Molecular dynamics simulation of cation motion in water-filled gramicidinlike pores.

A model calculation is carried out to study the potential energy profile of a sodium ion with several water molecules inside a simplified model of the gramicidin ion channel. The sodium ion is treated as a Lennard-Jones sphere with a point charge at its center. The Barnes polarizable water model is used to mimic the water molecules. A polarizable and deformable gramicidinlike channel is constructed based on the model obtained by Koeppe and Kimura. Potential minima and saddle points are located and the static energy barriers are computed. The potential minima at the two mouths of the channel exhibit an aqueous solvation structure very different from that at any of the interior minima. These sites are approximately 23.6 and 24.4 A apart for binding of a sodium ion and a cesium ion, respectively. Ionic motion from these exterior sites to the first interior minimum requires substantial rearrangement of the waters of solvation; this rearrangement may be the hydration/dehydration step in ionic permeation through the channel. Based on these results, a mechanism by which the sodium ion moves from the exterior binding site to the interior of the channel is proposed. Our model channel accommodates about eight water molecules and the transport of the ion and water within the channel is found to be single file. Results of less extensive calculations for Cs+ and Li+ ions in a channel with or without water are also reported.     

Molecular dynamics simulations of the gramicidin A-dimyristoylphosphatidylcholine system with an ion in the channel pore region

To investigate the process of ion permeation in an ion channel systematically, we performed molecular dynamics (MD) simulations on a gramicidin A (GA)-phospholipid model system with an ion in the channel pore region. Each of the three types of ions (Ca2+, Na+ Cl-) was placed at five different positions along the channel axis by replacing a water molecule. MD simulations were performed on each system at constant pressure and constant temperature. The MD trajectories showed that the Ca2+ and Na+ ions could stably fluctuate in the pore region, but the Cl- ion was pushed out because of the unfavorable interaction with the channel. This result is consistent with experimental data. It was also found that the conformation of the GA channel underwent a significant change due to the presence of the ion, and the two ends of the GA monomer were more flexible than its middle region. In particular, the dramatic change of local pore radius near the ion indicated this kind of deformation. The strong interaction between the ion and carbonyl oxygen atoms of GA was the major contributor to this change. Furthermore, it was found that the ethanolamine group of the GA molecule was the most flexible group in the GA channel and often observed to block the entrance of GA. These results imply that the deformation of channel structure plays a very important factor in ion permeation, and the ethanolamine group may play a key role in regulating ion entry into the pore. In conclusion, our results indicate that the ion has a dominant influence on the structure of the GA channel and that the flexibility of the ion channel is a crucial factor in the ion permeation process.     

短杆菌肽A-DMPC通道内离子输运的分子动力学模拟

用最近提出的构建膜体系初始构象的有效方法 ,构建了在DMPC脂膜环境下短杆菌肽A通道模型 (GA -DMPC)。通过对Na 、Ca2 、Cl-三种不同离子在GA -DMPC通道内不同位置的分子动力学模拟 ,研究离子在通道内输运过程中与通道及通道内水分子的相互作用 ,从分子动力学的角度阐明离子在通道内的输运机制。主要计算结果表明 :(1)离子在通道内的输运使GA的构象发生变化 ,GA的柔性是离子在通道内通透的重要因素 ;(2)Cl- 离子可扩大通道半径 ,Na 离子和Ca2 离子则减小通道半径。Cl-离子不能在GA通道内通透 ;(3)离子的出现使通道内水分子的偶极方向发生变化。上述结果均与实验相符。     

The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity

The cause of the anomalous mole fraction effect (AMFE) in calcium-selective ion channels is studied. An AMFE occurs when the conductance through a channel is lower in a mixture of salts than in the pure salts at the same concentration. The textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. Instead of this, we find that at its most basic level an AMFE reflects a channel's preferential binding selectivity for one ion species over another. The AMFE is explained by considering the charged and uncharged regions of the pore as electrical resistors in series: the AMFE is produced by these regions of high and low ion concentration changing differently with mole fraction due to the preferential ion selectivity. This is demonstrated with simulations of a model L-type calcium channel and a mathematical analysis of a simplistic point-charge model. The particle simulations reproduce the experimental data of two L-type channel AMFEs. Conditions under which an AMFE may be found experimentally are discussed. The resistors-in-series model provides a fundamentally different explanation of the AMFE than the traditional theory and does not require single filing, multiple occupancy, or momentum-correlated ion motion.     

Modeling of ion permeation in calcium and sodium channel selectivity filters

Structure-function studies have shown that it is possible to convert a sodium channel to a calcium-selective channel by a single amino acid substitution in the selectivity filter locus. Ion permeation through the "model selectivity filter" was modeled with a reduced set of functional groups representative of the constituent amino acid side chains. Force-field minimizations were conducted to obtain the energy profile of the cations as they get desolvated and bind to the "model selectivity filter." The calculations suggest that the ion selectivity in the calcium channel is due to preferential binding, whereas in the sodium channel it is due to exclusion. Energetics of displacement of a bound cation from the calcium "model selectivity filter" by another cation suggest that "multi-ion mechanism" reduces the activation barrier for ion permeation. Thus, the simple model captures qualitatively most of the conduction characteristics of sodium and calcium channels. However, the computed barriers for permeation are fairly large, suggesting that ion interaction with additional residues along the transport path may be essential to effect desolvation.     

Molecular dynamics study of the KcsA channel at 2.0-A resolution: stability and concerted motions within the pore

The stability of the KcsA channel accommodating more than one ion in the pore has been studied with molecular dynamics. We have used the very last X-ray structure of the KcsA channel at 2.0-A resolution determined by Zhou et al. [Nature 414 (2001) 43]. In this channel, six of the seven experimentally evidenced sites have been considered. We show that the protein remains very stable in the presence of four K+ ions (three in the selectivity filter and one in the cavity). The locations and the respective distances of the different K+ ions and water molecules (W), calculated within our KWKWKK sequence, also fits well with the experimental observations. The analysis of the K+ ions and water molecules displacements shows concerted file motions on the simulated time scale (approximately 1 ns), which could act as precursor to the diffusion of K+ ions inside the channel. A simple one-dimensional dynamical model is used to interpret the concerted motions of the ions and water molecules in the pore leading ultimately to ion transfer.     

The use of automated parameter searches to improve ion channel kinetics for neural modeling

The voltage and time dependence of ion channels can be regulated, notably by phosphorylation, interaction with phospholipids, and binding to auxiliary subunits. Many parameter variation studies have set conductance densities free while leaving kinetic channel properties fixed as the experimental constraints on the latter are usually better than on the former. Because individual cells can tightly regulate their ion channel properties, we suggest that kinetic parameters may be profitably set free during model optimization in order to both improve matches to data and refine kinetic parameters. To this end, we analyzed the parameter optimization of reduced models of three electrophysiologically characterized and morphologically reconstructed globus pallidus neurons. We performed two automated searches with different types of free parameters. First, conductance density parameters were set free. Even the best resulting models exhibited unavoidable problems which were due to limitations in our channel kinetics. We next set channel kinetics free for the optimized density matches and obtained significantly improved model performance. Some kinetic parameters consistently shifted to similar new values in multiple runs across three models, suggesting the possibility for tailored improvements to channel models. These results suggest that optimized channel kinetics can improve model matches to experimental voltage traces, particularly for channels characterized under different experimental conditions than recorded data to be matched by a model. The resulting shifts in channel kinetics from the original template provide valuable guidance for future experimental efforts to determine the detailed kinetics of channel isoforms and possible modulated states in particular types of neurons.     

Stochastic Markovian modeling of electrophysiology of ion channels: reconstruction of standard deviations in macroscopic currents

Markovian models of ion channels have proven useful in the reconstruction of experimental data and prediction of cellular electrophysiology. We present the stochastic Galerkin method as an alternative to Monte Carlo and other stochastic methods for assessing the impact of uncertain rate coefficients on the predictions of Markovian ion channel models. We extend and study two different ion channel models: a simple model with only a single open and a closed state and a detailed model of the cardiac rapidly activating delayed rectifier potassium current. We demonstrate the efficacy of stochastic Galerkin methods for computing solutions to systems with random model parameters. Our studies illustrate the characteristic changes in distributions of state transitions and electrical currents through ion channels due to random rate coefficients. Furthermore, the studies indicate the applicability of the stochastic Galerkin technique for uncertainty and sensitivity analysis of bio-mathematical models.     

Ion-specific diffusion rates through transmembrane protein channels. A molecular dynamics study

The migration of different alkali metal cations through a transmembrane model channel is simulated by means of the molecular dynamics technique. The parameters of the model are chosen in close relation to the gramicidin A channel. Coulomb- and van der Waals-type potentials between the ions and flexible carbonyl groups of the pore-forming molecule are used to describe the ion channel interaction. The diffusion properties of the ions are obtained from three-dimensional trajectory calculations. The diffusion rates for the different ions Li+, Na+, K+ and Rb+ are affected not only by the mass of the particles but also very strongly by their size. The latter effect is more pronounced for rigid channels, i.e., for binding vibrational frequencies of the CO groups with v greater than 400 cm-1. In this range the selectivity sequence for the diffusion rates is the inverse of that expected from normal rate theory but agrees with that found in experiments for gramicidin A.     

一个改进的马尔科夫模型

离子通道是细胞膜里的大分子孔道,是跨越细胞膜里的蛋白质大分子,是神经、肌肉等细胞膜兴奋性的基础。人体细胞均具有完成特殊功能的离子通道,构建离子通道,尤其其门控行为的动力学模型,对于研究离子通道的相关课题具有重要意义。离子通道的开关反映了蛋白质构象变化的动力学过程。本文介绍了细胞膜离子通道的基本内容和几种常用模型,并根据Markov链对离子通道门控行为的一个二态（闭、开）模型的Markov过程进行了改进,得到了包含失活状态的离子通道门控行为的Markov模型。     

Focused electric field across the voltage sensor of potassium channels

Voltage-gated ion channels respond to changes in membrane potential by movement of their voltage sensors across the electric field between cytoplasmic and extracellular solutions. The principal voltage sensors in these proteins are positively charged S4 segments. The absolute magnitude of S4 movement discriminates two competing classes of gating models. In one class, the movement is <10 Angstrom due to the fact that the electric field is focused by aqueous crevices in the channel protein. In an alternative model, based in part on the crystal structure of a potassium channel, the side chains of S4 arginines move their charges across the bilayer's electric field, a distance of >25 Angstrom. Here, using tethered charges attached to an S4 segment, we provide evidence that the electric field falls across a distance of <4 Angstrom, supporting a model in which the relative movement between S4 and the electric field is very small.     

Molecular dynamics study of the KcsA channel at 2.0-Å resolution: stability and concerted motions within the pore

The stability of the KcsA channel accommodating more than one ion in the pore has been studied with molecular dynamics. We have used the very last X-ray structure of the KcsA channel at 2.0-Å resolution determined by Zhou et al. [Nature 414 (2001) 43]. In this channel, six of the seven experimentally evidenced sites have been considered. We show that the protein remains very stable in the presence of four K⁺ ions (three in the selectivity filter and one in the cavity). The locations and the respective distances of the different K⁺ ions and water molecules (W), calculated within our KWKWKK sequence, also fits well with the experimental observations. The analysis of the K⁺ ions and water molecules displacements shows concerted file motions on the simulated time scale (≈1 ns), which could act as precursor to the diffusion of K⁺ ions inside the channel. A simple one-dimensional dynamical model is used to interpret the concerted motions of the ions and water molecules in the pore leading ultimately to ion transfer.     

Effects of Exogenous Electromagnetic Fields on a Simplified Ion Channel Model

In this paper, we calculate the effect of an exogenous perturbation (an electromagnetic field [EMF] oscillating in the range of microwave frequencies in the range of 1 GHz) on the flux of two ion species through a cylindrical ion channel, implementing a continuous model, the Poisson–Smoluchowski system of equations, to study the dynamics of charged particle density inside the channel. The method was validated through comparison with Brownian dynamics simulations, supposed to be more accurate but computationally more demanding, obtaining a very good agreement. No EMF effects were observed for low field intensities below the level for thermal effects, as the highly viscous regime and the simplicity of the channel do not exhibit resonance phenomena. For high intensities of the external field (>10⁵ V/m), we observed slightly different behavior of ion concentration oscillations and ion currents as a function of EMF orientation with respect to the channel axis.     

The peptaibol antiamoebin as a model ion channel: similarities to bacterial potassium channels.

Antiamoebin (AAM) is a polypeptide antibiotic that is capable of forming ion channels in phospholipid membranes: planar bilayer studies have suggested the channels are octamers. The crystal structure of a monomeric form of AAM has provided the basis for molecular modelling of an octameric helical bundle channel. The channel model is funnel-shaped due to a substantial bend in the middle of the polypeptide chain caused by the presence of several imino acids. Inter-monomer hydrogen bonds orientate a ring of glutamine side chains to form a constriction in the pore lumen. The channel lumen is lined both by side chains of Gln11 and by polypeptide backbone carbonyl groups. Electrostatic calculations on the model are compatible with a channel that transports cations across membranes. The AAM channel model is compared with the crystal structures of two bacterial (KcsA andMthK) potassium channels. AAM and the potassium channels exhibit common functional features, such as cation-selectivity and similar single channel conductances. Common structural features include being multimers, each formed from a bundle of eight transmembrane helices, with lengths roughly comparable to the thickness of lipid bilayers. In addition, they all have aromatic amino acids that lie at the bilayer interfaces and which may aid in the stabilization of the transmembrane helices, as well as narrower constrictions that define the ion binding sites or selectivity filters in the pore lumen. The commonality of structural and functional features in these channels thus suggests that antiamoebin is a good, simple model for more complex bacterial and eukaryotic ion channels, capable of providing insight into details of the mechanisms of ion transport and multimeric channel stability.     

Microscopic calculation of ion-transport rates in membrane channels

A method, based on rate theory, is described by which transport rates in ion channels can be calculated using only microscopic parameters, such as atomic coordinates, force constants and intermolecular energy parameters. The channel is treated as a system of elastically bound ligands interacting with the ion by coulombic and Lennard-Jones forces. Jump frequencies of the ion are obtained from the potential mean force which represents a thermal average over the different configurations of the ligand system. The method is illustrated by application to a special channel model, helical arrangement of dipolar ligands, which can be tilted toward the channel axis against harmonic restoring force. The jump frequency is found to be a non-monotonous function of ion radius. Furthermore, the ion specificity of the channel strongly depends on whether the ligand system is 'hard' or 'soft', i.e., on the extent to which the interaction with the ion can lead to a reorientation of the ligand groups.     

Brownian dynamics study of a multiply-occupied cation channel: application to understanding permeation in potassium channels.

The behavior of a multiply-occupied cation-selective channel has been computed by Brownian dynamics. The length, cross-section, ion-ion repulsion force, and ionic mobility within the channel are all estimated from data and physical reasoning. The only free parameter is a partition energy at the mouth of the channel, defining the free energy of an ion in the channel compared to the bath. It is presumed that this partition energy is associated with the energetics of exchanging a bulk hydration environment for a channel hydration environment. Varying the partition energy alone, keeping all other parameters fixed, gives approximately the full range of magnitudes of single channel conductances seen experimentally for K channels. Setting the partition energy at -11 kT makes the computed channel look similar to a squid axon K channel with respect to magnitude of conductance, shape of the I-V curve, non-unity of Ussing flux ratio exponents, decrease of current and increase of conductance with extracellular ion accumulation, and saturation at high ion concentration in the bathing solution. The model includes no preferred binding sites (local free energy minima) for ions in the channel. Therefore it follows that none of the above-mentioned properties of K channels are strong evidence for the existence of such sites. The model does not show supersaturation of current at very high bathing concentrations nor any pronounced voltage-dependence of the Ussing flux ratio exponent, suggesting that these features would require additional details not included in the model presented herein.     

Measuring extracellular ion gradients from single channels with ion-selective microelectrodes

Under many different conditions activated plasma membrane ion channels give rise to changes in the extracellular concentration of the permeant ion(s). The magnitude and duration of these changes are dependent on the electrochemical driving force(s) on the permeant ion(s) as well as conductance, open time, and channel density. We have modeled the change in the extracellular [K+] due to efflux through Ca2+-activated K+ channels, mSlo, to determine the range of parameters that would give rise to measurable signals in the surrounding media. Subsequently we have used extracellular, K+-selective microelectrodes to monitor localized changes in [K+]ext due to efflux through mSlo channels expressed in Xenopus oocytes. The rapid changes in [K+] show a close fit with the predicted model when the time response of the ion-selective microelectrode is taken into account, providing proof of the concept. Measurement of the change in extracellular ion concentration with ion-selective microelectrodes provides a noninvasive means for functional mapping of channel location and density, as well as characterizing the properties of ion channels in the plasma membrane.     

Voltage-dependent interaction of the peptaibol antibiotic zervamicin II with phospholipid vesicles

The effect of a transmembrane potential on ion channel formation by zervamicin II (ZER-II) was studied in a vesicular model system. The dissipation of diffusion potential caused by addition of ZER-II to small phosphatidylcholine vesicles was monitored using fluorescent (Safranine T) and optical (Oxonol YI) probes. Cis-positive potentials facilitated channel formation, while at cis-negative potentials, ion fluxes were inhibited. A potential-independent behavior of ZER-II was observed at high peptide concentrations, most likely due to its membrane modifying property.     

Gating kinetics of potassium channel in rat dorsal root ganglion neurons analyzed with fractal model

The kinetics of ion channels have been widely modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and kinetic rate constants connecting these states are constant. To study the gating kinetics of voltage-dependent K(+) channel in rat dorsal root ganglion neurons, K(+) channel current were recorded using cell-attached patch-clamp technique. The K(+) channel characteristic of kinetics were found to be statistically self-similar at different time scales as predicted by the fractal model. The fractal dimension D for the closed times and for the open times depend on the pipette potential. For the open and closed times of kinetic setpoint, it was found dependent on the applied pipette potential, which indicated that the ion channel gating kinetics had nonlinear kinetic properties. Thus, the open and closed durations, which had the voltage dependence of the gating of this ion channel, were well described by the fractal model.