Molecular dynamics and brownian dynamics investigation of ion permeation and anesthetic halothane effects on a proton-gated ion channel

Bacterial Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) is activated to cation permeation upon lowering the solution pH. Its function can be modulated by anesthetic halothane. In the present work, we integrate molecular dynamics (MD) and Brownian dynamics (BD) simulations to elucidate the ion conduction, charge selectivity, and halothane modulation mechanisms in GLIC, based on recently resolved X-ray crystal structures of the open-channel GLIC. MD calculations of the potential of mean force (PMF) for a Na(+) revealed two energy barriers in the extracellular domain (R109 and K38) and at the hydrophobic gate of transmembrane domain (I233), respectively. An energy well for Na(+) was near the intracellular entrance: the depth of this energy well was modulated strongly by the protonation state of E222. The energy barrier for Cl(-) was found to be 3-4 times higher than that for Na(+). Ion permeation characteristics were determined through BD simulations using a hybrid MD/continuum electrostatics approach to evaluate the energy profiles governing the ion movement. The resultant channel conductance and a near-zero permeability ratio (P(Cl)/P(Na)) were comparable to experimental data. On the basis of these calculations, we suggest that a ring of five E222 residues may act as an electrostatic gate. In addition, the hydrophobic gate region may play a role in charge selectivity due to a higher dehydration energy barrier for Cl(-) ions. The effect of halothane on the Na(+) PMF was also evaluated. Halothane was found to perturb salt bridges in GLIC that may be crucial for channel gating and open-channel stability, but had no significant impact on the single ion PMF profiles.     

Incidence of partial charges on ion selectivity in potassium channels

Potassium channels are membrane proteins known to select potassium over sodium ions at a high diffusion rate. We conducted ab initio calculations on a filter model of KcsA of about 300 atoms at the Hartree-Fock level of theory. Partial charges were derived from the quantum mechanically determined electrostatic potential either with Merz-Kollman or Hinsen-Roux schemes. Large polarization and/or charge transfer occur on potassium ions located in the filter, while the charges on sodium ions remain closer to unity. As a result, a weaker binding is obtained for K(+) ions. Using a simplified version of a permeation model based on the concerted-motion mechanism for ion translocation within the single-file ion channel [P. H. Nelson, J. Chem. Phys. 117, 11396 (2002)], we discuss how differences in polarization effects in the adducts with K(+) and Na(+) can play a role as for ionic selectivity and conductance.     

Energies of ions in water and nanopores within density functional theory

Accurate calculations of electrostatic potentials and treatment of substrate polarizability are critical for predicting the permeation of ions inside water-filled nanopores. The ab initio molecular dynamics method, based on density functional theory (DFT), accounts for the polarizability of materials, water, and solutes, and it should be the method of choice for predicting accurate electrostatic energies of ions. In practice, DFT coupled with the use of periodic boundary conditions in a charged system leads to large energy shifts. Results obtained using different DFT packages may vary because of the way pseudopotentials and long-range electrostatics are implemented. Using maximally localized Wannier functions, we apply robust corrections that yield relatively unambiguous ion energies in select molecular and aqueous systems and inside carbon nanotubes. Large binding energies are predicted for ions in metallic carbon nanotube arrays, while Na+ and Cl- energies are found to exhibit asymmetry in water that is smaller than but comparable with those computed using nonpolarizable water force fields.     

A size-modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage-dependent anion channel

We present a new size-modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage-dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.     

Mechanism of ion permeation in a model channel: Free energy surface and dynamics of K+ ion transport in an anion-doped carbon nanotube

The mechanism of the ion permeation is investigated for an anion-doped carbon nanotube, as a model of the K+ channel, by analyzing the free energy surface and the dynamics of the ion permeation through the model channel. It is found that the main rate-determining step is how an ion enters the channel. The entrance of the ion is mostly blocked by a water molecule located at this entrance. Only about 10% of K+ ions which reach the mouth of the channel can really enter the channel. The rejection rate sensitively depends on the location of this water molecule, which is easily controlled by the charge of the carbon nanotube; for example, the maximum permeation is obtained when the anion charge is at a certain value, -5.4e in the present model. At this charge, the facile translocation of the ion inside the channel is also induced due to the number of fluctuations of the ions inside the channel. Therefore, the so-called "Newton's balls", a toy model, combined with a simple ion diffusion model for explaining the fast ion permeation should be modified. The present analysis thus suggests that there exists an optimum combination of the length and the charge of the carbon nanotube for the most efficient ion permeation.     

Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs

Different microscopic and semimicroscopic approaches for calculations of electrostatic energies in macromolecules are examined. This includes the Protein Dipoles Langevin Dipoles (PDLD) method, the semimicroscopic PDLD (PDLD/S) method, and a free energy perturbation (FEP) method. The incorporation of these approaches in the POLARIS and ENZYMIX modules of the MOLARIS package is described in detail. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions, as well as the effects of the ionic strength and external pH. Determination of the hydrophobic energy involves an approach that considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. Ionic strength effects are studied by modeling the ionic environment around the given system using a grid of residual charges and evaluating the relevant interaction using Coulomb's law with the dielectric constant of water. The performance of the FEP calculations is significantly enhanced by using special boundary conditions and evaluating the long-range electrostatic contributions using the Local Reaction Field (LRF) model. A diverse set of electrostatic effects are examined, including the solvation energies of charges in proteins and solutions, energetics of ion pairs in proteins and solutions, interaction between surface charges in proteins, and effect of ionic strength on such interactions, as well as electrostatic contributions to binding and catalysis in solvated proteins. Encouraging results are obtained by the microscopic and semimicroscopic approaches and the problems associated with some macroscopic models are illustrated. The PDLD and PDLD/S methods appear to be much faster than the FEP approach and still give reasonable results. In particular, the speed and simplicity of the PDLD/S method make it an effective strategy for calculations of electrostatic free energies in interactive docking studies. Nevertheless, comparing the results of the three approaches can provide a useful estimate of the accuracy of the calculated energies. © 1993 John Wiley & Sons, Inc.     

Charge state of the fast gate in chloride channels: insights from electrostatic calculations in a schematic model

Fast gating is a unique property of chloride channels, where a permeating Cl(-) ion acts as its own ligand in opening the channel. The glutamate residue implicated in fast gating normally carries a unit negative charge. Whether this charge needs to be protonated to enable permeation of a Cl(-) ion is an important question that will affect how models of chloride channels are constructed. We investigate the energetic consequences of the charge state of this glutamate residue from continuum electrostatics using a schematic cylindrical channel model. Both analytical solutions of the Poisson equation for an infinite cylinder and numerical ones for a finite cylinder are employed in the calculations.     

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.     

Hyperconjugation Is the Source of Helicity in Perfluorinated n-Alkanes

Hyperconjugative, steric, and electrostatic effects were evaluated as possible sources of the helicity in linear perfluorinated alkanes through analysis of natural bond orbitals and classical electrostatics. Contrary to previous rationalizations, which indicate dominating steric or electrostatic effects, this analysis indicates that hyperconjugative stabilization through σ_CC→σ*_CF interactions are the underlying driving force for the origin of the observed helicity in perfluoroalkanes.     

Hyperconjugation Is the Source of Helicity in Perfluorinated n‐Alkanes

Hyperconjugative, steric, and electrostatic effects were evaluated as possible sources of the helicity in linear perfluorinated alkanes through analysis of natural bond orbitals and classical electrostatics. Contrary to previous rationalizations, which indicate dominating steric or electrostatic effects, this analysis indicates that hyperconjugative stabilization through σ_CC→σ*_CF interactions are the underlying driving force for the origin of the observed helicity in perfluoroalkanes.     

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.     

Why are the Ca2+ and K+ binding energies of formaldehyde and ammonia reversed with respect to their proton affinities?

The binding energies (BEs) of alkali metal monocations and alkaline-earth metal dications to a series of small oxygen and nitrogen bases have been evaluated by means of CCSD(T) calculations on B3-LYP optimized structures. These calculations were carried out both using all-electron basis sets, and additionally using an effective-core potential (ECP) to describe the inner electrons of the metal. A theoretical model aiming at analyzing the effects on the binding energy trends of electrostatic, polarization, and covalent contributions, as well as geometry distortion, was employed. From this analysis, we conclude that although the neutral-ion interaction energy for alkali and alkaline-earth metal cations is dominated by electrostatic contributions, in many cases the correct basicity trends are only attained once polarization effects are also included in the model. This is indeed the case when Ca2+ and K+ are bound to ammonia and formaldehyde. Geometry distortions triggered by polarization are also necessary, in some cases, to obtain the correct basicity trends. In addition, in particular for alkaline-earth dications, the energy associated with covalent interactions sometimes dictates the basicity trend. Our observations imply that simple models based on ion-dipole interactions, that are frequently used in the literature to explain affinity trends in ion-molecule reactions, are generally not likely to be reliable.     

Unfavorable electrostatic and steric interactions in DNA polymerase β E295K mutant interfere with the enzyme's pathway

Mutations in DNA polymerase β (pol β) have been associated with approximately 30% of human tumors. The E295K mutation of pol β has been linked to gastric carcinoma via interference with base excision repair. To interpret the different behavior of E295K as compared to wild-type pol β in atomic and energetic detail, we resolve a binary crystal complex of E295K at 2.5 ? and apply transition path sampling (TPS) to delineate the closing pathway of the E295K pol β mutant. Conformational changes are important components in the enzymatic pathway that lead to and ready the enzyme for the chemical reaction. Our analyses show that the closing pathway of E295K mutant differs from the wild-type pol β in terms of the individual transition states along the pathway, associated energies, and the active site conformation in the final closed form of the mutant. In particular, the closed state of E295K has a more distorted active site than the active site in the wild-type pol β. In addition, the total energy barrier in the conformational closing pathway is 65 ± 11 kJ/mol, much higher than that estimated for both correct (e.g., G:C) and incorrect (e.g., G:A) wild-type pol β systems (42 ± 8 and 45 ± 7 kJ/mol, respectively). In particular, the rotation of Arg258 is the rate-limiting step in the conformational pathway of E295K due to unfavorable electrostatic and steric interactions. The distorted active site in the closed relative to open state and the high energy barrier in the conformational pathway may explain in part why the E295K mutant is observed to be inactive. Interestingly, however, following the closing of the thumb but prior to the rotation of Arg258, the E295K mutant complex has a similar energy level as compared to the wild-type pol β. This suggests that the E295K mutant may associate with DNA with similar affinity, but it may be hampered in continuing the process of chemistry. Supporting experimental data come from the observation that the catalytic activity of wild-type pol β is hampered when E295K is present: this may arise from the competition between E295K and wild-type enzyme for the DNA. These combined results suggest that the low insertion efficiency of E295K mutant as compared to wild-type pol β may be related to a closed form distorted by unfavorable electrostatic and steric interactions between Arg258 and other key residues. The active site is thus less competent for proceeding to the chemical reaction, which may also involve a higher reaction barrier than the wild-type or may not be possible in this mutant. Our analysis also suggests further experiments for other mutants to test the above hypothesis and dissect the roles of steric and electrostatic factors on enzyme behavior.     

Universal solvation model based on conductor‐like screening model

Atomic surface tensions are parameterized for use with solvation models in which the electrostatic part of the calculation is based on the conductor‐like screening model (COSMO) and the semiempirical molecular orbital methods AM1, PM3, and MNDO/d. The convergence of the calculated polarization free energies with respect to the numerical parameters of the electrostatic calculations is first examined. The accuracy and precision of the calculated values are improved significantly by adjusting two parameters that control the segmentation of the solvent‐accessible surface that is used for the calculations. The accuracy of COSMO calculations is further improved by adopting an optimized set of empirical electrostatic atomic radii. Finally, the electrostatic calculation is combined with SM5‐type atomic surface tension functionals that are used to compute the nonelectrostatic portions of the solvation free energy. All parameterizations are carried out using rigid (R) gas‐phase geometries; this combination (SM5‐type surface tensions, COSMO electrostatics, and rigid geometries) is called SM5CR. Six air–water and 76 water–solvent partition coefficients are added to the training set of air–solvent data points previously used to parameterize the SM5 suite of solvation models, thereby bringing the total number of data points in the training set to 2266. The model yields free energies of solvation and transfer with mean unsigned errors of 0.63, 0.59, and 0.61 kcal/mol for AM1, PM3, and MNDO/d, respectively, over all 2217 data points for neutral solutes in the training set and mean unsigned errors of 3.0, 2.7, and 3.1 kcal/mol, respectively, for 49 data points for the ions. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 340–366, 2000     

从能量和信息理论视角理解单取代烷烃的异构化

对直链烷烃和支链烷烃的相对稳定性统一的解释仍然没有定论,并且一直在进行着。以单取代的烷烃体系C_nH_2n+1―R (n = 3, 4, 5, 6;R = OH, OCH₃, NH₂, NO₂, F, Cl, CN, CHO)为例,本文对支链效应的有效性和本质进行了研究。与传统的基于轨道的描述不同的是,本文采用了密度泛函理论的总能量和基于新能量分配方案的能量分量[见Liu, S. B. J. Chem. Phys. 2007, 126, 244103]。新型能量分解方法计算结果表明,静电效应和立体效应等对支链效应的存在都起着重要作用,但是它们均不能单独用来解释支链效应的本质。用双变量(静电势和空间位阻)组合,发现单取代烷烃衍生物的异构化反应主要影响因子是静电势作用,空间位阻效应的影响是次要的。此外还发现了香农熵差与Fisher信息差之间的线性关系,未能发现总能量差或者分能量差值和Fisher信息或者Shannon熵之间的关系。这与前人发现是一致的。     

Thermochemical stabilities and structures of the cluster ions OCS+, S2+, H+(OCS), and C2H5+ with OCS molecules in the gas phase

The gas-phase clustering reactions of OCS+, S2+, H+(OCS), and C2H5+ ions with carbonyl sulfide (OCS) molecules were studied using a pulsed electron-beam high-pressure mass spectrometer and applying density functional theory (DFT) calculations. In the cluster ions OCS+(OCS)(n) and H+(OCS)(OCS)(n), a moderately strong, here referred to as "semi-covalent", bond was formed with n = 1. However, the nature of bonding changed from semi-covalent to electrostatic with n = 1 --> 2. The bond energy of S2(+)(OCS) was determined experimentally to be 12.9 +/- 1 kcal/mol, which is significantly smaller than that of the isovalent S2(+)(CS2) complex (30.9 +/- 1.5 kcal/mol). DFT based calculations predicted the presence of several isomeric structures for H+(OCS)(OCS)(n) complexes. The bond energies in the C2H5+(OCS)(n) clusters showed an irregular decrease for n = 1 --> 2 and 7 --> 8. The nonclassical bridge structure for the free C2H5+ isomerized to form a semi-covalent bond with one OCS ligand, [H3CCH2...SCO]+, i.e., reverted to classical structure. However, the nonclassical bridge structure of C2H5+ was preserved in the cluster ions C2H5+(OCS)(n) below 140 K attributable to the lack of thermal energy for the isomerization. DFT calculations revealed that stability orders of the geometric isomers of H+(OCS)(OCS)(n) and C2H5+(OCS)(n) changed with increasing n values.     

Statistical thermodynamics of mixtures of polar liquids in the model of hindered rotation of molecules

The model of hindered rotation of molecules was used to calculate the internal energy of mixtures of dipolar hard spheres. A comparison of the analytic equations obtained with the data of Monte Carlo simulations and hypernetted chain theory calculations showed the importance of various correlation effects caused by electrostatic and steric forces.