Ion currents through pores. The roles of diffusion and external access steps in determining the currents through narrow pores

Temperature dependence of proton permeation through a voltage-gated proton channel

Voltage-gated proton channels are found in many different types of cells, where they facilitate proton movement through the membrane. The mechanism of proton permeation through the channel is an issue of long-term interest, but it remains an open question. To address this issue, we examined the temperature dependence of proton permeation. Under whole cell recordings, rapid temperature changes within a few milliseconds were imposed. This method allowed for the measurement of current amplitudes immediately before and after a temperature jump, from which the ratios of these currents (Iratio) were determined. The use of Iratio for evaluating the temperature dependence minimized the contributions of factors other than permeation. Temperature jumps of various degrees (DeltaT, -15 to 15 degrees C) were applied over a wide temperature range (4-49 degrees C), and the Q10s for the proton currents were evaluated from the Iratios. Q10 exhibited a high temperature dependence, varying from 2.2 at 10 degrees C to 1.3 at 40 degrees C. This implies that processes with different temperature dependencies underlie the observed Q10. A novel resistivity pulse method revealed that the access resistance with its low temperature dependence predominated in high temperature ranges. The measured temperature dependence of Q10 was decomposed into Q10 of the channel and of the access resistances. Finally, the Q10 for proton permeation through the voltage-gated proton channel itself was calculated and found to vary from 2.8 at 5 degrees C to 2.2 at 45 degrees C, as expected for an activation enthalpy of 64 kJ/mol. The thermodynamic features for proton permeation through proton-selective channels were discussed for the underlying mechanism.

Voltage-gated proton channels and other proton transfer pathways

Proton channels exist in a wide variety of membrane proteins where they transport protons rapidly and efficiently. Usually the proton pathway is formed mainly by water molecules present in the protein, but its function is regulated by titratable groups on critical amino acid residues in the pathway. All proton channels conduct protons by a hydrogen-bonded chain mechanism in which the proton hops from one water or titratable group to the next. Voltage-gated proton channels represent a specific subset of proton channels that have voltage- and time-dependent gating like other ion channels. However, they differ from most ion channels in their extraordinarily high selectivity, tiny conductance, strong temperature and deuterium isotope effects on conductance and gating kinetics, and insensitivity to block by steric occlusion. Gating of H(+) channels is regulated tightly by pH and voltage, ensuring that they open only when the electrochemical gradient is outward. Thus they function to extrude acid from cells. H(+) channels are expressed in many cells. During the respiratory burst in phagocytes, H(+) current compensates for electron extrusion by NADPH oxidase. Most evidence indicates that the H(+) channel is not part of the NADPH oxidase complex, but rather is a distinct and as yet unidentified molecule.

Thallous ion movements through gramicidin channels incorporated in lipid monolayers supported by mercury

The potential independent limiting flux of hydrated Tl(+) ions through gramicidin (GR) channels incorporated in phospholipid monolayers self assembled on a hanging mercury-drop electrode is shown to be controlled both by diffusion and by a dehydration step. Conversely, the potential independent limiting flux of dehydrated Tl(+) ions stemming from Tl amalgam electro-oxidation is exclusively controlled by diffusion of thallium atoms within the amalgam. Modulating the charge on the polar heads of dioleoylphosphatidylserine (DOPS) by changing pH affects the limiting flux of hydrated Tl(+) ions to a notable extent, primarily by electrostatic interactions. The dipole potential of DOPS and dioleoylphosphatidylcholine (DOPC), positive toward the hydrocarbon tails, does not hinder the translocation step of Tl(+) ions to such an extent as to make it rate limiting. Consequently, incorporation in the lipid monolayer of phloretin, which decreases such a positive dipole potential, does not affect the kinetics of Tl(+) flux through GR channels. In contrast, the increase in the positive dipole potential produced by the incorporation of ketocholestanol causes the translocation step to contribute to the rate of the overall process. A model providing a quantitative interpretation of the kinetics of diffusion, dehydration-hydration, translocation, and charge transfer of the Tl(+)/Tl(0)(Hg) couple through GC channels incorporated in mercury-supported phospholipid monolayers is provided. A cut-off disk model yielding the profile of the local electrostatic potential created by an array of oriented dipoles located in the lipid monolayer along the axis of a cylindrical ion channel is developed.

Cellular microtransport processes: intercellular, intracellular, and aggregate behavior

Ionic and molecular transfer among cells occurs by a variety of transport processes operative at different length scales. Cell membrane permeability and electrical conductance derive from channel proteins producing pores at the molecular (ultrastructural) scale. Intracellular mobility involves the dynamics of motion through the complex ultrastructure of the cytoplasm. These phenomena unite in the larger-scale (microscopic) process of gross intercellular transfer. When such movement occurs among sufficiently many cells, it in turn begins to reflect their average collective (macroscopic) behavior as bulk tissue. This article surveys selected aspects of intercellular and intracellular transport, with emphasis on detailed mechanistic theory, experimental probes of cellular permeability, and systematic transcendence from small to large length scales.

Noncontact dipole effects on channel permeation. IV. Kinetic model of 5F-Trp(13) gramicidin A currents

Nonlinear least squares fitting was used to assign rate constants for the three-barrier, two-site, double-occupancy, single-filing kinetic model for previously reported current-voltage relations of (5F-Indole)Trp(13) gramicidin A and gramicidin A channels (, 75:2830-2844). By judicious coupling of parameters, it was possible to reduce the parameter space from 64 parameters to 24, and a reasonable fit consistent with other experimental data was obtained. The main features of the fit were that fluorination increased the rate constant for translocation by a factor of 2.33, consistent with a free energy change in the translocation barrier of -0.50 kcal/mol, and increased first-ion binding affinity by a factor of 1.13, primarily by decreasing the first-ion exit rate constant. The translocation rate constant was 5.62 times slower in diphytanoyl phosphatidylcholine (DPhPC) bilayers than in monoolein (GMO) bilayers (coupled for the four combinations of peptide and salt), suggesting a 44.2-mV difference in the projection of the interfacial dipole into the channel. Thus fluorination caused increased currents in DPhPC bilayers, where a high interfacial dipole potential makes translocation more rate limiting because the translocation barrier was reduced, and decreased currents in GMO bilayers, where ion exit or entry is rate limiting because these barriers were increased.

Can we use rate constants and state models to describe ion transport through gramicidin channels?

Can we use rate constants and state models to describe ion transport through gramicidin channels? Maybe, but only if rate constants are just proportionality constants between rates and probabilities of observing states of the channel. This approach is natural if the system of channel plus ions (plus water) is almost always in one or another of a small number of identifiable states. Many features of ion transport through gramicidin, including the conductance-concentration relationship, concentration-dependent permeability ratios, anomalous mole fraction effect and to some extent flux ratio exponents, are consistent with a description in which there are four occupation 'states' of the pore: only water; an ion at one end; an ion at the other; and ions at both ends. Current-voltage relationships can (and must) also be fitted, but until there is a theory to predict the potential dependence of the rate constants this success will remain hollow. Other features have resisted interpretation. These include the failures to determine 'binding constants' consistent with all the data; the variation of flux ratio exponents with ion type; and, probably, the variation of the currents with asymmetrical ion concentrations. Nevertheless, state models still have one attractive feature, they allow consideration of the effects that one ion within the pore has on the movements of another.

Effects of buffer concentration on voltage-gated H+ currents: does diffusion limit the conductance?

The single-channel proton conductance of the voltage-gated H(+)-selective channel, like that of the F0 component of the H(+)-ATPase, is nearly constant over a wide range of pH encompassing the physiological range. To examine the possible contributions of buffer diffusion and buffer-channel proton transfer reactions to this phenomenon, the effects of buffer concentration on voltage-activated H+ currents were explored in voltage-clamped rat alveolar epithelial cells. Changes in the external buffer concentration ([B]o), evaluated using the whole-cell configuration, had only small effects on H+ currents (IH). Lowering [B]o from 100 to 1 mM did not alter the voltage-activation curve or reversal potential (Vrev) but reduced IH, typically by 10-30%. Changes in internal buffer concentration ([B]i), examined in inside-out patches, usually altered IH more distinctly and subtly changed the kinetics. Overall, the effects of changing buffer concentration were small and subtle. The maximum attenuation of the single-channel H+ current at 1 mM buffer was estimated to be approximately 20% at either mouth of the H+ channel. Therefore, the rate-determining step in H+ permeation is neither deprotonation of buffer at the inner mouth of the channel nor protonation of buffer at the external surface. Evidently the rate of H+ permeation through the channel is itself small enough that diffusion of buffer in bulk solution does not directly limit the conductance significantly.

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.

The effects of space charge on the ionic currents through biological membranes

In this paper, the ions moving through an ion-selective membrane are regarded as a space charge. The repulsive action among the ions attenuates the ion current through the membrane. For a quantitative description of this effect on the relation between the ion current, the ion concentrations and the membrane voltage, the usual assumption of a constant electric field within the membrane is replaced by that of an inconstant field influenced by the moving ions. This can be done either by inserting the Poisson equation into the Nernst-Planck equation or by directly calculating the Coulomb forces, e.g. between two ions moving through a narrow channel. An attenuation factor is defined and its dependence on membrane thickness, dielectric number, membrane voltage, and ion concentrations is exactly calculated; its dependence on the cross section of an assumed channel is necessary for the current through the channel to be appreciably attenuated by saturation effects. The saturation effect described differs from the Michaelis-Menten kinetics in that no absolute maximum effect is attained.

Effects of double-layer polarization on ion transport

It has been proposed that changes in ionic strength will alter the shape of current-voltage relations for ion transport across a lipid membrane. To investigate this effect, we measured currents across glyceryl monooleate membranes at applied potentials between 10 and 300 mV using either gramicidin and 1 mM NaCl or valinomycin and 1 mM KCl. A bridge circuit with an integrator as null detector was used to separate the capacitative and ionic components of the current. The changes in the current-voltage relations when ionic strength is varied between 1 and 100 mM are compared with predictions of Gouy-Chapman theory for the effects of these variations on polarization of the electrical diffuse double-layer. Double-layer polarization accounts adequately for the changes observed using membranes made permeable by either gramicidin or valinomycin.