Steered Molecular Dynamics Simulations of Na+ Permeation across the Gramicidin A Channel

Interactions and Transport of a Bioconjugated Peptide Targeting the Mitomembrane

The Szeto-Schiller (SS) peptides are a subclass of cell-penetrating peptides that can specifically target mitochondria and mediate conditions caused by mitochondrial dysfunction. In this work, we constructed an iron-chelating SS peptide and studied its interaction with a mitochondrial-mimicking membrane using atomistic molecular dynamics (MD) simulations. We report that the peptide/membrane interaction is thermodynamically favorable, and the localization of the peptide to the membrane is driven by electrostatic interactions between the cationic residues and the anionic phospholipid headgroups. The insertion of the peptide into the membrane is driven by hydrophobic interactions between the aromatic side chains in the peptide and the lipid acyl tails. We also probed the translocation of the peptide across the membrane by applying nonequilibrium steered MD simulations and resolved the translocation pathway, free energy profile, and metastable states. We explored four distinct orientations of the peptide along the translocation pathway and found that one orientation was energetically more favorable than the other orientations. We tested a significantly slower pulling velocity on the most thermodynamically favorable system and compared metastable states during peptide translocation. We found that the peptide can optimize hydrophobic interactions with the membrane by having aromatic side chains interacting with the lipid acyl tails instead of forming π-π interactions with each other. The mechanistic insights emerging from our work will potentially facilitate improved peptide design with enhanced activity.

Molecular properties of Ca2+ transport through TRPV2 channel: a molecular dynamics simulations study

TRPV channels are a category of nonselective cation channels that are activated by heat and ligands and permeate monovalent and divalent ions. The mechanism of Ca2+ transfer through TRPV2 channel is not well known. Here, we investigated the reaction coordination and energy fluctuation of Ca2+ transition in TRPV2 channel by steered molecular dynamics (SMD) simulations and potential of mean force (PMF) calculation. Results showed that electrostatic interactions between Ca2+ and residues of the first and second gates had main roles in ions transfer through the channel. Also, we recognized important amino acids in this path. Moreover, results indicated that enter and exit of calcium ions need to overcome barrier energies in the first and second gates.Communicated by Ramaswamy H. Sarma.

Predicting Ion Channel Conductance via Dissipation-Corrected Targeted Molecular Dynamics and Langevin Equation Simulations

Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, here we applied dissipation-corrected targeted molecular dynamics in combination with Langevin equation simulations to potassium diffusion through the gramicidin A channel as a test system. Performing a nonequilibrium principal component analysis on backbone dihedral angles, we find coupled protein-ion dynamics to occur during ion transfer. The dissipation-corrected free energy profiles correspond well to predictions from other biased simulation methods. The incorporation of an external electric field in Langevin simulations enables the prediction of macroscopic observables in the form of I-V characteristics.

The penetration of human defensin 5 (HD5) through bacterial outer membrane: simulation studies

Human α-defensin 5 (HD5) is one of cationic antimicrobial peptides which plays a crucial role in an innate immune system in human body. HD5 shows the killing activity against a broad spectrum of pathogenic bacteria by making a pore in a bacterial membrane and penetrating into a cytosol. Nonetheless, its pore-forming mechanisms remain unclear. Thus, in this work, the constant-velocity steered molecular dynamics (SMD) simulation was used to simulate the permeation of a dimeric HD5 into a gram-negative lipopolysaccharide (LPS) membrane model. Arginine-rich HD5 is found to strongly interact with a LPS surface. Upon arrival, arginines on HD5 interact with lipid A head groups (a top part of LPS) and then drag these charged moieties down into a hydrophobic core resulting in the formation of water-filled pore. Although all arginines are found to interact with a membrane, Arg13 and Arg32 appear to play a dominant role in the HD5 adsorption on a gram-negative membrane. Furthermore, one chain of a dimeric HD5 is required for HD5 adhesion. The interactions of arginine-lipid A head groups play a major role in adhering a cationic HD5 on a membrane surface and retarding a HD5 passage in the meantime.

Study on the Assembly Mechanisms and Transport Properties of Transmembrane End-Charged Cyclic Peptide Nanotubes

In this work, two end-charged cyclic peptide nanotubes (CPNTs) embedded in 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) were designed to simulate transmembrane ion channels. Density functional theory (DFT) computations at the level of M06-2X/6-31G give different assembling modes of the negatively charged ELWL-CPNT and positively charged RLWL-CPNT as (L-L)(D-L)(D-D)(L-L)(D-D)(L-L)(D-D) and (D-D)(L-L)(D-D)(L-L)(D-D)(L-L)(D-D), respectively. Molecular dynamics (MD) simulations indicate that a charge at a CPNT end obviously affects the structure of the channel water chain and the diffusion behavior of K⁺. The regions with the highest probability of H-bond defects in the channel water chains are gap5 and gap2 in ELWL/POPE-CPNT and RLWL/POPE-CPNT, respectively. K⁺ can easily enter either CPNT by desolvation, and behaves more actively in RLWL/POPE-CPNT, shuttling rapidly and frequently between an α-plane zone and an adjacent midplane region. Results of this work reveal that a charge at the end of an ionic channel may significantly alter the transport characteristics of the channel.

Deciphering the Structure of the Gramicidin A Channel in the Presence of AOT Reverse Micelles in Pentane Using Molecular Dynamics Simulations

Structural studies of proteins and, in particular, integral membrane proteins (IMPs) using solution NMR spectroscopy approaches are challenging due to not only their inherent structural complexities but also the fact that they need to be solubilized in biomimetic environments (such as micelles), which enhances the slow molecular reorientation. To deal with these difficulties and increase the effective rate of molecular reorientation, the encapsulation of IMPs in the aqueous core of the reverse micelle (RM) dissolved in a low-viscosity solvent has been proven to be a viable approach. However, the effect of the reverse micelle (RM) environment on the IMP structure and function is little known. To gain insight into these aspects, this article presents a series of atomistic unconstrained molecular dynamics (MD) of a model ion channel (gramicidin A, gA) with RMs formed with anionic surfactant diacyl chain bis(2-ethylhexyl) sodium succinate (AOT) in pentane at a water-to-surfactant molar ratio (W₀) of 6. The simulations were carried out with different protocols and starting conditions for a total of 2.4 μs and were compared with other MDs used with the gA channel inserted in models of the SDS micelle or the DMPC membrane. We show here that in the presence of AOT RMs the gA dimer did not look like the "dumbbell-like" model anticipated by experiments, where the C-terminal parts of the gA are capped with two RMs and the rest of the dimer is protected from the oil solvent by the AOT acyl chains. In contrast, the MD simulations reveal that the AOT, Na⁺, and water formed two well-defined and elongated RMs attached to the C-terminal ends of the gA dimer, while the rest is in direct contact with the pentane. The initial β^6.3 secondary structure of the gA is well conserved and filled with 6-9 waters, as in SDS micelles or the DMPC membrane. Finally, the water movement inside the gA is strongly affected by the presence of RMs at each extremity, and no passage of water molecules through the gA channel is observed even after a long simulation period, whereas the opposite was found for gA in SDS and DMPC.

The Role of Structural Polymorphism in Driving the Mechanical Performance of the Alzheimer's Beta Amyloid Fibrils

Alzheimer's Disease (AD) is related with the abnormal aggregation of amyloid β-peptides Aβ₁₋₄₀ and Aβ₁₋₄₂, the latter having a polymorphic character which gives rise to U- or S-shaped fibrils. Elucidating the role played by the nanoscale-material architecture on the amyloid fibril stability is a crucial breakthrough to better understand the pathological nature of amyloid structures and to support the rational design of bio-inspired materials. The computational study here presented highlights the superior mechanical behavior of the S-architecture, characterized by a Young's modulus markedly higher than the U-shaped architecture. The S-architecture showed a higher mechanical resistance to the enforced deformation along the fibril axis, consequence of a better interchain hydrogen bonds' distribution. In conclusion, this study, focusing the attention on the pivotal multiscale relationship between molecular phenomena and material properties, suggests the S-shaped Aβ₁₋₄₂ species as a target of election in computational screen/design/optimization of effective aggregation modulators.

A Polarizable Atomic Multipole-Based Force Field for Molecular Dynamics Simulations of Anionic Lipids

In all of the classical force fields, electrostatic interaction is simply treated and explicit electronic polarizability is neglected. The condensed-phase polarization, relative to the gas-phase charge distributions, is commonly accounted for in an average way by increasing the atomic charges, which remain fixed throughout simulations. Based on the lipid polarizable force field DMPC and following the same framework as Atomic Multipole Optimized Energetics for BiomoleculAr (AMOEBA) simulation, the present effort expands the force field to new anionic lipid models, in which the new lipids contain DMPG and POPS. The parameters are compatible with the AMOEBA force field, which includes water, ions, proteins, etc. The charge distribution of each atom is represented by the permanent atomic monopole, dipole and quadrupole moments, which are derived from the ab initio gas phase calculations. Many-body polarization including the inter- and intramolecular polarization is modeled in a consistent manner with distributed atomic polarizabilities. Molecular dynamics simulations of the two aqueous DMPG and POPS membrane bilayer systems, consisting of 72 lipids with water molecules, were then carried out to validate the force field parameters. Membrane width, area per lipid, volume per lipid, deuterium order parameters, electron density profile, electrostatic potential difference between the center of the bilayer and water are all calculated, and compared with limited experimental data.

Toward high permeability, selectivity and controllability of water desalination with FePc nanopores

Efficient and controllable water desalination with a nanoporous 2D Fe phthalocyanine (FePc) membrane was demonstrated by molecular dynamics simulations.

Exploration of Protein Conformational Change with PELE and Meta-Dynamics

Atomistic molecular simulation methods are now able to explore complex protein or protein-ligand dynamical space in a tractable way with methods such as meta-dynamics or adaptive biasing force. However, many of these methods either require a careful selection of reaction coordinates or the knowledge of an initial pathway of some kind. Thus, it is important that effective methods are developed to produce this pathway data in an efficient fashion. PELE, a proven protein-ligand sampling code, has been developed to provide rapid protein sampling in highly flexible cases, using a reduced network model eigen problem approach. The resulting method is able to rapidly sample configuration space with very general driving information. When applied to ubiquitin, PELE was able to reproduce RMSD and average force data found in molecular dynamics simulations. PELE was also applied to explore the opening/closing transition of T4 lysozyme. A meta-dynamics exploration using a low energy pathway validated that the configurations explored by PELE represent the most populated regions of phase space. PELE and meta-dynamics explorations also discovered a low free energy region where a large cross-domain helix of T4 lysozyme is broken in two. There is previous NMR evidence for the validity of this unfolded helix region.

Transfer of the K+ cation across a water/dichloromethane interface: a steered molecular dynamics study with implications in cation extraction

In this paper we report the characterization of the dichloromethane (DCM)/water interface in terms of density profile, width, and surface structure. The use of steered molecular dynamics (SMD) to study the transfer of the K(+) cation from the organic layer to the water layer is also described. The corresponding free energy is in semiquantitative agreement with published experimental and theoretical results. The transference of the K(+) cation from the water layer toward the DCM layer occurs with concomitant water transport as a water microdroplet that detaches itself from the water layer after ca. 16 Å of penetration into the organic layer by breaking the thin water thread that unites both. Complexation of the water microdroplet by a polyethylene-glycol type podand induces the loss of water molecules from the water microdroplet to bulk DCM and, eventually, to the water layer.

A High-Throughput Steered Molecular Dynamics Study on the Free Energy Profile of Ion Permeation through Gramicidin A

Steered molecular dynamics (SMD) simulations for the calculation of free energies are well suited for high-throughput molecular simulations on a distributed infrastructure due to the simplicity of the setup and parallel granularity of the runs. However, so far, the computational cost limited the estimation of the free energy typically over just a few pullings, thus impeding the evaluation of statistical uncertainties involved. In this work, we performed two thousand pulls for the permeation of a potassium ion in the gramicidin A pore by all-atom molecular dynamics in order to assess the bidirectional SMD protocol with a proper amount of sampling. The estimated free energy profile still shows a statistical error of several kcal/mol, while the work distributions are estimated to be non-Gaussian at pulling speeds of 10 Å/ns. We discuss the methodology and the confidence intervals in relation to increasing amounts of computed trajectories and how different permeation pathways for the potassium ion, knock-on and sideways, affect the sampling and the free energy estimation.

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.

Higher susceptibility to halothane modulation in open- than in closed-channel alpha4beta2 nAChR revealed by molecular dynamics simulations

The neuronal alpha4beta2 nicotinic acetylcholine receptor (nAChR) is a potential molecular target for general anesthetics. It is unclear, however, whether anesthetic action produces the same effect on the open and closed channels. Computations parallel to our previous open channel study (J. Phys. Chem. B 2009, 113, 12581) were performed on the closed-channel alpha4beta2 nAChR to investigate the conformation-dependent anesthetic effects on channel structures and dynamics. Flexible ligand docking and over 20 ns molecular dynamics simulations revealed similar halothane-binding sites in the closed and open channels. The sites with relatively high binding affinities (approximately -6.0 kcal/mol) were identified at the interface of extracellular (EC) and transmembrane (TM) domains or at the interface between alpha4 and beta2 subunits. Despite similar sites for halothane binding, the closed-channel conformation showed much less sensitivity than the open channel to the structural and dynamical perturbations from halothane. Compared to the systems without anesthetics, the amount of water inside the pore decreased by 22% in the presence of halothane in the open channel but only by 6% in the closed channel. Comparison of the nonbonded interactions at the EC/TM interfaces suggested that the beta2 subunits were more prone than the alpha4 subunits to halothane binding. In addition, our data support the notion that halothane exerts its effect by disturbing the quaternary structure and dynamics of the channel. The study concludes that sensitivity and global dynamics responsiveness of alpha4beta2 nAChR to halothane are conformation dependent. The effect of halothane on the global dynamics of the open-channel conformation might also account for the action of other inhaled general anesthetics.

Reconstructing potentials of mean force from short steered molecular dynamics simulations of Vpu from HIV-1

Vpu from human immunodeficiency virus type-1 (HIV-1) is an 81 amino acid type I integral membrane protein. Vpu forms ion conducting homooligomeric assemblies. To assess the energy landscape of an ion traversing the channel or pore single ion potentials of mean force (PMF) are reconstructed from short (1.2 ns) steered molecular dynamics (SMD) simulations using the Langevin equation of motion. For the simulations a section of the first 32 amino acids including the transmembrane domain of the Vpu protein is used. The values for the friction coefficient are estimated as a function of time using the velocity autocorrelation method. The PMFs of K(+), Na(+), and C(-) adopt a wave like pattern with a maximum around the hydrophobic stretch of the pore and a minimum at the hydrophilic site (C terminus). Independent of the pore size the amplitude of the PMF of at least one cation is always the lowest.

Molecular simulation of ion transport in silica nanopores

Ion distribution and transport of KCl aqueous solutions at the junction of hydrophobic and hydrophilic regions inside silica nanopores were studied by using two kinds of molecular simulation: grand canonical Monte Carlo (GCMC) simulations and nonequilibrium molecular dynamics (NEMD) simulations. The nanopores were 2 nm diameter silica pores in which surface functional groups, -SiOH, had been modified by hydrophobic surface functional groups, -SiCH(3), within three different lengths along the pore direction (z-direction), L(z0) = 0, 2, and 4 nm. If L(z0) is long enough, water could not enter the hydrophobic region, but for all L(z0) studied here, water entered the hydrophobic region. When an external electric field was applied along the z-direction, ions could not pass through the hydrophobic region when the external electric field was less than a threshold level, E(0), whereas the ionic current increased relatively linearly with increasing electric field strength above E(0). In 2 nm diameter fluidic pores, the electrical potential barrier appeared at the junction between the hydrophilic and hydrophobic regions due to the difference in dipole moment of the surface functional groups, although the overall surface charge of the pore was neutral. This junction formed an electrical potential threshold, and the ionic current could be modulated by adjusting the external electric field.

Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations

Alkali (Li(+), Na(+), K(+), Rb(+), and Cs(+)) and halide (F(-), Cl(-), Br(-), and I(-)) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Aqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4P EW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.

Four-alpha-helix bundle with designed anesthetic binding pockets. Part II: halothane effects on structure and dynamics

As a model of the protein targets for volatile anesthetics, the dimeric four-alpha-helix bundle, (Aalpha(2)-L1M/L38M)(2), was designed to contain a long hydrophobic core, enclosed by four amphipathic alpha-helices, for specific anesthetic binding. The structural and dynamical analyses of (Aalpha(2)-L1M/L38M)(2) in the absence of anesthetics (another study) showed a highly dynamic antiparallel dimer with an asymmetric arrangement of the four helices and a lateral accessing pathway from the aqueous phase to the hydrophobic core. In this study, we determined the high-resolution NMR structure of (Aalpha(2)-L1M/L38M)(2) in the presence of halothane, a clinically used volatile anesthetic. The high-solution NMR structure, with a backbone root mean-square deviation of 1.72 A (2JST), and the NMR binding measurements revealed that the primary halothane binding site is located between two side-chains of W15 from each monomer, different from the initially designed anesthetic binding sites. Hydrophobic interactions with residues A44 and L18 also contribute to stabilizing the bound halothane. Whereas halothane produces minor changes in the monomer structure, the quaternary arrangement of the dimer is shifted by about half a helical turn and twists relative to each other, which leads to the closure of the lateral access pathway to the hydrophobic core. Quantitative dynamics analyses, including Modelfree analysis of the relaxation data and the Carr-Purcell-Meiboom-Gill transverse relaxation dispersion measurements, suggest that the most profound anesthetic effect is the suppression of the conformational exchange both near and remote from the binding site. Our results revealed a novel mechanism of an induced fit between anesthetic molecule and its protein target, with the direct consequence of protein dynamics changing on a global rather than a local scale. This mechanism may be universal to anesthetic action on neuronal proteins.

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.

1-Alkanols and membranes: a story of attraction

Although 1-alkanols have long been known to act as penetration enhancers and anesthetics, the mode of operation is not yet understood. In this study, long-time molecular dynamics simulations have been performed to investigate the effect of 1-alkanols of various carbon chain lengths onto the structure and dynamics of dimyristoylphosphatidylcholine bilayers. The simulations were complemented by microcalorimetry, continuous bleaching and film balance experiments. In the simulations, all investigated 1-alkanols assembled inside the lipid bilayer within tens of nanoseconds. Their hydroxyl groups bound preferentially to the lipid carbonyl group and the hydrocarbon chains stretched into the hydrophobic core of the bilayer. Both molecular dynamics simulations and experiments showed that all 1-alkanols drastically affected the bilayer properties. Insertion of long-chain 1-alkanols decreased the area per lipid while increasing the thickness of the bilayer and the order of the lipids. The bilayer elasticity was reduced and the diffusive motion of the lipids within the bilayer plane was suppressed. On the other hand, integration of ethanol into the bilayer enlarged the area per lipid. The bilayer became softer and lipid diffusion was enhanced.

Steered Molecular Dynamics Studies of the Potential of Mean Force of a Na+ or K+ Ion in a Cyclic Peptide Nanotube

Potential of mean force (PMF) profiles of a single Na+ or K+ ion passing through a cyclic peptide nanotube, cyclo[-(D-Ala-Glu-D-Ala-Gln)2-], in water are calculated to provide insight into ion transport and to understand the conductance difference between these two ions. The PMF profiles are obtained by performing steered molecular dynamics (SMD) simulations that are based on the Jarzynski equality. The computed PMF profiles for both ions show barriers of around 2.4 kcal/mol at the channel entrances and exits and energy wells in the middle of the tube. The energy barriers, so-called dielectric energy barriers, arise due to the desolvation of water molecules when ions move across the nanotube, and the energy wells appear as a result of attractive interactions between the cations and negatively charged carbonyl oxygens on the backbone of the tube. We find more and deeper energy wells in the PMF profile for Na+ than for K+, which suggests that Na+ ions have a longer residence time inside the nanotube and that permeation of Na+ ions is reduced compared to K+ ions. Calculations of the radial distribution functions (RDF) between the ions and oxygens in the water molecules and in carbonyl groups on the tube and an investigation of the orientations of the carbonyl groups show that, in contrast with the dynamic carbonyl groups observed in the selectivity filter of the KcsA ion channel, the carbonyl groups in the cyclic peptide nanotube are relatively rigid, with only slight reorientation of the carbonyl groups as the cations pass through. The rigidity of the carbonyl groups in the cyclic peptide nanotube can be attributed to their role in hydrogen bonding, which is responsible for the tube structure. Comparison of the PMF profiles with the electrostatic energy profiles calculated from the Poisson-Boltzmann (PB) equation, a dielectric continuum model, reveals that the dielectric continuum model breaks down in the confined region within the tube that governs ion transport.

Free-energy reconstruction from experiments performed under different biasing programs

Recently developed nonequilibrium statistical physics relationships, including Jarzynski's equality and the Crooks fluctuation theorem, have been used to calculate equilibrium thermodynamic properties using data from both laboratory and computational experiments. Although Jarzynski's derivation does not include an explicit time dependency, prior work utilizing the relationship to reconstruct free-energy surfaces has combined data from experiments performed under identical conditions. Here, a formalism is developed for combining data from a variety of biasing protocols, as in dynamic force spectroscopy experiments. The method is then demonstrated on data from simulations conducted under a wide range of pulling velocities and with a random biasing protocol.