Computational studies of the gramicidin channel

The Potential of Cyclodextrins as Inhibitors for the BM2 Protein: An In Silico Investigation

The influenza BM2 transmembrane domain (BM2TM), an acid-activated proton channel, is an attractive antiviral target due to its essential roles during influenza virus replication, whereas no effective inhibitors have been reported for BM2. In this study, we draw inspiration from the properties of cyclodextrins (CDs) and hypothesize that CDs of appropriate sizes may possess the potential to act as inhibitors of the BM2TM proton channel. To explore this possibility, molecular dynamics simulations were employed to assess their inhibitory capabilities. Our findings reveal that CD4, CD5, and CD6 are capable of binding to the BM2TM proton channel, resulting in disrupted water networks and reduced hydrogen bond occupancy between H19 and the solvent within the BM2TM channel necessary for proton conduction. Notably, CD4 completely obstructs the BM2TM water channel. Based on these observations, we propose that CD4, CD5, and CD6 individually contribute to diminishing the proton transfer efficiency of the BM2 protein, and CD4 demonstrates promising potential as an inhibitor for the BM2 proton channel.

Modern Alchemical Free Energy Methods for Drug Discovery Explained

This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.

Protein Motifs for Proton Transfers That Build the Transmembrane Proton Gradient

Biological membranes are barriers to polar molecules, so membrane embedded proteins control the transfers between cellular compartments. Protein controlled transport moves substrates and activates cellular signaling cascades. In addition, the electrochemical gradient across mitochondrial, bacterial and chloroplast membranes, is a key source of stored cellular energy. This is generated by electron, proton and ion transfers through proteins. The gradient is used to fuel ATP synthesis and to drive active transport. Here the mechanisms by which protons move into the buried active sites of Photosystem II (PSII), bacterial RCs (bRCs) and through the proton pumps, Bacteriorhodopsin (bR), Complex I and Cytochrome c oxidase (CcO), are reviewed. These proteins all use water filled proton transfer paths. The proton pumps, that move protons uphill from low to high concentration compartments, also utilize Proton Loading Sites (PLS), that transiently load and unload protons and gates, which block backflow of protons. PLS and gates should be synchronized so PLS proton affinity is high when the gate opens to the side with few protons and low when the path is open to the high concentration side. Proton transfer paths in the proteins we describe have different design features. Linear paths are seen with a unique entry and exit and a relatively straight path between them. Alternatively, paths can be complex with a tangle of possible routes. Likewise, PLS can be a single residue that changes protonation state or a cluster of residues with multiple charge and tautomer states.

Characterizing the Water Wire in the Gramicidin Channel Found by Monte Carlo Sampling Using Continuum Electrostatics and in Molecular Dynamics Trajectories with Conventional or Polarizable Force Fields

Water molecules play a key role in all biochemical processes. They help define the shape of proteins, and they are reactant or product in many reactions and are released as ligands are bound. They facilitate the transfer of protons through transmembrane proton channel, pump and transporter proteins. Continuum electrostatics (CE) force fields used by program Multiconformation CE (MCCE) capture electrostatic interactions in biomolecules with an implicit solvent, which captures the averaged solvent water equilibrium properties. Hybrid CE methods can use explicit water molecules within the protein surrounded by implicit solvent. These hybrid methods permit the study of explicit hydrogen bond networks within the protein and allow analysis of processes such as proton transfer reactions. Yet hybrid CE methods have not been rigorously tested. Here, we present an explicit treatment of water molecules in the Gramicidin A (gA) channel using MCCE and compare the resulting distributions of water molecules and key hydration features against those obtained with explicit solvent Molecular Dynamics (MD) simulations with the nonpolarizable CHARMM36 and polarizable Drude force fields. CHARMM36 leads to an aligned water wire in the channel characterized by a large absolute net water dipole moment; the MCCE and Drude analysis lead to a small net dipole moment as the water molecules change orientation within the channel. The correct orientation is not as yet known, so these calculations identify an open question.

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.

Bilayer thickness determines the alignment of model polyproline helices in lipid membranes

Our understanding of protein folds relies fundamentally on the set of secondary structures found in the proteomes. Yet, there also exist intriguing structures and motifs that are underrepresented in natural biopolymeric systems. One example is the polyproline II helix, which is usually considered to have a polar character and therefore does not form membrane spanning sections of membrane proteins. In our work, we have introduced specially designed polyproline II helices into the hydrophobic membrane milieu and used 19F NMR to monitor the helix alignment in oriented lipid bilayers. Our results show that these artificial hydrophobic peptides can adopt several different alignment states. If the helix is shorter than the thickness of the hydrophobic core of the membrane, it is submerged into the bilayer with its long axis parallel to the membrane plane. The polyproline helix adopts a transmembrane alignment when its length exceeds the bilayer thickness. If the peptide length roughly matches the lipid thickness, a coexistence of both states is observed. We thus show that the lipid thickness plays a determining role in the occurrence of a transmembrane polyproline II helix. We also found that the adaptation of polyproline II helices to hydrophobic mismatch is in some notable aspects different from α-helices. Finally, our results prove that the polyproline II helix is a competent structure for the construction of transmembrane peptide segments, despite the fact that no such motif has ever been reported in natural systems.

Artificial Gramicidins

Gramicidin A, gA is a natural protein channel with a well-established, simple structure, and function: cations and water are transported together along the channel. Importantly, the dipolar orientation of water molecules within the pore can influence the ionic translocation. The need for simple artificial systems biomimicking the gA functions has been desired and they were until last decade unknown. Several interesting papers highlighted in this minireview have been published and supramolecular systems described here can be considered as primitive gA mimics. The dynamics of ions/water and protons confined within gA channels is difficult to structurally analyze and simpler artificial systems designed at the atomic level would have a crucial relevance for understanding such translocation scenarios at the molecular level. The directional ordering of confined water-wires or ions, as observed inside primitive gA channels is reminiscent with specific interactions between water and the natural gA. This dipolar orientation may induce specific dielectric properties which most probably influence the biological recognition at bio-interfaces or translocation of charge species along artificial channel pathways.

Scaling Behavior of Ionic Transport in Membrane Nanochannels

Ionic conductance in membrane channels exhibits a power-law dependence on electrolyte concentration ( G ∼ c^α). The many scaling exponents, α, reported in the literature usually require detailed interpretations concerning each particular system under study. Here, we critically evaluate the predictive power of scaling exponents by analyzing conductance measurements in four biological channels with contrasting architectures. We show that scaling behavior depends on several interconnected effects whose contributions change with concentration so that the use of oversimplified models missing critical factors could be misleading. In fact, the presence of interfacial effects could give rise to an apparent universal scaling that hides the channel distinctive features. We complement our study with 3D structure-based Poisson-Nernst-Planck (PNP) calculations, giving results in line with experiments and validating scaling arguments. Our findings not only provide a unified framework for the study of ion transport in confined geometries but also highlight that scaling arguments are powerful and simple tools with which to offer a comprehensive perspective of complex systems, especially those in which the actual structure is unknown.

Trypsin-Ligand binding affinities calculated using an effective interaction entropy method under polarized force field

Molecular dynamics (MD) simulation in the explicit water is performed to study the interaction mechanism of trypsin-ligand binding under the AMBER force field and polarized protein-specific charge (PPC) force field combined the new developed highly efficient interaction entropy (IE) method for calculation of entropy change. And the detailed analysis and comparison of the results of MD simulation for two trypsin-ligand systems show that the root-mean-square deviation (RMSD) of backbone atoms, B-factor, intra-protein and protein-ligand hydrogen bonds are more stable under PPC force field than AMBER force field. Our results demonstrate that the IE method is superior than the traditional normal mode (Nmode) method in the calculation of entropy change and the calculated binding free energy under the PPC force field combined with the IE method is more close to the experimental value than other three combinations (AMBER-Nmode, AMBER-IE and PPC-Nmode). And three critical hydrogen bonds between trypsin and ligand are broken under AMBER force field. However, they are well preserved under PPC force field. Detailed binding interactions of ligands with trypsin are further analyzed. The present work demonstrates that the polarized force field combined the highly efficient IE method is critical in MD simulation and free energy calculation.

Classical Molecular Dynamics with Mobile Protons

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

Large-scale molecular dynamics simulation: Effect of polarization on thrombin-ligand binding energy

Molecular dynamics (MD) simulations lasting 500 ns were performed in explicit water to investigate the effect of polarization on the binding of ligands to human α-thrombin based on the standard nonpolarizable AMBER force field and the quantum-derived polarized protein-specific charge (PPC). The PPC includes the electronic polarization effect of the thrombin-ligand complex, which is absent in the standard force field. A detailed analysis and comparison of the results of the MD simulation with experimental data provided strong evidence that intra-protein, protein-ligand hydrogen bonds and the root-mean-square deviation of backbone atoms were significantly stabilized through electronic polarization. Specifically, two critical hydrogen bonds between thrombin and the ligand were broken at approximately 190 ns when AMBER force field was used and the number of intra-protein backbone hydrogen bonds was higher under PPC than under AMBER. The thrombin-ligand binding energy was computed using the molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) method, and the results were consistent with the experimental value obtained using PPC. Because hydrogen bonds were unstable, it was failed to predict the binding affinity under the AMBER force field. Furthermore, the results of the present study revealed that differences in the binding free energy between AMBER and PPC almost comes from the electrostatic interaction. Thus, this study provides evidence that protein polarization is critical to accurately describe protein-ligand binding.

Artificial water channels – incipient innovative developments

This Feature Article discusses the incipient developments of the first artificial water channels, including only systems that integrate synthetic elements in their water selective translocation unit.

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.

M2 proton channel: toward a model of a primitive proton pump

Transmembrane proton transfer was essential to early cellular systems in order to transduce energy for metabolic functions. The reliable, efficient and controlled generation of proton gradients became possible only with the emergence of active proton pumps. On the basis of features shared by most modern proton pumps we identify the essential mechanistic steps in active proton transport. Further, we discuss the mechanism of action of a small, transmembrane M2 proton channel from influenza A virus as a model for proton transport in protocells. The M2 channel is a 94-residue long, α-helical tetramer that is activated at low pH and exhibits high selectivity and directionality. A shorter construct, built of transmembrane fragments that are only 24 amino acids in length, exhibits very similar proton transport properties. Molecular dynamics simulations on the microsecond time-scale carried out for the M2 channel provided atomic level details on the activation of the channel in response to protonation of the histidine residue, His37. The pathway of proton conduction is mediated by His37, which accepts and donates protons at different interconverting conformation states when pH is lower than 6.5. The Val27 and Trp41 gates and the salt bridge between Asp44 and Arg45 further enhance the directionality of proton transport. It is argued that the architecture and the mechanism of action similar to that found in the M2 channel might have been the perfect starting point for evolution towards the earliest proton pumps, indicating that active proton transport could have readily emerged from simple, passive proton channels.

Multisite ion model in concentrated solutions of divalent cations (MgCl2 and CaCl2): osmotic pressure calculations

Accurate force field parameters for ions are essential for meaningful simulation studies of proteins and nucleic acids. Currently accepted models of ions, especially for divalent ions, do not necessarily reproduce the right physiological behavior of Ca(2+) and Mg(2+) ions. Saxena and Sept (J. Chem. Theor. Comput. 2013, 9, 3538-3542) described a model, called the multisite-ion model, where instead of treating the ions as an isolated sphere, the charge was split into multiple sites with partial charge. This model provided accurate inner shell coordination of the ion with biomolecules and predicted better free energies for proteins and nucleic acids. Here, we expand and refine the multisite model to describe the behavior of divalent ions in concentrated MgCl2 and CaCl2 electrolyte solutions, eliminating the unusual ion-ion pairing and clustering of ions which occurred in the original model. We calibrate and improve the parameters of the multisite model by matching the osmotic pressure of concentrated solutions of MgCl2 to the experimental values and then use these parameters to test the behavior of CaCl2 solutions. We find that the concentrated solutions of both divalent ions exhibit the experimentally observed behavior with correct osmotic pressure, the presence of solvent separated ion pairs instead of direct ion pairs, and no aggregation of ions. The improved multisite model for (Mg(2+) and Ca(2+)) can be used in classical simulations of biomolecules at physiologically relevant salt concentrations.

Anatomy of enzyme channels

Background

Enzyme active sites can be connected to the exterior environment by one or more channels passing through the protein. Despite our current knowledge of enzyme structure and function, surprisingly little is known about how often channels are present or about any structural features such channels may have in common.

Results

Here, we analyze the long channels (i.e. >15 Å) leading to the active sites of 4,306 enzyme structures. We find that over 64% of enzymes contain two or more long channels, their typical length being 28 Å. We show that amino acid compositions of the channel significantly differ both to the composition of the active site, surface and interior of the protein.

Conclusions

The majority of enzymes have buried active sites accessible via a network of access channels. This indicates that enzymes tend to have buried active sites, with channels controlling access to, and egress from, them, and that suggests channels may play a key role in helping determine enzyme substrate.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0379-x) contains supplementary material, which is available to authorized users.

An artificial primitive mimic of the Gramicidin-A channel

Gramicidin A (gA) is the simplest known natural channel, and important progress in improving conduction activity has previously been obtained with modified natural gAs. However, simple artificial systems mimicking the gA functions are unknown. Here we show that gA can be mimicked using a simple synthetic triazole or 'T-channel' forming compound (TCT), having similar constitutional functions as the natural gAs. As in gA channels, the carbonyl moieties of the TCT, which point toward the T-channel core and surround the transport direction, are solvated by water. The net-dipolar alignment of water molecules along the chiral pore surfaces influences the conduction of protons/ions, envisioned to diffuse along dipolar hydrophilic pathways. Theoretical simulations and experimental assays reveal that the conduction through the T-channel, similar to that in gA, presents proton/water conduction, cation/anion selectivity and large open channel-conductance states. T-channels--associating supramolecular chirality with dipolar water alignment--represent an artificial primitive mimic of gA.

From natural to bioassisted and biomimetic artificial water channel systems

Within biological systems, natural channels and pores transport metabolites across the cell membranes. Researchers have explored artificial ion-channel architectures as potential mimics of natural ionic conduction. All these synthetic systems have produced an impressive collection of alternative artificial ion-channels. Amazingly, researchers have made far less progress in the area of synthetic water channels. The development of synthetic biomimetic water channels and pores could contribute to a better understanding of the natural function of protein channels and could offer new strategies to generate highly selective, advanced water purification systems. Despite the imaginative work by synthetic chemists to produce sophisticated architectures that confine water clusters, most synthetic water channels have used natural proteins channels as the selectivity components, embedded in the diverse arrays of bioassisted artificial systems. These systems combine natural proteins that present high water conductance states under natural conditions with artificial lipidic or polymeric matrixes. Experimental results have demonstrated that natural biomolecules can be used as bioassisted building blocks for the construction of highly selective water transport through artificial membranes. A next step to further the potential of these systems was the design and construction of simpler compounds that maintain the high conduction activity obtained with natural compounds leading to fully synthetic artificial biomimetic systems. Such studies aim to use constitutional selective artificial superstructures for water/proton transport to select functions similar to the natural structures. Moving to simpler water channel systems offers a chance to better understand mechanistic and structural behaviors and to uncover novel interactive water-channels that might parallel those in biomolecular systems. This Account discusses the incipient development of the first artificial water channels systems. We include only systems that integrate synthetic elements in their water selective translocation unit. Therefore, we exclude peptide channels because their sequences derive from the proteins in natural channels. We review many of the natural systems involved in water and related proton transport processes. We describe how these systems can fit within our primary goal of maintaining natural function within bioassisted artificial systems. In the last part of the Account, we present several inspiring breakthroughs from the last decade in the field of biomimetic artificial water channels. Researchers have synthesized and tested hydrophobic, hydrophilic and hybrid nanotubular systems. All these examples demonstrate how the novel interactive water-channels can parallel biomolecular systems. At the same time these simpler artificial water channels offer a means of understanding the molecular-scale hydrodynamics of water for many biological scenarios.

Molecular dynamics study of the proposed proton transport pathways in [FeFe]-hydrogenase

Possible proton transport pathways in Clostridium pasteurianum (CpI) [FeFe]-hydrogenase were investigated with molecular dynamics simulations. This study was undertaken to evaluate the functional pathway and provide insight into the hydrogen bonding features defining an active proton transport pathway. Three pathways were evaluated, two of which consist of water wires and one of predominantly amino acid residues. Our simulations suggest that protons are not transported through water wires. Instead, the five-residue motif (Glu282, Ser319, Glu279, H2O, Cys299) was found to be the likely pathway, consistent with previously made experimental observations. The pathway was found to have a persistent hydrogen bonded core (residues Cys299 to Ser319), with less persistent hydrogen bonds at the ends of the pathway for both H2 release and H2 uptake. Single site mutations of the four residues have been shown experimentally to deactivate the enzyme. The theoretical evaluation of these mutations demonstrates redistribution of the hydrogen bonds in the pathway, resulting in enzyme deactivation. Finally, coupling between the protein dynamics near the proton transport pathway and the redox partner binding regions was also found as a function of H2 uptake and H2 release states, which may be indicative of a correlation between proton and electron movement within the enzyme.

Gramicidin A backbone and side chain dynamics evaluated by molecular dynamics simulations and nuclear magnetic resonance experiments. I: molecular dynamics simulations

Gramicidin A (gA) channels provide an ideal system to test molecular dynamics (MD) simulations of membrane proteins. The peptide backbone lines a cation-selective pore, and due to the small channel size, the average structure and extent of fluctuations of all atoms in the peptide will influence ion permeation. This raises the question of how well molecular mechanical force fields used in MD simulations and potential of mean force (PMF) calculations can predict structure and dynamics as well as ion permeation. To address this question, we undertook a comparative study of nuclear magnetic resonance (NMR) observables predicted by fully atomistic MD simulations on a gA dimer embedded in a sodium dodecyl sulfate (SDS) micelle with measurements of the gA dimer backbone and tryptophan side chain dynamics using solution-state (15)N NMR on gA dimers in SDS micelles (Vostrikov, V. V.; Gu, H.; Ingólfsson, H. I.; Hinton, J. F.; Andersen, O. S.; Roux, B.; Koeppe, R. E., II. J. Phys. Chem. B2011, DOI 10.1021/jp200906y , accompanying article). This comparison enables us to examine the robustness of the MD simulations done using different force fields as well as their ability to predict important features of the gA channel. We find that MD is able to predict NMR observables, including the generalized order parameters (S(2)), the (15)N spin-lattice (T(1)) and spin-spin (T(2)) relaxation times, and the (1)H-(15)N nuclear Overhauser effect (NOE), with remarkable accuracy. To examine further how differences in the force fields can affect the channel conductance, we calculated the PMF for K(+) and Na(+) permeation through a gA channel in a dimyristoylphosphatidylcholine (DMPC) bilayer. In this case, we find that MD is less successful in quantitatively predicting the single-channel conductance.

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.

A statistical mechanical theory of proton transport kinetics in hydrogen-bonded networks based on population correlation functions with applications to acids and bases

Extraction of relaxation times, lifetimes, and rates associated with the transport of topological charge defects in hydrogen-bonded networks from molecular dynamics simulations is a challenge because proton transfer reactions continually change the identity of the defect core. In this paper, we present a statistical mechanical theory that allows these quantities to be computed in an unbiased manner. The theory employs a set of suitably defined indicator or population functions for locating a defect structure and their associated correlation functions. These functions are then used to develop a chemical master equation framework from which the rates and lifetimes can be determined. Furthermore, we develop an integral equation formalism for connecting various types of population correlation functions and derive an iterative solution to the equation, which is given a graphical interpretation. The chemical master equation framework is applied to the problems of both hydronium and hydroxide transport in bulk water. For each case it is shown that the theory establishes direct links between the defect's dominant solvation structures, the kinetics of charge transfer, and the mechanism of structural diffusion. A detailed analysis is presented for aqueous hydroxide, examining both reorientational time scales and relaxation of the rotational anisotropy, which is correlated with recent experimental results for these quantities. Finally, for OH(-)(aq) it is demonstrated that the "dynamical hypercoordination mechanism" is consistent with available experimental data while other mechanistic proposals are shown to fail. As a means of going beyond the linear rate theory valid from short up to intermediate time scales, a fractional kinetic model is introduced in the Appendix in order to describe the nonexponential long-time behavior of time-correlation functions. Within the mathematical framework of fractional calculus the power law decay ∼t(-σ), where σ is a parameter of the model and depends on the dimensionality of the system, is obtained from Mittag-Leffler functions due to their long-time asymptotics, whereas (stretched) exponential behavior is found for short times.

A combined experimental and theoretical study of ion solvation in liquid N-methylacetamide

Most current biomolecular simulations are based on potential energy functions that treat the electrostatic energy as a sum of pairwise Coulombic interactions between effective fixed atomic charges. This approximation, in which many-body induced polarization effects are included in an average way, is expected to be satisfactory for a wide range of systems, but less accurate for processes involving the transfer and partition of ions among heterogeneous environments. The limitations of these potential energy functions are perhaps most obvious in studies of ion permeation through membrane channels. In many cases, the pore is so narrow that the permeating ion must shed most of its surrounding water molecules and the large energetic loss due to dehydration must be compensated by coordination with protein atoms. Interactions of cations with protein backbone carbonyl oxygens, in particular, play a critical role in several important biological channels. As a first step toward meeting the challenge of developing an accurate explicit accounting for induced polarization effects, the present work combines experiments and computation to characterize the interactions of alkali and halide ions with N-methylacetamide chosen to represent the peptide bond. From solubility measurements, we extract the solvation free energies of KCl and NaCl in liquid N-methylacetamide. Polarizable models based on the Drude oscillator are then developed and compared with available experimental and ab initio data. The good agreement for a range of structural and thermodynamic properties in the gas and condensed phases suggests that the polarizable models provide an accurate representation of ion-amide interactions in biological systems.

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.

Influenza M2 proton channels

M2 of the influenza virus is an intriguing transmembrane protein that forms a minuscule proton channel in the viral envelope. Its recognized function is to equilibrate pH across the viral membrane during cell entry and across the trans-Golgi membrane of infected cells during viral maturation. It is vital for viral replication and it is a target for the anti-influenza drugs, amantadine and rimantadine. Recently, high resolution structures of M2 channels of both flu A and B have been obtained, providing the desperately needed structural details for understanding the mechanism of proton conductance. In particular, the establishment of the functional solution NMR system of the proton channels enabled simultaneous high resolution structure characterization and measurement of channel dynamics coupled to channel activity. This review summarizes our current understanding of how protons are conducted through the M2 channel from a structural point of view, as well as the modes by which important channel gating elements function during proton conduction.

Systematic study of anharmonic features in a principal component analysis of gramicidin A

We use principal component analysis (PCA) to detect functionally interesting collective motions in molecular-dynamics simulations of membrane-bound gramicidin A. We examine the statistical and structural properties of all PCA eigenvectors and eigenvalues for the backbone and side-chain atoms. All eigenvalue spectra show two distinct power-law scaling regimes, quantitatively separating large from small covariance motions. Time trajectories of the largest PCs converge to Gaussian distributions at long timescales, but groups of small-covariance PCs, which are usually ignored as noise, have subdiffusive distributions. These non-Gaussian distributions imply anharmonic motions on the free-energy surface. We characterize the anharmonic components of motion by analyzing the mean-square displacement for all PCs. The subdiffusive components reveal picosecond-scale oscillations in the mean-square displacement at frequencies consistent with infrared measurements. In this regime, the slowest backbone mode exhibits tilting of the peptide planes, which allows carbonyl oxygen atoms to provide surrogate solvation for water and cation transport in the channel lumen. Higher-frequency modes are also apparent, and we describe their vibrational spectra. Our findings expand the utility of PCA for quantifying the essential features of motion on the anharmonic free-energy surface made accessible by atomistic molecular-dynamics simulations.

Concerted hydrogen-bond dynamics in the transport mechanism of the hydrated proton: a first-principles molecular dynamics study

First-principles molecular dynamics calculations performed in a fully converged basis set are used to reveal new details about the mechanism of the anomalous proton-transport process in water, a fundamental question dating back over 200 years. By separating actual structural diffusion from simple rattling events, wherein a proton shuttles forth and back in a hydrogen bond, it is found that the former are driven by a concerted mechanism in which hydronium begins to accept a hydrogen bond from a donor water molecule while the proton-receiving water molecule simultaneously loses one of its acceptor hydrogen bonds. The kinetics of the process are found to be in good agreement with recent experiments.