Prediction of ion channel transport from Grote—Hynes and Kramers theories

Generalized Langevin equation based Grote—Hynes (GH) theory and Langevin equation based Kramers theory are used to calculate the transmission coefficient for K⁺ diffusion through a model of the biological potassium ion channel IRK1, which contains a high potential barrier in the selectivity filter. The ion friction kernel is determined from a molecular dynamics (MD) simulation of the force on a stationary ion at the barrier top. The GH and Kramers estimates of the transmission coefficient are compared with those obtained from MD simulations of ion diffusion at the barrier top of the IRK1 channel. It is found that the GH estimate agrees with the value determined by rigorous MD, but the Kramers estimate is about 40% too small. The success or failure of GH and Kramers theories for various other systems is discussed and compared with these results.     

Test of rate theory transmission coefficient algorithms. An application to ion channels

The determination of rate constants is an important problem in many areas of chemical physics. Transition state theory (TST) is often used in estimating the rate constants. However TST neglects recrossings of the transition state by the reaction coordinate. The transmission coefficient is a correction to the TST estimate which accounts for the influence of recrossing dynamics. The transmission coefficient is calculated by generating activated trajectories which cross the transition state. This article investigates the correctness and efficiency of several current numerical algorithms for estimating the transmission coefficient, as well as a new one presented here. We use these algorithms to estimate the transmission coefficient for K⁺ diffusion through a model inward rectifier potassium (IRK1) ion channel.     

Langevin approach for stochastic Hodgkin–Huxley dynamics with discretization of channel open fraction

The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K⁺$10{\text{K}}^{+}$ channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.     

离子与通道相互作用对NaK 通道通透特性影响的研究

以NaK 通道的三维精细结构为基础,从理论上阐述了NaK 通道对钠离子、钾离子、铷离子以及钙离子的通透机理,钡离子可以作为NaK 通道阻断剂的微观机理,我们的研究结果表明,通道与离子的相互作用是决定通道对不同离子选择性的基础, 反映通道与离子相互作用的位能曲线是通道对不同离子通透性的外在表现. 关键词： NaK 通道 密度泛函 布朗动力学 通透性     

In-Medium Kaon Potential and Nuclear Equation of State Measured in Nucleus–Nucleus Collisions

The kaon production in heavy ion collisions at intermediate energies provides a sensitive probe to study the in-medium properties and nuclear equation of state of hadrons. Properties of kaons in dense hadronic matter are important for a better understanding of both, the possible restoration of chiral symmetry in dense hadronic matter and the properties of nuclear matter at high densities. We investigated the in-medium kaon potential and nuclear equation of state by transverse mass spectra of K ⁺ mesons in heavy ion collisions. We use quantum molecular dynamics (QMD) models based on covariant kaon dynamics to simulate ${_{28}^{58}Ni +_{28}^{58}Ni}$ collisions at 1.93 A GeV, to analyze the transverse mass spectra of K ⁺. Calculated results with a repulsive in-medium K ⁺N potential can reasonably describe the features of KaoS data. They also shown that the transverse mass spectrum of K ⁺ mesons is a sensitive observable to probe the kaon in-medium potential in dense nuclear matter.     

Analysis of Cation-Dependent DNA (G<Subscript>3</Subscript>T<Subscript>1</Subscript>)<Subscript>4</Subscript> Shape Change Using Fluorescence Correlation Spectroscopy

In G-rich DNA, it is well known that the form changes from single-strand DNA to G-quadruplex due to cations. In this study, we analyze the diffusion coefficient and fluorescence intensity obtained by fluorescence correlation spectroscopy for short G-rich DNA of the (G₃T₁)₄ sequence labeled as 5-Carboxytetramethylrhodamine (TAMRA) with variation of the K⁺ ion concentration. At a K⁺ ion concentration of more than 200 mM, the single-strand DNA was changed to the G-quadruplex. The size of the G-quadruplex decreased to 86% than the size of the single strand DNA at K⁺ ion concentration of 0 M. The size of the G-quadruplex and the fluorescence intensity of TAMRA attached to the DNA were constant with an increase in the K⁺ ion concentration between 200 and 800 mM. This means that the size of the DNA and the fluorescence intensity of the TAMRA are not affected by the K⁺ ion concentration at the G-quadruplex structure because the binding structure of DNA and TAMRA dye leads to stability at a concentration of less than 100 mM K⁺. Based on our short G-rich DNA results, longer G-rich DNA is analyzed for the diffusion coefficient of the DNA and the fluorescence intensity variation of fluorescence dye attached to the DNA.     

Effect of substitution of K ions on the structural and electrical properties of nanocrystalline MgAl2O4 spinel oxide

Potassium substituted nanosized magnesium aluminates having a nominal composition Mg_1−xK_xAl₂O₄ where x=0.0, 0.25, 0.5, 0.75, 1.0 have been synthesized by the chemical co-precipitation method. The samples have been characterized by means of X-ray diffraction (XRD), scanning electron microscope (SEM), and dc electrical resistivity measurements. The XRD results reveal that the samples are spinel single phase cubic close packed crystalline materials. The calculated crystallite size ranges between 6 and 8 nm. The behaviour of the lattice constant seems to deviate from the Vegard's law. While X-ray density clearly increases, the bulk density and consequently, the percentage porosity do not exhibit a significant change on increasing the K⁺ content. The SEM micrographs suggest homogeneous distribution of the nanocrystallites in the samples. The dc electrical resistivity exhibits a typical semiconducting behaviour. Substitution of a Mg²⁺ ion by a K⁺ ion provides an extra hole to the system, which forms small polaron. Thermally activated hopping of these small polarons is believed to be the conduction mechanism in the Mg_1−xK_xAl₂O₄. The activation energy of hopping of small polarons has been calculated and found K⁺ ions content dependent.     

Analysis of K+/Na+ selectivity of KcsA potassium channel with reference interaction site model theory

As a preliminary approach, we have successfully analysed K⁺/Na⁺ selectivity of the KcsA potassium channel for the most selective ion occupancy state (1010) at the atomic level by using the reference interaction site model (RISM) integral equation theory [Q. Cui, V.H. Smith, Chem. Phys. Lett. 365, 110 (2002)]. With similar methods, in this paper, we analyse seven other most relevant ion occupancy states: (0101), (0110), (1001), (1000), (0100), (0010) and (0001). By analysing all the most relevant states, we are able to characterize some dynamic properties of the systems. More detailed solvation structures of the selectivity filter are presented and more solvation energetic data are obtained and compared with the available molecular dynamics simulation data. We predict consistent results with the simulations in that ions are best dehydrated at binding site 2. For ion occupancy states of most interest, we obtain good relative solvation free energies in comparison with the simulation data. The results in this paper further support the conclusion in our previous paper that the selectivity filter favours K⁺ over Na⁺ from the point of view of solvation.     

Charge state effect on K-shell ionization of aluminum by 600–3400 keV xenonq+ (12 < q < 29) ion collisions

K-shell X-ray spectra of Al were measured by the interaction of 600–3400 keV Xe ^q+ (q = 12–29) ions with Al surface. The X-ray yields per incident ion were deduced and the K-shell ionization cross-sections were obtained from the experimental yield data. With the same incident energy, the K-shell ionization cross-sections of Al excited by Xe ^q+ (q < 26) ions were of the same order of magnitude, while for q = 26 and 29 Xe ion collisions, they were, respectively, about two and ten times larger. Taking into account the binding-energy-modification and the recoil effect of target atoms, the binary encounter approximation (BEA) theory was consistent with the experimental data for q < 26 Xe ion collisions, but it underestimated those excited by q = 26 and 29 Xe ions. This indicates that the K-shell ionization of target induced by Xe ^q+(q < 26) ions was mainly due to the direct Coulomb excitation. However for q = 26 and 29 Xe ions collisions, the transfer of 3d vacancies of projectile to the 1s orbital of target via rotational coupling of the 3dπ, δ-3dσ molecular orbitals, which were formed in the ion-atom quasi-molecule, may cause a considerable contribution to the enhancement of ionization. In addition to the well known Auger and X-ray transition, our experiments proved that the molecular orbital transition (“side-feeding”) mechanism is also a significant channel for de-excitation of hollow atoms formed below the surface.     

Kaon production in heavy ion collisions — Which observable is best suited to observe in-medium potentials?

A review of kaon production in heavy ion collisions at incident energies of 1–2 A GeV is presented. Two conflicting interpretations are discussed: Microscopic transport models can describe most of the observed features when in-medium modifications of kaons are taken into account. In contrast, statistical models in a canonical formulation are able to describe the particle yields only by using masses of free hadrons. Different inverse slope parameters and unequal azimuthal distributions are observed for K⁺ and K^- mesons. Interpretations are discussed.     

Using ion exchange to control the mechanical strength of Naβ-alumina ceramics

We employed Naβ-alumina ceramics as a candidate of structural material of which strength can be controllable. Mechanical strength of Naβ-alumina ceramics revealed to be enhanced up to 50% by ion exchange of Na⁺ by larger K⁺. Maximum mechanical strength was as large as 450 MPa that can be easily degraded by simple annealing at moderate temperature. Such large strength maintained on service could make it useful as structural material. Furthermore it is advantageous for recycling because it can be easily broken after annealing. The increase in mechanical strength on ion exchange was not dependent on the composition of β-alumina but dependent on the internal stress developed due to the difference in the cation sizes. After showing maximum strength, prolonged ion exchange time leads to strength degradation due to the crack generation. When NaK-β-alumina ceramics was used instead of Naβ-alumina, ion exchange time showing maximum strength and degree of strength degradation had been changed.     

Ultrasonically assisted synthesis of barium stannate incorporated graphitic carbon nitride nanocomposite and its analytical performance in electrochemical sensing of 4-nitrophenol

We describe the ultrasonic assisted preparation of barium stannate-graphitic carbon nitride nanocomposite (BSO-gCN) by a simple method and its application in electrochemical detection of 4-nitrophenol via electro-oxidation. A bath type ultrasonic cleaner with ultrasonic power and ultrasonic frequency of 100 W and 50 Hz, respectively, was used for the synthesis of BSO-gCN nanocomposite material. The prepared BSO-gCN nanocomposite was characterized by employing several spectroscopic and microscopic techniques such as X-ray diffraction, X-ray photoelectron spectroscopy, fourier transform infra-red, field emission scanning electron microscopy, and high resolution transmission electron microscopy, to unravel the structural and electronic features of the prepared nanocomposite. The BSO-gCN was drop-casted on a pre-treated glassy carbon electrode (GCE), and their sensor electrode was utilized for electrochemical sensing of 4-nitrophenol (4-NP). The BSO-gCN modified GCE exhibited better electrochemical sensing behavior than the bare GCE and other investigated electrodes. The electroanalytical parameters such as charge transfer coefficient (α = 0.5), the rate constant for electron transfer (k_s = 1.16 s⁻¹) and number of electron transferred were calculated. Linear sweep voltammetry (LSV) exhibited increase in peak current linearly with 4-NP concentration in the range between 1.6 and 50 μM. The lowest detection limit (LoD) was calculated to be 1 μM and sensitivity of 0.81 μA μM⁻¹ cm⁻²_. A 100-fold excess of various ions, such as Ca²⁺, Na⁺, K⁺, Cl⁻, I⁻, CO₃²⁻, NO₃, NH₄⁺ and SO₄²⁻ did not able to interfere with the determination of 4-NP and high sensitivity for detecting 4-NP in real samples was achieved. This newly developed BSO-gCN could be a potential candidate for electrochemical sensor applications.     

Theoretical calculation for the high pressure properties of alkali fluorides

Abstract

The overlap repulsive potentials of ion pairs (Li ⁺?F^?, Na⁺?F^? and K⁺?F^?) are calculated by means of generalized Heitler-London method and the numerical results are fitted in the Born-Mayer form, i.e. Dexp (—αR), Then the parameter D for each pair potential is modified to satisfy the crystal equilibrium condition at the experimentally known lattice constant. The redetermined repulsive potentials are applied to calculate the cohesive energies, bulk moduli, equations of state and NaC1–to-CsC1 structural phase transition pressures of LiF, NaF and KF crystals. The results obtained are compared with some other theoretical values and the available experimental data, and good agreement is reached.     

Modeling and simulation of Li-ion conduction in poly(ethylene oxide)

Polyethylene oxide (PEO) containing a lithium salt (e.g., LiI) serves as a solid polymer electrolyte (SPE) in thin-film batteries and its ionic conductivity is a key parameter of their performance. We model and simulate Li⁺ ion conduction in a single PEO molecule. Our simplified stochastic model of ionic motion is based on an analogy between protein channels of biological membranes that conduct Na⁺, K⁺, and other ions, and the PEO helical chain that conducts Li⁺ ions. In contrast with protein channels and salt solutions, the PEO is both the channel and the solvent for the lithium salt (e.g., LiI). The mobile ions are treated as charged spherical Brownian particles. We simulate Smoluchowski dynamics in channels with a radius of ca. 0.1 nm and study the effect of stretching and temperature on ion conductivity. We assume that each helix (molecule) forms a random angle with the axis between these electrodes and the polymeric film is composed of many uniformly distributed oriented boxes that include molecules with the same direction. We further assume that mechanical stretching aligns the molecular structures in each box along the axis of stretching (intra-box alignment). Our model thus predicts the PEO conductivity as a function of the stretching, the salt concentration and the temperature. The computed enhancement of the ionic conductivity in the stretch direction is in good agreement with experimental results. The simulation results are also in qualitative agreement with recent theoretical and experimental results.     

Cu+ ion conductivity of K2Cu(CNS)3

K₂Cu(CNS)₃ is found to be a Cu⁺ ion conductor with a room temperature (30°C) conductivity of ～5×10^?3ω^?1 cm^?1. The phase structure of the CuCNS + KCNS system and data on temperature variation of the conductivity of K₂Cu(CNS)₃ is reported. The related compound KAg(CNS)₂ is found to be a Ag⁺ ion conductor.     

Spectral Properties, Cation Selectivity, and Dynamic Efficiency of Fluorescent Alkali Ion Indicators in Aqueous Solution Around Neutral pH

The spectral properties of two fluorescent alkali ion indicators, the commercially available cryptand CD222 and a new bipyridyl-type cryptand, F[bpy.bpy.2], bearing the trifluorocoumarino residue are investigated in aqueous solution as a function of pH as well as around neutral pH in the presence of alkali and alkaline earth cations. From the values of the acidity constants it is concluded that bridgehead nitrogen deprotonation occurs at a much lower pH for CD222 (pK _a below 5.5) than for F[bpy.bpy.2]. Spectrofluorometric titrations with salts of NH⁺ ₄, TI⁺, and alkali as well as alkaline earth cations indicate that both indicators are K⁺ selective. F[bpy.bpy.2] shows the higher K⁺/Na⁺ selectivity and larger fluorescence intensity changes but the slower dynamic response. Under suitable conditions, alkali ion binding by CD222 can occur in less than 1 ms.     

Changes in Ion Selectivity Following the Asymmetrical Addition of Charge to the Selectivity Filter of Bacterial Sodium Channels

Voltage-gated sodium channels (NaVs) play fundamental roles in eukaryotes, but their exceptional size hinders their structural resolution. Bacterial NaVs are simplified homologues of their eukaryotic counterparts, but their use as models of eukaryotic Na⁺ channels is limited by their homotetrameric structure at odds with the asymmetric Selectivity Filter (SF) of eukaryotic NaVs. This work aims at mimicking the SF of eukaryotic NaVs by engineering radial asymmetry into the SF of bacterial channels. This goal was pursued with two approaches: the co-expression of different monomers of the NaChBac bacterial channel to induce the random assembly of heterotetramers, and the concatenation of four bacterial monomers to form a concatemer that can be targeted by site-specific mutagenesis. Patch-clamp measurements and Molecular Dynamics simulations showed that an additional gating charge in the SF leads to a significant increase in Na⁺ and a modest increase in the Ca²⁺ conductance in the NavMs concatemer in agreement with the behavior of the population of random heterotetramers with the highest proportion of channels with charge −5e. We thus showed that charge, despite being important, is not the only determinant of conduction and selectivity, and we created new tools extending the use of bacterial channels as models of eukaryotic counterparts.     

Antikaon production in proton-nucleus reactions and the K− properties in nuclear matter

We calculate the momentum-dependent potentials for K⁺ and K⁻ mesons in a dispersion approach at nuclear density ϱ₀ using the information from the vacuum K⁺N and K⁻N scattering amplitudes, however, leaving out the resonance contributions for the in-medium analysis. Whereas the K⁺ potential is found to be repulsive (≈ + 25 MeV) and to show only a moderate momentum dependence, the K⁻ self-energy at normal nuclear matter density turns out to be ≈ − 140 ± 25 MeV at zero momentum roughly in line with K⁻ atomic data, however, decreases rapidly in magnitude for higher momenta. The antikaon production in p + A reactions is calculated within a coupled channel transport approach and compared to the data at KEK including different assumptions for the antikaon potentials. Furthermore, detailed predictions are made for p+¹²C and p+²⁰⁷Pb reactions at 2.5 GeV in order to determine the momentum-dependent antikaon potential experimentally.     

Modeling and simulation of Li-ion conduction in poly(ethylene oxide)

Polyethylene oxide (PEO) containing a lithium salt (e.g., LiI) serves as a solid polymer electrolyte (SPE) in thin-film batteries and its ionic conductivity is a key parameter of their performance. We model and simulate Li⁺ ion conduction in a single PEO molecule. Our simplified stochastic model of ionic motion is based on an analogy between protein channels of biological membranes that conduct Na⁺, K⁺, and other ions, and the PEO helical chain that conducts Li⁺ ions. In contrast with protein channels and salt solutions, the PEO is both the channel and the solvent for the lithium salt (e.g., LiI). The mobile ions are treated as charged spherical Brownian particles. We simulate Smoluchowski dynamics in channels with a radius of ca. 0.1 nm and study the effect of stretching and temperature on ion conductivity. We assume that each helix (molecule) forms a random angle with the axis between these electrodes and the polymeric film is composed of many uniformly distributed oriented boxes that include molecules with the same direction. We further assume that mechanical stretching aligns the molecular structures in each box along the axis of stretching (intra-box alignment). Our model thus predicts the PEO conductivity as a function of the stretching, the salt concentration and the temperature. The computed enhancement of the ionic conductivity in the stretch direction is in good agreement with experimental results. The simulation results are also in qualitative agreement with recent theoretical and experimental results.     

Hofmeister series and ionic effects of alkali metal ions on DNA conformation transition in normal and less polarised water solvent

Normal and less polarised water models are used as the solvent to investigate Hofmeister effects and alkali metal ionic effects on dodecamer d(CGCGAATTCGCG) B-DNA with atomic dynamics simulations. As normal water solvent is replaced by less polarised water, the Hofmeister series of alkali metal ions is changed from Li⁺ > Na⁺ ? K⁺ ? Cs⁺ ? Rb⁺ to Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺. In less polarised water, DNA experiences the B→A conformational transition for the lighter alkali metal counterions (Li⁺, Na⁺ and K⁺). However, it keeps B form for the heavier ions (Rb⁺ and Cs⁺). We find that the underlying cause of the conformation transition for these alkali metal ions except K⁺ is the competition between water molecules and counterions coupling to the free oxygen atoms of the phosphate groups. For K⁺ ions, the ‘economics’ of phosphate hydration and ‘spine of hydration’ are both concerned with the DNA helixes changing.