Energetics of ion permeation, rejection, binding, and block in gramicidin A from free energy simulations

Thermodynamics of Transition Metal Ion Binding to Proteins

Modeling the thermodynamics of a transition metal (TM) ion assembly be it in proteins or in coordination complexes affords us a better understanding of the assembly and function of metalloclusters in diverse application areas including metal organic framework design, TM-based catalyst design, the trafficking of TM ions in biological systems, and drug design in metalloprotein platforms. While the structural details of TM ions bound to metalloproteins are generally well understood via experimental and computational approaches, accurate studies describing the thermodynamics of TM ion binding are rare. Herein, we demonstrate that we can obtain accurate structural and absolute binding free energies of Co²⁺ and Ni²⁺ to the enzyme glyoxalase I using an optimized 12-6-4 (m12-6-4) potential. Critically, this model simultaneously reproduces the solvation free energy of the individual TM ions and reproduces the thermodynamics of TM ion-ligand coordination as well as the thermodynamics of TM ion binding to a protein active site unlike extant models. We find the incorporation of the thermodynamics associated with protonation state changes for the TM ion (un)binding to be crucial. The high accuracy of m12-6-4 potential in this study presents an accurate route to explore more complicated processes associated with TM cluster assembly and TM ion transport.

Molecular mechanisms of pore formation and membrane disruption by the antimicrobial lantibiotic peptide Mutacin 1140

The emergence of antibiotic-resistance is a major concern to global human health and identification of novel antibiotics is critical to mitigate the threat.

Study on the Application of the Combination of TMD Simulation and Umbrella Sampling in PMF Calculation for Molecular Conformational Transitions

Free energy calculations of the potential of mean force (PMF) based on the combination of targeted molecular dynamics (TMD) simulations and umbrella samplings as a function of physical coordinates have been applied to explore the detailed pathways and the corresponding free energy profiles for the conformational transition processes of the butane molecule and the 35-residue villin headpiece subdomain (HP35). The accurate PMF profiles for describing the dihedral rotation of butane under both coordinates of dihedral rotation and root mean square deviation (RMSD) variation were obtained based on the different umbrella samplings from the same TMD simulations. The initial structures for the umbrella samplings can be conveniently selected from the TMD trajectories. For the application of this computational method in the unfolding process of the HP35 protein, the PMF calculation along with the coordinate of the radius of gyration (R_g) presents the gradual increase of free energies by about 1 kcal/mol with the energy fluctuations. The feature of conformational transition for the unfolding process of the HP35 protein shows that the spherical structure extends and the middle α-helix unfolds firstly, followed by the unfolding of other α-helices. The computational method for the PMF calculations based on the combination of TMD simulations and umbrella samplings provided a valuable strategy in investigating detailed conformational transition pathways for other allosteric processes.

Computational Investigation of the Effect of Lipid Membranes on Ion Permeation in Gramicidin A

Membrane proteins are embedded in a lipid bilayer and interact with the lipid molecules in subtle ways. This can be studied experimentally by examining the effect of different lipid bilayers on the function of membrane proteins. Understanding the causes of the functional effects of lipids is difficult to dissect experimentally but more amenable to a computational approach. Here we perform molecular dynamics simulations and free energy calculations to study the effect of two lipid types (POPC and NODS) on the conductance of the gramicidin A (gA) channel. A larger energy barrier is found for the K⁺ potential of mean force in gA embedded in POPC compared to that in NODS, which is consistent with the enhanced experimental conductance of cations in gA embedded in NODS. Further analysis of the contributions to the potential energy of K⁺ reveals that gA and water molecules in gA make similar contributions in both bilayers but there are significant differences between the two bilayers when the lipid molecules and interfacial waters are considered. It is shown that the stronger dipole moments of the POPC head groups create a thicker layer of interfacial waters with better orientation, which ultimately is responsible for the larger energy barrier in the K⁺ PMF in POPC.

Force fields for simulating the interaction of surfaces with biological molecules

The interaction of biomolecules with solid interfaces is of fundamental importance to several emerging biotechnologies such as medical implants, anti-fouling coatings and novel diagnostic devices. Many of these technologies rely on the binding of peptides to a solid surface, but a full understanding of the mechanism of binding, as well as the effect on the conformation of adsorbed peptides, is beyond the resolution of current experimental techniques. Nanoscale simulations using molecular mechanics offer potential insights into these processes. However, most models at this scale have been developed for aqueous peptide and protein simulation, and there are no proven models for describing biointerfaces. In this review, we detail the current research towards developing a non-polarizable molecular model for peptide-surface interactions, with a particular focus on fitting the model parameters as well as validation by choice of appropriate experimental data.

Mechanism of Ion Permeation in Mammalian Voltage-Gated Sodium Channels

Recent determination of the crystal structures of bacterial voltage-gated sodium (NaV) channels have raised hopes that modeling of the mammalian counterparts could soon be achieved. However, there are substantial differences between the pore domains of the bacterial and mammalian NaV channels, which necessitates careful validation of mammalian homology models constructed from the bacterial NaV structures. Such a validated homology model for the NaV1.4 channel was constructed recently using the extensive mutagenesis data available for binding of μ-conotoxins. Here we use this NaV1.4 model to study the ion permeation mechanism in mammalian NaV channels. Linking of the DEKA residues in the selectivity filter with residues in the neighboring domains is found to be important for keeping the permeation pathway open. Molecular dynamics simulations and potential of mean force calculations reveal that there is a binding site for a Na+ ion just inside the DEKA locus, and 1-2 Na+ ions can occupy the vestibule near the EEDD ring. These sites are separated by a low free energy barrier, suggesting that inward conduction occurs when a Na+ ion in the vestibule goes over the free energy barrier and pushes the Na+ ion in the filter to the intracellular cavity, consistent with the classical knock-on mechanism. The NaV1.4 model also provides a good description of the observed Na+/K+ selectivity.

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.

New Insights into the Molecular Mechanism of E-Cadherin-Mediated Cell Adhesion by Free Energy Calculations

Three-dimensional domain swapping is an important mode of protein association leading to the formation of stable dimers. Monomers associating via this mechanism mutually exchange a domain to form a homodimer. Classical cadherins, an increasingly important target for anticancer therapy, use domain swapping to mediate cell adhesion. However, despite its importance, the molecular mechanism of domain swapping is still debated. Here, we study the conformational changes that lead to activation and dimerization via domain swapping of E-cadherin. Using state-of-the-art enhanced sampling atomistic simulations, we reconstruct its conformational free energy landscape, obtaining the free energy profile connecting the inactive and active form. Our simulations predict that the E-cadherin monomer populates the open and closed forms almost equally, which is in agreement with the proposed "selected fit" mechanism in which monomers in an active conformational state bind to form a homodimer, analogous to the conformational selection mechanism often observed in ligand-target binding. Moreover, we find that the open state population is increased in the presence of calcium ions at the extracellular boundary, suggesting their possible role as allosteric activators of the conformational change.

Systematic study of binding of μ-conotoxins to the sodium channel NaV1.4

Voltage-gated sodium channels (NaV) are fundamental components of the nervous system. Their dysfunction is implicated in a number of neurological disorders, such as chronic pain, making them potential targets for the treatment of such disorders. The prominence of the NaV channels in the nervous system has been exploited by venomous animals for preying purposes, which have developed toxins that can block the NaV channels, thereby disabling their function. Because of their potency, such toxins could provide drug leads for the treatment of neurological disorders associated with NaV channels. However, most toxins lack selectivity for a given target NaV channel, and improving their selectivity profile among the NaV1 isoforms is essential for their development as drug leads. Computational methods will be very useful in the solution of such design problems, provided accurate models of the protein-ligand complex can be constructed. Using docking and molecular dynamics simulations, we have recently constructed a model for the NaV1.4-μ-conotoxin-GIIIA complex and validated it with the ample mutational data available for this complex. Here, we use the validated NaV1.4 model in a systematic study of binding other μ-conotoxins (PIIIA, KIIIA and BuIIIB) to NaV1.4. The binding mode obtained for each complex is shown to be consistent with the available mutation data and binding constants. We compare the binding modes of PIIIA, KIIIA and BuIIIB to that of GIIIA and point out the similarities and differences among them. The detailed information about NaV1.4-μ-conotoxin interactions provided here will be useful in the design of new NaV channel blocking peptides.

Molecular dynamics study of binding of µ-conotoxin GIIIA to the voltage-gated sodium channel Na(v)1.4

Homology models of mammalian voltage-gated sodium (NaV) channels based on the crystal structures of the bacterial counterparts are needed to interpret the functional data on sodium channels and understand how they operate. Such models would also be invaluable in structure-based design of therapeutics for diseases involving sodium channels such as chronic pain and heart diseases. Here we construct a homology model for the pore domain of the NaV1.4 channel and use the functional data for the binding of µ-conotoxin GIIIA to NaV1.4 to validate the model. The initial poses for the NaV1.4-GIIIA complex are obtained using the HADDOCK protein docking program, which are then refined in molecular dynamics simulations. The binding mode for the final complex is shown to be in broad agreement with the available mutagenesis data. The standard binding free energy, determined from the potential of mean force calculations, is also in good agreement with the experimental value. Because the pore domains of NaV1 channels are highly homologous, the model constructed for NaV1.4 will provide an excellent template for other NaV1 channels.

Density-functional theory study of gramicidin A ion channel geometry and electronic properties

Understanding the mechanisms underlying ion channel function from the atomic-scale requires accurate ab initio modelling as well as careful experiments. Here, we present a density functional theory (DFT) study of the ion channel gramicidin A (gA), whose inner pore conducts only monovalent cations and whose conductance has been shown to depend on the side chains of the amino acids in the channel. We investigate the ground state geometry and electronic properties of the channel in vacuum, focusing on their dependence on the side chains of the amino acids. We find that the side chains affect the ground state geometry, while the electrostatic potential of the pore is independent of the side chains. This study is also in preparation for a full, linear scaling DFT study of gA in a lipid bilayer with surrounding water. We demonstrate that linear scaling DFT methods can accurately model the system with reasonable computational cost. Linear scaling DFT allows ab initio calculations with 10,000-100,000 atoms and beyond, and will be an important new tool for biomolecular simulations.

Investigation of polarization effects in the gramicidin A channel from ab initio molecular dynamics simulations

Polarization is an important component of molecular interactions and is expected to play a particularly significant role in inhomogeneous environments such as pores and interfaces. Here we investigate the effects of polarization in the gramicidin A ion channel by performing quantum mechanics/molecular mechanics molecular dynamics (MD) simulations and comparing the results with those obtained from classical MD simulations with non-polarizable force fields. We consider the dipole moments of backbone carbonyl groups and channel water molecules as well as a number of structural quantities of interest. The ab initio results show that the dipole moments of the carbonyl groups and water molecules are highly sensitive to the hydrogen bonds (H-bonds) they participate in. In the absence of a K(+) ion, water molecules in the channel are quite mobile, making the H-bond network highly dynamic. A central K(+) ion acts as an anchor for the channel waters, stabilizing the H-bond network and thereby increasing their average dipole moments. In contrast, the K(+) ion has little effect on the dipole moments of the neighboring carbonyl groups. The weakness of the ion-peptide interactions helps to explain the near diffusion-rate conductance of K(+) ions through the channel. We also address the sampling issue in relatively short ab initio MD simulations. Results obtained from a continuous 20 ps ab initio MD simulation are compared with those generated by sampling ten windows from a much longer classical MD simulation and running each window for 2 ps with ab initio MD. Both methods yield similar results for a number of quantities of interest, indicating that fluctuations are fast enough to justify the short ab initio MD simulations.

Computational studies of marine toxins targeting ion channels

Toxins from marine animals offer novel drug leads for treatment of diseases involving ion channels. Computational methods could be very helpful in this endeavour in several ways, e.g., (i) constructing accurate models of the channel-toxin complexes using docking and molecular dynamics (MD) simulations; (ii) determining the binding free energies of toxins from umbrella sampling MD simulations; (iii) predicting the effect of mutations from free energy MD simulations. Using these methods, one can design new analogs of toxins with improved affinity and selectivity properties. Here we present a review of the computational methods and discuss their applications to marine toxins targeting potassium and sodium channels. Detailed examples from the potassium channel toxins—ShK from sea anemone and κ-conotoxin PVIIA—are provided to demonstrate capabilities of the computational methods to give accurate descriptions of the channel-toxin complexes and the energetics of their binding. An example is also given from sodium channel toxins (µ-conotoxin GIIIA) to illustrate the differences between the toxin binding modes in potassium and sodium channels.

Molecular dynamics simulations of membrane proteins

Membrane proteins control the traffic across cell membranes and thereby play an essential role in cell function from transport of various solutes to immune response via molecular recognition. Because it is very difficult to determine the structures of membrane proteins experimentally, computational methods have been increasingly used to study their structure and function. Here we focus on two classes of membrane proteins-ion channels and transporters-which are responsible for the generation of action potentials in nerves, muscles, and other excitable cells. We describe how computational methods have been used to construct models for these proteins and to study the transport mechanism. The main computational tool is the molecular dynamics (MD) simulation, which can be used for everything from refinement of protein structures to free energy calculations of transport processes. We illustrate with specific examples from gramicidin and potassium channels and aspartate transporters how the function of these membrane proteins can be investigated using MD simulations.

Position of the third Na+ site in the aspartate transporter GltPh and the human glutamate transporter, EAAT1

Glutamate transport via the human excitatory amino acid transporters is coupled to the co-transport of three Na(+) ions, one H(+) and the counter-transport of one K(+) ion. Transport by an archaeal homologue of the human glutamate transporters, Glt(Ph), whose three dimensional structure is known is also coupled to three Na(+) ions but only two Na(+) ion binding sites have been observed in the crystal structure of Glt(Ph). In order to fully utilize the Glt(Ph) structure in functional studies of the human glutamate transporters, it is essential to understand the transport mechanism of Glt(Ph) and accurately determine the number and location of Na(+) ions coupled to transport. Several sites have been proposed for the binding of a third Na(+) ion from electrostatic calculations and molecular dynamics simulations. In this study, we have performed detailed free energy simulations for Glt(Ph) and reveal a new site for the third Na(+) ion involving the side chains of Threonine 92, Serine 93, Asparagine 310, Aspartate 312, and the backbone of Tyrosine 89. We have also studied the transport properties of alanine mutants of the coordinating residues Threonine 92 and Serine 93 in Glt(Ph), and the corresponding residues in a human glutamate transporter, EAAT1. The mutant transporters have reduced affinity for Na(+) compared to their wild type counterparts. These results confirm that Threonine 92 and Serine 93 are involved in the coordination of the third Na(+) ion in Glt(Ph) and EAAT1.

Free energy simulations of ligand binding to the aspartate transporter Glt(Ph)

Glutamate/Aspartate transporters cotransport three Na(+) and one H(+) ions with the substrate and countertransport one K(+) ion. The binding sites for the substrate and two Na(+) ions have been observed in the crystal structure of the archeal homolog Glt(Ph), while the binding site for the third Na(+) ion has been proposed from computational studies and confirmed by experiments. Here we perform detailed free energy simulations of Glt(Ph), giving a comprehensive characterization of the substrate and ion binding sites, and calculating their binding free energies in various configurations. Our results show unequivocally that the substrate binds after the binding of two Na(+) ions. They also shed light into Asp/Glu selectivity of Glt(Ph), which is not observed in eukaryotic glutamate transporters.

Comparative study of the energetics of ion permeation in Kv1.2 and KcsA potassium channels

Biological ion channels rely on a multi-ion transport mechanism for fast yet selective permeation of ions. The crystal structure of the KcsA potassium channel provided the first microscopic picture of this process. A similar mechanism is assumed to operate in all potassium channels, but the validity of this assumption has not been well investigated. Here, we examine the energetics of ion permeation in Shaker Kv1.2 and KcsA channels, which exemplify the six-transmembrane voltage-gated and two-transmembrane inward-rectifier channels. We study the feasibility of binding a third ion to the filter and the concerted motion of ions in the channel by constructing the potential of mean force for K(+) ions in various configurations. For both channels, we find that a pair of K(+) ions can move almost freely within the filter, but a relatively large free-energy barrier hinders the K(+) ion from stepping outside the filter. We discuss the effect of the CMAP dihedral energy correction that was recently incorporated into the CHARMM force field on ion permeation dynamics.

Proton transport in biological systems can be probed by two-dimensional infrared spectroscopy

We propose a new method to determine the proton transfer (PT) rate in channel proteins by two-dimensional infrared (2DIR) spectroscopy. Proton transport processes in biological systems, such as proton channels, trigger numerous fundamental biochemical reactions. Due to the limitation in both spatial and time resolution of the traditional experimental approaches, describing the whole proton transport process and identifying the rate limiting steps at the molecular level is challenging. In the present paper, we focus on proton transport through the Gramicidin A channel. Using a kinetic PT model derived from all-atom molecular dynamics simulations, we model the amide I region of the 2DIR spectrum of the channel protein to examine its sensitivity to the proton transport process. We demonstrate that the 2DIR spectrum of the isotope-labeled channel contain information on the PT rate, which may be extracted by analyzing the antidiagonal linewidth of the spectral feature related to the labeled site. Such experiments in combination with detailed numerical simulations should allow the extraction of site dependent PT rates, providing a method for identifying possible rate limiting steps for proton channel transfer.

The gramicidin channel ion permeation free-energy profile: direct and indirect effects of CHARMM force field improvements

A revised CHARMM force field for tryptophan residues is studied as well as a new grid-based correction algorithm, called CMAP, using molecular dynamics simulations of gramicidin A (1JNO) embedded in a lipid bilayer (DMPC) with 1 mol/kg NaCl or KCl saline solution. The conformational stability of the interfacial side chains is studied, which shows good stability on the 10 ns time scale. The revised force field for the tryptophan side chain produces, in the decomposition, a Na(+) PMF(Trp) profile that is consonant with the prediction from the experimental results, analyzed with rate theory by Durrant et al. (2006), but in stark contrast to the prediction of the original CHARMM force field, version 22. However, the effect is diluted in the PMF profile due to indirect effects mediated by other components of the system (polypeptide, lipid molecules, ions, and water molecules). CMAP corrections to the L-amino acids help reduce the excessive translocation barrier. Decomposition demonstrates that this effect is due to effects on the K(+) PMF(H(2)O) profile rather than on the K(+) PMF(gA) profile. The results have been confirmed to be robust using an alternative umbrella-potential method. Further force field balancing efforts (direct and indirect) are required for future studies to evaluate whether these effects give rise to predictions that are consistent with those observables extracted from real experiments.

Importance of the peptide backbone description in modeling the selectivity filter in potassium channels

A dihedral energy correction (CMAP) term has been recently included in the CHARMM force field to obtain a more accurate description of the peptide backbone. Its importance in improving dynamical properties of proteins and preserving their stability in long molecular-dynamics simulations has been established for several globular proteins. Here we investigate its role in maintaining the structure and function of two potassium channels, Shaker K(v)1.2 and KcsA, by performing molecular-dynamics simulations with and without the CMAP correction in otherwise identical systems. We show that without CMAP, it is not possible to maintain the experimentally observed orientations of the carbonyl groups in the selectivity filter in Shaker, and the channel loses its selectivity property. In the case of KcsA, the channel retains some selectivity even without CMAP because the carbonyl orientations are relatively better preserved compared to Shaker.

Computational studies of gramicidin permeation: an entry way sulfonate enhances cation occupancy at entry sites

The impact on the cation-transport free-energy profile of replacing the C-terminal ethanolamine in the gramicidin A channel with a taurine residue is studied using molecular dynamics simulations of gramicidin A (1JNO) embedded in a lipid bilayer (DMPC) with 1 mol/kg NaCl saline solution. The potential of mean force for ion transport is obtained by umbrella sampling. The presence of a negatively charged sulfonate group at the entrance of the gramicidin channel affects the depth and the location of the binding sites, producing a strong attraction for the cations in the bulk. The potential of mean force by the sulfonate acting directly through electrostatics and van der Waals interactions on the test ion is highly modulated by indirect effects (i.e., sulfonate effects on other components of the system that, in turn, affect the ion free-energy profile in the channel). Because the "entry" sites are located symmetrically at both entry and exit of the channel, the deeper free-energy wells should inhibit exit. Given that the channel has increased conductance experimentally, the simulation results suggest that the channel conductance is normally entry limited.

Potential of mean force calculations of ligand binding to ion channels from Jarzynski's equality and umbrella sampling

Potential of mean force (PMF) calculations provide a reliable method for determination of the absolute binding free energies for protein-ligand systems. The common method used for this purpose -- umbrella sampling with weighted histogram analysis -- is computationally very laborious, which limits its applications. Recently, a much simpler alternative for PMF calculations has become available, namely, using Jarzynski's equality in steered molecular dynamics simulations. So far, there have been a few comparisons of the two methods and mostly in simple systems that do not reflect the complexities of protein-ligand systems. Here, we use both methods to calculate the PMF for ion permeation and ligand binding to ion channels. Comparison of results indicate that Jarzynski's method suffers from relaxation problems in complex systems and would require much longer simulation times to yield reliable PMFs for protein-ligand systems.

Comment on "Free energy simulations of single and double ion occupancy in gramicidin A" [J. Chem. Phys. 126, 105103 (2007)]

In a recent article published by Bastug and Kuyucak [J. Chem. Phys.126, 105103 (2007)] investigated the microscopic factors affecting double ion occupancy in the gramicidin channel. The analysis relied largely on the one-dimensional potential of mean force of ions along the axis of the channel (the so-called free energy profile of the ion along the channel axis), as well as on the calculation of the equilibrium association constant of the ions in the channel binding sites. It is the purpose of this communication to clarify this issue.

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.

Electric field effects on membranes: Gramicidin A as a test ground

Electric fields due to transmembrane potential differences or ionic gradients across the membrane are presumably crucial for many reactions across membranes or close to membranes like signal transduction, control of ion channels or the generation of neural impulses. Molecular dynamics simulations have been used to study the influence of external electric fields on a mixed gramicidin/phospholipid bilayer system. At high field strengths, formation of membrane electropores occurred both close and distal to the gramicidin. Gramicidin was found to stabilize the membrane adjacent to the protein but also at larger distances of up to 2-3 nm. As a result, membrane pore formation was found to be significantly suppressed for the mixed gramicidin/DMPC system. Moderate field strengths only weakly affected the structure and dynamics of the gramicidin. Spontaneous potassium passage events in external electric fields were observed for both the head-to-head helical conformation as well as for the double helical conformation of gramicidin A. The double-helical conformation was found to facilitate ion passage compared to the head-to-head helical dimer.