Ion transport in the gramicidin channel: molecular dynamics study of single and double occupancy

Statistical mechanics of polarizable force fields based on classical Drude oscillators with dynamical propagation by the dual-thermostat extended Lagrangian

Polarizable force fields based on classical Drude oscillators offer a practical and computationally efficient avenue to carry out molecular dynamics (MD) simulations of large biomolecular systems. To treat the polarizable electronic degrees of freedom, the Drude model introduces a virtual charged particle that is attached to its parent nucleus via a harmonic spring. Traditionally, the need to relax the electronic degrees of freedom for each fixed set of nuclear coordinates is achieved by performing an iterative self-consistent field (SCF) calculation to satisfy a selected tolerance. This is a computationally demanding procedure that can increase the computational cost of MD simulations by nearly one order of magnitude. To avoid the costly SCF procedure, a small mass is assigned to the Drude particles, which are then propagated as dynamic variables during the simulations via a dual-thermostat extended Lagrangian algorithm. To help clarify the significance of the dual-thermostat extended Lagrangian propagation in the context of the polarizable force field based on classical Drude oscillators, the statistical mechanics of a dual-temperature canonical ensemble is formulated. The conditions for dynamically maintaining the dual-temperature properties in the case of the classical Drude oscillator are analyzed using the generalized Langevin equation.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Gramicidin A Channel Formation Induces Local Lipid Redistribution I: Experiment and Simulation

Integral membrane protein function can be modulated by the host bilayer. Because biological membranes are diverse and nonuniform, we explore the consequences of lipid diversity using gramicidin A channels embedded in phosphatidylcholine (PC) bilayers composed of equimolar mixtures of di-oleoyl-PC and di-erucoyl-PC (dC_18:1+dC_22:1, respectively), di-palmitoleoyl-PC and di-nervonoyl-PC (dC_16:1+dC_24:1, respectively), and di-eicosenoyl-PC (pure dC_20:1), all of which have the same average bilayer chain length. Single-channel lifetime experiments, molecular dynamics simulations, and a simple lipid compression model are used in tandem to gain insight into lipid redistribution around the channel, which partially alleviates the bilayer deformation energy associated with channel formation. The average single-channel lifetimes in the two-component bilayers (95 ± 10 ms for dC_18:1+dC_22:1 and 195 ± 20 ms for dC_16:1+dC_24:1) were increased relative to the single-component dC_20:1 control bilayer (65 ± 10 ms), implying lipid redistribution. Using a theoretical treatment of thickness-dependent changes in channel lifetimes, the effective local enrichment of lipids around the channel was estimated to be 58 ± 4% dC_18:1 and 66 ± 2% dC_16:1 in the dC_18:1+dC_22:1 and dC_16:1+dC_24:1 bilayers, respectively. 3.5-μs molecular dynamics simulations show 66 ± 2% dC_16:1 in the first lipid shell around the channel in the dC_16:1+dC_24:1 bilayer, but no significant redistribution (50 ± 4% dC_18:1) in the dC_18:1+dC_22:1 bilayer; these simulated values are within the 95% confidence intervals of the experimental averages. The strong preference for the better matching lipid (dC_16:1) near the channel in the dC_16:1+dC_24:1 mixture and lesser redistribution in the dC_18:1+dC_22:1 mixture can be explained by the energetic cost associated with compressing the lipids to match the channel's hydrophobic length.

Conformational changes during permeation of Na+ through a modified cyclic peptide nanotube promote energy landscape roughness

Using a metadynamics approach, we investigate the potential of mean force for Na⁺ permeation inside a cyclic peptide nanotube (CPN) with modified interior as a function of ion position, coordination number, and lumen chemistry. We show that functionalizing the lumen of a CPN with a methyl-benzoic acid group introduces non-periodic variations in the internal energy of the nanotube, which dictate the overall free energy roughness during the permeation of Na⁺. These non-periodic variations arise from the structural dynamics of the functional group, where changes in the dihedral angles induced by the proximity of the ion give rise to conformational changes that increase landscape roughness and thereby decrease transport rate. Our computational framework emphasizes the advantages of using the coordination number as a collective variable to investigate the available conformations during ion permeation through CPNs, and reveals new structure-function relations for chemically tunable CPNs, paving the way for rational design of nano-porous systems with tunable selectivity and flux.

C-terminal tail insertion of Bcl-xL in membrane occurs via partial unfolding and refolding cycle associating microsolvation

Insertion of the Bcl-x_L C-terminal into the mitochondrial outer membrane is found to be guided by the partial unfolding–refolding cycle, assisted by micro-solvation.

Spontaneous Formation of KCl Aggregates in Biomolecular Simulations: A Force Field Issue?

Realistic all-atom simulation of biological systems requires accurate modeling of both the biomolecules and their ionic environment. Recently, ion nucleation phenomena leading to the rapid growth of KCl or NaCl clusters in the vicinity of biomolecular systems have been reported. To better understand this phenomenon, molecular dynamics simulations of KCl aqueous solutions at three (1.0, 0.25, and 0.10 M) concentrations were performed. Two popular water models (TIP3P and SPC/E) and two Lennard-Jones parameter sets (AMBER and Dang) were combined to produce a total of 80 ns of molecular dynamics trajectories. Results suggest that the use of the Dang cation Lennard-Jones parameters instead of those adopted by the AMBER force-field produces a more accurate description of the ionic solution. In the later case, formation of salt aggregates is probably indicative of an artifact resulting from misbalanced force-field parameters. Because similar results were obtained with two different water parameter sets, the simulations exclude a water model dependency in the formation of anomalous ionic clusters. Overall, the results strongly suggest that for accurate modeling of ions in biomolecular systems, great care should be taken in choosing balanced ionic parameters even when using the most popular force-fields. These results invite a reexamination of older data obtained using available force-fields and a thorough check of the quality of current parameters sets by performing simulations at finite (>0.25 M) instead of minimal salt conditions.

Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels

Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are known. The experimental data of both channels are then used to verify and explain novel features of PNPF as compared with previous PNP models. The PNPF currents are in accord with the experimental I-V (V for applied voltages) data of the gramicidin A channel and I-C (C for bath concentrations) data of the calcium channel with 10(-8)-fold bath concentrations that pose severe challenges in theoretical simulations.

Modelling of noble anaesthetic gases and high hydrostatic pressure effects in lipid bilayers

Our objective was to study molecular processes that might be responsible for inert gas narcosis and high-pressure nervous syndrome. The classical molecular dynamics trajectories (200 ns) of dioleoylphosphatidylcholine (DOPC) bilayers simulated by the Berger force field were evaluated for water and the atomic distribution of noble gases around DOPC molecules in the pressure range of 1-1000 bar and at a temperature of 310 K. Xenon and argon have been tested as model gases for general anaesthetics, and neon has been investigated for distortions that are potentially responsible for neurological tremors in hyperbaric conditions. The analysis of stacked radial pair distribution functions of DOPC headgroup atoms revealed the explicit solvation potential of the gas molecules, which correlates with their dimensions. The orientational dynamics of water molecules at the biomolecular interface should be considered as an influential factor, while excessive solvation effects appearing in the lumen of membrane-embedded ion channels could be a possible cause of inert gas narcosis. All the noble gases tested exhibit similar order parameter patterns for both DOPC acyl chains, which are opposite of the patterns found for the order parameter curve at high hydrostatic pressures in intact bilayers. This finding supports the 'critical volume' hypothesis of anaesthesia pressure reversal. The irregular lipid headgroup-water boundary observed in DOPC bilayers saturated with neon in the pressure range of 1-100 bar could be associated with the possible manifestation of neurological tremors at the atomic scale. The non-immobiliser neon also demonstrated the highest momentum impact on the normal component of the DOPC diffusion coefficient representing the monolayer undulation rate, which indicates that enhanced diffusivity rather than atomic size is the key factor.

Paradoxical one-ion pore behavior of the long β-helical peptide of marine cytotoxic polytheonamide B

The cytotoxic 48-mer peptide, polytheonamide B (pTB), from a marine sponge forms a β^6.3-helix with an inner diameter of 4 Å and a length of 45 Å, features that allow the selective permeation of monovalent cations across targeted cell membranes. To characterize this long, narrow pore, electrophysiological examination using a planar lipid bilayer method was performed. The single-channel current amplitude exhibited saturation for concentrated Cs⁺ or K⁺ solution, and the reversal potential in mixed solutions did not exhibit any anomalous mole-fraction behavior. These results suggest the one-ion permeation mechanism. This is in contrast to the short (26 Å) β^6.3-helical gramicidin channel, which holds two ions simultaneously. The paradoxical one-ion permeation through the long pTB channel was modeled with a discrete-state Markov model. Ions permeate through the channel by stepping between two binding sites in the pore, but never occupy these sites simultaneously in either pure or mixed ion solution.

Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the two methods are essentially equivalent; i.e., they have comparable accuracies for the same number of elements. We find that ions in water--charges embedded in a high-dielectric medium--are harder to compute accurately than charges in a low-dielectric medium.

Propeptides are sufficient to regulate organelle-specific pH-dependent activation of furin and proprotein convertase 1/3

The proprotein convertases (PCs) furin and proprotein convertase 1/3 (PC1) cleave substrates at dibasic residues along the eukaryotic secretory/endocytic pathway. PCs are evolutionarily related to bacterial subtilisin and are synthesized as zymogens. They contain N-terminal propeptides (PRO) that function as dedicated catalysts that facilitate folding and regulate activation of cognate proteases through multiple-ordered cleavages. Previous studies identified a histidine residue (His69) that functions as a pH sensor in the propeptide of furin (PRO(FUR)), which regulates furin activation at pH~6.5 within the trans-Golgi network. Although this residue is conserved in the PC1 propeptide (PRO(PC1)), PC1 nonetheless activates at pH~5.5 within the dense core secretory granules. Here, we analyze the mechanism by which PRO(FUR) regulates furin activation and examine why PRO(FUR) and PRO(PC1) differ in their pH-dependent activation. Sequence analyses establish that while both PRO(FUR) and PRO(PC1) are enriched in histidines when compared with cognate catalytic domains and prokaryotic orthologs, histidine content in PRO(FUR) is ~2-fold greater than that in PRO(PC1), which may augment its pH sensitivity. Spectroscopy and molecular dynamics establish that histidine protonation significantly unfolds PRO(FUR) when compared to PRO(PC1) to enhance autoproteolysis. We further demonstrate that PRO(FUR) and PRO(PC1) are sufficient to confer organelle sensing on folding and activation of their cognate proteases. Swapping propeptides between furin and PC1 transfers pH-dependent protease activation in a propeptide-dictated manner in vitro and in cells. Since prokaryotes lack organelles and eukaryotic PCs evolved from propeptide-dependent, not propeptide-independent prokaryotic subtilases, our results suggest that histidine enrichment may have enabled propeptides to evolve to exploit pH gradients to activate within specific organelles.

Application of electrochemical impedance spectroscopy to the study of surface processes

The application of Electrochemical Impedance Spectroscopy to the study of surface electrode processes is reviewed. The impedance expressions and the physical meaning of the parameters included in them are shown for three surface processes: adsorption kinetics, diffusion towards partially blocked electrodes and surface confined redox reactions. The models are applied to selected examples, showing the capability of Electrochemical Impedance Spectroscopy to obtain fundamental kinetic information of these processes. A review with 83 references.

Energetics of double-ion occupancy in the gramicidin A channel

To understand the energetics of double-ion occupancy in gramicidin A (gA) channels, the 2D potential of mean force (PMF) is calculated for two ions at different positions along the channel axis. The cross sections of this 2D PMF are compared with available one-ion PMFs to highlight the effect of one ion on the permeation dynamics of the other. It is found that, if the first ion stays on one side in the channel, the second ion has to pass over an additional barrier to move into the outer binding site. At the same time, both outer and inner binding sites for the second ion become shallower than those in the one-ion PMF. The calculated ion-ion repulsion for a doubly occupied channel is about 2 kcal/mol, in good agreement with previous experimental estimates. The number of water molecules inside the channel and their dipole moment are calculated to interpret the energetics of double-ion occupancy. As the first ion moves into the outer binding site and then further into the channel, the oxygen atoms of the single-file water column in the channel are oriented to point toward the ion. The observed dipole moment distribution of a singly occupied channel has only one sharp peak, and the water alignment is essentially perfect once the ion is in the inner binding site. For this reason, there is an energy penalty to accommodate a second ion at the opposite end of the channel.

Molecular insights on the cyclic peptide nanotube-mediated transportation of antitumor drug 5-fluorouracil

Self-assembled cyclic peptide nanotubes (CPNs) show a potential use in drug delivery. In this study, the CPN composed of (Trp-D-Leu)(4)-Gln-D-Leu was synthesized and tested for the transport of the antitumor drug 5-fluorouracil (5-FU). CPN-mediated release of 5-FU from liposomes experimentally tested the transportation function of the synthetic CPNs. To explore the transportation mechanism of CPNs, computational studies have been performed on the CPN models stacked by 8 subunits, including conventional molecular dynamics (CMD) simulations, and steered molecular dynamics (SMD) simulations in the environment of hydrated dimyristoylphosphatidylcholine (DMPC) lipid bilayer. Our CMD simulations demonstrated that the ortho-CPN is the most stable nanotube, in which the Gln residue is in the ortho-position relative to other residues. The calculated diffusion coefficient value for inner water molecules was 1.068 × 10(-5) cm(2)·s(-1), almost half that of the bulky water and 24 times faster than that of the typical gramicidin A channel. The CPN conserved its hollow structure along the 10 ns CMD simulations, with a tile angle of 50° relative to the normal of DMPC membrane. Results from SMD simulations showed that the 5-FU molecule was transported by hopping through different potential energy minima distributed along subunits, and finally exited the nanotube by escaping from the kink region at the last two subunits. The hopping of 5-FU was driven by switching from hydrophobic interactions between 5-FU and the interior wall of the nanotube to hydrogen bonding interactions of 5-FU with the backbone carbonyl group and amide group of ortho-CPN. The calculated binding free energy profile of 5-FU interacting with the CPN indicated that there was an energy well near the outer end of the nanotube.

Application of the fuzzy-oil-drop model to membrane protein simulation

The analysis of structural properties and biological activity of membrane proteins requires long lasting simulation of molecular dynamics. The large number of atoms present in protein molecule, membrane (phospholipids), and water environment makes the simulation of large scale. The implementation of simplified model representing the natural environment for membrane proteins is presented and compared with the vacuum simulation and simulation in the presence of water molecules and membrane phospholipids presented explicite. The comparative structural analysis and computational times for these three models makes the simplified model promising.

Standardizing the atomic description, axis and centre of biological ion channels

A general representation of the atomic co-ordinates of a biological ion channel is obtained from a definition of channel axis and centre. Through rotation and translation of the channel, its centre becomes the origin of the standard co-ordinate system, and the channel axis becomes the system's z-axis. A method for determining the channel axis and centre based on the concepts of mass centre and mass moment of inertia is presented. The method for determining the channel axis can be directly applied to channels that adhere to two specific conditions regarding their geometry and mass distribution. Specific examples are given for Gramicidin A (GA), and the mammalian potassium channel Kv 1.2. For channels that do not adhere to these conditions, minor modifications of these procedures can be applied in determining the channel axis. Specific examples are given for the outer membrane bacterial porin OmpF, and for the staphylococcal pore-forming toxin alpha-hemolysin (alpha HL). The definitions and procedures presented are made in an effort to establish a standard basis for performing, sharing, and comparing computations in a consistent manner.

Solution of the Poisson-Nernst-Planck equations in the cell-substrate interface

Electrogenic cells are able to generate electrical signals which can be measured by various invasive electrophysiological methods such as patch-clamp or sharp microelectrode recordings. Growing cells on the surfaces of e.g. metal microelectrodes or field-effect transistors allows the recording of an extracellular component of these signals. For an understanding of such extracellular signals it is mandatory to get detailed topographical as well as electrical information about the cell-sensor interface. In a first approximation, this interface can be described by a flat disk between cell membrane and sensor surface. For a correct description of the signals, the electrodiffusion of ions in this interface is modeled by using the stationary Poisson-Nernst-Planck equations. We solve the equations analytically, and derive expressions for the potential, the ionic charge densities, and the seal resistance. The results provide a method for determining the distance h between sensor surface and cell membrane. For human embryonic kidney cells, we receive h approximately 70 nm. Comparison with literature shows good agreement.

Free energy simulations of single and double ion occupancy in gramicidin A

Simultaneous occupancy of the two binding sites in gramicidin A by monovalent cations is a well known property of this channel, but the energetic feasibility of this process in molecular dynamics simulations has not been established so far. Here the authors study the energetics of single and double ion occupancy in gramicidin A by constructing the potential of mean force for single and pair of cations. As representatives of small and large ions, they consider both Na+ and K+ ions in the calculations. Binding constants of ions are estimated from the free energy profiles. Comparisons with the experimental results indicate 3-4 kT discrepancy in the binding energies. They also study the coordination of the ions in their respective binding sites and the dynamic behavior of the channel water during the double ion binding process.

Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields

We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.

Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels

Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.

Gramicidin channels

Gramicidin channels are mini-proteins composed of two tryptophan-rich subunits. The conducting channels are formed by the transbilayer dimerization of nonconducting subunits, which are tied to the bilayer/solution interface through hydrogen bonds between the indole NH groups and the phospholipid backbone and water. The channel structure is known at atomic resolution and the channel's permeability characteristics are particularly well defined: gramicidin channels are selective for monovalent cations, with no measurable permeability to anions or polyvalent cations; ions and water move through a pore whose wall is formed by the peptide backbone; and the single-channel conductance and cation selectivity vary when the amino acid sequence is varied, even though the permeating ions make no contact with the amino acid side chains. Given the amount of experimental information that is available--for both the wild-type channels and for channels formed by amino acid-substituted gramicidin analogues--gramicidin channels provide important insights into the microphysics of ion permeation through bilayer-spanning channels. For the same reason, gramicidin channels constitute the system of choice for evaluating computational strategies for obtaining mechanistic insights into ion permeation through the complex channels formed by integral membrane proteins.

Role of ions on structure and stability of a synthetic gramicidin ion channel in solution. A molecular dynamics study

We performed a molecular dynamics (MD) simulation to the investigate structure and stability of a synthetic gramicidin-like peptide in solution with and without ions. The starting structures of the MD simulations were taken from two recently solved NMR structures of this peptide in isotropic solution, which forms stable monomers or dimers in the presence or absence of ions, respectively. The monomeric structure is channel-like and is assumed to be stabilized by the presence of two Cs(+) ions bound in the channel, each one close to one channel entrance. In our MD simulations, we observed how the Cs(+) ions bind in the channel formed by the monomeric gramicidin-like peptide using implicit solvent and explicit ions with a concentration of 2 M. MD simulations were performed with and without explicit ions but with an implicit solvent model defined by the generalized Born approximation, which was used to mimic the dielectric properties of the solvent and to speed up the computations.

Protons may leak through pure lipid bilayers via a concerted mechanism

Protons are known to permeate pure lipid bilayers at a rate that is anomalous compared to those of other small monovalent cations. The prevailing mechanism via which they cross the membrane is still unclear, and it is unknown how to probe the mechanism directly by experiment. One of the more popular theories assumes the formation of membrane-spanning single-file water wires providing a matrix along which the protons can "hop" over the barrier. However, free energy calculations on such structures (without the presence of an excess proton) suggest that this mechanism alone cannot account for the observed permeation rates. We use the multistate empirical valence bond method to directly study water structures surrounding a (delocalized) excess proton on its way through the membrane. We find that membrane-spanning networks, rather than single-file chains, are formed around the proton. We also find that such structures are considerably stabilized in the presence of the proton, with lifetimes of several hundreds of picoseconds. The observed structures are suggestive of a new, concerted, mechanism and provide some direction for further investigation.

Computer simulations of membrane proteins

Computer simulations are rapidly becoming a standard tool to study the structure and dynamics of lipids and membrane proteins. Increasing computer capacity allows unbiased simulations of lipid and membrane-active peptides. With the increasing number of high-resolution structures of membrane proteins, which also enables homology modelling of more structures, a wide range of membrane proteins can now be simulated over time spans that capture essential biological processes. Longer time scales are accessible by special computational methods. We review recent progress in simulations of membrane proteins.

Molecular docking of the scorpion toxin Tc1 to the structural model of the voltage-gated potassium channel Kv1.1 from human Homo sapiens

In this study, structural model of the pore loop region of the voltage-gated potassium channel Kv1.1 from human Homo sapiens was constructed based on the crystallographic structure of KcsA by structural homology. The pore loop region of Kv1.1 exhibits similar folds as that of KcsA. The structural feature of the selectivity filter of Kv1.1 is nearly identical to that of KcsA, whereas most of the structural variations occur in the turret as well as in the inner and outer helices. Molecular docking experiments of the scorpion toxin Tc1 from Tityus cambridgei to the outer vestibule of KcsA as well as Kv1.1 were subsequently performed with various initial Tc1 orientations. Tc1 was found to form the most stable complexes with these two K+ channels when the side chain of Lys14 occupies the pore of the selectivity filter through electrostatic interaction. Tc1 binds preferentially towards Kv1.1 than KcsA due to stronger hydrophobic and electrostatic interactions formed between the toxin and the selectivity filter and outer vestibule of Kv1.1. Furthermore, surface complementarity of the outer vestibules of the channels to the Tc1 spatial conformations also plays an important role in stabilizing both the Tc1/KcsA and Tc1/Kv1.1 complexes.

Structure prediction of small transmembrane helix bundles

In this work, we will introduce a novel computational approach to predict the structures of small helical hetero-oligomeric transmembrane bundles. The approach is based on the generation and evaluation of a large library of randomly generated helix bundle conformations. This library will be evaluated by energy-dependent distributions of the structural parameters of the conformations. The approach enables us to model a subunit of cytochrome c oxidase (occ), consisting of four TM helices, to an accuracy of 1.7A and the transducer protein of the sensory Rhodopsin II-transducer complex to an accuracy of 2.3A when including two transducer-contacting Rhodopsin helices. As the approach does not afford a unique solution for each protein, experimental data would be needed to discriminate the possible models. In addition to predicting the structure of helix bundles, one can also gain insight into possible higher-energy conformations or flexible regions of the protein.

A set of homology models of pore loop domain of six eukaryotic voltage-gated potassium channels Kv1.1-Kv1.6

Homology models of the pore loop domain of six eukaryotic potassium channels, Kv1.1-Kv1.6, were generated based on the crystallographic structure of KcsA. The results of amino acid sequence alignment indicate that these Kv channels are composed of two structurally and functionally independent domains: the N-terminal 'voltage sensor' domain and the C-terminal 'pore loop' domain. The homology models reveal that the pore loop domains of these Kv channels exhibit similar folds to those of KcsA. The structural features and specific packing of aromatic residues around the selectivity filter of these Kv channels are nearly identical to those of KcsA, whereas most of the structural variations occur in the turret as well as in the inner and outer helices. The distribution of polar and nonpolar side chains on the surfaces of the KcsA and Kv channels reveals that they exhibit a segregation of side chains common to most integral membrane proteins. As the hydrogen bond between Glu71 and Asp80 in KcsA plays an important role in stabilizing the channel, the substituted Val residue in the Kv family corresponding to Glu71 of KcsA stabilizes the channel by making hydrophobic contact with Tyr residue from the signature sequence of the selectivity filter. The homology models of these Kv channels provide particularly attractive subjects for further structure-based studies.

Energetics of ion conduction through the gramicidin channel

The free energy governing K(+) conduction through gramicidin A channels is characterized by using over 0.1 micros of all-atom molecular dynamics simulations with explicit solvent and membrane. The results provide encouraging agreement with experiments and insights into the permeation mechanism. The free energy surface of K(+), as a function of both axial and radial coordinates, is calculated. Correcting for simulation artifacts due to periodicity and the lack of hydrocarbon polarizability, the calculated single-channel conductance for K(+) ions is 0.8 pS, closer to experiment than any previous calculation. In addition, the estimated single ion dissociation constants are within the range of experimental determinations. The relatively small free energy barrier to ion translocation arises from a balance of large opposing contributions from protein, single-file water, bulk electrolyte, and membrane. Mean force decomposition reveals a remarkable ability of the single-file water molecules to stabilize K(+) by -40 kcal/mol, roughly half the bulk solvation free energy. The importance of the single-file water confirms the conjecture of Mackay et al. [Mackay, D. H. J., Berens, P. H., Wilson, K. R. & Hagler, A. T. (1984) Biophys. J. 46, 229-248]. Ion association with the channel involves gradual dehydration from approximately six to seven water molecules in the first shell, to just two inside the narrow pore. Ion permeation is influenced by the orientation of the single-file water column, which can present a barrier to conduction and give rise to long-range coupling of ions on either side of the pore. Small changes in the potential function, including contributions from electronic polarization, are likely to be sufficient to obtain quantitative agreement with experiments.

Effect of channel geometry on the electrostatic potential in acetylcholine channels

We study the effect of channel geometry on the potential barrier encountered by ions as they permeate the acetylcholine receptor channel. Among the various channel geometries which have been used to represent the acetylcholine receptor channel include the cylinder and the toroidal catenary. The main reasons for those choices appear to be the facilitation of separation of the Poisson equation, rather than biological considerations. We consider a novel and realistic acetylcholine channel geometry, and calculate the electrostatic potential profiles within it, and compare our results with results from other channel geometries.

Voltage-gated proton channels and other proton transfer pathways

Proton channels exist in a wide variety of membrane proteins where they transport protons rapidly and efficiently. Usually the proton pathway is formed mainly by water molecules present in the protein, but its function is regulated by titratable groups on critical amino acid residues in the pathway. All proton channels conduct protons by a hydrogen-bonded chain mechanism in which the proton hops from one water or titratable group to the next. Voltage-gated proton channels represent a specific subset of proton channels that have voltage- and time-dependent gating like other ion channels. However, they differ from most ion channels in their extraordinarily high selectivity, tiny conductance, strong temperature and deuterium isotope effects on conductance and gating kinetics, and insensitivity to block by steric occlusion. Gating of H(+) channels is regulated tightly by pH and voltage, ensuring that they open only when the electrochemical gradient is outward. Thus they function to extrude acid from cells. H(+) channels are expressed in many cells. During the respiratory burst in phagocytes, H(+) current compensates for electron extrusion by NADPH oxidase. Most evidence indicates that the H(+) channel is not part of the NADPH oxidase complex, but rather is a distinct and as yet unidentified molecule.

Ion permeation through the gramicidin channel: atomically detailed modeling by the Stochastic Difference Equation

Atomically detailed descriptions of ionic solution, membrane, and the gramicidin channel are used to compute molecular dynamics trajectories of ion permeation. The microsecond trajectories are calculated with the Stochastic Difference Equation (SDE), which provides approximate solutions to the equations of motions (with filtered high-frequency modes) of extended timescales. The relative permeations of lithium, sodium, and potassium are estimated by using a novel, kinetic cycle protocol and are compared with experiment. The transport through native gramicidin and one fluoro-valine variant is considered as well. Qualitative agreement between theory and experiment is obtained. The faster permeation rate of sodium compared to lithium is reproduced in the calculations. The calculations also reproduce the slower diffusion through a gramicidin with fluorinated valine compared to native gramicidin. The calculations are inconclusive about the relative rates of potassium and sodium. The experiment suggests that potassium permeates more quickly. We directly probe the kinetics of a biophysical process at a relevant time window without reducing the atomically detailed description of the system. The calculations were able to capture subtle balances between binding and diffusion that determine permeation rates. The same model gave the correct ordering of diffusion rates for cases in which electrostatic binding has opposite effects and must be supplemented by dynamic factors. Diffusion rates are faster when favorable electrostatic interactions of ions in the channel (compared to the solvent) are observed. Studies of a gramicidin variant suggest an opposite effect, in which permeation is faster for the less polar channel, indicating dynamic effects. Although both trends can be explained qualitatively, it is not possible to predict (before doing the SDE calculations) which factor is more important.

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.

Computational studies of the gramicidin channel

Ion channels are highly specific membrane-spanning protein structures which serve to facilitate the passage of selected ions across the lipid barrier. In the past decade, molecular dynamics simulations based on atomic models and realistic microscopic interactions with explicit solvent and membrane lipids have been used to gain insight into the function of these complex systems. These calculations have considerably expanded our view of ion permeation at the microscopic level. This Account will mainly focus on computational studies of the gramicidin A channel, one of the simplest and best characterized molecular pore.

Cellular microtransport processes: intercellular, intracellular, and aggregate behavior

Ionic and molecular transfer among cells occurs by a variety of transport processes operative at different length scales. Cell membrane permeability and electrical conductance derive from channel proteins producing pores at the molecular (ultrastructural) scale. Intracellular mobility involves the dynamics of motion through the complex ultrastructure of the cytoplasm. These phenomena unite in the larger-scale (microscopic) process of gross intercellular transfer. When such movement occurs among sufficiently many cells, it in turn begins to reflect their average collective (macroscopic) behavior as bulk tissue. This article surveys selected aspects of intercellular and intracellular transport, with emphasis on detailed mechanistic theory, experimental probes of cellular permeability, and systematic transcendence from small to large length scales.

Noncontact dipole effects on channel permeation. V. Computed potentials for fluorinated gramicidin

Experimental and theoretical calculations indicate that the dipole moment of the four Trp side chains in gramicidin A (gA) channels modify channel conductance through long-range electrostatic interactions. Electrostatic ion/side-chain interaction energies along the channel were computed with CHARMM using ab initio atom charges for native and 4-, 5-, or 6-fluorinated Trp side chains. The bulk water reaction to the polar side chains was included using the method of images as implemented by, and channel waters in idealized structures were included. Ion/Trp interaction energies were approximately -0.6 kcal/mol throughout the channel for all four of the native Trp pairs. Channel waters produced a modest reduction in the magnitude of interactions, essentially offsetting images representing the bulk water outside the channel. The effects of side-chain fluorination depended on ring position and, to a lesser extent, residue number. Compared with native Trp, 5-fluorination reduces the translocation barrier with minor effects on the exit barrier. In contrast, 6-fluorination primarily reduces exit barrier. 4-Fluorination produces a more complex double-well energy profile. Effects of measured side-chain movements resulting from fluorination or change in lipid bilayer were negligible whereas thermal side chain librations cause large effects, especially in the region of the ion-binding sites.

Conformations of an adenine bulge in a DNA octamer and its influence on DNA structure from molecular dynamics simulations

Molecular dynamics simulations have been applied to the DNA octamer d(GCGCA-GAAC). d(GTTCGCGC), which has an adenine bulge at the center to determine the pathway for interconversion between the stacked and extended forms. These forms are known to be important in the molecular recognition of bulges. From a total of ~35 ns of simulation time with the most recent CHARMM27 force field a variety of distinct conformations and subconformations are found. Stacked and fully looped-out forms are in excellent agreement with experimental data from NMR and x-ray crystallography. Furthermore, in a number of conformations the bulge base associates with the minor groove to varying degrees. Transitions between many of the conformations are observed in the simulations and used to propose a complete transition pathway between the stacked and fully extended conformations. The effect on the surrounding DNA sequence is investigated and biological implications of the accessible conformational space and the suggested transition pathway are discussed, in particular for the interaction of the MS2 replicase operator RNA with its coat protein.

Design and characterization of gramicidin channels

This article summarizes methods for the chemical synthesis and biophysical characterization of gramicidins with varying sequences and labels. The family of gramicidin channels has developed into a powerful model system for understanding fundamental properties, interactions, and dynamics of proteins and lipids generally, and ion channels specifically, in biological membranes.

Molecular dynamics of the KcsA K(+) channel in a bilayer membrane

Molecular dynamics (MD) simulations of an atomic model of the KcsA K(+) channel embedded in an explicit dipalmitoylphosphatidylcholine (DPPC) phospholipid bilayer solvated by a 150 mM KCl aqueous salt solution are performed and analyzed. The model includes the KcsA K(+) channel, based on the recent crystallographic structure of, Science. 280:69-77), 112 DPPC, K(+) and Cl(-) ions, as well as over 6500 water molecules for a total of more than 40,000 atoms. Three K(+) ions are explicitly included in the pore. Two are positioned in the selectivity filter on the extracellular side and one in the large water-filled cavity. Different starting configurations of the ions and water molecules in the selectivity filter are considered, and MD trajectories are generated for more than 4 ns. The conformation of KcsA is very stable in all of the trajectories, with a global backbone root mean square (RMS) deviation of less than 1.9 A with respect to the crystallographic structure. The RMS atomic fluctuations of the residues surrounding the selectivity filter on the extracellular side of the channel are significantly lower than those on the intracellular side. The motion of the residues with aromatic side chains surrounding the selectivity filter (Trp(67), Trp(68), Tyr(78), and Tyr(82)) is anisotropic with the smallest RMS fluctuations in the direction parallel to the membrane plane. A concerted dynamic transition of the three K(+) ions in the pore is observed, during which the K(+) ion located initially in the cavity moves into the narrow part of the selectivity filter, while the other two K(+) ions move toward the extracellular side. A single water molecule is stabilized between each pair of ions during the transition, suggesting that each K(+) cation translocating through the narrow pore is accompanied by exactly one water molecule, in accord with streaming potential measurements (, Biophys. J. 55:367-371). The displacement of the ions is coupled with the structural fluctuations of Val(76) and Gly(77), in the selectivity filter, as well as the side chains of Glu(71), Asp(80), and Arg(89), near the extracellular side. Thus the mechanical response of the channel structure at distances as large as 10-20 A from the ions in the selectivity filter appears to play an important role in the concerted transition.

Modeling of ion permeation in calcium and sodium channel selectivity filters

Structure-function studies have shown that it is possible to convert a sodium channel to a calcium-selective channel by a single amino acid substitution in the selectivity filter locus. Ion permeation through the "model selectivity filter" was modeled with a reduced set of functional groups representative of the constituent amino acid side chains. Force-field minimizations were conducted to obtain the energy profile of the cations as they get desolvated and bind to the "model selectivity filter." The calculations suggest that the ion selectivity in the calcium channel is due to preferential binding, whereas in the sodium channel it is due to exclusion. Energetics of displacement of a bound cation from the calcium "model selectivity filter" by another cation suggest that "multi-ion mechanism" reduces the activation barrier for ion permeation. Thus, the simple model captures qualitatively most of the conduction characteristics of sodium and calcium channels. However, the computed barriers for permeation are fairly large, suggesting that ion interaction with additional residues along the transport path may be essential to effect desolvation.

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants. The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues. Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.

Accelerated diffusion of Na+ in a hydrophobic region revealed by molecular dynamics simulations of a synthetic ion channel

To get insight into the significance of the hydrophobic lining on the ion permeation, we performed molecular dynamics simulations on a Na(+) permeation through a de novo synthetic hydrophobic channel. Electrophysiological study has suggested that the channel is formed from a tail-to-tail associated dimer of a cyclic octa-peptide coupled with hydrophobic acyl chains. The acyl chains line the channel pore while the cyclic peptide forms the channel entrance [Z. Qi, M. Sokabe, K. Donowaki, H. Ishida, Biophys. J. 76 (1999) 631]. Molecular dynamics simulation of water in the channel indicated that the inferred structure is physically reasonable [Z. Qi, M. Sokabe, Biophys. Chem. 71 (1998) 35]. In the present study, the potential energy profile of the Na(+) and the energy contributions from each component of the system at different positions along the channel axis were calculated. An energy well instead of a peak is located at the central hydrophobic cavity of the channel, due to its ability of accommodating at least five water molecules to hydrate the ion. Interestingly, the ion diffuses much faster in the hydrophobic acyl chain region, particularly in the central hydrophobic cavity, than it does in the peptide ring region and even surprisingly faster than that in the bulk phase. These results provide a physical basis for an idea that the hydrophobic lining of the K(+) channel [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, Science 280 (1998) 69] plays an active role to facilitate the ion permeation through the channel pore.