Imaging alpha-hemolysin with molecular dynamics: ionic conductance, osmotic permeability, and the electrostatic potential map

Ion selectivity of alpha-hemolysin with beta-cyclodextrin adapter. II. Multi-ion effects studied with grand canonical Monte Carlo/Brownian dynamics simulations

In a previous study of ion selectivity of alpha-hemolysin (alphaHL) in complex with beta-cyclodextrin (betaCD) adapter, we calculated the potential of mean force (PMF) and characterized the self-diffusion coefficients of isolated K(+) and Cl(-) ions using molecular dynamics simulations (Y. Luo et al., "Ion Selectivity of alpha-Hemolysin with beta-Cyclodextrin Adapter: I. Single Ion Potential of Mean Force and Diffusion Coefficient"). In the present effort, these results pertaining to single isolated ions in the wide aqueous pore are extended to take into account multi-ion effects. The grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) algorithm is used to simulate ion currents through the wild-type alphaHL ion channel, as well as two engineered alphaHL mutants, with and without the cyclic oligosaccaride betaCD lodged in the lumen of the pore. The GCMC/BD current-voltage curves agree well with experimental results and show that betaCD increases the anion selectivity of alphaHL. Comparisons between multi-ion PMFs from GCMC/BD simulations and single-ion PMFs demonstrate that multi-ion effects and pore shape are crucial for explaining this behavior. It is concluded that the narrow betaCD adapter increases the anion selectivity of alphaHL because it reduces the pore radius locally, which decreases the ionic screening and the dielectric shielding of the strong electrostatic field induced by a nearby ring of positively charged alphaHL side chains.

Regulated attachment method for reconstituting lipid bilayers of prescribed size within flexible substrates

A new method called the regulated attachment method (RAM) for reproducibly forming lipid bilayers within flexible substrates has been developed that enables precise control over the size of the bilayer. This technique uses a deformable flexible substrate to open and close an aperture that subdivides aqueous volumes submersed in an organic solvent. Phospholipids incorporated as vesicles in the aqueous phase self-assemble at the oil/water interface to form lipid monolayers that encapsulate each aqueous volume. Controlled attachment of opposing lipid monolayers is achieved by regulating the dimensions of the aperture in the substrate that separates the adjacent aqueous volumes. In this manner, the size of a lipid bilayer formed within a flexible substrate is a function of the substrate and aperture dimensions, and not determined by the sizes or shapes of the aqueous volumes. Lipid bilayers formed within the prototype flexible substrate exhibit DC resistances consistently higher than 10 GOmega and can survive 20-30x changes in area without rupture. Furthermore, RAM permits lipid bilayers to be completely unzipped after thinning by applying sufficient force to fully close the dividing aperture and even allows the introduction of species, such as alamethicin channels, into preformed lipid bilayers via controlled injection through an intersecting channel within the substrate. Controlling the size of the interface through indirect interactions with the supporting substrate offers a new platform for assembling durable lipid bilayers. We envision that this technology can be scaled to higher dimensions consisting of multiple apertures required for creating aqueous networks partitioned by functional lipid bilayers and to smaller length scales to produce very small lipid bilayers capable of hosting single proteins.

Molecular control of ionic conduction in polymer nanopores

Polymeric nanopores show unique transport properties and have attracted a great deal of scientific interest as a test system to study ionic and molecular transport at the nanoscale. By means of all-atom molecular dynamics, we simulated the ion dynamics inside polymeric polyethylene terephthalate nanopores. For this purpose, we established a protocol to assemble atomic models of polymeric material into which we sculpted a nanopore model with the key features of experimental devices, namely a conical geometry and a negative surface charge density. Molecular dynamics simulations of ion currents through the pore show that the protonation state of the carboxyl group of exposed residues have a considerable effect on ion selectivity, by affecting ionic densities and electrostatic potentials inside the nanopores. The role of high concentrations of Ca2+ ions was investigated in detail.

Probing single nanometer-scale pores with polymeric molecular rulers

We previously demonstrated that individual molecules of single-stranded DNA can be driven electrophoretically through a single Staphylococcus aureus alpha-hemolysin ion channel. Polynucleotides thread through the channel as extended chains and the polymer-induced ionic current blockades exhibit stable modes during the interactions. We show here that polynucleotides can be used to probe structural features of the alpha-hemolysin channel itself. Specifically, both the pore length and channel aperture profile can be estimated. The results are consistent with the channel crystal structure and suggest that polymer-based "molecular rulers" may prove useful in deducing the structures of nanometer-scale pores in general.

Continuum electrostatic calculations of the pKa of ionizable residues in an ion channel: dynamic vs. static input structure

We have computed the pK(a)'s of the ionizable residues of a protein ion channel, the Staphylococcus aureus toxin alpha-hemolysin, by using two types of input structures, namely the crystal structure of the heptameric alpha-hemolysin and a set of over four hundred snapshots from a 4.38 ns Molecular Dynamics simulation of the protein inserted in a phospholipid planar bilayer. The comparison of the dynamic picture provided by the Molecular Simulation with the static one based on the X-ray crystal structure of the protein embedded in a lipid membrane allows analyzing the influence of the fluctuations in the protein structure on its ionization properties. We find that the use of the dynamic structure provides interesting information about the sensitivity of the computed pK(a) of a given residue to small changes in the local structure. The calculated pK(a) are consistent with previous indirect estimations obtained from single-channel conductance and selectivity measurements.

Deciphering ionic current signatures of DNA transport through a nanopore

Within just a decade from the pioneering work demonstrating the utility of nanopores for molecular sensing, nanopores have emerged as versatile systems for single-molecule manipulation and analysis. In a typical setup, a gradient of the electrostatic potential captures charged solutes from the solution and forces them to move through a single nanopore, across an otherwise impermeable membrane. The ionic current blockades resulting from the presence of a solute in a nanopore can reveal the type of the solute, for example, the nucleotide makeup of a DNA strand. Despite great success, the microscopic mechanisms underlying the functionality of such stochastic sensors remain largely unknown, as it is not currently possible to characterize the microscopic conformations of single biomolecules directly in a nanopore and thereby unequivocally establish the causal relationship between the observables and the microscopic events. Such a relationship can be determined using molecular dynamics-a computational method that can accurately predict the time evolution of a molecular system starting from a given microscopic state. This article describes recent applications of this method to the process of DNA transport through biological and synthetic nanopores.

Structure and functional characterization of Vibrio parahaemolyticus thermostable direct hemolysin

Thermostable direct hemolysin (TDH) is a major virulence factor of Vibrio parahaemolyticus that causes pandemic foodborne enterocolitis mediated by seafood. TDH exists as a tetramer in solution, and it possesses extreme hemolytic activity. Here, we present the crystal structure of the TDH tetramer at 1.5 A resolution. The TDH tetramer forms a central pore with dimensions of 23 A in diameter and approximately 50 A in depth. Pi-cation interactions between protomers comprising the tetramer were indispensable for hemolytic activity of TDH. The N-terminal region was intrinsically disordered outside of the pore. Molecular dynamic simulations suggested that water molecules permeate freely through the central and side channel pores. Electron micrographs showed that tetrameric TDH attached to liposomes, and some of the tetramer associated with liposome via one protomer. These findings imply a novel membrane attachment mechanism by a soluble tetrameric pore-forming toxin.

Ion selectivity of alpha-hemolysin with a beta-cyclodextrin adapter. I. Single ion potential of mean force and diffusion coefficient

The alpha-hemolysin (alphaHL) is a self-assembling exotoxin that binds to the membrane of a susceptible host cell and causes its death. Experimental studies show that electrically neutral beta-cyclodextrin (betaCD) can insert into the alphaHL channel and significantly increase its anion selectivity. To understand how betaCD can affect ion selectivity, molecular dynamics simulations and potential of mean force (PMF) calculations are carried out for different alphaHL channels with and without the betaCD adapter. A multiscale approach based on the generalized solvent boundary potential is used to reduce the size of the simulated system. The PMF profiles reveal that betaCD has no anion selectivity by itself but can increase the Cl(-) selectivity of the alphaHL channel when lodged into the pore lumen. Analysis shows that betaCD causes a partial desolvation of ions and affects the orientation of nearby charged residues. The ion selectivity appears to result from increased electrostatic interaction between the ion and the channel due to a reduction in dielectric shielding by the solvent. These observations suggest a reasonable explanation of the ion selectivity and provide important information for further ion channel modification.

High-chloride concentrations abolish the binding of adenine nucleotides in the mitochondrial ADP/ATP carrier family

The ADP/ATP carrier (AAC) is a very effective membrane protein that mediates the exchange of ADP and ATP across the mitochondrial membrane. In vivo transport measurements on the AAC overexpressed in Escherichia coli demonstrate that this process can be severely inhibited by high-chloride concentrations. Molecular-dynamics simulations reveal a strong modification of the topology of the local electric field related to the number of chloride ions inside the cavity. Halide ions are shown to shield the positive charges lining the internal cavity of the carrier by accurate targeting of key basic residues. These specific amino acids are highly conserved as highlighted by the analysis of multiple AAC sequences. These results strongly suggest that the chloride concentration acts as an electrostatic lock for the mitochondrial AAC family, thereby preventing adenine nucleotides from reaching their dedicated binding sites.

Simulation of spontaneous substrate binding revealing the binding pathway and mechanism and initial conformational response of GlpT

Glycerol 3-phosphate transporter (GlpT) mediates the import of glycerol 3-phosphate (G3P) using the gradient of inorganic phosphate (P(i)). To study the process and mechanism of substrate binding and to investigate the protein's initial response, we performed equilibrium simulations of wild-type GlpT and several of its mutant forms in membranes in the presence of all physiologically relevant substrates (P(i)(-), P(i)(2-), G3P(-), and G3P(2-)). The simulations capture spontaneous substrate binding of GlpT, driven by the positive electrostatic potential of the lumen. K80 is found to act as a "hook" making the first encounter with the substrate and guiding it toward the binding site, where it binds tightly to R45, a key binding site residue that acts as a "fork" holding the substrate. R269 establishes no direct contact with the substrate during the simulations, a surprising behavior given its structural pseudosymmetry to R45. In all substrate-bound systems, partial closing of the cytoplasmic half of GlpT was observed. The substrate appears to stabilize the partially occluded state, as in the two apo simulations either no closing was observed or the protein reverted to its open form toward the end of the simulation, whereas in all substrate-bound systems, a stable partially closed state was produced. Along with the modulation of the periplasmic salt bridge network, these substrate-induced events destabilize the periplasmic half while inducing a closure in the cytoplasmic half, thus capturing the early stages of the proposed rocker-switch mechanism in GlpT.

Ionic current flow through ZnO nanotubes

The control of ionic current (electrolyte) flow through zinc oxide (ZnO) nanotubes is investigated. We studied a structure operating like a field effect transistor with a tunable ionic flow. The main investigation tool used was molecular dynamics simulation. We complemented the molecular dynamics simulation with the site binding method in order to study the effect of the double layer on the ionic current flowing through the nanotube. We achieved this by considering the electrolyte solution as a virtual semiconductor wire. The double layer capacitance and surface charge of the inner walls of the ZnO nanotube have been calculated. The results indicate that ZnO nanotubes can be tuned to operate as ion selectors. ZnO nanotubes exhibit enhanced functionality with characteristics similar to those of the nanopore membrane.

Understanding ion conductance on a molecular level: an all-atom modeling of the bacterial porin OmpF

All-atom molecular dynamics simulations of the ion current through OmpF, the major porin in the outer membrane of Escherichia coli, were performed. Starting from the crystal structure, the all-atom modeling allows us to calculate a parameter-free ion conductance in semiquantitative agreement with experiment. Discrepancies between modeling and experiment occur, e.g., at salt concentrations above 1 M KCl or at high temperatures. At lower salt concentrations, the ions have separate pathways along the channel surface. The constriction zone in the channel contains, on one side, a series of positively charges (R42, R82, R132), and on the opposite side, two negatively charged residues (D113, E117). Mutations generated in the constriction zone by removing cationic residues enhance the otherwise small cation selectivity, whereas removing the anionic residues reverses the selectivity. Reduction of the negatively charged residues decreases the conductance by half, whereas cationic residues enhance the conductance. Experiments on mutants confirm the results of the molecular-level simulations.

Theory of single-file multiparticle diffusion in narrow pores

Single-file diffusion of multiple strongly interacting particles in a one-dimensional pore is described within a general analytical framework. The theory accounts for nonequilibrium conditions, explicit particle-particle interactions, external potential acting on the particles and the fluctuations of the number of particles due to their exchange with external equilibrium reservoirs. It is shown that the problem can be reduced to a closed hierarchical set of partial differential equations of increasing dimensionality, which can be solved numerically. Our framework allows computing any macroscopic characteristic of multiparticle diffusion in the pore. It is shown that the pore occupancy probabilities and the current are rational functions of external concentrations in the steady state. The theory is tested on a simplified model of the narrow rigid pore inspired by the selectivity filter of biological ion channel. Perspectives and limitations of the theory are discussed.

Structure, dynamics, and ion conductance of the phospholamban pentamer

A 52-residue membrane protein, phospholamban (PLN) is an inhibitor of an adenosine-5'-triphosphate-driven calcium pump, the Ca2+-ATPase. Although the inhibition of Ca2+-ATPase involves PLN monomers, in a lipid bilayer membrane, PLN monomers form stable pentamers of unknown biological function. The recent NMR structure of a PLN pentamer depicts cytoplasmic helices extending normal to the bilayer in what is known as the bellflower conformation. The structure shows transmembrane helices forming a hydrophobic pore 4 A in diameter, which is reminiscent of earlier reports of possible ion conductance through PLN pentamers. However, recent FRET measurements suggested an alternative structure for the PLN pentamer, known as the pinwheel model, which features a narrower transmembrane pore and cytoplasmic helices that lie against the bilayer. Here, we report on structural dynamics and conductance properties of the PLN pentamers from all-atom (AA) and coarse-grained (CG) molecular dynamics simulations. Our AA simulations of the bellflower model demonstrate that in a lipid bilayer membrane or a detergent micelle, the cytoplasmic helices undergo large structural fluctuations, whereas the transmembrane pore shrinks and becomes asymmetric. Similar asymmetry of the transmembrane region was observed in the AA simulations of the pinwheel model; the cytoplasmic helices remained in contact with the bilayer. Using the CG approach, structural dynamics of both models were investigated on a microsecond timescale. The cytoplasmic helices of the CG bellflower model were observed to fall against the bilayer, whereas in the CG pinwheel model the conformation of the cytoplasmic helices remained stable. Using steered molecular dynamics simulations, we investigated the feasibility of ion conductance through the pore of the bellflower model. The resulting approximate potentials of mean force indicate that the PLN pentamer is unlikely to function as an ion channel.

Transitions between closed and open conformations of TolC: the effects of ions in simulations

Bacteria, such as Escherichia coli, use multidrug efflux pumps to export toxic substrates through their cell membranes. Upon formation of an efflux pump, the aperture of its outer membrane protein TolC opens and thereby enables the extrusion of substrate molecules. The specialty of TolC is its ability to dock to different transporters, making it a highly versatile export protein. Within this study, the transition between two conformations of TolC that are both available as crystal structures was investigated using all-atom molecular dynamics simulations. To create a partially open conformation from a closed one, the stability of the periplasmic aperture was weakened by a double point mutation at the constricting ring, which removes some salt bridges and hydrogen bonds. These mutants, which showed partial opening in previous experiments, did not spontaneously open during a 20-ns equilibration at physiological values of the KCl solution. Detailed analysis of the constricting ring revealed that the cations of the solvent were able to constitute ionic bonds in place of the removed salt bridges, which inhibited the opening of the aperture in simulations. To remove the ions from these binding positions within the available simulation time, an extra force was applied onto the ions. To keep the effect of this additional force rather flexible, it was applied in form of an artificial external electric field perpendicular to the membrane. Depending on the field direction and the ion concentration, these simulations led to a partial opening. In experiments, this energy barrier for the ions can be overcome by thermal fluctuations on a longer timescale.

Nanoscopic description of biomembrane electrostatics: results of molecular dynamics simulations and fluorescence probing

Electrostatic fields generated on and inside biological membranes are recognized to play a fundamental role in key processes of cell functioning. Their understanding requires an adequate description on the level of elementary charges and the reconstruction of electrostatic potentials by integration over all elementary interactions. Out of all the available research tools, only molecular dynamics simulations are capable of this, extending from the atomic to the mesoscopic level of description on the required time and space scale. A complementary approach is that offered by molecular probe methods, with the application of electrochromic dyes. Highly sensitive to intermolecular interactions, they generate integrated signals arising from electric fields produced by elementary charges at the sites of their location. This review is an attempt to provide a critical analysis of these two approaches and their present and potential applications. The results obtained by both methods are consistent in that they both show an extremely complex profile of the electric field in the membrane. The nanoscopic view, with two-dimensional averaging over the bilayer plane and formal separation of the electrostatic potential into surface (Psi(s)), dipole (Psi(d)) and transmembrane (Psi(t)) potentials, is constructive in the analysis of different functional properties of membranes.

Characterizing rare-event property distributions via replicate molecular dynamics simulations of proteins

As computational resources increase, molecular dynamics simulations of biomolecules are becoming an increasingly informative complement to experimental studies. In particular, it has now become feasible to use multiple initial molecular configurations to generate an ensemble of replicate production-run simulations that allows for more complete characterization of rare events such as ligand-receptor unbinding. However, there are currently no explicit guidelines for selecting an ensemble of initial configurations for replicate simulations. Here, we use clustering analysis and steered molecular dynamics simulations to demonstrate that the configurational changes accessible in molecular dynamics simulations of biomolecules do not necessarily correlate with observed rare-event properties. This informs selection of a representative set of initial configurations. We also employ statistical analysis to identify the minimum number of replicate simulations required to sufficiently sample a given biomolecular property distribution. Together, these results suggest a general procedure for generating an ensemble of replicate simulations that will maximize accurate characterization of rare-event property distributions in biomolecules.

The multiple faces of self-assembled lipidic systems

Lipids, the building blocks of cells, common to every living organisms, have the propensity to self-assemble into well-defined structures over short and long-range spatial scales. The driving forces have their roots mainly in the hydrophobic effect and electrostatic interactions. Membranes in lamellar phase are ubiquitous in cellular compartments and can phase-separate upon mixing lipids in different liquid-crystalline states. Hexagonal phases and especially cubic phases can be synthesized and observed in vivo as well. Membrane often closes up into a vesicle whose shape is determined by the interplay of curvature, area difference elasticity and line tension energies, and can adopt the form of a sphere, a tube, a prolate, a starfish and many more. Complexes made of lipids and polyelectrolytes or inorganic materials exhibit a rich diversity of structural morphologies due to additional interactions which become increasingly hard to track without the aid of suitable computer models. From the plasma membrane of archaebacteria to gene delivery, self-assembled lipidic systems have left their mark in cell biology and nanobiotechnology; however, the underlying physics is yet to be fully unraveled.PACS Codes: 87.14.Cc, 82.70.Uv.

Ionic Current Rectification Through Silica Nanopores

Nanopores immersed in electrolytic solution and under the influence of an electric field can produce ionic current rectification, where ionic currents are higher for one voltage polarity than for the opposite polarity, resulting in an asymmetric current-voltage (I-V) curve. This behavior has been observed in polymer and silicon-based nanopores as well as in theoretically studied continuum models. By means of atomic level molecular dynamics (MD) simulations, we have performed a systematic investigation of KCl conductance in silica nanopores with a total simulation time of 680 ns. We found that ion-binding spots at the silica surfaces, such as dangling atoms, have effects on the ion concentration and electrostatic potential inside the nanopore, producing asymmetric I-V curves. Conversely, silica surfaces without ion-binding spots produce symmetric I-V curves.

Microscopic mechanics of hairpin DNA translocation through synthetic nanopores

Nanoscale pores have proved useful as a means to assay DNA and are actively being developed as the basis of genome sequencing methods. Hairpin DNA (hpDNA), having both double-helical and overhanging coil portions, can be trapped in a nanopore, giving ample time to execute a sequence measurement. In this article, we provide a detailed account of hpDNA interaction with a synthetic nanopore obtained through extensive all-atom molecular dynamics simulations. For synthetic pores with minimum diameters from 1.3 to 2.2 nm, we find that hpDNA can translocate by three modes: unzipping of the double helix and--in two distinct orientations--stretching/distortion of the double helix. Furthermore, each of these modes can be selected by an appropriate choice of the pore size and voltage applied transverse to the membrane. We demonstrate that the presence of hpDNA can dramatically alter the distribution of ions within the pore, substantially affecting the ionic current through it. In experiments and simulations, the ionic current relative to that in the absence of DNA can drop below 10% and rise beyond 200%. Simulations associate the former with the double helix occupying the constriction and the latter with accumulation of DNA that has passed through the constriction.

The potential and challenges of nanopore sequencing

A nanopore-based device provides single-molecule detection and analytical capabilities that are achieved by electrophoretically driving molecules in solution through a nano-scale pore. The nanopore provides a highly confined space within which single nucleic acid polymers can be analyzed at high throughput by one of a variety of means, and the perfect processivity that can be enforced in a narrow pore ensures that the native order of the nucleobases in a polynucleotide is reflected in the sequence of signals that is detected. Kilobase length polymers (single-stranded genomic DNA or RNA) or small molecules (e.g., nucleosides) can be identified and characterized without amplification or labeling, a unique analytical capability that makes inexpensive, rapid DNA sequencing a possibility. Further research and development to overcome current challenges to nanopore identification of each successive nucleotide in a DNA strand offers the prospect of 'third generation' instruments that will sequence a diploid mammalian genome for approximately $1,000 in approximately 24 h.

The roles of pore ring and plug in the SecY protein-conducting channel

The protein-conducting channel, or translocon, is an evolutionarily conserved complex that allows nascent proteins to cross a cellular membrane or integrate into it. The crystal structure of an archaeal translocon, the SecY complex, revealed that two elements contribute to sealing the channel: a small "plug" domain blocking the periplasmic region of the channel, and a pore ring composed of six hydrophobic residues acting as a constriction point at the channel's center. To determine the independent functions of these two elements, we have performed molecular dynamics simulations of the native channel as well as of two recently structurally resolved mutants in which portions of their plugs were deleted. We find that in the mutants, the instability in the plug region leads to a concomitant increase in flexibility of the pore ring. The instability is quantified by the rate of water permeation in each system as well as by the force required for oligopeptide translocation. Through a novel simulation in which the interactions between the plug and water were independently controlled, we find that the role of the plug in stabilizing the pore ring is significantly more important than its role as a purely steric barrier.

Synthetic ion channels via self-assembly: a route for embedding porous polyoxometalate nanocapsules in lipid bilayer membranes

Porous polyoxometalate nanocapsules of Keplerate type are known to exhibit the functionality of biological ion channels; however, their use as an artificial ion channel is tempered by the high negative charge of the capsules, which renders their spontaneous incorporation into a lipid bilayer membrane unlikely. In this Letter we report coarse-grained molecular dynamics simulations that demonstrate a route for embedding negatively charged nanocapsules into lipid bilayer membranes via self-assembly. A homogeneous mixture of water, cationic detergent, and phospholipid was observed to spontaneously self-assemble around the nanocapsule into a layered, liposome-like structure, where the nanocapsule was enveloped by a layer of cationic detergent followed by a layer of phospholipid. Fusion of such a layered liposome with a lipid bilayer membrane was observed to embed the nanocapsule into the lipid bilayer. The resulting assembly was found to remain stable even after the surface of the capsule was exposed to electrolyte. In the latter conformation, water was observed to flow into and out of the capsule as Na(+) cations entered, suggesting that a polyoxometalate nanocapsule can form a functional synthetic ion channel in a lipid bilayer membrane.

Mechanosensitive channel MscS in the open state: modeling of the transition, explicit simulations, and experimental measurements of conductance

Mechanosensitive channels of small conductance (MscS) are ubiquitous turgor pressure regulators found in many walled cells and some intracellular organelles. Escherichia coli MscS acting as a tension-activated osmolyte release valve shows a nonsaturable conductance (1.2 nS in a 39 mS/cm electrolyte) and weak preference for anions. Pursuing the transition pathways in this channel, we applied the extrapolated motion protocol (cycles of displacements, minimizations, and short simulations) to the previously generated compact resting conformation of MscS. We observed tilting and straightening of the kinked pore-forming TM3 helices during the barrel expansion. Extended all-atom simulations confirmed the stability of the open conformation in the bilayer. A 53° spontaneous axial rotation of TM3s observed after equilibration increased the width and polarity of the pore allowing for stable voltage-independent hydration and presence of both cations and anions throughout the pore. The resultant open state, characterized by a pore 1.6 nm wide, satisfied the experimental conductance and in-plane expansion. Applied transmembrane electric field (±100 to ±200 mV) in simulations produced a flow of both K⁺ and Cl⁻, with Cl⁻ current dominating at higher voltages. Electroosmotic water flux strongly correlated with the chloride current (∼8 waters per Cl⁻). The selectivity and rectification were in agreement with the experimental measurements performed in the same range of voltages. Among the charged residues surrounding the pore, only K169 was found to contribute noticeably in the rectification. We conclude that (a) the barrel expansion involving tilting, straightening, and rotation of TM3s provides the geometry and electrostatics that accounts for the conductive properties of the open pore; (b) the observed regimen of ion passage through the pore is similar to electrodiffusion, thus macroscopic estimations closely approximate the experimental and molecular dynamics-simulated conductances; (c) increased interaction of the opposing ionic fluxes at higher voltages may result in selectivities stronger than measured near the reversal potential.

Ion flux through membrane channels--an enhanced algorithm for the Poisson-Nernst-Planck model

A novel algorithmic scheme for numerical solution of the 3D Poisson-Nernst-Planck model is proposed. The algorithmic improvements are universal and independent of the detailed physical model. They include three major steps: an adjustable gradient-based step value, an adjustable relaxation coefficient, and an optimized segmentation of the modeled space. The enhanced algorithm significantly accelerates the speed of computation and reduces the computational demands. The theoretical model was tested on a regular artificial channel and validated on a real protein channel-alpha-hemolysin, proving its efficiency.

Theory of DNA translocation through narrow ion channels and nanopores with charged walls

Translocation of a single-stranded DNA molecule through genetically engineered alpha -hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild-type alpha -hemolysin channels. We assume that the wall charges compensate a fraction x of the bare charge q_{b} of the DNA piece residing in the channel. Our predictions are as follows. (i) At small concentration of salt the blocked ion current decreases with x . (ii) The effective charge q_{s} of the DNA piece, which is very small at x=0 (neutral channel) grows with x and at x=1 reaches q_{b} . (iii) The rate of DNA capture by the channel grows exponentially with x . Our theory is also applicable to translocation of a double-stranded DNA molecular in narrow solid state nanopores with positively charged walls.

Binding of ADP in the mitochondrial ADP/ATP carrier is driven by an electrostatic funnel

The ADP/ATP carrier (AAC) is a membrane protein of paramount importance for the energy-fueling function of the mitochondria, transporting ADP from the intermembrane space to the matrix and ATP in the opposite direction. On the basis of the high-resolution, 2.2-A structure of the bovine carrier, a total of 0.53 micros of classical molecular dynamics simulations were conducted in a realistic membrane environment to decipher the early events of ADP (3-) translocation across the inner membrane of the mitochondria. Examination of apo-AAC underscores the impermeable nature of the carrier, impeding passive transport of permeants toward the matrix. The electrostatic funnel illuminated from three-dimensional mapping of the electrostatic potential forms a privileged passageway anticipated to drive the diphosphate nucleotide rapidly toward the bottom of the internal cavity. This conjecture is verified in the light of repeated, independent numerical experiments, whereby the permeant is dropped near the mouth of the mitochondrial carrier. Systematic association of ADP (3-) to the crevice of the AAC, an early event in its transport across the inner membrane, is accompanied by the formation of an intricate network of noncovalent bonds. Simulations relying on the use of an adaptive biasing force reveal for the first time that the proposed binding site corresponds to a minimum of the free energy landscape delineating the translocation of ADP (3-) in the carrier. The present work paves the way to the design of novel nucleotides and new experiments aimed at unveiling key structural features in the chronology of ADP/ATP transport across the mitochondrial membrane.

The membrane potential and its representation by a constant electric field in computer simulations

A theoretical framework is elaborated to account for the effect of a transmembrane potential in computer simulations. It is shown that a simulation with a constant external electric field applied in the direction normal to the membrane is equivalent to the influence of surrounding infinite baths maintained to a voltage difference via ion-exchanging electrodes connected to an electromotive force. It is also shown that the linearly-weighted displacement charge within the simulation system tracks the net flow of charge through the external circuit comprising the electromotive force and the electrodes. Using a statistical mechanical reduction of the degrees of freedom of the external system, three distinct theoretical routes are formulated and examined for the purpose of characterizing the free energy of a protein embedded in a membrane that is submitted to a voltage difference. The W-route is constructed from the variations in the voltage-dependent potential of mean force along a reaction path connecting two conformations of the protein. The Q-route is based on the average displacement charge as a function of the conformation of the protein. Finally, the G-route considers the relative charging free energy of specific residues, with and without applied membrane potentials. The theoretical formulation is illustrated with a simple model of an ion crossing a vacuum slab surrounded by two aqueous bulk phases and with a fragment of the voltage-sensor of the KvAP potassium channel.

Electrostatic funneling of substrate in mitochondrial inner membrane carriers

Exchange of ATP and ADP across mitochondrial membrane replenishes the cytoplasm with newly synthesized ATP and provides the mitochondria with the substrate ADP for oxidative phosphorylation. The sole means of this exchange is the mitochondrial ADP/ATP carrier (AAC), a membrane protein that is suggested to cycle between two conformationally distinct states, cytosolic-open (c-state) and matrix-open (m-state), thereby shuttling nucleotides across the inner mitochondrial membrane. However, the c-state is the only structurally resolved state, and the binding site of ADP remains elusive. Here, we present approximately 0.3 mus of all-atom MD simulations of the c-state revealing rapid, spontaneous binding of ADP to deeply positioned binding sites within the AAC lumen. To our knowledge, a complete ligand-binding event has heretofore not been described in full atomic detail in unbiased simulations. The identified ADP-bound state and additional simulations shed light on key structural elements and the initial steps involved in conversion to the m-state. Electrostatic analysis of trajectories reveals the presence of an unusually strong positive electrostatic potential in the lumen of AAC that appears to be the main driving force for the observed spontaneous binding of ADP. We provide evidence that the positive electrostatic potential is likely a common attribute among the entire family of mitochondrial carriers. In addition to playing a key role in substrate recruitment and translocation, the electropositivity of mitochondrial carriers might also be critical for their binding to the negatively charged environment of the inner mitochondrial membrane.

Charge parameterization of the metal centers in cytochrome c oxidase

Reliable atomic point charges are of key importance for a correct description of the electrostatic interactions when performing classical, force field based simulations. Here, we present a systematic procedure for point charge derivation, based on quantum mechanical methodology suited for the systems at hand. A notable difference to previous procedures is to include an outer region around the actual system of interest. At the cost of increasing the system sizes, here up to 265 atoms, including the surroundings achieves near-neutrality for the systems as well as structural stability, important factors for reliable charge distributions. In addition, the common problem of converting between C--H bonds and C--C bonds at the border vanishes. We apply the procedure to the four redox-active metal centers of cytochrome c oxidase: Cu(A), haem a, haem a(3), and Cu(B). Several relevant charge and ligand states are considered. Charges for two different force fields, CHARMM and AMBER, are presented.

Model-based prediction of the alpha-hemolysin structure in the hexameric state

The alpha-hemolysin toxin self-assembles in lipid bilayers to form water-filled pores. In recent years, alpha-hemolysin has received great attention, mainly due to its possible usage as a sensing element. We measured the ion currents through single alpha-hemolysin channels and confirmed the presence of two different subpopulations of channels with conductance levels of 465 +/- 30 pS and 280 +/- 30 pS. Different oligomerization states could be responsible for these two conductances. In fact, a heptameric structure of the channel was revealed by x-ray crystallography, whereas atomic force microscopy revealed a hexameric structure. Due to the low resolution of atomic force microscopy the atomic details of the hexameric structure are still unknown, and are here predicted by computational methods. Several possible structures of the hexameric channel were defined, and were simulated by molecular dynamics. The conductances of these channel models were computed by a numerical method based on the Poisson-Nernst-Planck electrodiffusion theory, and the values were compared to experimental data. In this way, we identified a model of the alpha-hemolysin hexameric state with conductance characteristics consistent with the experimental data. Since the oligomerization state of the channel may affect its behavior as a molecular sensor, knowing the atomic structure of the hexameric state will be useful for biotechnological applications of alpha-hemolysin.

Molecular dynamics simulation of Kv channel voltage sensor helix in a lipid membrane with applied electric field

In this article, we present the results of the molecular dynamics simulations of amphiphilic helix peptides of 13 amino-acid residues, placed at the lipid-water interface of dipalmitoylphosphatidylcholine bilayers. The peptides are identical with, or are derivatives of, the N-terminal segment of the S4 helix of voltage-dependent K channel KvAP, containing four voltage-sensing arginine residues (R1-R4). Upon changing the direction of the externally applied electric field, the tilt angle of the wild-type peptide changes relative to the lipid-water interface, with the N-terminus heading up with an outward electric field. These movements were not observed using an octane membrane in place of the dipalmitoylphosphatidylcholine membrane, and were markedly suppressed by 1), substituting Phe located one residue before the first arginine (R1) with a hydrophilic residue (Ser, Thr); or 2), changing the periodicity rule of Rs from at-every-third to at-every-fourth position; or 3), replacing R1 with a lysine residue (K). These and other findings suggest that the voltage-dependent movement requires deep positioning of Rs when the resting (inward) electric field is present. Later, we performed simulations of the voltage sensor domain (S1-S4) of Kv1.2 channel. In simulations with a strong electric field (0.1 V/nm or above) and positional restraints on the S1 and S2 helices, S4 movement was observed consisting of displacement along the S4 helix axis and a screwlike axial rotation. Gating-charge-carrying Rs were observed to make serial interactions with E183 in S1 and E226 in S2, in the outer water crevice. A 30-ns-backward simulation started from the open-state model gave rise to a structure similar to the recent resting-state model, with S4 moving vertically approximately 6.7 A. The energy landscape around the movement of S4 appears very ragged due to salt bridges formed between gating-charge-carrying residues and negatively charged residues of S1, S2, and S3 helices. Overall, features of S3 and S4 movements are consistent with the recent helical-screw model. Both forward and backward simulations show the presence of at least two stable intermediate structures in which R2 and R3 form salt bridges with E183 or E226, respectively. These structures are the candidates for the states postulated in previous gating kinetic models, such as the Zagotta-Hoshi-Aldrich model, to account for more than one transition step per subunit for activation.

Control of cation permeation through the nicotinic receptor channel

We used molecular dynamics (MD) simulations to explore the transport of single cations through the channel of the muscle nicotinic acetylcholine receptor (nAChR). Four MD simulations of 16 ns were performed at physiological and hyperpolarized membrane potentials, with and without restraints of the structure, but all without bound agonist. With the structure unrestrained and a potential of −100 mV, one cation traversed the channel during a transient period of channel hydration; at −200 mV, the channel was continuously hydrated and two cations traversed the channel. With the structure restrained, however, cations did not traverse the channel at either membrane potential, even though the channel was continuously hydrated. The overall results show that cation selective transport through the nAChR channel is governed by electrostatic interactions to achieve charge selectivity, but ion translocation relies on channel hydration, facilitated by a trans-membrane field, coupled with dynamic fluctuations of the channel structure.

Communication between a cell and its environment relies on channel-forming proteins to provide a low energy pathway for ions to move in and out. Although channel-forming proteins are essential to all life forms, the atomic-scale mechanisms that enable ions to pass through the channel remain elusive due to the lack of experimental approaches to monitor the protein and ion in real time and at atomic resolution. A powerful alternative approach is molecular dynamics (MD) simulation based on the laws of physics applied to the increasing body of protein structures resolved at atomic resolution. Here we present all-atom MD simulations applied to the nicotinic acetylcholine receptor (nAChR) that initiates voluntary movement in skeletal muscle. By focusing on individual permeant cations, we find that selective cation translocation occurs in stages: cations are first selected through a series of oppositely charged residues within the protein vestibule leading to a narrow hydrophobic constriction, but then hydration of the narrow region and dynamic fluctuations of the protein enable the cation to pass through. The findings provide a general framework for understanding how ions are selected for transport based on charge, and how the dynamic interplay between water, the ion, and the channel protein enable rapid ion translocation through the broad class of channel-forming proteins with hydrophobic barriers.

Single molecule measurements within individual membrane-bound ion channels using a polymer-based bilayer lipid membrane chip

The measurement of single poly(ethylene glycol) (PEG) molecules interacting with individual bilayer lipid membrane-bound ion channels is presented. Measurements were performed within a polymer microfluidic system including an open-well bilayer lipid membrane formation site, integrated Ag/AgCl reference electrodes for on-chip electrical measurements, and multiple microchannels for independent ion channel and analyte delivery. Details of chip fabrication, bilayer membrane formation, and alpha-hemolysin ion channel incorporation are discussed, and measurements of interactions between the membrane-bound ion channels and single PEG molecules are presented.

Simulations of electrophoretic RNA transport through transmembrane carbon nanotubes

The study of interactions between carbon nanotubes and cellular components, such as membranes and biomolecules, is fundamental for the rational design of nanodevices interfacing with biological systems. In this work, we use molecular dynamics simulations to study the electrophoretic transport of RNA through carbon nanotubes embedded in membranes. Decorated and naked carbon nanotubes are inserted into a dodecane membrane and a dimyristoylphosphatidylcholine lipid bilayer, and the system is subjected to electrostatic potential differences. The transport properties of this artificial pore are determined by the structural modifications of the membrane in the vicinity of the nanotube openings and they are quantified by the nonuniform electrostatic potential maps at the entrance and inside the nanotube. The pore is used to transport electrophoretically a short RNA segment and we find that the speed of translocation exhibits an exponential dependence on the applied potential differences. The RNA is transported while undergoing a repeated stacking and unstacking process, affected by steric interactions with the membrane headgroups and by hydrophobic interaction with the walls of the nanotube. The RNA is structurally reorganized inside the nanotube, with its backbone solvated by water molecules near the axis of the tube and its bases aligned with the nanotube walls. Upon exiting the pore, the RNA interacts with the membrane headgroups and remains attached to the dodecane membrane while it is expelled into the solvent in the case of the lipid bilayer. The results of the simulations detail processes of molecular transport into cellular compartments through manufactured nanopores and they are discussed in the context of applications in biotechnology and nanomedicine.

Theoretical study of sequence-dependent nanopore unzipping of DNA

We theoretically investigate the unzipping of DNA electrically driven through a nanometer-size pore. Taking the DNA base sequence explicitly into account, the unpairing and translocation process is described by a biased random walk in a one-dimensional energy landscape determined by the sequential basepair opening. Distributions of translocation times are numerically calculated as a function of applied voltage and temperature. We show that varying these two parameters changes the dynamics from a predominantly diffusive behavior to a dynamics governed by jumps over local energy barriers. The work suggests experimentally studying sequence effects, by comparing the average value and standard deviation of the statistical distribution of translocation times.