Mechanism of ion permeation and selectivity in a voltage gated sodium channel

The rapid and selective transport of Na(+) through sodium channels is essential for initiating action potentials within excitable cells. However, an understanding of how these channels discriminate between different ion types and how ions permeate the pore has remained elusive. Using the recently published crystal structure of a prokaryotic sodium channel from Arcobacter butzleri, we are able to determine the steps involved in ion transport and to pinpoint the location and likely mechanism used to discriminate between Na(+) and K(+). Na(+) conduction is shown to involve the loosely coupled "knock-on" movement of two solvated ions. Selectivity arises due to the inability of K(+) to fit between a plane of glutamate residues with the preferred solvation geometry that involves water molecules bridging between the ion and carboxylate groups. These mechanisms are different to those described for K(+) channels, highlighting the importance of developing a separate mechanistic understanding of Na(+) and Ca(2+) channels.     

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.     

Molecular dynamics investigation of the effects of a water surface on the aggregation of bent-core molecules

Molecular dynamics simulations are used to determine how the presence of a water surface affects the way that bent-core surfactant molecules interact with one another. The simulations are carried out for isolated pairs of bent-core molecules, and for pairs of bent-core molecules on a water surface. The results show that the water surface fundamentally alters the nature of the interaction between the bent-core molecules: a stable complex is formed when the two molecules are on the water surface, but not for an isolated pair of molecules. This difference occurs because the water surface constrains the internal structure and orientation of the molecules, which makes the packing of the molecules into a stable complex more thermodynamically favorable.     

Molecular dynamics investigation of bent-core molecules on a water surface

Molecular dynamics simulations are carried out for bent-core molecules at water surfaces. The water surface is shown to alter the equilibrium molecular structure significantly by causing a different class of torsional states to become more favorable. The equilibrium structure is also altered by the substitution of chlorine atoms for hydrogen atoms on the central phenyl ring in that this substitution forces the bent core to remain in a single torsional state rather than be delocalized among several torsional states. The consequences of these structural changes on the chirality and packing of these molecules on water surfaces are discussed.     

Molecular dynamics of oligofluorenes: a dielectric spectroscopy investigation

The molecular dynamics were investigated in a series of "defect-free" oligofluorenes up to the polymer by dielectric spectroscopy (DS). The method is very sensitive to the presence of keto "defects" that when incorporated on the backbone give rise to poor optical and electronic properties. Two dielectrically active processes were found (beta and alpha process). The latter process (alpha) displays strongly temperature dependent relaxation times and temperature- and molecular weight-dependent spectral broadening associated with intramolecular correlations. The glass temperature (Tg) obeys the Fox-Flory equation and the polymer Tg is obtained by DS at 332 K. The effective dipole moment associated with the alpha process is 0.27 +/- 0.03 D.     

Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel

The recently developed multiscale coarse-graining (MS-CG) method (Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469; J. Chem. Phys. 2005, 123, 134105) is used to build a mixed all-atom and coarse-grained (AA-CG) model of the gramicidin A (gA) ion channel embedded in a dimyristoylphosphatidylcholine (DMPC) lipid bilayer and water environment. In this model, the gA peptide was described in full atomistic detail, while the lipid and water molecules were described using coarse-grained representations. The atom-CG and CG-CG interactions in the mixed AA-CG model were determined using the MS-CG method. Molecular dynamics (MD) simulations were performed using the resulting AA-CG model. The results from simulations of the AA-CG model compare very favorably to those from all-atom MD simulations of the entire system. Since the MS-CG method employs a general and systematic approach to obtain effective interactions from the underlying all-atom models, the present approach to rigorously develop mixed AA-CG models has the potential to be extended to many other systems.     

Dynamic light scattering,a probe of brownian particle dynamics

The principles and techniques of dynamic light scattering (DLS) are outlined and its application to the study of suspensions of interacting colloidal particles is discussed. We show how, under appropriate conditions, DLS can measure long-time collective and self-diffusion coefficients as well as study short-time motions (characterized by the cumulants). These theoretical considerations are illustrated by experimental data. Finally, we discuss the relevance of certain characteristic timescales to theories of the diffusion of interacting particles.     

A molecular dynamics investigation of the titration of a trivalent aqueous ion

We carried out a series of molecular dynamics simulations of the hydrolysis of a model trivalent metal ion in aqueous solution. We use a dissociative model for water and examine the spontaneous speciation of M³⁺ into M(OH) _n ^(3-n)+ (n =1,4) both in neutral solution and as a function of added protons and hydroxide ions. The species distributions in neutral solution correspond reasonably well with those expected for real trivalent metal ions at neutral pH. However, the change in the species distributions as a function of either added protons or hydroxide ions is much less than expected with very large concentrations of protons or hydroxide ions required to shift the species equilibria in either direction. The influence of added protons and hydroxide ions on the species distributions appears to be proportional to the average charge of the hydrolysis couples, being highest for the 3+/2+ couple and lowest for the 1+/0 and 0/1- couples. Proton exchange rates vary with proton/hydroxide ion concentration giving a minimum at intermediate values ([H+]≈ 0.166) with increasing rates at both lower and higher pH.     

Electric-field-controlled water and ion permeation of a hydrophobic nanopore

The permeation of hydrophobic, cylindrical nanopores by water molecules and ions is investigated under equilibrium and out-of-equilibrium conditions by extensive molecular-dynamics simulations. Neglecting the chemical structure of the confining pore surface, we focus on the effects of pore radius and electric field on permeation. The simulations confirm the intermittent filling of the pore by water, reported earlier under equilibrium conditions for pore radii larger than a critical radius R(c). Below this radius, water can still permeate the pore under the action of a strong electric field generated by an ion concentration imbalance at both ends of the pore embedded in a structureless membrane. The water driven into the channel undergoes considerable electrostriction characterized by a mean density up to twice the bulk density and by a dramatic drop in dielectric permittivity which can be traced back to a considerable distortion of the hydrogen-bond network inside the pore. The free-energy barrier to ion permeation is estimated by a variant of umbrella sampling for Na(+), K(+), Ca(2+), and Cl(-) ions, and correlates well with known solvation free energies in bulk water. Starting from an initial imbalance in ion concentration, equilibrium is gradually restored by successive ion passages through the water-filled pore. At each passage the electric field across the pore drops, reducing the initial electrostriction, until the pore, of radius less than R(c), closes to water and hence to ion transport, thus providing a possible mechanism for voltage-dependent gating of hydrophobic pores.     

Equivalence of two approaches for modeling ion permeation through a transmembrane channel with an internal binding site

Ion permeation through transmembrane channels has traditionally been modeled using two different approaches. In one approach, the translocation of the permeant ion through the channel pore is modeled as continuous diffusion and the rate of ion transport is obtained from solving the steady-state diffusion equation. In the other approach, the translocation of the permeant ion through the pore is modeled as hopping along a discrete set of internal binding sites and the rate of ion transport is obtained from solving a set of steady-state rate equations. In a recent work [Zhou, J. Phys. Chem. Lett. 1, 1973 (2010)], the rate constants for binding to an internal site were further calculated by modeling binding as diffusion-influenced reactions. That work provided the foundation for bridging the two approaches. Here we show that, by representing a binding site as an energy well, the two approaches indeed give the same result for the rate of ion transport.     

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.     

Molecular dynamics of a model of one ion in 225 polar molecules

Calculations are reported which explore the effect of an ion on the arrangement and motion of the surrounding solvent molecules in a highly polar medium. It is found that the ion and its nearest neighbours are strongly associated and this also applies - to a lesser extent - to groups of solvent molecules.     

Molecular dynamics study of polarization effects on AgI

Three different models of AgI are studied by molecular dynamics simulations. The first one is the rigid ion model (RIM) with the effective pair potential of the Vashishta and Rahman form and the parametrization proposed by Shimojo and Kobayashi. The other two are polarizable ion models in which the induced polarization effects have been added to the RIM effective pair potential. In one of them (PIM1), only the anions are assumed to be polarizable by the local electric field. In the other one (PIM2s), the silver polarization is also included, and a short-range overlap-induced polarization opposes the electrically induced dipole moments. This short-range polarization is proved to be necessary to avoid overpolarization when both species are assumed to be polarizable. The three models reproduce the superionic character of alpha-AgI at 573 K and the liquid behavior of molten AgI at 923 K. The averaged spatial distribution of the cations in the alpha-phase obtained for PIM1 appears to be in better agreement with experimental data analysis. The PIM1 also reproduces the structure factor prepeak at about 1 A(-1) observed from neutron diffraction data of molten AgI. The three models retain in the liquid phase the superionic character of alpha-AgI, as the mobility of the cations is significantly larger than that for the anions. The ionic conductivity for the polarizable ion models is in better agreement with experimental data for alpha-AgI and molten AgI.     

Molecular dynamics investigation of a density-driven glass transition in a liquid crystal system

Molecular dynamics simulations are carried out to address the density-driven glass transition in a system of rodlike particles that interact with the Gay-Berne potential. Since crystallization occurs in this system on the time scale of the simulations, direct simulation of the glass transition is not possible. Instead, glasses with isotropic orientational order are heated to a temperature T, and the relaxation times by which nematic orientational order develops are determined. These relaxation times appear to diverge at a critical density rho(c); i.e., the system can equilibrate at rhorho(c) (at the temperature T). The relaxation times follow a power-law scaling as the critical density is approached, suggesting that this density-driven glass transition concurs with mode coupling theory.     

Molecular dynamics study on ion diffusion in LiFePO4 olivine materials

Molecular dynamics (MD) simulations have been employed to investigate the ionic diffusion and the structure of LiFePO 4 cathode material. The results correspond well with the published experimental observations. The simulation results indicated that the diffusion of lithium ions was thermally activated and more significant than those of other ions. Compared with other cathode materials, the shifts of ions were less significant in LiFePO 4. This suggested that LiFePO 4 was more thermally stable. The snapshots of the positions of lithium atoms over a range of the steps provided a microscopic picture and the picture showed the lithium ions migrated through one-dimension channels.     

Molecular dynamics studies on yttrium(III) ion diffusion in a cesium chloride melt

Molecular dynamics modeling was used to study diffusion parameters of yttrium(III) ions in cesium chloride melt at the temperature range 900–1200 K.     

Molecular dynamics investigation of oxygen vacancy diffusion in rutile

Oxygen vacancy diffusion in rutile was studied by Born-Oppenheimer molecular dynamics techniques in the framework of the semiempirical molecular orbital method MSINDO. Migration of an oxygen vacancy from the rutile (110) surface towards the bulk was simulated. The metadynamics technique was employed to accelerate the diffusion processes. In this way, transition state structures and activation energies for the diffusion processes were obtained. Rate constants and the time scale of diffusion processes were estimated for different temperatures using the calculated activation energy. It was found that the vacancies in the bulk are less stable than on the surface. The feasibility of oxygen vacancy diffusion under experimental conditions is discussed.     

Molecular dynamics study of dynamical heterogeneity in ion conducting glasses

Molecular dynamics (MD) simulations of lithium metasilicate (Li₂SiO₃) glass have been performed. Dynamic heterogeneity of lithium ions has been examined in detail over 4 ns at 700 K. Particles showing displacements less than the distance at the first minimum of g(r)^Li-Li during a given time T(=920 ps) were defined as type A. Particles showing a displacement greater than the distance of the first minimum of g(r)^Li-Li during T were defined as type B. The type A particles show slow dynamics in accordance with a long tail of waiting time distribution of jump motion and localized jumps within neighboring sites (fractons), while the type B particles show fast dynamics related to the cooperative jumps with strong forward correlation probability (Lévy flights). The mutual changes of two kinds of dynamics with a relatively long time scale have been observed. The 'mixed alkali effect' in the LiKSiO₃ system can be explained by the mutual interception of jump paths. The paths of lithium and potassium are nearly independent in a relatively short time scale while the mixing of the jump paths occurs in a long time scale. The mixed alkali system also shows a kind of heterogeneity. The heterogeneity can be realized only when the 'memory' of the characteristics of the dynamics is longer than the relaxation time for the mixing. Observation of the heterogeneity also depends on the time (or spatial) resolution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Molecular dynamics study of polarizable ion models for molten AgBr

Three different polarizable ion models for molten AgBr have been studied by molecular dynamics simulations. The three models are based on a rigid ion model (RIM) with a pair potential of the type proposed by Vashishta and Rahman for alpha-AgI, to which the induced dipole polarization of the ions is added. In the first (PIM1) the dipole moments are only induced by the local electric field, while in the other two (PIM1s and PIM2s) a short-range overlap induced polarization opposes the electrically induced dipole moments. In the PIM1 and the PIM1s only the anions are assumed polarizable, while in the PIM2s both species are polarizable. Long molecular dynamics simulations show that the PIM2s is an unphysical model since, for some improbable but possible critical configurations, the ions become infinitely polarized. The results of using the PIM1, the PIM1s, as well as those of the simple RIM, have been compared for the static structure and ionic transport properties. The PIM1 reproduces the broad main peak of the total structure factor present in the neutron diffraction data, although the smoothed three-peak feature of this broad peak is slightly overestimated. The structural results for the PIM1s are intermediate between those for the RIM and the PIM1, but fail to reproduce the experimental features within the broad principal peak. Concerning the ionic transport properties, the value of the conductivity obtained using PIM1 is in good agreement with experimental values, while the self-diffusion coefficients and the conductivity for the PIM1s are lower than the corresponding values using the PIM1 and the RIM.