Permeation in ionic channels: a statistical rate theory approach.

A novel way to model permeation through ionic channels is formulated. Our method does not require that equilibrium exists in the channel or at the channel interfaces. In addition, the potential profile does not need to be specified and the assumption of constant field across the membrane does not need to be made. Our formulation relies on statistical rate theory for its development and uses a form of the electrochemical potential which assumes that the ions are in solution. We show that the conductance and the degree of nonlinearity are dependent on the relative equilibrium exchange rates in the channel and at the interfaces. Nonlinear current-voltage plots can be obtained in symmetric solutions as well as a nonunity exponent for the Ussing flux ratio. Due to the dependence of the partition coefficient on solubility, it is highly unlikely that the intracellular and extracellular partition coefficients are the same. A manifestation of unequal partition coefficients is a current reversal at a membrane voltage that is different from the Nernst potential of the current-carrying ionic species.     

A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel.

A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed.     

The passage of an ion through a synthetic ion channel

The simulated system consisted of a fatty acid bilayer membrane dividing two electrolyte layers each containing ions, and a channel composed of linked 15-crown-5 ether rings. The Na⁺ and F^?  ions in the aqueous electrolyte layers were too large to enter the channel, but the Li⁺ ions entered and were transported. Conditions that optimised the passive, electric-field-induced transport of Li⁺ ions through the channel were investigated. It was calculated and rationalised that the higher the numerical value of the electrostatic charge on the oxygen atoms of the crown ether rings, the more easily does the channel convey the Li⁺ ions.     

Three-dimensional Poisson-Nernst-Planck theory studies: influence of membrane electrostatics on gramicidin A channel conductance

A recently introduced real-space lattice methodology for solving the three-dimensional Poisson-Nernst-Planck equations is used to compute current-voltage relations for ion permeation through the gramicidin A ion channel embedded in membranes characterized by surface dipoles and/or surface charge. Comparisons to a variety of experimental results, presented herein, have proven largely successful. Strengths and weaknesses of the method are discussed.     

Permeation of neutral molecules through calcium channel in sarcoplasmic reticulum vesicles.

Permeation of neutral molecules as well as Ca2+ through the Ca2+ channel in sarcoplasmic reticulum vesicles has been studied by the tracer and/or by the light scattering methods. In the absence of KCl, the Ca2+ channel was found not to be able to pass neutral molecules such as glucose, xylose, and glycine under the condition that the channel was open, although the channel could pass Ca2+. On the other hand, submolar concentrations of KCl made the channel become permeable to neutral molecules as well as Ca2+. Since the effect of KCl could be replaced by NaCl and KNO3, but not by sucrose and glucose, this effect of KCl is considered to be due to ionic strength and not to osmotic pressure. These results suggest that low ionic strength transforms the Ca2+ channel protein in such a manner as to block the permeation of neutral molecules without modifying the gating mechanism of the channel.     

Permeation of water through the KcsA K+ channel

Previous studies have reported that the KcsA potassium channel has an osmotic permeability coefficient of 4.8 x 10(-12) cm3/s, giving it a significantly higher osmotic permeability coefficient than that of some membrane channels specialized in water transport. This high osmotic permeability is proposed to occur when the channel is depleted of potassium ions, the presence of which slow down the water permeation process. The atomic structure of the potassium-depleted KcsA channel and the mechanisms of water permeation have not been well characterized so far. Here, all-atom molecular dynamics simulations, in conjunction with an umbrella sampling strategy and a nonequilibrium approach to simulate pressure gradients are employed to illustrate the permeation of water in the absence of ions through the KcsA K+ channel. Equilibrium molecular dynamics simulations (95 ns combined total length) identified a possible structure of the potassium-depleted KcsA channel, and umbrella sampling calculations (160 ns combined total length) revealed that this structure is not permeable by water molecules moving along the channel axis. The simulation of a pressure gradient across the channel (30 ns combined total length) identified an alternative permeation pathway with a computed osmotic permeability of approximately (2.7 +/- 0.9) x 10(-13) cm3/s. Water fluxes along this pathway did not proceed through collective water motions or transitions to vapor state. All of the major results of this study were robust against variations in a wide set of simulation parameters (force field, water model, membrane model, and channel conformation).     

Poisson-Nernst-Planck Models of Nonequilibrium Ion Electrodiffusion through a Protegrin Transmembrane Pore

Protegrin peptides are potent antimicrobial agents believed to act against a variety of pathogens by forming nonselective transmembrane pores in the bacterial cell membrane. We have employed 3D Poisson-Nernst-Planck (PNP) calculations to determine the steady-state ion conduction characteristics of such pores at applied voltages in the range of −100 to +100 mV in 0.1 M KCl bath solutions. We have tested a variety of pore structures extracted from molecular dynamics (MD) simulations based on an experimentally proposed octomeric pore structure. The computed single-channel conductance values were in the range of 290–680 pS. Better agreement with the experimental range of 40–360 pS was obtained using structures from the last 40 ns of the MD simulation, where conductance values range from 280 to 430 pS. We observed no significant variation of the conductance with applied voltage in any of the structures that we tested, suggesting that the voltage dependence observed experimentally is a result of voltage-dependent channel formation rather than an inherent feature of the open pore structure. We have found the pore to be highly selective for anions, with anionic to cationic current ratios (I_Cl−/I_K+) on the order of 10³. This is consistent with the highly cationic nature of the pore but surprisingly in disagreement with the experimental finding of only slight anionic selectivity. We have additionally tested the sensitivity of our PNP model to several parameters and found the ion diffusion coefficients to have a significant influence on conductance characteristics. The best agreement with experimental data was obtained using a diffusion coefficient for each ion set to 10% of the bulk literature value everywhere inside the channel, a scaling used by several other studies employing PNP calculations. Overall, this work presents a useful link between previous work focused on the structure of protegrin pores and experimental efforts aimed at investigating their conductance characteristics.     

钾离子通道两态跳跃的通透机制

采用两态跳跃模型研究离子通道的通透机制,从两态动力学方程得到了平衡态下的能斯特方程、稳态条件下的米氏动力学关系。得出：若电压小于100mV,电导-电压关系是线性的;在电流-浓度关系中,电流具有饱和特性。这些与实验结果是一致的。此外,还讨论了钾离子通道到达稳态前的暂态过程,并用特征时间来描述这一过程。发现采用两态跳跃模型用较少的参数就可以说明离子通透的机制。     

Permeation mechanism of a two-state potassium channel

A two-state hopping model was proposed to study the permeation of ion channel.The Nemst equation in equilibrium and the Michaelis-Menten relation in steady state were derived from the two-state kinetic model.The currentvoltage relationship obtained in the symmetrical solutions case was linear when the applied potential was less than 100 mV,which met Ohm's law.The conductance-concentration relationship exhibited the saturation property.Moreover,the characteristic time reaching the steady state of the KcsA channel was also discussed.     

Permeation mechanism of a two-state potassium channel

A two-state hopping model was proposed to study the permeation of ion channel. The Nernst equation in equilibrium and the Michaelis-Menten relation in steady state were derived from the two-state kinetic model. The current-voltage relationship obtained in the symmetrical solutions case was linear when the applied potential was less than 100 mV, which met Ohm’s law. The conductance-concentration relationship exhibited the saturation property. Moreover, the characteristic time reaching the steady state of the KcsA channel was also discussed. Translated from Acta Biophysica Sinica, 2005, 21(4): 289–294 [译自: 生物物理学报]     

Membrane dipole potential modulates proton conductance through gramicidin channel: movement of negative ionic defects inside the channel.

The effect of membrane dipole potential on gramicidin channel activity in bilayer lipid membranes (BLMs) was studied. Remarkably, it appeared that proton conductance of gramicidin A (gA) channels responded to modulation of the dipole potential oppositely as compared with gA alkali metal cation conductance. In particular, the addition of phloretin, known to reduce the membrane dipole potential, resulted in a decrease in gA proton conductance, on one hand, and an increase in gA alkali metal conductance, on the other hand, whereas 6-ketocholestanol, the agent raising the membrane dipole potential, provoked an increase in gA proton conductance as opposed to a decrease in the alkali metal cation conductance. The peculiarity of the 6-ketocholestanol effect consisted in its dependence on the H(+) concentration. The experiments with the impermeant dipolar compound, phloridzin, showed that the response of proton transport through gramicidin channels to varying the membrane dipole potential did not change qualitatively if the dipole potential of only one monolayer or both monolayers of the BLM was altered. In contrast to gA proton conductance, the single-channel lifetime changed similarly with varying the membrane dipole potential, regardless of the kind of permeant cations (protons or potassium ions). The results of this study could be tentatively accounted for by an assumption that one of the rate-limiting steps of proton conduction through gramicidin channels represents, in fact, movement of negatively charged species (negative ionic defects) across a membrane.     

Permeation of sodium through calcium channels of an insect muscle membrane.

The contribution of Na ions to the electrically excited response was studied in the muscle fibres of mealworm larvae, Tenebrio molitor, using microelectrode techniques. When Ca ions were omitted from the external solution, no action potential could be elicited. However, addition of Na ions to Ca-free medium rendered the fibre excitable again. The amplitude of these action potentials increased with a slope of about 40 mV for a 10-fold elevation of external Na concentrations. Tetrodotoxin had no effect on the initiation of the spike, and Co ions completely suppressed it. Therefore, it seems likely that a Ca-channel, which is utilized by both Na and Ca ions, is the sole factor responsible for the action potential in the mealworm larval muscle fibre membrane.     

Permeation of Ca2+ and monovalent cations through an outwardly rectifying channel in maize root stelar cells

A depolarization-activated outwardly-rectifying channel (OR),most likely involved in the passive release of K⁺ from the rootsymplasm into the stelar apoplast (for subsequent transportto the shoot via the xylem vessels), has been characterizedin the plasma membrane of maize root stelar cells (Roberts andTester, 1995). In the present study, the selectivity of thischannel was further characterized using single channel current-voltagecurves generated using a voltage ramp protocol. This protocolpermitted the accurate and unambiguous measurement of the reversalpotentials of currents resulting from single channel openings.Using the voltage ramp protocol, it was shown that the OR allowsboth K⁺ efflux and Ca²⁺ influx at potentials positive of E_Kand negative of E_Ca. The OR had a P_Ca/P_K of 1.72–0.21decreasing as extracellular Ca²⁺ was increased. The permeabilityof the OR for monovalent cations other than K⁺ was also investigated.In biionic conditions, a relative permeability sequence of was determined (i.e. Eisenman sequenceIV). The physiological implications of the selectivity of theOR are discussed. Key words: Maize roots, K⁺ channel selectivity, Ca²⁺ permeation     

Molecular dynamics simulation of a synthetic ion channel.

A molecular dynamics simulation has been performed on a synthetic membrane-spanning ion channel, consisting of four alpha-helical peptides, each of which is composed of the amino acids leucine (L) and serine (S), with the sequence Ac-(LSLLLSL)3-CONH2. This four-helix bundle has been shown experimentally to act as a proton-conducting channel in a membrane environment. In the present simulation, the channel was initially assembled as a parallel bundle in the octane portion of a phase-separated water/octane system, which provided a membrane-mimetic environment. An explicit reversible multiple-time-step integrator was used to generate a dynamical trajectory, a few nanoseconds in duration for this composite system on a parallel computer, under ambient conditions. After more than 1 ns, the four helices were found to adopt an associated dimer state with twofold symmetry, which evolved into a coiled-coil tetrameric structure with a left-handed twist. In the coiled-coil state, the polar serine side chains interact to form a layered structure with the core of the bundle filled with H2O. The dipoles of these H2O molecules tended to align opposite the net dipole of the peptide bundle. The calculated dipole relaxation function of the pore H2O molecules exhibits two reorientation times. One is approximately 3.2 ps, and the other is approximately 100 times longer. The diffusion coefficient of the pore H2O is about one-third of the bulk H2O value. The total dipole moment and the inertia tensor of the peptide bundle have been calculated and reveal slow (300 ps) collective oscillatory motions. Our results, which are based on a simple united atom force-field model, suggest that the function of this synthetic ion channel is likely inextricably coupled to its dynamical behavior.     

Correlation character of ionic current fluctuations: analysis of ion current through a voltage-dependent potassium single channel

The gating of ion channels has widely been modeled by assuming the transition between open and closed states is a memoryless process. Nevertheless, the statistical analysis of an ionic current signal recorded from voltage dependence K(+) single channel is presented. Calculating the sample auto-correlation function of the ionic current based on the digitized signals, rather than the sequence of open and closed states duration time. The results provide evidence for the existence of memory. For different voltages, the ion channel current fluctuation has different correlation attributions. The correlations in data generated by simulation of two Markov models, on one hand, auto-correlation function of the ionic current shows a weaker memory, after a delayed period of time, the attribute of memory does not exist; on the other hand, the correlation depends on the number of states in the Markov model. For V(p)=-60 mV pipette potential, spectral analysis of ion channel current was conducted, the result indicates that the spectrum is not a flat spectrum, the data set from ionic current fluctuations shows considerable variability with a broad 1/f -like spectrum, alpha=1.261+/-0.24. Thus the ion current fluctuations give information about the kinetics of the channel protein, the results suggest the correlation character of ion channel protein nonlinear kinetics regardless of whether the channel is in open or closed state.     

Permeation of Na+ through a delayed rectifier K+ channel in chick dorsal root ganglion neurons

In whole-cell patch clamp recordings from chick dorsal root ganglion neurons, removal of intracellular K+ resulted in the appearance of a large, voltage-dependent inward tail current (Icat). Icat was not Ca2+ dependent and was not blocked by Cd2+, but was blocked by Ba2+. The reversal potential for Icat shifted with the Nernst potential for [Na+]. The channel responsible for Icat had a cation permeability sequence of Na+ >> Li+ >> TMA+ > NMG+ (PX/PNa = 1:0.33:0.1:0) and was impermeable to Cl-. Addition of high intracellular concentrations of K+, Cs+, or Rb+ prevented the occurrence of Icat. Inhibition of Icat by intracellular K+ was voltage dependent, with an IC50 that ranged from 3.0-8.9 mM at membrane potentials between -50 and -110 mV. This voltage- dependent shift in IC50 (e-fold per 52 mV) is consistent with a single cation binding site approximately 50% of the distance into the membrane field. Icat displayed anomolous mole fraction behavior with respect to Na+ and K+; Icat was inhibited by 5 mM extracellular K+ in the presence of 160 mM Na+ and potentiated by equimolar substitution of 80 mM K+ for Na+. The percent inhibition produced by both extracellular and intracellular K+ at 5 mM was identical. Reversal potential measurements revealed that K+ was 65-105 times more permeant than Na+ through the Icat channel. Icat exhibited the same voltage and time dependence of inactivation, the same voltage dependence of activation, and the same macroscopic conductance as the delayed rectifier K+ current in these neurons. We conclude that Icat is a Na+ current that passes through a delayed rectifier K+ channel when intracellular K+ is reduced to below 30 mM. At intracellular K+ concentrations between 1 and 30 mM, PK/PNa remained constant while the conductance at -50 mV varied from 80 to 0% of maximum. These data suggest that the high selectivity of these channels for K+ over Na+ is due to the inability of Na+ to compete with K+ for an intracellular binding site, rather than a barrier that excludes Na+ from entry into the channel or a barrier such as a selectivity filter that prevents Na+ ions from passing through the channel.     

Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels.

L-type Ca channels contain a cluster of four charged glutamate residues (EEEE locus), which seem essential for high Ca specificity. To understand how this highly charged structure might produce the currents and selectivity observed in this channel, a theory is needed that relates charge to current. We use an extended Poisson-Nernst-Planck (PNP2) theory to compute (mean) Coulombic interactions and thus to examine the role of the mean field electrostatic interactions in producing current and selectivity. The pore was modeled as a central cylinder with tapered atria; the cylinder (i.e., "pore proper") contained a uniform volume density of fixed charge equivalent to that of one to four carboxyl groups. The pore proper was assigned ion-specific, but spatially uniform, diffusion coefficients and excess chemical potentials. Thus electrostatic selection by valency was computed self-consistently, and selection by other features was also allowed. The five external parameters needed for a system of four ionic species (Na, Ca, Cl, and H) were determined analytically from published measurements of thre limiting conductances and two critical ion concentrations, while treating the pore as a macroscopic ion-exchange system in equilibrium with a uniform bath solution. The extended PNP equations were solved with these parameters, and the predictions were compared to currents measured in a variety of solutions over a range of transmembrane voltages. The extended PNP theory accurately predicted current-voltage relations, anomalous mole fraction effects in the observed current, saturation effects of varied Ca and Na concentrations, and block by protons. Pore geometry, dielectric permittivity, and the number of carboxyl groups had only weak effects. The successful prediction of Ca fluxes in this paper demonstrates that ad hoc electrostatic parameters, multiple discrete binding sites, and logistic assumptions of single-file movement are all unnecessary for the prediction of permeation in Ca channels over a wide range of conditions. Further work is needed, however, to understand the atomic origin of the fixed charge, excess chemical potentials, and diffusion coefficients of the channel. The Appendix uses PNP2 theory to predict ionic currents for published "barrier-and-well" energy profiles of this channel.