Steered molecular dynamics simulations of Na+ permeation across the gramicidin A channel

The potential of mean forces (PMF) governing Na+ permeation through gramicidin A (gA) channels with explicit water and membrane was characterized using steered molecular dynamics (SMD) simulations. Constant-force SMD with a steering force parallel to the channel axis revealed at least seven energy wells in each monomer of the channel dimer. Except at the channel dimer interface, each energy well is associated with at least three and at most four backbone carbonyl oxygens and two water oxygens in a pseudo-hexahedral or pseudo-octahedral coordination with the Na+ ion. Repeated constant-velocity SMD by dragging a Na+ ion from each energy well in opposite directions parallel to the channel axis allowed the computation of the PMF across the gA channel, revealing a global minimum corresponding to Na+ binding sites near the entrance of gA at +/-9.3 A from the geometric center of the channel. The effect of volatile anesthetics on the PMF was also analyzed in the presence of halothane molecules. Although the accuracy of the current PMF calculation from SMD simulations is not yet sufficient to quantify the PMF difference with and without anesthetics, the comparison of the overall PMF profiles nevertheless confirms that the anesthetics cause insignificant changes to the structural makeup of the free energy wells along the channel and the overall permeation barrier. On average, the PMF appears less rugged in the outer part of the channel in the presence of anesthetics, consistent with our earlier finding that halothane interaction with anchoring residues makes the gA channel more dynamic. A causal relationship was observed between the reorientation of the coordinating backbone carbonyl oxygen and Na+ transit from one energy well to another, suggesting the possibility that even minute changes in the conformation of pore-lining residues due to dynamic motion could be sufficient to trigger the ion permeation. Because some of the carbonyl oxygens contribute to Na+ coordination in two adjacent energy wells, our SMD results reveal that the atomic picture of ion "hopping" through a gA channel actually involves a Na+ ion being carried in a relay by the coordinating oxygens from one energy well to the next. Steered molecular dynamics complements other computational approaches as an attractive means for the atomistic interpretation of experimental permeation studies.     

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.     

The Crystal Structure of a Potassium Channel— A New Era in the Chemistry of Biological Signaling

The similarity to crown ethers is apparent when the arrangement of the oxygen atoms of the carbonyl groups of the protein backbone in the structure of the potassium channel (see schematic drawing of a section of the structure) found in the bacterium Streptomyces lividans is considered. This particular part of the channel pore acts as the selectivity filter, with the permeability of the channel for K⁺ being as much as 10 000 times greater than for the Na⁺ ion. In fact, in this area of the structure two K⁺ ions are located, a feature that enables high flux through the channel.     

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.     

Identification of active sites of biomolecules. 1. Methyl-alpha-mannopyranoside and Fe(III)

Car-Parrinello molecular dynamics (CPMD) simulations, DFT chemical reactivity index calculations, and mass spectrometric measurements are combined in an integrated effort to elucidate the details of the coordination of a transition-metal ion to a carbohydrate. The impact of the interaction with the FeIII ion on the glycosidic linkage conformation of methyl-alpha-d-mannopyranoside is studied by classical molecular dynamics (MD) and CPMD simulations. This study shows that FeIII interacts with specific hydroxyl oxygen atoms of the carbohydrate, affecting the ground state carbohydrate conformation. These conformational details are discussed in terms of a set of supporting experiments involving electrospray ionization mass spectrometry, and CPMD simulations clearly indicate that the specific conformational preference is due to intramolecular hydrogen bonding. Classical MD simulations proved insensitive to these important chemical properties. Thus, we demonstrate the importance of chemical reactivity calculations and CPMD simulations in predicting the active sites of biological molecules toward metal cations.     

Cooperative transport in a potassium ion channel

Our current understanding of ion permeation through the selectivity filter of the KcsA potassium channel is based on the concept of a multi-ion transport mechanism. The details of this concerted movement, however, are not well understood. In the present paper we report on molecular dynamics simulations which provides new insights. It is shown that ion translocation is based on the collective hopping of ions and water molecules which is mediated by the flexible charged carbonyl groups lining the backbone of the pore. In particular, there is strong evidence for pairwise translocations where one ion and one water molecule form a bound state. We suggest a physical explanation of the observed phenomena employing a simple lattice model. It is argued that the water molecules can act as rectifiers during the hopping of ion-water pairs.     

Thermodynamics of ion binding and occupancy in potassium channels

Potassium channels modulate various cellular functions through efficient and selective conduction of K⁺ ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K⁺ ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated by ab initio calculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations.

Polarization shapes the energy landscape of ion conduction in potassium channels.     

Glycosidic linkage conformation of methyl-alpha-mannopyranoside

We study the preferred conformation of the glycosidic linkage of methyl-alpha-mannopyranoside in the gas phase and in aqueous solution. Results obtained utilizing Car-Parrinello molecular dynamics (CPMD) simulations are compared to those obtained from classical molecular dynamics (MD) simulations. We describe classical simulations performed with various water potential functions to study the impact of the chosen water potential on the predicted conformational preference of the glycosidic linkage of the carbohydrate in aqueous solution. In agreement with our recent studies, we find that results obtained with CPMD simulations differ from those obtained from classical simulations. In particular, this study shows that the trans (t) orientation of the glycosidic linkage of methyl-alpha-mannopyranoside is preferred over its gauche anticlockwise (g-) orientation in aqueous solution. CPMD simulations indicate that this preference is due to intermolecular hydrogen bonding with surrounding water molecules, whereas no such information could be demonstrated by classical MD simulations. This study emphasizes the importance of ab initio MD simulations for studying the structural properties of carbohydrates in aqueous solution.     

Role of water molecules in the KcsA protein channel by molecular dynamics calculations

Molecular dynamics simulations supported by electrostatic calculations have been conducted on the KcsA channel to determine the role of water molecules in the pore. Starting from the X-ray structure of the KcsA channel in its closed state at 2.0 angstroms resolution, the opening of the pore towards a conformation built on the basis of EPR results is studied. We show that water molecules act as a structural element for the K+ ions inside the filter and the hydrophobic cavity of the channel. In the filter, water tends to enhance the depth of the wells occupied by the K+ ions, while in the cavity there is a strong correlation between the water molecules and the cavity ion. As a consequence, the protein remains very stable in the presence of three K+ ions in the selectivity filter and one in the cavity. The analysis of the dynamics of water molecules in the cavity reveals preferred orientations of the dipoles along the pore axis, and a correlated behavior between this dipole orientation and the displacement of the K+ ion during the gating process.     

Preferred conformation of the glycosidic linkage of methyl-beta-mannose

The conformational preference of the glycosidic linkage of methyl-beta-mannose was studied in the gas phase and in aqueous solution by ab initio calculations, and by molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) simulations. MD simulations were performed with various water potential functions to study the impact of the chosen water potential on the predicted conformational preference of the glycosidic linkage of the carbohydrate in solution. This study shows that the trans (t) orientation of the glycosidic linkage of methyl-beta-mannose is preferred over its gauche clockwise (g+) orientation in solution. CPMD simulations clearly indicate that this preference is due to intermolecular hydrogen bonding with surrounding water molecules, whereas no such information could be demonstrated by MD simulations. This study demonstrates the importance of ab initio molecular dynamics simulations in studying the structural properties of carbohydrate-water interactions.     

Functional dynamics of ion channels: modulation of proton movement by conformational switches

Detailed comparative studies of proton relay in native and chemically modified gramicidin channels provide a unique opportunity to uncover the structural basis of biological proton transport. The function of ion channels hinges on their ability to provide surrogate solvation in narrow pore filters so as to overcome the dielectric barrier presented by biological membranes. In the potassium channel KcsA and in the cation channel gramicidin, permeant selectivity and mobility are determined by the proteinaceous matrix via hydrogen bonding, charge-dipole, and dipole-dipole interactions. In particular, main-chain carbonyl groups in these pore interiors play an essential role in the solvation of alkali ions and of protons. In this study, molecular dynamics simulations reveal how the translocation of H(+) is controlled by nanosecond conformational transitions exchanging distorted states of the peptidic backbone in the single-file region of a dioxolane-linked analogue of the gramicidin dimer. These results underline the functional role of channel dynamics and provide a mechanism for the modulation of proton currents by fluctuating dipoles.     

Influence of <Emphasis Type="Italic">gauche</Emphasis> effect on uncharged oxime reactivators for the reactivation of tabun-inhibited AChE: quantum chemical and steered molecular dynamics studies

The neutral oxime reactivator RS194B with a seven-membered ring has shown better efficacy towards the tabun-inhibited AChE than that of RS69N with a six-membered ring and RS41A with a five-membered ring. The difference in the efficacy of these reactivators has remained unexplored. We report here the origin of the difference of efficacy of these reactivators based on the conformational analysis, quantum chemical calculations and steered molecular dynamics (SMD) simulations. The conformational analysis using B3LYP/6-31G(d) level of theory revealed that RS41A and RS194B are more stable in gauche conformation due to the gauche effect (–N–C–C–N– bonds) whereas RS69N prefers anti-conformation. The SMD simulations show that RS194B retains in more stable gauche conformation inside the active gorge of AChE during different time intervals that experiences more hydrogen bonding, hydrophobic interactions with the catalytic anionic site (CAS) residues and weaker interactions with the peripheral anionic site (PAS) residues compared to RS41A and RS69N. In an effort to design an even superior reactivator, RS194B-S has been chosen with a subtle change in the geometry of RS194B by replacing the carbonyl oxygen with the sulfur atom. The newly designed reactivator RS194B-S can also be a promising candidate to reactivate tabun-inhibited AChE.     

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

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

LiTFSI structure and transport in ethylene carbonate from molecular dynamics simulations

Molecular dynamics (MD) simulations using a many-body polarizable force field were performed on ethylene carbonate (EC) doped with lithium bistrifluoromethanesulfonamide (LiTFSI) salt as a function of temperature and salt concentration. At 313 K Li+ was coordinated by 2.7-3.2 EC carbonyl oxygen atoms and 0.67-1.05 TFSI- oxygen atoms at EC:Li = 10 and 20 salt concentrations. In completely dissociated electrolytes, however, Li+ was solvated by approximately 3.8 carbonyl oxygen atoms from EC on average. The probability of ions to participate ion aggregates decreased exponentially with an increase in the size of the aggregate. Ion and solvent self-diffusion coefficients and conductivity predicted by MD simulations were in good agreement with experiments. Approximately half of the charge was transported by charged ion aggregates with the other half carried by free (uncomplexed by counterion) ions. Investigation of the Li+ transport mechanism revealed that contribution from the Li+ diffusion together with its coordination shell to the total Li+ transport is similar to the contribution arising from Li+ exchanging solvent molecules in its first coordination shell with solvents from the outer shells.     

Quantum mechanical calculations on selectivity in the KcsA channel: the role of the aqueous cavity

We have carried out quantum calculations on selected residues at the intracellular side of the selectivity filter of the KcsA potassium channel, using the published X-ray coordinates as starting points. The calculations involved primarily the side chains of residues lining the aqueous cavity on the intracellular side of the selectivity filter, in addition to water molecules, plus a K+ or Na+ ion. The results showed unambiguously that Na+ significantly distorts the symmetry of the channel at the entrance to the selectivity filter (at the residue T75), while K+ does so to a much smaller extent. In all, three ion positions have been calculated: the S4 (lowest) position at the bottom of the selectivity filter, the top of the cavity, and the midpoint of the cavity; Na+ is trapped at the cavity top, while K+ is cosolvated by the selectivity filter carbonyl groups plus threonine hydroxyl groups so that it can traverse the filter. Only one water molecule remains in the K+ solvation shell at the upper position in the cavity; this solvation shell also contains four threonine (T75) hydroxyl oxygens and two backbone carbonyls, while Na+ is solvated by five molecules of water and one oxygen from threonine hydroxyls. T75 at the entrance to the selectivity filter has a key role in recognition of the alkali ion, and T74 has secondary importance. The energetic basis for the preferential bonding of potassium by these residues is briefly discussed, based on additional calculations. Taken together, the results suggest that Na+ would have difficulty entering the cavity, and if it did, it would not be able to enter the selectivity filter.     

What induces pocket openings on protein surface patches involved in protein–protein interactions?

We previously showed for the proteins BCL-X_L, IL-2, and MDM2 that transient pockets at their protein–protein binding interfaces can be identified by applying the PASS algorithm to molecular dynamics (MD) snapshots. We now investigated which aspects of the natural conformational dynamics of proteins induce the formation of such pockets. The pocket detection protocol was applied to three different conformational ensembles for the same proteins that were extracted from MD simulations of the inhibitor bound crystal conformation in water and the free crystal/NMR structure in water and in methanol. Additional MD simulations studied the impact of backbone mobility. The more efficient CONCOORD or normal mode analysis (NMA) techniques gave significantly smaller pockets than MD simulations, whereas tCONCOORD generated pockets comparable to those observed in MD simulations for two of the three systems. Our findings emphasize the influence of solvent polarity and backbone rearrangements on the formation of pockets on protein surfaces and should be helpful in future generation of transient pockets as putative ligand binding sites at protein–protein interfaces. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Dynamic mechanism of fatty acid transport across cellular membranes through FadL: molecular dynamics simulations

FadL is an important member of the family of fatty acid transport proteins within membranes. In this study, 11 conventional molecular dynamics (CMD) and 25 steered molecular dynamics (SMD) simulations were performed to investigate the dynamic mechanism of transport of long-chain fatty acids (LCFAs) across FadL. The CMD simulations addressed the intrinsically dynamic behavior of FadL. Both the CMD and SMD simulations revealed that a fatty acid molecule can move diffusively to a high-affinity site (HAS) from a low-affinity site (LAS). During this process, the swing motion of the L3 segment and the hydrophobic interaction between the fatty acid and FadL could play important roles. Furthermore, 22 of the SMD simulations revealed that fatty acids can pass through the gap between the hatch domain and the transmembrane domain (TMD) by different pathways. SMD simulations identified nine possible pathways for dodecanoic acid (DA) threading the barrel of FadL. The binding free energy profiles between DA and FadL along the MD trajectories indicate that all of the possible pathways are energetically favorable for the transport of fatty acids; however, one pathway (path VI) might be the most probable pathway for DA transport. The reasonability and reliability of this study were further demonstrated by correlating the MD simulation results with the available mutagenesis results. On the basis of the simulations, a mechanism for the full-length transport process of DA from the extracellular side to the periplasmic space mediated by FadL is proposed.     

Molecular dynamics study of the influence of calcium ions on the conformation of gelsolin S2 domain

Gelsolin is an actin-severing protein whose action is promoted by Ca²⁺ ions and inhibited by binding to lipid phosphoinositides incorporated in the inner leaflet of the plasma membrane inner lipid bilayer. In this study, we carried out molecular dynamics (MD) simulations to investigate the influence of calcium cations on the conformation of gelsolin S2 domain. First, gelsolin S2 domain taken from the crystal structure of apo-gelsolin (PDB code: 1D0N) was subjected to three 1100 ps MD simulations in a periodic water box with the 5.0 force field at T=298 K. In the first simulation (S2_Ca²⁺) excess concentration of Ca²⁺ was applied, in the second one (S2_phys) the concentration of Ca²⁺ ions was physiological and in the third one (S2_w) no Ca²⁺ ions were added. The results of MD simulations showed high conformational flexibility of the N-terminal part of the S2 domain. S2_w deviated from the starting structure considerably more that S2_phys and S2_Ca²⁺ suggesting that Ca²⁺ ions stabilize the conformation of the S2 domain of gelsolin.