Current noise generated by electrogenic ion pumps

Active ion transport by ATP-or light-driven pumps involves a sequence of elementary steps such as binding and release of ions, as well as conformational transitions of the pump protein. At the microscopic level the individual reaction steps occur at random intervals, and therefore the current generated by electrogenic pumps fluctuates around a mean value. In this paper, a theoretical treatment of the electrical noise associated with active ion transport is given. The analysis, which is based on the calculation of the correlation function, yields the spectral intensity S₁ of current noise as a function of frequency, f. The shape of S_I(f) contains information on the rate constants as well as on the magnitude of the charge displacements occuring during single reaction steps. The contribution of electrogenic pumps to the total voltage noise of the cell may be estimated from S_I(f) and from the frequency-dependent impedance of the cell membrane.     

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion.

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.     

Autocorrelation analysis of hydrophobic ion current noise in lipid bilayer membranes.

The autocorrelation function of a given process is related to its spectral density by the Wiener-Khintchine theorem, and both expressions contain the same information. We report here a measurement of the current noise produced in a lipid bilayer membrane doped with hydrophobic anions of dipicrylamine. The results are in good agreement both with relaxation measurements on the same membrane and with an analysis of the spectral density of the current noise for this system which has been presented by other workers. Although measurement of the spectral density function is generally more complete for technical reasons, the autocorrelation function provides, for the case studied here, more physical insight into the underlying charge transport mechanism. We find that the measured autocorrelation function is negative at short, but nonzero, times. This is a consequence of the operative conductance mechanism in this case, which cannot carry current continuously in the same direction without compensatory reverse flow.     

Free-energy relationships in ion channels activated by voltage and ligand

Many ion channels are modulated by multiple stimuli, which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part because of the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained by measuring the charge-voltage (Q-V) relationship in zero ligand condition and the ligand binding curve at highly depolarizing membrane voltages. Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the Q-V curves at multiple ligand concentrations. When a single reference ligand binding curve is available, this relationship allows us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the Q-V curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand- and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in a polymodal ion channel.     

Characterization of the ion channels formed by poliovirus in planar lipid membranes.

The steps in poliovirus infection leading to viral entry and uncoating are not well understood. Current evidence suggests that the virus first binds to a plasma membrane-bound receptor present in viable cells, leading to a conformational rearrangement of the viral proteins such that the virus crosses the membrane and releases the genomic RNA. The studies described in this report were undertaken to determine if poliovirus (160S) as well as one of the subviral particles (135S) could interact with membranes lacking poliovirus receptors in an effort to begin to understand the process of uncoating of the virus. We report that both forms of viral particles, 160S and 135S, interact with lipid membranes and induce the formation of ion-permeable channels in a manner that does not require acid pH. The channels induced by the viral particles 160S have a voltage-dependent conductance which depends on the ionic composition of the medium. Our findings raise the possibility that viral entry into cells may be mediated by direct interaction of viral surface proteins with membrane lipids.     

Open channel noise. II. A test for coupling between current fluctuations and conformational transitions in the acetylcholine receptor.

The first paper of this series demonstrated that the open-channel currents in the acetylcholine receptors in cultured rat muscle show fluctuations on a time scale of approximately 1 ms. In this paper the hypothesis is tested that these fluctuations are coupled to the gating mechanism that opens and closes the channel. Such a coupling could arise if the channel current and the energy barrier for gating transitions both showed fluctuations having a common origin such as a motion of part of the receptor molecule. A test for coupled fluctuations is made by averaging approximately 1,000 channel opening or closing transitions to search for the small relaxation in the current that is predicted. At a resolution of approximately 1% of the single-channel current amplitude, no such relaxation is observed. It is concluded that any coupled fluctuations are small; fluctuations in the energy barrier for the open-closed conformational transition must be smaller than about 0.3 kT.     

Long-range interactions, voltage sensitivity, and ion conduction in S4 segments of excitable channels.

Forces acting on the S4 segments of the channel, the voltage-sensing structures, are analyzed. The conformational change in the Na channel is modeled as a helix-coil transition in the four S4 segments, coupled to the membrane voltage by electrical forces. In the model, repulsions between like charges make the S4 segment unstable, but field-dependent forces hold it in an alpha-helix configuration at resting potential. At threshold depolarization, the S4 helices cooperatively expand into random coils, breaking the hydrogen bonds connecting adjacent loops of the alpha helices. Exposed electron pairs left on the carbonyl oxygens constitute sites at which cations can bind selectively. The first hydrogen bond to break is at the channel exterior, then the second breaks, and so on in a zipper-like motion along the entire segment. The Na+ ions hop from one site to the next until all H bonds are broken and all sites are filled with ions. This completes the pathway over which the permeant ions move through the channel, driven by the electrochemical potential difference across the membrane. This microscopic mechanism is consistent with the thermodynamic explanation of ion-channel gating previously formulated as the ferroelectric-superionic transition hypothesis.     

Formation of ion channels in planar lipid bilayer membranes by synthetic basic peptides.

We made use of a planar lipid bilayer system to examine the action of synthetic basic peptides which model the prepiece moiety of mitochondrial protein precursors and have antibacterial activity against Gram-positive bacteria. The sequences of the peptides used were as follows: Ac-(Ala-Arg-Leu)3-NHCH3 (3(3], Ac-(Leu-Ala-Arg-Leu)2-NHCH3 (4(2], Ac-(Leu-Ala-Arg-Leu)3-NHCH3 (4(3], Ac-(Leu-Leu-Ala-Arg-Leu)2-NHCH3 (5(2]. These peptides interacted differently with planar lipid bilayer membranes and membrane conductance increased by the formation of ion channels. The effects of the peptides on the macroscopic current-increase and on the probability of channel formation, at the single channel level were in the order of 4(3) greater than 4(2) approximately 5(2) much greater than 3(3), a finding which correlates with the antibacterial activity of these peptides. The micromolar (microM) order concentration at which the channel was formed resembles that causing antibacterial activity. Thus, the peptide antibacterial activity may occur through an increase in ion permeability of the bacterial membrane. The single-channel properties were investigated in detail using 4(3), the peptide with the highest ion channel-forming activity. Many types of channels were observed with respect to conductance (2-750 pS) and voltage dependency of gating. However, the channels were all cation-selective. These results suggest that the ion channels formed by peptide 4(3) may be able to take on a variety of conformations and/or assembly.     

Orchestration of neuronal migration by activity of ion channels,neurotransmitter receptors,and intracellular Ca2+ fluctuations

The real-time observation of cell movement in acute cerebellar slices reveals that granule cells alter their shape concomitantly with changes in the mode and rate of migration as they traverse different cortical layers. Although the origin of local environmental cues responsible for these position-specific changes in migratory behavior remains unclear, several signaling mechanisms involved in controlling granule cell movement have emerged. The onset of one such mechanism is marked by the expression of voltage-gated ion channels and neurotransmitter receptors in postmitotic cells prior to the initiation of their migration. Granule cells start their radial migration after the expression of N-type Ca²⁺ channels and the N-methyl-D -aspartate subtype of glutamate receptors on the plasmalemmal surface. Blockade of the channel or receptor activity significantly decreases the rate of cell movement, indicating that the activation of these membrane constituents provides an essential signal for the translocation of granule cells. Another signal that controls the rate of cell migration is embedded in the combined amplitude and frequency components of Ca²⁺ fluctuations in the somata of migrating granule cells. Interestingly, each phase of Ca²⁺ fluctuation controls a separate phase of saltatory movement in the granule cells: The cells move forward during the phase of transient Ca²⁺ elevation and remain stationary during the troughs. Consequently, the changes in the amplitude and frequency components of Ca²⁺ fluctuations directly affect granule cell movement: Reducing the amplitude or frequency of Ca²⁺ fluctuations slows down the speed of cell movement, while the enhancement of these components accelerates migration. These findings suggest that signaling molecules present in the local cellular milieu encountered on the migratory route control the shape and motility of granule cells by modifying Ca²⁺ fluctuations in the soma through the activation of specific ion channels and neurotransmitter receptors. © 1998 John Wiley & Sons, Inc. J Neurobiol 37: 110–130, 1998     

Novel voltage clamp to record small, fast currents from ion channels expressed in Xenopus oocytes.

The present report describes a novel technique for voltage-clamping amphibian oocytes in which part of the membrane is isolated by a vaseline gap and the cytoplasmic fluid is exchanged by cutting or permeabilizing the remaining membrane. The main features of this open-oocyte, vaseline-gap voltage clamp are: (a) low current noise (1 nA at 3 kHz), (b) control of the ionic composition of both the internal and external media, (c) fast time resolution (20-100 microseconds time constant of decay of the capacity transient) and (d) stable recordings for several hours. These features allow reliable measurements of tail or gating currents and the new method is especially suitable when either of these currents must be measured to test the effects of mutations introduced into the cDNAs of cloned ion channels.     

Cluster organization of ion channels formed by the antibiotic syringomycin E in bilayer lipid membranes.

The cyclic lipodepsipeptide, syringomycin E, when incorporated into planar lipid bilayer membranes, forms two types of channels (small and large) that are different in conductance by a factor of sixfold. To discriminate between a cluster organization-type channel structure and other possible different structures for the two channel types, their ionic selectivity and pore size were determined. Pore size was assessed using water-soluble polymers. Ion selectivity was found to be essentially the same for both the small and large channels. Their reversal (zero current) potentials with the sign corresponding to anionic selectivity did not differ by more than 3 mV at a twofold electrolyte gradient across the bilayer. Reduction in the single-channel conductance induced by poly(ethylene glycol)s of different molecular weights demonstrated that the aqueous pore sizes of the small and large channels did not differ by more than 2% and were close to 1 nm. Based on their virtually identical selectivity and size, we conclude that large syringomycin E channels are clusters of small ones exhibiting synchronous opening and closing.     

Primary structure of peptides and ion channels. Role of amino acid side chains in voltage gating of melittin channels.

Melittin produces a voltage-dependent increase in the conductance of planar lipid bilayers. The conductance increases when the side of the membrane to which melittin has been added (cis-side) is made positive. This paper reports observations on the effect of modifying two positively charged amino acid residues within the NH2-terminal region of the molecule: lysine at position 7 (K7), and the NH2-terminal glycine (G1). We have synthesized melittin analogues in which K7 is replaced by asparagine (K7-N), G1 is blocked by a formyl group (G1-f), and in which both modifications of the parent compound were introduced (G1-f, K7-N). The time required to reach peak conductance during a constant voltage pulse was shorter in membranes exposed to the analogues than in membranes modified by melittin. The apparent number of monomers producing a conducting unit for [K7-N]-melittin and [G1-f]-melittin, eight, was found to be greater than the one for [G1-f], K7-N]-melittin and for melittin itself, four. The apparent gating charge per monomer was less for the analogues, 0.5-0.3 than for melittin, one. Essentially similar results were obtained with melittin analogues in which the charge on K7 or G1 or both was blocked by an uncharged N-linked spin label. These results show that the positive charges in the NH2-terminal region of melittin play a major but not exclusive role in the voltage gating of melittin channels in bilayers.     

Modification of sodium inactivation in myelinated nerve by Anemonia toxin II and iodate. Analysis of current fluctuations and current relaxations

(1) Na+ currents and Na+ current fluctuations were measured in single myelinated nerve fibres of Rana esculenta under voltage-clamp conditions. The process of Na+ inactivation was modified by external treatment with 7 microM Anemonia Toxin II or by internal application of 20 or 40 mM IO3(-). (2) At depolarization of 24 and 32 mV the spectral density of Na+ current fluctuations could be described as the sum of two contributions, Sh(f) and Sm(f), representing the spectrum from fluctuations of the inactivation (h) and activation (m) gates, respectively. At higher depolarizations of 40 and 48 mV the low frequency (h) fluctuations could be better fitted by the sum, Sh1(f)+Sh2(f), of two separate Lorentzian functions. (3) The Na+ current and the variance of Na+ current fluctuations between 150 and 450 ms after depolarization are increased by one order of magnitude after application of Anemonia Toxin II or IO3(-). (4) The kinetics of Na+ current inactivation were described as A1 x exp(-t/tau h1) + A2 x exp(-t/tau h2) + B. The constant, tau h1, of fast Na+ inactivation was the same in normal and modified nerve fibres. The slow inactivation time constant, tau h2, increased with increasing depolarizations in modified fibres but decreased under control conditions. In all cases tau h2 showed a similar voltage dependence as the time constant found by fitting the low frequency fluctuations of Na+ current with one Lorentzian function, Sh(f). (5) It is concluded that Anemonia Toxin II and IO3(-) modify a fraction of Na+ channels in an all-or-none manner. A lower limit of the number of modified Na+ channels is estimated from the Na+ current and the variance Na+ current fluctuations. 7 microM external Anemonia Toxin II modifies more than 17% and 20 or 40 mM internal IO3(-) more than 8% of all Na+ channels. The inactivation gates in modified channels experience an electric field different from that in normal fibres.     

Generalized transition state method and continuous diffusion in multi-dimensional systems with relation to ion transport in channels of biological membranes

An exact expression for the escape rate of a particle in a multi-dimensional system, with respect to an arbitrary reaction coordinate, is derived from first principles according to the transition state method, using a simple geometrical argument. It is shown how the mutual coupling of all degrees of freedom due to the interaction forces leads to the appearance of an effective mass and the potential of the mean force. The same relevant quantities dominate the effective one-particle Fokker-Planck equation, which is derived by a similar projection procedure from the multi-dimensional transport equation. In the limit of a large, position-dependent friction the respective effective Smoluchowski equation is obtained. It allows for the discussion of a diffusing particle which is subject to a temperature bath only through the coupled motion with the constituent lattice particles, or ligands in the case of a molecular ion channel. This treatment is of particular importance for the analysis of ion transport in membrane pores in which the ionic motion is mediated by internal ligand motion.