: 1:1 aluminum phyllosilicate), globular montmorillonite (Mt: 2:1 aluminum phyllosilicate), globular bentonite (Bent: 2:1 aluminum phyllosilicate), and fibrous sepiolite (Sep: 2:1 inverted ribbons of magnesium phyllosilicate), were selected as the base materials. Due to the distinct characteristics of the selected clay, the derived clay/AuNP composites resulted in different physical morphologies, AuNP sizes and loadings, matrix hydrophobicity, and active AChE loading per electrode. These, in turn, caused divergent electrochemical responses for the pesticide determination; hence, no other enzymes apart from AChE were necessary for the fabrication of distinct biosensors. Physical and chemical characterizations of clay/AuNPs were conducted using scanning electron microscopy, transmission electron microscopy, thermogravimetric analysis, and X-ray photoelectron spectroscopy techniques. The electrochemical information was recorded by cyclic voltammetry and amperometry techniques. The enzyme inhibition results obtained from the pesticides were treated and used as input data to obtain PCA results. The four fabricated clay/AuNPs/AChE biosensors were able to discriminate chlorpyrifos and carbaryl and their concentration levels for synthetic pesticides and real samples. It was disclosed that a high enzyme inhibition and a high hydrophobic modified-electrode material affect a highly sensitive pesticide biosensor. The hydrophobic/hydrophilic character of the modified-electrode material plays a major role in discriminating the pesticide types and their concentration levels by the proposed single-enzyme sensor system. The PCA results illustrated that PC2 described the different types of pesticides, and PC1 showed the level of pesticide concentration with high first two principal components. The mixed pesticides could be identified at an especially low total concentration of 0.5 ng/mL in real samples.

Nanoconfined Fluids: Uniqueness of Water Compared to Other Liquids

Nanoconfinement can drastically change the behavior of liquids, puzzling us with counterintuitive properties. It is relevant in applications, including decontamination and crystallization control. However, it still lacks a systematic analysis for fluids with different bulk properties. Here we address this gap. We compare, by molecular dynamics simulations, three different liquids in a graphene slit pore: (1) A simple fluid, such as argon, described by a Lennard-Jones potential; (2) an anomalous fluid, such as a liquid metal, modeled with an isotropic core-softened potential; and (3) water, the prototypical anomalous liquid, with directional HBs. We study how the slit-pore width affects the structure, thermodynamics, and dynamics of the fluids. All the fluids show similar oscillating properties by changing the pore size. However, their free-energy minima are quite different in nature: (i) are energy-driven for the simple liquid; (ii) are entropy-driven for the isotropic core-softened potential; and (iii) have a changing nature for water. Indeed, for water, the monolayer minimum is entropy driven, at variance with the simple liquid, while the bilayer minimum is energy driven, at variance with the other anomalous liquid. Also, water has a large increase in diffusion for subnm slit pores, becoming faster than bulk. Instead, the other two fluids have diffusion oscillations much smaller than water, slowing down for decreasing slit-pore width. Our results, clarifying that water confined at the subnm scale behaves differently from other (simple or anomalous) fluids under similar confinement, are possibly relevant in nanopores applications, for example, in water purification from contaminants.

Accurate modeling of a biological nanopore with an extended continuum framework

Despite the broad success of biological nanopores as powerful instruments for the analysis of proteins and nucleic acids at the single-molecule level, a fast simulation methodology to accurately model their nanofluidic properties is currently unavailable. This limits the rational engineering of nanopore traits and makes the unambiguous interpretation of experimental results challenging. Here, we present a continuum approach that can faithfully reproduce the experimentally measured ionic conductance of the biological nanopore Cytolysin A (ClyA) over a wide range of ionic strengths and bias potentials. Our model consists of the extended Poisson-Nernst-Planck and Navier-Stokes (ePNP-NS) equations and a computationally efficient 2D-axisymmetric representation for the geometry and charge distribution of the nanopore. Importantly, the ePNP-NS equations achieve this accuracy by self-consistently considering the finite size of the ions and the influence of both the ionic strength and the nanoscopic scale of the pore on the local properties of the electrolyte. These comprise the mobility and diffusivity of the ions, and the density, viscosity and relative permittivity of the solvent. Crucially, by applying our methodology to ClyA, a biological nanopore used for single-molecule enzymology studies, we could directly quantify several nanofluidic characteristics difficult to determine experimentally. These include the ion selectivity, the ion concentration distributions, the electrostatic potential landscape, the magnitude of the electro-osmotic flow field, and the internal pressure distribution. Hence, this work provides a means to obtain fundamental new insights into the nanofluidic properties of biological nanopores and paves the way towards their rational engineering.

Mesoscopic method to study water flow in nanochannels with different wettability

Molecular dynamics (MD) simulations is currently the most popular and credible tool to model water flow in nanoscale where the conventional continuum equations break down due to the dominance of fluid-surface interactions. However, current MD simulations are computationally challenging for the water flow in complex tube geometries or a network of nanopores, e.g., membrane, shale matrix, and aquaporins. We present a novel mesoscopic lattice Boltzmann method (LBM) for capturing fluctuated density distribution and a nonparabolic velocity profile of water flow through nanochannels. We incorporated molecular interactions between water and the solid inner wall into LBM formulations. Details of the molecular interactions were translated into true and apparent slippage, which were both correlated to the surface wettability, e.g., contact angle. Our proposed LBM was tested against 47 published cases of water flow through infinite-length nanochannels made of different materials and dimensions-flow rates as high as seven orders of magnitude when compared with predictions of the classical no-slip Hagen-Poiseuille (HP) flow. Using the developed LBM model, we also studied water flow through finite-length nanochannels with tube entrance and exit effects. Results were found to be in good agreement with 44 published finite-length cases in the literature. The proposed LBM model is nearly as accurate as MD simulations for a nanochannel, while being computationally efficient enough to allow implications for much larger and more complex geometrical nanostructures.

Soft and ion-conducting hydrogel artificial tongue for astringency perception

Artificial tongues have been receiving increasing attention for the perception of five basic tastes. However, it is still challenging to fully mimic human tongue-like performance for tastes such as astringency. Mimicking the mechanism of astringency perception on the human tongue, we use a saliva-like chemiresistive ionic hydrogel anchored to a flexible substrate as a soft artificial tongue. When exposed to astringent compounds, hydrophobic aggregates form inside the microporous network and transform it into a micro/nanoporous structure with enhanced ionic conductivity. This unique human tongue-like performance enables tannic acid to be detected over a wide range (0.0005 to 1 wt %) with high sensitivity (0.292 wt %^-1) and fast response time (~10 s). As a proof of concept, our sensor can detect the degree of astringency in beverages and fruits using a simple wipe-and-detection method, making a powerful platform for future applications involving humanoid robots and taste monitoring devices.

Structure, Thermodynamics, and Dynamics of Thin Brine Films in Oil-Brine-Rock Systems

Thin brine films are ubiquitous in oil-brine-rock systems such as oil reservoirs and play a crucial role in applications such as enhanced oil recovery. We report the results of molecular simulations of brine films that are confined between model oil (n-decane) and rock (neutral or negatively charged quartz slabs), with a focus on their structure, electrical double layers (EDLs), disjoining pressure, and dynamics. As brine films are squeezed to ∼0.7 nm (∼3 water molecule layers), the structures of the water-rock and water-oil interfaces change only marginally, except that the oil surface above the brine film becomes less diffuse. As the film is thinned from ∼1.0 to ∼0.7 nm, ions are enriched (depleted) near the rock (oil) surface, especially at a bath ion concentration of 0.1 M. These changes are caused primarily by the reduced dielectric screening of water and the weakened ion hydration near water-oil interfaces and, to a smaller extent, by the increased confinement. When the brine film is ∼1.0 nm thick, hydration and EDL forces contribute to the disjoining pressure between the charged rock and the oil. The EDL forces are reduced substantially as the ion concentration increases from 0.1 to 1.0 M, and the magnitude of the reduction is close to that predicted by the Poisson-Boltzmann equation. When the brine film is thinned from ∼1.0 to ∼0.7 nm, the disjoining pressure increases by ∼10 MPa, which is mostly due to an increase in the hydration forces. The first layer of water on the rock surface is nearly stagnant, even in 0.74 nm-thick brine films, whereas the viscosity of water beyond the first layer is bulk-like, and the slip coefficient of oil-water interfaces is close to that under unconfined conditions. The insights that are obtained here help lay a foundation for the rational application of technologies such as low-salinity waterflooding.

Inner surface modification of 1.76 nm diameter (13,13) carbon nanotubes and the desalination behavior of its reverse osmosis membrane

100% desalination was achieved with high water conductance by adding –CH₂COO⁻ and –CH₂NH₃⁺ to the interior of CNTs, to imitate the protein Aquaporin-4.

Effects of confinement between attractive and repulsive walls on the thermodynamics of an anomalous fluid

We study via molecular-dynamics simulations the thermodynamics of an anomalous fluid confined in a slit pore with one wall structured and attractive and another unstructured and repulsive. We find that the phase diagram of the homogeneous part of the confined fluid is shifted to higher temperatures, densities, and pressures with respect to the bulk, but it can be rescaled on the bulk case. We calculate a moderate increase of mobility of the homogeneous confined fluid that we interpret as a consequence of the layering due to confinement and the collective modes due to long-range correlations. We show that, as in bulk, the confined fluid has structural, diffusion, and density anomalies that order in the waterlike hierarchy, and a liquid-liquid critical point (LLCP). The overall anomalous region moves to higher temperatures, densities, and pressure, and the LLCP displaces to higher temperature compared to bulk. Motivated by experiments, we calculate also the phase diagram not just for the homogeneous part of the confined fluid but for the entire fluid in the pore, and we show that it is shifted toward higher pressures but preserves the thermodynamics, including the LLCP. Because our model has waterlike properties, we argue that in experiments with supercooled water confined in slit pores with a width of >3 nm if hydrophilic and of >1.5 nm if hydrophobic, the existence of the LLCP could be easier to test than in bulk, where it is not directly accessible.

Simulations of outer membrane channels and their permeability

Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Mechanisms of transfer of bioactive molecules through the cell membrane by electroporation

A short review of biophysical mechanisms for electrotransfer of bioactive molecules through the cell membrane by using electroporation is presented. The concept of transient hydrophilic aqueous pores and membrane electroporation mechanisms of single cells and cells in suspension models are analyzed. Alongside the theoretical approach, some peculiarities of drug and gene electrotransfer into cells and applications in clinical trials are discussed.

Wetting behavior of nonpolar nanotubes in simple dipolar liquids for varying nanotube diameter and solute-solvent interactions

Atomistic simulations of model nonpolar nanotubes in a Stockmayer liquid are carried out for varying nanotube diameter and nanotube-solvent interactions to investigate solvophobic interactions in generic dipolar solvents. We have considered model armchair type single-walled nonpolar nanotubes with increasing radii from (5,5) to (12,12). The interactions between solute and solvent molecules are modeled by the well-known Lennard-Jones and repulsive Weeks-Chandler-Andersen potentials. We have investigated the density profiles and microscopic arrangement of Stockmayer molecules, orientational profiles of their dipole vectors, time dependence of their occupation, and also the translational and rotational motion of solvent molecules in confined environments of the cylindrical nanopores and also in their external peripheral regions. The present results of structural and dynamical properties of Stockmayer molecules inside and near atomistically rough nonpolar surfaces including their wetting and dewetting behavior for varying interactions provide a more generic picture of solvophobic effects experienced by simple dipolar liquids without any specific interactions such as hydrogen bonds.

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore

In this article, uncertainty quantification is applied to molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. We consider a silica pore model connecting two reservoirs containing a solution of sodium (Na(+)) and chloride (Cl(-)) ions in water. An ad hoc concentration control algorithm is developed to simulate a concentration driven counter flow of ions through the pore, with the ionic flux being the main observable extracted from the MD system. We explore the sensitivity of the system to two physical parameters of the pore, namely, the pore diameter and the gating charge. First we conduct a quantitative analysis of the impact of the pore diameter on the ionic flux, and interpret the results in terms of the interplay between size effects and ion mobility. Second, we analyze the effect of gating charge by treating the charge density over the pore surface as an uncertain parameter in a forward propagation study. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of intrinsic noise and quantify the impact of parametric uncertainty on the MD predictions. We highlight the challenges arising from the heterogeneous nature of the system, given the several components involved, and from the substantial effect of the intrinsic thermal noise.

Permeation and block of the Kv1.2 channel examined using brownian and molecular dynamics

Using both Brownian and molecular dynamics, we replicate many of the salient features of Kv1.2, including the current-voltage-concentration profiles and the binding affinity and binding mechanisms of charybdotoxin, a scorpion venom. We also elucidate how structural differences in the inner vestibule can give rise to significant differences in its permeation characteristics. Current-voltage-concentration profiles are constructed using Brownian dynamics simulations, based on the crystal structure 2A79. The results are compatible with experimental data, showing similar conductance, rectification, and saturation with current. Unlike KcsA, for example, the inner pore of Kv1.2 is mainly hydrophobic and neutral, and to explore the consequences of this, we investigate the effect of mutating neutral proline residues at the mouth of the inner vestibule to charged aspartate residues. We find an increased conductance, less inward rectification, and quicker saturation of the current-voltage profile. Our simulations use modifications to our Brownian dynamics program that extend the range of channels that can be usefully modeled. Using molecular dynamics, we investigate the binding of the charybdotoxin scorpion venom to the outer vestibule of the channel. A potential of mean force is derived using umbrella sampling, giving a dissociation constant within a factor of ∼2 to experimentally derived constants. The residues involved in the toxin binding are in agreement with experimental mutagenesis studies. We thus show that the experimental observations on the voltage-gated channel, including the toxin-channel interaction, can reliably be replicated by using the two widely used computational tools.

Efficiency of the delivery of small charged molecules into cells in vitro

The effectiveness of the delivery of small charged molecules, including anticancer drugs into MH22 hepatoma cells in vitro was investigated. It was shown that for each kind of small molecules one can find a specific set of pulse strength-duration combinations that define electrotransfer of chosen compounds into the same amount of electroporated cells. Analysis of experimental data from the point of theory of hydrophilic aqueous pores and the estimation of the contribution of the electrostatic Born's energy to the change in free energy suggests that the main factors defining small molecules transfer through the membrane are: the charge and size of molecules, the permittivities of external medium, membrane material, and the electropores respectively as well as the size of electropores. The joint impact of all mentioned factors on transfer efficiency is essential.

THz investigations of condensed phase biomolecular systems

Terahertz (THz) spectroscopic investigations of crystalline dipeptide nanotubes are discussed in the frequency region from 0.6 (2 cm(-1)) to 3 THz (100 cm(-1)). The THz region provides access to collective modes of biomolecular systems and is therefore sensitive to the large scale motions important for understanding the impact of environmental stimuli in biomolecular systems. The focus of this chapter is on THz spectral changes observed in this region when crystals of alanyl isoleucine (AI) and isoleucyl alanine (IA) nanotubes are exposed to water. Of biological significance is the water permeability through hydrophobic pore regions as exemplified in the disparate behavior of these two dipeptide nanotubes. AI is known from X-ray studies and confirmed here to act reversibly to the exchange of water while IA does not accept water into its pore region. Both quantum chemical and classical calculations are performed to better understand the subtle balance that determines guest molecule absorption and conduction through these hydrophobic channels. Examination of the vibrational character of the THz modes with and without water suggests water mode coupling/decoupling with collective modes of the nanotube may play an important role in the permeability dynamics.

Determinants of water permeability through nanoscopic hydrophilic channels

Naturally occurring pores show a variety of polarities and sizes that are presumably directly linked to their biological function. Many biological channels are selective toward permeants similar or smaller in size than water molecules, and therefore their pores operate in the regime of single-file water pores. Intrinsic factors affecting water permeability through such pores include the channel-membrane match, the structural stability of the channel, the channel geometry and channel-water affinity. We present an extensive molecular dynamics study on the role of the channel geometry and polarity on the water osmotic and diffusive permeability coefficients. We show that the polarity of the naturally occurring peptidic channels is close to optimal for water permeation, and that the water mobility for a wide range of channel polarities is essentially length independent. By systematically varying the geometry and polarity of model hydrophilic pores, based on the fold of gramicidin A, the water density, occupancy, and permeability are studied. Our focus is on the characterization of the transition between different permeation regimes in terms of the structure of water in the pores, the average pore occupancy and the dynamics of the permeating water molecules. We show that a general relationship between osmotic and diffusive water permeability coefficients in the single-file regime accounts for the time averaged pore occupancy, and that the dynamics of the permeating water molecules through narrow non single file channels effectively behaves like independent single-file columns.

Poisson-Nernst-Planck models of nonequilibrium ion electrodiffusion through a protegrin transmembrane pore

Protegrin peptides are potent antimicrobial agents believed to act against a variety of pathogens by forming nonselective transmembrane pores in the bacterial cell membrane. We have employed 3D Poisson-Nernst-Planck (PNP) calculations to determine the steady-state ion conduction characteristics of such pores at applied voltages in the range of −100 to +100 mV in 0.1 M KCl bath solutions. We have tested a variety of pore structures extracted from molecular dynamics (MD) simulations based on an experimentally proposed octomeric pore structure. The computed single-channel conductance values were in the range of 290–680 pS. Better agreement with the experimental range of 40–360 pS was obtained using structures from the last 40 ns of the MD simulation, where conductance values range from 280 to 430 pS. We observed no significant variation of the conductance with applied voltage in any of the structures that we tested, suggesting that the voltage dependence observed experimentally is a result of voltage-dependent channel formation rather than an inherent feature of the open pore structure. We have found the pore to be highly selective for anions, with anionic to cationic current ratios (I_Cl−/I_K+) on the order of 10³. This is consistent with the highly cationic nature of the pore but surprisingly in disagreement with the experimental finding of only slight anionic selectivity. We have additionally tested the sensitivity of our PNP model to several parameters and found the ion diffusion coefficients to have a significant influence on conductance characteristics. The best agreement with experimental data was obtained using a diffusion coefficient for each ion set to 10% of the bulk literature value everywhere inside the channel, a scaling used by several other studies employing PNP calculations. Overall, this work presents a useful link between previous work focused on the structure of protegrin pores and experimental efforts aimed at investigating their conductance characteristics.

Protegrins are small peptides with strong antimicrobial properties, believed to kill bacteria primarily by forming nonselective pores in the bacterial membrane. This nonspecific and highly effective mechanism of action has created significant excitement about the use of protegrins as therapeutic antibiotics. However, a lack of understanding of the fundamental processes that lead to pore formation and bacterial death has proven to be a major bottleneck in the rational design of protegrin-based antibiotics. In the present work, we have carried out computational investigations of the diffusion of ions through a protegrin pore. We have thereby provided a connection between previous experimental and simulation work aimed at elucidating the structure of the protegrin pore and earlier experimental work investigating the ion transport characteristics of protegrin pores. The ion diffusion characteristics of protegrin pores are likely to be important in their ability to kill bacteria, as the uncontrolled flow of ions through a bacterial membrane will result in membrane depolarization and the loss of vital membrane functions. The present work thus represents an important first step in modeling and quantifying the timeline of events that lead to the killing of bacteria by protegrins. Furthermore, the computational tools that we have presented herein are easily extendible to similar systems, in particular other antimicrobial peptides.

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson-Nernst-Planck theory, the force encountered by permeant ions is calculated by solving Poisson's equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current-voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2-10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.

Hydrogen bond dynamics and microscopic structure of confined water inside carbon nanotubes

We have investigated the density and temperature dependences of microscopic structure and hydrogen bond dynamics of water inside carbon nanotubes (CNTs) using molecular dynamics simulation. The CNTs are treated as rigid, and smoothly truncated extended simple point charge water model is adopted. The results show that as the overall density increases, the atomic density profiles of water inside CNTs become sharper, the peaks shift closer to the wall, and a new peak of hydrogen atomic density appears between the first (outermost) and second layer. The intermittent hydrogen bond correlation function C(HB)(t) of water inside CNTs decays slower than that of bulk water, and the rate of decay decreases as the tube diameter decreases. C(HB)(t) clearly decays more slowly for the first layer of water than for other regions inside CNTs. The C(HB)(t) of the interlayer hydrogen bonds decays faster than those of the other regions and even faster than that of the bulk water. On the other hand, the hydrogen bond lifetimes of the first layer are shorter than those of the inner layer(s). Interlayer hydrogen bond lifetimes are clearly shorter than those of the constituent layers. As a whole, the hydrogen bond lifetimes of water inside CNTs are shorter than those of bulk water, while the relaxation of C(HB)(t) is slower for the confined water than for bulk water. In other words, hydrogen bonds of water inside CNTs break more easily than those of bulk water, but the water molecules remain in each other's vicinity and can easily reform the bonds.

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.

The mechanism of water diffusion in narrow carbon nanotubes

Carbon nanotubes show exceptional physical properties that render them promising candidates as building blocks for nanostructured materials. Many ambitious applications, ranging from gene therapy to membrane separations, require the delivery of fluids, in particular aqueous solutions, through the interior of carbon nanotubes. To foster these and other applications, it is necessary to understand the thermodynamic and transport properties of water confined within long narrow carbon nanotubes. Previous theoretical work considered either short carbon nanotubes or short periods of time. By conducting molecular dynamics simulations in the microcanonical ensemble for water confined in infinitely long carbon nanotubes of diameter 1.08 nm, we show here that confined water molecules diffuse through a fast ballistic motion mechanism for up to 500 ps at room temperature. By comparing the results obtained for the diffusion of water to those obtained for the diffusion of a reference Lennard-Jones fluid, we prove here that long-lasting hydrogen bonds are responsible for the ballistic diffusion of water clusters in narrow carbon nanotubes, as opposed to spatial mismatches between pore-fluid and fluid-fluid attractive interactions which, as shown previously by others, are responsible for the concerted motion of simple fluids in molecular sieves. Additionally we prove here for the first time that, despite the narrow diameter of the carbon nanotubes considered which may suggest the existence of single-file diffusion, when the trajectories of confined water are studied at time scales in excess of 500 ps, a Fickian-type diffusion mechanism prevails. Our results are important for designing nano fluidic apparatuses to develop, for example, novel drug-delivery devices.

Electrostatic properties of the mechanosensitive channel of small conductance MscS

The mechanosensitive channel of small conductance (MscS) belongs to a family of membrane proteins that are gated in response to changes in membrane tension, thereby protecting the cell from hypo-osmotic shock. Here we report on passive ion transport simulations of MscS in a POPC bilayer using a coarse-grained particle-based description based on the Boltzmann transport Monte Carlo method. Single channel current-voltage curves are computed over hundreds of nanoseconds for channel conformations derived from all-atom molecular dynamics simulations reaching an overall simulation time of over 5 micros. Channel conformations similar to that of the crystal structure exhibit low conductance, whereas conformations reached after opening the channel by means of steered molecular dynamics simulations match experimentally determined conductances. However, while experiments indicate a slight preference for anionic currents, the simulated channel strongly selects anions over cations and the direction of rectification at high voltages is opposite to what is observed in experiments. Three-dimensional maps of time-averaged ion distribution and equilibrium occupancy profiles constructed from trajectory data indicate separation of anions and cations inside and in the immediate vicinity of the large cytoplasmic domain of MscS, in accordance with earlier molecular dynamics simulations. This separation arises from the distribution of ionizable residues of MscS and suggests a specific, yet unknown, functional purpose.

Acidity of a Cu-Bound Histidine in the Binuclear Center of CytochromecOxidase

Cytochrome c oxidase (CcO) is a crucial enzyme in the respiratory chain. Its function is to couple the reduction of molecular oxygen, which takes place in the Fea3-CuB binuclear center, to proton translocation across the mitochondrial membrane. Although several high-resolution structures of the enzyme are known, the molecular basis of proton pumping activation and its mechanism remain to be elucidated. We examine a recently proposed scheme (J. Am. Chem. Soc. 2004, 126, 1858; FEBS Lett. 2004, 566, 126) that involves the deprotonation of the CuB-bound imidazole ring of a histidine (H291 in mammalian CcO) as a key element in the proton pumping mechanism. The central feature of that proposed mechanism is that the pKa values of the imidazole vary significantly depending on the redox state of the metals in the binuclear center. We use density functional theory in combination with continuum electrostatics to calculate the pKa values, successively in bulk water and within the protein, of the Cu-bound imidazole in various Cu- and Cu-Fe complexes. From pKas in bulk water, we derived a value of -266.34 kcal.mol(-1) for the proton solvation free energy (Delta). This estimate is in close agreement with the experimental value of -264.61 kcal.mol(-1) (J. Am. Chem. Soc. 2001, 123, 7314), which reinforces the conclusion that Delta is more negative than previous values used for pKa calculations. Our approach, on the basis of the study of increasingly more detailed models of the CcO binuclear center at different stages of the catalysis, allows us to examine successively the effect of each of the two metals' redox states and of solvation on the acidity of imidazole, whose pKa is approximately 14 in bulk water. This analysis leads to the following conclusions: first, the effect of Cu ligation on the imidazole acidity is negligible regardless of the redox state of the metal. Second, results obtained for Cu-Fe complexes in bulk water indicate that Cu-bound imidazole pKa values lie within the range of 14.8-16.6 throughout binuclear redox states corresponding to the catalytic cycle, demonstrating that the effect of the Fe oxidation states is also negligible. Finally, the low-dielectric CcO proteic environment shifts the acid-base equilibrium toward a neutral imidazole, further increasing the corresponding pKa values. These results are inconsistent with the proposed role of the Cu-bound histidine as a key element in the pumping mechanism. Limitations of continuum solvation models in pKa calculations are discussed.

Three computational methods for studying permeation, selectivity and dynamics in biological ion channels

The cell membrane, confining some ions and molecules on one side and exchanging others with the other side, is the ultimate unit of the physiology of life. The delicate task of regulating the transport of ions across the membrane is carried out by biological nanotubes called 'ion channels'. Recently, there have been enormous strides in our understanding of the structure-function relationships of biological ion channels. The molecular structures of several ion channels have been determined from crystallographic analysis, including potassium channels, mechanosensitive channels, a chloride channel, as well as gramicidin channels and porins. It is expected that the X-ray structures of other ion channels will soon follow these discoveries, ushering in a new era of ion channel studies in which predicting the function of channels from their atomic structures will become the main quest. In parallel to these experimental findings, there have been important advances in computational biophysics. Here we summarize three theoretical approaches that have been utilized to understand the dynamics of ion permeation across bio-nanotubes, highlighting their advantages and shortcomings, and briefly describe some of the salient properties of ion channels uncovered through computational studies.

Transport of a liquid water and methanol mixture through carbon nanotubes under a chemical potential gradient

In this work, we report a dual-control-volume grand canonical molecular dynamics simulation study of the transport of a water and methanol mixture under a fixed concentration gradient through nanotubes of various diameters and surface chemistries. Methanol and water are selected as fluid molecules since water represents a strongly polar molecule while methanol is intermediate between nonpolar and strongly polar molecules. Carboxyl acid (-COOH) groups are anchored onto the inner wall of a carbon nanotube to alter the hydrophobic surface into a hydrophilic one. Results show that the transport of the mixture through hydrophilic tubes is faster than through hydrophobic nanotubes although the diffusion of the mixture is slower inside hydrophilic than hydrophobic pores due to a hydrogen network. Thus, the transport of the liquid mixture through the nanotubes is controlled by the pore entrance effect for which hydrogen bonding plays an important role.

Ion permeation through the alpha-hemolysin channel: theoretical studies based on Brownian dynamics and Poisson-Nernst-Plank electrodiffusion theory

Identification of the molecular interaction governing ion conduction through biological pores is one of the most important goals of modern electrophysiology. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) and three-dimensional Poisson-Nernst-Plank (3d-PNP) electrodiffusion algorithms offer powerful and general approaches to study of ion permeation through wide molecular pores. A detailed analysis of ion flows through the staphylococcal alpha-hemolysin channel based on series of simulations at different concentrations and transmembrane potentials is presented. The position-dependent diffusion coefficient is approximated on the basis of a hydrodynamic model. The channel conductance calculated by GCMC/BD is approximately 10% higher than (electrophysiologically measured) experimental values, whereas results from 3d-PNP are always 30-50% larger. Both methods are able to capture all important electrostatic interactions in equilibrium conditions. The asymmetric conductance upon the polarity of the transmembrane potential observed experimentally is reproduced by GCMC/BD and 3d-PNP. The separation of geometrical and energetic influence of the channel on ion conduction reveals that such asymmetries arise from the permanent charge distribution inside the pore. The major determinant of the asymmetry is unbalanced charge in the triad of polar residues D127, D128, and K131. The GCMC/BD or 3d-PNP calculations reproduce also experimental reversal potentials and permeability rations in asymmetric ionic solutions. The weak anionic selectivity of the channel results from the presence of the salt bridge between E111 and K147 in the constriction zone. The calculations also reproduce the experimentally derived dependence of the reversible potential to the direction of the salt gradient. The origin of such effect arises from the asymmetrical distribution of energetic barriers along the channel axis, which modulates the preferential ion passage in different directions.

The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores

A hydrophobic constriction site can act as an efficient barrier to ion and water permeation if its diameter is less than the diameter of an ion's first hydration shell. This hydrophobic gating mechanism is thought to operate in a number of ion channels, e.g. the nicotinic receptor, bacterial mechanosensitive channels (MscL and MscS) and perhaps in some potassium channels (e.g. KcsA, MthK and KvAP). Simplified pore models allow one to investigate the primary characteristics of a conduction pathway, namely its geometry (shape, pore length, and radius), the chemical character of the pore wall surface, and its local flexibility and surface roughness. Our extended (about 0.1 micros) molecular dynamic simulations show that a short hydrophobic pore is closed to water for radii smaller than 0.45 nm. By increasing the polarity of the pore wall (and thus reducing its hydrophobicity) the transition radius can be decreased until for hydrophilic pores liquid water is stable down to a radius comparable to a water molecule's radius. Ions behave similarly but the transition from conducting to non-conducting pores is even steeper and occurs at a radius of 0.65 nm for hydrophobic pores. The presence of water vapour in a constriction zone indicates a barrier for ion permeation. A thermodynamic model can explain the behaviour of water in nanopores in terms of the surface tensions, which leads to a simple measure of 'hydrophobicity' in this context. Furthermore, increased local flexibility decreases the permeability of polar species. An increase in temperature has the same effect, and we hypothesize that both effects can be explained by a decrease in the effective solvent-surface attraction which in turn leads to an increase in the solvent-wall surface free energy.

Liquid-vapor oscillations of water in hydrophobic nanopores

Water plays a key role in biological membrane transport. In ion channels and water-conducting pores (aquaporins), one-dimensional confinement in conjunction with strong surface effects changes the physical behavior of water. In molecular dynamics simulations of water in short (0.8 nm) hydrophobic pores the water density in the pore fluctuates on a nanosecond time scale. In long simulations (460 ns in total) at pore radii ranging from 0.35 to 1.0 nm we quantify the kinetics of oscillations between a liquid-filled and a vapor-filled pore. This behavior can be explained as capillary evaporation alternating with capillary condensation, driven by pressure fluctuations in the water outside the pore. The free-energy difference between the two states depends linearly on the radius. The free-energy landscape shows how a metastable liquid state gradually develops with increasing radius. For radii > approximately 0.55 nm it becomes the globally stable state and the vapor state vanishes. One-dimensional confinement affects the dynamic behavior of the water molecules and increases the self diffusion by a factor of 2-3 compared with bulk water. Permeabilities for the narrow pores are of the same order of magnitude as for biological water pores. Water flow is not continuous but occurs in bursts. Our results suggest that simulations aimed at collective phenomena such as hydrophobic effects may require simulation times >50 ns. For water in confined geometries, it is not possible to extrapolate from bulk or short time behavior to longer time scales.

Role of the dielectric constants of membrane proteins and channel water in ion permeation

Using both analytical solutions obtained from simplified systems and numerical results from more realistic cases, we investigate the role played by the dielectric constant of membrane proteins epsilon(p) and pore water epsilon(w) in permeation of ions across channels. We show that the boundary and its curvature are the crucial factors in determining how an ion's potential energy depends on the dielectric constants near an interface. The potential energy of an ion outside a globular protein has a dominant 1/epsilon(w) dependence, but this becomes 1/epsilon(p) for an ion inside a cavity. For channels, where the boundaries are in between these two extremes, the situation is more complex. In general, we find that variations in epsilon(w) have a much larger impact on the potential energy of an ion compared to those in epsilon(p). Therefore a better understanding of the effective epsilon(w) values employed in channel models is desirable. Although the precise value of epsilon(p) is not a crucial determinant of ion permeation properties, it still needs to be chosen carefully when quantitative comparisons with data are made.

Intermittent permeation of cylindrical nanopores by water

Molecular-dynamics simulations of water molecules in nanometer sized cylindrical channels connecting two reservoirs show that the permeation of water is very sensitive to the channel radius and to electric polarization of the embedding material. At threshold, the permeation is intermittent on a nanosecond time scale, and strongly enhanced by the presence of an ion inside the channel, providing a possible mechanism for gating. Confined water remains surprisingly fluid and bulklike. Its behavior differs strikingly from that of a reference Lennard-Jones fluid, which tends to contract into a highly layered structure inside the channel.

Recent advances in ion channel research

The field of ion channels has entered into a rapid phase of development in the last few years, partly due to the breakthroughs in determination of the crystal structures of membrane proteins and advances in computer simulations of biomolecules. These advances have finally enabled the long-dreamed goal of relating function of a channel to its underlying molecular structure. Here we present simplified accounts of the competing permeation theories and then discuss their application to the potassium, gramicidin A and calcium channels.