Voltage-gated proton channels were studied under voltage clamp in excised, inside-out patches of human eosinophils, at various pHi with pHo 7.5 or 6.5 pipette solutions. H+ current fluctuations were observed consistently when the membrane was depolarized to voltages that activated H+ current. At pHi ≤ 5.5 the variance increased nonmonotonically with depolarization to a maximum near the midpoint of the H+ conductance-voltage relationship, gH-V, and then decreased, supporting the idea that the noise is generated by H+ channel gating. Power spectral analysis indicated Lorentzian and 1/f components, both related to H+ currents. Unitary H+ current amplitude was estimated from stationary or quasi-stationary variance,

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
⁠. We analyze
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
data obtained at various voltages on a linearized plot that provides estimates of both unitary conductance and the number of channels in the patch, without requiring knowledge of open probability. The unitary conductance averaged 38 fS at pHi 6.5, and increased nearly fourfold to 140 fS at pHi 5.5, but was independent of pHo. In contrast, the macroscopic gH was only 1.8-fold larger at pHi 5.5 than at pHi 6.5. The maximum H+ channel open probability during large depolarizations was 0.75 at pHi 6.5 and 0.95 at pHi 5.5. Because the unitary conductance increases at lower pHi more than the macroscopic gH, the number of functional channels must decrease. Single H+ channel currents were too small to record directly at physiological pH, but at pHi ≤ 5.5 near Vthreshold (the voltage at which gH turns on), single channel–like current events were observed with amplitudes 7–16 fA.

## Introduction

Voltage-gated proton channels differ in several respects from other voltage-gated ion channels. Indeed, it is still debated whether they are ion channels or carriers. Like ion channels, H+ channels conduct protons passively down their electrochemical gradient, and independently of other ionic species. They probably do not meet a narrow definition of an ion channel as a water-filled pore through which ions diffuse, because the mechanism of permeation is believed to be radically different. Proton channels appear to conduct by a Grotthuss-like mechanism in which protons hop across a hydrogen-bonded chain spanning the membrane (Nagle and Morowitz, 1978; DeCoursey, 2003). Several distinctive properties of voltage-gated proton channels are likely a consequence of this unique conduction mechanism. H+ channels are extremely selective for H+ (PH/Pcation > 106) (DeCoursey and Cherny, 1994). H+ conduction has much greater temperature dependence (Byerly and Suen, 1989; Kuno et al., 1997; DeCoursey and Cherny, 1998) and stronger deuterium isotope effects (DeCoursey and Cherny, 1997) than the vast majority of ion channels. Nevertheless, H+ permeates passively down its electrochemical gradient, and H+ channels exhibit time- and voltage-dependent gating, and thus resemble ion channels more than other transporters. If proton channels are genuine voltage-gated ion channels, their gating ought to generate current fluctuations that could be used to estimate the single channel conductance. The H+ current fluctuations described here provide strong evidence of gating, a defining property of ion channels, and thus support the designation of voltage-gated proton channels as genuine ion channels

Three groups have attempted to detect H+ current fluctuations previously (Byerly and Suen, 1989; Bernheim et al., 1993; DeCoursey and Cherny, 1993). In the best case, the signal-to-noise ratio (S/N = the ratio of H+ current variance to the “background” variance when H+ channels are closed or blocked) was very poor, 0.5 (DeCoursey and Cherny, 1993). Byerly and Suen (1989) established an upper bound at <50 fS at pHi 5.9. No excess fluctuations were seen (S/N = 0), but the data had to be filtered at 1 kHz because of the rapid gating kinetics in snail neurons. Bernheim et al. (1993) filtered at 5 kHz, and from a 6% reduction of variance in the presence of Cd2+ (S/N = 0.06), they estimated the conductance to be 90 fS at pHi 5.5 (Bernheim et al., 1993). DeCoursey and Cherny (1993) improved S/N to 0.5 and estimated the unitary conductance at pHi 6.0 in human neutrophils to be ∼10 fS. All of these estimates were compromised by poor S/N and should be considered very rough. Here we report noise measurements in which S/N was routinely >100 and sometimes >1,000. In whole-cell studies, stationary H+ current fluctuations can only be recorded just above Vthreshold because prolonged H+ currents deplete intracellular buffer and change pHi (Thomas and Meech, 1982; DeCoursey, 1991). To avoid this problem, we studied noise in excised inside-out patches. An additional benefit is that this approach enables varying pHi in the same experiment.

## Materials And Methods

### Eosinophil Isolation

Venous blood was drawn from healthy adult volunteers under informed consent according to procedures approved by our Institutional Review Board and in accordance with federal regulations. Neutrophils were isolated by density gradient centrifugation as described previously (DeCoursey et al., 2001) with one modification. In the two cycles of hypotonic lysis performed for removal of the red blood cells, isotonicity was restored by the addition of 2× concentrated Hank's balanced salt solution (HBSS)* (without Ca2+ or Mg2+) containing 5 mM HEPES, pH 7.4. Eosinophils were isolated from the neutrophil preparation by negative selection using anti-CD16 immunomagnetic beads as described by the manufacturer (Miltenyi Biotec, Inc.). The eosinophils were suspended in HEPES (10 mM)-buffered HBSS (with Ca2+ and Mg2+), pH 7.4, containing 1 mg/ml human serum albumin (HEPES-HBSS-HSA buffer). Eosinophil purity was routinely >98% as determined by counting Wright-stained cytospin preparations.

### Solutions

External and internal solutions contained 100 or 200 mM buffer supplemented with tetramethylammonium methanesulfonate (TMAMeSO3) to bring the osmolality to ∼300 mosmol kg−1. Solutions contained 2 mM MgCl2 and 1 mM EGTA. Solutions were titrated to the desired pH with tetramethylammonium hydroxide (TMAOH) or methanesulfonic acid (for solutions using BisTris as a buffer). A stock solution of TMAMeSO3 was made by neutralizing TMAOH with methanesulfonic acid. The following buffers were used near their pKa (at 20°C) for measurements at the following pH: pH 4.1, phosphate (phosphoric acid neutralized with TMAOH); pH 5.0, Homopipes (homopiperazine-N,N'-bis-2-(ethanesulfonic acid), pKa 4.61); pH 5.5–6.0 Mes (pKa 6.15); pH 6.5 Bis-Tris (bis[2-hydroxyethyl]imino-tris[hydroxymethyl]methane, pKa 6.50); pH 7.5 HEPES (pKa 7.55). Buffers were purchased from Sigma-Aldrich, except for Homopipes (Research Organics). In about half the experiments, solutions with 200 mM HEPES for pH 7.5 or 200 mM Mes for pH 5.5 and 6.5 were used. These solutions contained 2 mM MgCl2 and 2 mM EGTA and were titrated to the desired pH with n-methyl-D-glucamine or with TMAOH.

#### TΩ seals.

The seal resistance in this study was typically in the TΩ (1012 Ω) range. Our solutions were designed to minimize extraneous conductances by use of impermeant ions and to maximize control of pH by use of high buffer concentrations. The ionic strength was lower than more conventional solutions, especially for the 200 mM buffer solutions. Consequently, the conductivity of these solutions measured at 25°C with a Fisher Digital Conductivity Meter (Fisher Scientific) was low: 7.2–9.8 mS/cm for the 100 mM buffer solutions and 2.7–7.3 mS/cm for the 200 mM buffer solutions, compared, for example, with 15.9 mS/cm for Ringer's and 22.4 mS/cm for isotonic K+ Ringer's solutions. Both the low conductivity and the paucity of permeant ions may have contributed to the high seal resistances obtained. The patch resistance at voltages negative to the threshold for activating H+ currents averaged 1.33 ± 0.18 TΩ (mean ± SEM, n = 20) in patches studied with 100//100 mM buffer (out//in). With the 200//200 mM buffer solutions, the patch resistance was no higher, 1.32 ± 0.15 TΩ (n = 21). There was no significant difference between resistances measured in any two combinations of solutions. High resistance patches are not cell specific; a 0.9 TΩ resistance was obtained in an alveolar epithelial cell patch studied with similar solutions (Fig. 15 of DeCoursey, 2003). Resistances up to 4 TΩ were reported by Benndorf (1994), using hypertonic solutions (conductivity 36.6 mS/cm) and tiny pipette openings of only 0.2 μm (∼70 MΩ pipette resistance even with the highly conductive solution). Our pipettes had “normal” geometry and typically a 5–15 MΩ tip resistance.

### Electrophysiology

All measurements were made using the inside-out patch configuration. Inside-out patches were formed by obtaining a tight seal and then lifting the pipette into the air briefly. Micropipettes were pulled using a Flaming Brown automatic pipette puller (Sutter Instruments Co.) from 7052 glass (Garner Glass Co.), coated with Sylgard 184 (Dow Corning Corp.), and heat polished. Electrical contact with the pipette solution was achieved by a thin sintered Ag-AgCl pellet (In Vivo Metric Systems) attached to a Teflon-encased silver wire. A reference electrode made from a Ag-AgCl pellet was connected to the bath through an agar bridge made with Ringer's solution. The current signal from the patch clamp (List Electronic) was passed through a secondary 8-pole lowpass Bessel filter (Frequency Devices model 902LPF) that was used to filter and amplify the signal by 20 dB, generally with a −3 dB cutoff frequency of 10–20 Hz. The minimum increment of digitization with a gain of 2,000 or 5,000 was ∼2.2 fA or ∼0.9 fA, respectively. The current was recorded simultaneously on both an Indec Laboratory Data Acquisition and Display System (Indec Corporation) and on a PC-based system with our own software written for the L780 ADC board (Measurement Computing Corp.). Seals were formed with Ringer's solution (in mM: 160 NaCl, 4.5 KCl, 2 CaCl2, 1 MgCl2, 5 HEPES, pH 7.4) in the bath, and the zero current potential established after the pipette was in contact with the cell. Then the bath was exchanged with one of the solutions described above. Bath temperature was controlled by Peltier devices, and monitored by a resistance temperature detector element (Omega Scientific) in the bath. The experiments were done at 21°C.

To calculate conductance, it is necessary to estimate the reversal potential, Vrev. This was done by conventional tail current analysis in patches in which the currents were large enough that tail currents could be resolved. In other patches, Vrev was estimated from the voltage at which H+ current first became activated, Vthreshold, according to the empirical relationship between Vrev and Vthreshold reported in Fig. 11 of DeCoursey and Cherny (1997), which appears to apply to voltage-gated proton channels in all cells (Fig. 19 in DeCoursey, 2003).

Conventions. We refer to pH in the format pHo//pHi. In the inside-out patch configuration the solution in the pipette sets pHo, defined as the pH of the solution bathing the original extracellular surface of the membrane, and the bath solution sets pHi. Currents and voltages are presented in the normal sense, that is, upward currents represent current flowing outward through the membrane from the original intracellular surface, and potentials are expressed by defining as 0 mV the original bath solution. Data are presented without correction for leak current or liquid junction potentials.

### Evaluation of Adequacy of Noise Sample Duration

If a current sample is too short in relation to the time constants of the kinetic processes responsible for generating the noise, then σ2 will be underestimated (Diggle, 1990). To estimate the extent to which σ2 is underestimated by using finite records we pooled successive single records to form longer composite records and then determined σ2 as a function of sample length for each composite record. Plots like those in Fig. 1 were fitted with the following empirical function:

$\mathrm{{\sigma}}^{2}=A_{0}+A_{1}\left(1{-}e^{{-}{t}/{\mathrm{{\tau}}_{1}}}\right)+A_{2}\left(1{-}e^{{-}{t}/{\mathrm{{\tau}}_{2}}}\right)\mathrm{,}$

or one of its reduced forms (single exponential, exponential plus straight line). Models were chosen by considering the probability of Student's t values for the parameter estimates, followed by visual inspection. The “true” value of σ2 (σ2) was then estimated by extrapolating the saturating (exponential) components as t → ∞. 61 composite records were obtained from seven different patches, and included various suprathreshold voltages at pHo 7.5 and 6.5, and pHi 5.0, 5.5, and 6.5. Single record lengths ranged from 12 to 50 s, but were mostly 12–20 s. Composite-record lengths ranged from 16 to 166 s (two 16 s single records are included).

Values of σ2(single-record)/σ2 ranged from 0.72 to 1.34, with a median of 0.99. [Some values of σ2(single-record)/σ2 exceed unity because of scatter and/or the presence of a linear component.] Hence, errors in σ2 resulting from the use of finite (single) records appear to be negligible. Furthermore, there was no evidence that this error varied with pHi. The presence of a linear (nonsaturating) component in 20 composite records (e.g., Fig. 1 B) apparently reflects the presence of 1/f noise, since the slope of the linear component was positively correlated with the band-limited variance of 1/f noise (unpublished data).

### Spectral Analysis

For the determination of power spectra, the mean current was first subtracted from the current records. Records in which the current increased were fitted by linear or rising exponential functions, which were subtracted to eliminate spurious trends. The resulting residual time series were then analyzed by one of two methods. For pH regimes 7.5//5.0 and 7.5//5.5 (relatively fast kinetics), power spectra were obtained with program “spctrm” in Press et al. (1992). This program divides the data into at least two segments, estimates the spectral density for each segment using an FFT (fast Fourier transform), and then takes the average. Where several successive records at a given voltage were available, each record was treated as a segment. This gives the lowest frequency obtainable, because equally spaced data are required. Hence, the length of a segment (the reciprocal of which determines the lowest frequency) cannot exceed the length of a record when there are gaps between records. With this lower frequency limit, Lorentzian plateaus often were not detected for pH regimes 7.5//6.5 and 6.5//6.5, presumably because the slower gating kinetics shifted the Lorentzian component to lower frequencies than those resolved. Accordingly, a second method for determining power spectra was used for these data that allowed successive records (including gaps) to be treated as a single record, thus reducing the lower frequency limit of the spectrum. Gaps between records pose no problem for the estimation of the autocovariance function, which was calculated according to Eq. 2.5.5 in Diggle (1990). The one-sided spectral density was then obtained as the Fourier cosine transform of the autocovariance (Blackman-Tukey method) as described by Otnes and Enochson (1978). The reliability of both methods for estimating power spectra was checked with simulated data for a two-state kinetic scheme.

To correct for filtering, spectra were divided by the square modulus of the transfer function for an eight-pole low-pass Bessel filter using equation 3.11 and coefficients in Tietze and Schenk (1978). This had a negligible effect on most of the spectrum, but it did allow curve-fitting up to about the cutoff frequency of the filter (typically 20 Hz); data above this frequency were discarded. The data were then binned in log10(f) intervals of 0.2 (where f is the frequency in Hz) before fitting with various functions by nonlinear least squares. The most general function employed treats the one-sided spectral density G(f) as the sum of Lorentzian, 1/f and white components:

$G\left(F\right)=\frac{4\mathrm{{\tau}}_{\mathrm{L}}\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}}{1+\left(2\mathrm{{\pi}{\tau}}_{\mathrm{L}}f\right)^{2}}+\frac{A}{f^{m}}+B\mathrm{,}$

where

$$\mathrm{{\sigma}}_{\mathrm{L}}^{2}$$
is the current variance attributed to open/closed transitions of the channels, τL is the “Lorentzian” time constant defined as (2πfc)−1, where fc is the corner (half-power) frequency, and m, A, and B are constants. In practice, estimates of m were in the range 0.7 to 1.4; noise of this type is generally described as 1/f (Neumcke, 1978; DeFelice, 1981). Various reduced models were then fitted by removing one or more of these adjustable parameters. Initial selection of a minimum-parameter model was made using F-tests as described by Gallant (1975) and Walpole and Myers (1978). The fits were then checked visually and t-value probabilities for parameter estimates were inspected; in a few cases, the initial choice of minimum-parameter model was overridden.

### Online Supplemental Material

The online supplemental material evaluates quantitatively the possibility that pH changes due to H+ current might occur under the conditions of these experiments, and we estimate the errors introduced. Analysis of simulated y-gH plots (e.g., Fig. 6) suggests that the errors in γH and N due to proton depletion/accumulation are relatively small and essentially independent of pHi and pHo. For typical values, γH was overestimated by 1–4% while N was underestimated by 2–10%. We also estimate that local pH changes due to current flow will be established within 0.1–1.2 s.

## Results

### H+ Channel Gating Generates Current Fluctuations

The currents in excised patches were distinctly noisier when the H+ conductance was activated. Fig. 2 illustrates currents recorded during pulses or prolonged depolarizations in the same inside-out patch of membrane from a human eosinophil, at three different pHi (the bath solution faces the intracellular side of the membrane). The threshold voltage, Vthreshold, at which H+ current is first activated is exquisitely sensitive to pH, becoming more negative at lower pHi, as in all other cells with voltage-gated proton channels (Byerly et al., 1984; DeCoursey, 2003). The patch currents exhibit little noise at subthreshold voltages, but become markedly noisier when small outward H+ current is activated just above Vthreshold.

In Fig. 3, chord conductance-voltage (gH-V) relationships from the experiment in Fig. 2 are plotted. The curves show that the quasisteady-state gH-V relationship is well described by a Boltzmann function. The slope factors are 5–8 mV, somewhat steeper than most estimates of 7–14 mV in whole-cell studies using shorter pulses (DeCoursey and Cherny, 1994; Cherny et al., 2001). The average slope factors were 8.16 ± 0.52 mV (mean ± SEM, n = 13) at pH 7.5//5.5 and 6.99 ± 0.48 mV (n = 16) at pH 7.5//6.5 (P > 0.1). The present values are probably more reliable for two reasons. First, they are more nearly steady-state, because they were measured after long times at each voltage. Second, H+ currents in excised patches are less distorted than in whole-cell configuration by pH changes that occur during current flow, due to depletion of protonated buffer (see online supplemental material).

As evident in Fig. 3, lowering pHi shifts the gH-V relationship toward more negative voltages and increases gH,max. The average shift in Vthreshold between pHi 6.5 and 5.5 was −36 ± 5 mV (mean ± SD, n = 9) and the average shift in the midpoint of the gH-V relationship was −31 ± 9 mV (n = 8). Thus, in most patches, there was a larger shift in Vthreshold than in the patch illustrated. Although this patch is not ideally representative in all respects, we use it in many figures in this paper because it was a rare patch in which we were able to record extensive data at three pHi and it exhibits, at least qualitatively, all of the behaviors that characterize this system. The limiting gH, gH,max, consistently increased at lower pHi. Rundown, which was often observed during long experiments (e.g., gH,max might decrease 50%), compromises our comparison of gH,max and of the number of channels in the patch, N, at different pHi. However, measurements made before and after pHi changes indicate that the macroscopic gH,max has a relatively weak dependence on pHi. On average, in nine patches in which sufficient data were recorded at both pH, gH,max was 1.78 ± 0.10 (mean ± SE) times larger at pHi 5.5 than 6.5 in each patch. This comparison was done with pH changes in both directions and the measurements were fairly close together in time to minimize effects of rundown.

Current fluctuations can be quantified by their variance, σ2. Variance measured in the patch illustrated in Figs. 2 and 3 is plotted in Fig. 4. Each data point represents a 12-s sample of current, collected during prolonged sojourns at each voltage. Comparison of Figs. 3 and 4 confirms that σ2 increases precisely at the voltage at which the gH becomes activated at each pHi. At subthreshold voltages the variance is ≤10−28 A2. It is noteworthy that the signal-to-noise ratio (S/N, defined in introduction) at lower pHi is >100 at many voltages, which is a two-order-of-magnitude improvement over previous studies (Byerly and Suen, 1989; Bernheim et al., 1993; DeCoursey and Cherny, 1993). In some patches, S/N was >1,000.

Several features indicate that the noise is related to the activation of H+ channels. First, when pHi was varied, which shifted the gH-V relationship, the current always became noisy (i.e., σ2 increased) at Vthreshold. Second, no other detectable ion-specific conductance is evident in eosinophil patches under these ionic conditions. During depolarizing pulses, the current turns on from a small initial level, indicating that practically all of the outward current is the result of voltage- and time-dependent gating. Finally, σ2 increases rapidly with depolarization above Vthreshold, but at larger depolarizing voltages, σ2 does not increase in proportion, and at pHi 5.5 or 5.0, actually decreases. Strikingly, σ2 is maximal near the midpoint of the gH-V relationship at pHi 5.5 or 5.0 (symbols labeled V1/2 in Fig. 4). If the noise were generated by some process other than channel gating fluctuations, one would expect σ2 to increase with the current amplitude (DeFelice, 1981; Kogan, 1996). The 1/f component of σ2 that is associated with ion transport through open ion channels often increases with I 2 (Conti et al., 1975; DeCoursey et al., 1984). To the extent that we observe a distinct maximum in the σ2-V relationship (Fig. 4), any such component must be dwarfed by σ2 generated by H+ channel gating, that is expected to have a Lorentzian spectrum (see Power spectra). In fact, the σ2 contained within the Lorentzian component alone, plotted as open symbols in Fig. 4, is similar to the total σ2 except at large depolarizations. As shown in Fig. 5, the voltage dependence of the current variance behaves precisely as one would predict from a simple gating model.

Ideally, the variance due to H+ channel gating,

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
⁠, would be measured under stationary conditions. At lower pHi, the activation time course (turn-on) of H+ current was relatively rapid and accordingly these data appeared to be stationary. More rigorous tests of stationarity, in which the variance was estimated at different times during prolonged records also revealed no clear trends in σ2. However, activation was much slower at pHi 6.5, and up to several minutes were required at some voltages before stationarity was achieved. H+ current data that increased slowly during each successive record were “corrected” for the slow drift by subtracting a fitted single exponential curve. We discarded the first several records in which IH increased more rapidly and used only the last few records, treating each one separately (i.e., with its own IH, Popen, and
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
). In Fig. 1 (materials and methods) we showed empirically that
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
measured during 12–20-s current records included >90% of the total
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
that is expected to be obtained with much longer records.

### Calculation of iH from Stationary Variance of H+ Currents

Accepting that the current fluctuations originate in H+ channel gating, we would like to estimate the single channel H+ current, iH, and related properties (the number of channels in the patch, N, and the open probability, Popen). iH can be calculated from (Hille, 2001):

$i_{\mathrm{H}}=\frac{\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}}{I_{\mathrm{H}}\left(1{-}P_{\mathrm{open}}\right)}\mathrm{,}$
(1)

where

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
is the H+ current variance, and IH is the mean H+ current. Except for Popen, these parameters are directly measurable, although it is necessary to distinguish the contributions to current and variance that originate in H+ channels from background current or noise. The total σ2 was essentially independent of voltage at subthreshold voltages where H+ channels are closed (Fig. 4). Therefore, we subtracted the average σ2 at subthreshold voltages from that measured at voltages where H+ channels were open. This approach was used by Byerly and Suen (1989). Another approach is to inhibit H+ current with Zn2+ of Cd2+ and to consider the resulting σ2 to be the background at that voltage (Bernheim et al., 1993). We avoided this approach because Zn2+ sometimes reduced both the background leak current and σ2 at voltages where H+ channels were closed, and at high concentrations Zn2+ apparently caused membrane damage that increased σ2 spuriously. In a few patches, the maximal H+ current was <1 pA and the fluctuations attributable to H+ channel gating were comparable with background levels (i.e., S/N ≈ 1). However, in most patches, S/N > 100, and sometimes S/N > 1,000, hence the subtraction of background variance had negligible effect. Determination of IH required subtraction of leak current. Leak current at subthreshold voltages was usually Ohmic, and we extrapolated it to estimate the leak at each voltage where noise was measured. The most difficult parameter to estimate was Popen. In preliminary analyses, we approximated Popen as gH measured during the noise record normalized to gH,max from a family of pulses, which presumes that the maximum value of Popen (Pmax) approaches 1.0 for large depolarizations. For measurements just above Vthreshold where Popen is small, this assumption will cause only a small overestimation of iH. However, knowledge of Popen becomes important at more positive voltages where gH approaches saturation. For this reason, previous attempts to estimate iH were restricted to voltages near Vthreshold (Bernheim et al., 1993; DeCoursey and Cherny, 1993). Eventually, we adopted a procedure of data analysis (see below) that obviates the need to guess Popen.

### What is the Limiting Popen at Large Depolarizations?

The calculation of iH requires an estimate of Popen (Eq. 1). Although gH may be proportional to Popen (after correction for rectification), it provides no information about Pmax. However, the voltage dependence of the

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
does provide evidence about Pmax. Current fluctuations generate variance in proportion to the frequency of gating events, which is proportional to the product Popen(1-Popen) (Conti and Neher, 1980; Hille, 2001). Thus, gating transitions will occur most often and
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
will be maximal near Popen = 0.5 (if Pmax > 0.5). Fig. 5 (bottom) illustrates the voltage dependence of σ2 calculated with a simple gating model using parameters typical of voltage-gated proton channels, assuming different values of Pmax (Fig. 5, top). Although this heuristic model obviously ignores complexities of H+ channel gating, it describes the main features of the data remarkably well. If Pmax is 1.0, σ2 increases to a maximum near the midpoint of the gH-V relationship and then decreases to 0 at large voltages where Popen → 1. If Pmax is 0.1 or 0.5, the variance increases monotonically and almost linearly with depolarization (on a linear scale). If Pmax is 0.8 there is a clear inflection, and if Pmax is 0.9 the variance peaks and then decreases before increasing again. The Pmax at which nonmonotonic
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
-V behavior occurs depends somewhat on k, the slope factor of the gH-V relationship. The appearance of these curves is also influenced by the relative positions of Vrev and the gH-V relationship.

Comparison of the voltage dependence of actual σ2 data (Fig. 4) with the model variance (Fig. 5) indicates that Pmax ≥ ∼0.9 at low pHi. In most patches studied at pH ≤ 5.5,

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
reached a clear maximum with increasing depolarization, and then decreased before eventually increasing again. The maximum
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
occurred near or slightly positive to V1/2, indicated near the X axis in Fig. 4, precisely as expected from the simple model in Fig. 5. At pHi 6.5, we did not see a clear maximum in
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
, but usually a monotonic increase in
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
with depolarization, although the increase was often more gradual during large depolarizations (i.e., positive to V1/2 in Fig. 4). This behavior is suggestive of Pmax ≤ 0.8. A more quantitative analysis of Pmax is described in the next section.

### Obtaining γH and N from a Linearized Plot of All Data

It is possible to obtain γH and N simultaneously without foreknowledge of Popen by plotting

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
data obtained at multiple voltages in a simple format. From Sesti and Goldstein (1998):

$\mathit{y}=\mathrm{{\gamma}}_{\mathrm{H}}{-}N^{{-}1}g_{\mathrm{H}}\mathrm{,}$
(2)

where

$y=\frac{\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}}{I_{\mathrm{H}}\left(V{-}V_{\mathrm{rev}}\right)}\mathrm{.}$
(3)

Hence, provided γH is constant (e.g., no rectification) and N is constant (e.g., no rundown) a plot of y versus gH should be linear. The Y intercept is the unitary conductance, γH, and the slope is −1/N. The intercept on the X axis is γHN, the maximum possible gH if all channels were open simultaneously (which may be greater than the observed gH,max). In practice, within the limits of experimental error, linear y-gH plots were obtained, as in Fig. 6. For pHi 6.5, the slope was often small and sometimes not significantly different from zero. In such cases N could not be determined reliably, although γH could still be estimated.

We adopted the y-gH plot because (a) through N, it provides an estimate of Popen without requiring assuming an arbitrary value, and (b) it makes use of all the data over a range of voltages that include low to high Popen. Different errors are expected to occur at both extremes of Popen as well as at intermediate values. Near Vthreshold, both IH and σ2 are close to background levels, and thus are poorly determined. During large depolarizations, iH might be attenuated due to pH changes that result from prolonged H+ flux through the patch. This error is considered in the online supplemental material , and shown to have had little impact on the results. At intermediate voltages, the estimated IH using Eq. 1 depends strongly on the limiting Popen value. Attempting to use Eq. 1 directly on individual records would require guessing Popen. By including all the data in plots such as in Fig. 6, we can estimate N, from which Popen can be calculated.

In Fig. 7, Popen is plotted for the same patch as in other figures. To approach true steady-state, we plot only the estimate from the final record at each voltage. The results are quite similar to the simple gH-V relationships in Fig. 3. The additional information obtained from Fig. 7 is the limiting value for Popen, Pmax. Average values of Pmax are given in Table I. Consistent with the behavior predicted from Figs. 4 and 5, Pmax is 0.95 at pHi ≤5.5, and at pHi 6.5, Pmax is 0.75. Almost all H+ channels open during large depolarizations at low pHi, but Pmax decreases at higher pHi.

The single-channel conductance, γH, is already determined from the y-gH plot (Fig. 6). However, in Fig. 8 the unitary currents calculated for each noise sample are plotted. The lines are not fitted to these data but simply illustrate the values for γH obtained from the y-gH plots. Single channel H+ currents are a few femtoamperes at pHi 6.5, and increase markedly at lower pHi. Mean values obtained for γH are given in Table I. Lowering pHi from 6.5 to 5.5 increased γH by 3.7-fold on average. Although only a few measurements were made at pH 6.5//6.5, the similar γH obtained at pH 7.5//6.5 suggests that γH depends only on pHi and not on pHo.

### Direct Measurement of Single-channel H+ Currents

Consistent with previous studies (Byerly and Suen, 1989; Bernheim et al., 1993; DeCoursey and Cherny, 1993), we were unable to detect single H+ channel currents directly when pHi was 6.5 or higher. However, at pHi 5.5 there were tiny step-like fluctuations in the current in some patches (Fig. 9). Putative unitary currents could be resolved only near Vthreshold, where just a few channels opened at a time. In Fig. 9, channel-like events are present at −60 and −70 mV, but at −50 mV too many channels are open to resolve discrete levels. The amplitude of the events at −60 mV is ∼10 fA, estimated as the difference in local mean current when the channel is judged to be open or closed. The

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
analysis (y-gH plot) of this patch indicated that iH was ∼5 fA at −60 mV. Apparent single-channel currents in seven other patches under similar conditions were 7–16 fA, which is about twice as large as estimates obtained from variance analysis, although it is evident that the amplitudes are not clearly resolved. To our knowledge, these are the smallest single-channel currents identified by direct voltage-clamp measurement of any channel. Decker and Levitt (1988) resolved 25-fA H+ currents through gramicidin channels.

### Frequency Dependence of H+ Current Fluctuations

Power spectra were obtained from a subset of the data comprising 11 datasets from 7 different patches. Lorentzian spectral components could be identified under all pH regimes (Fig. 10), although detection of the Lorentzian plateau was difficult for pHi 6.5 (Fig. 10 B). The Lorentzian noise appeared to “turn on” when IH became activated, and the variance contained within the Lorentzian component,

$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
(Fig. 11, ▴), showed similar voltage dependence to the total current variance (
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
= open,
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
= solid symbols in Fig. 4). Thus, the
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
-V relationship exhibited a maximum for pHi 5.0 and pHi 5.5 (Fig. 11 A), but increased monotonically with V for pHi 6.5 (Fig. 11 B). In addition to the Lorentzian noise, 1/f (Fig. 11, ○) and white noise (▾, Fig. 11) were also often observed. Both of these components increased monotonically with V. The 1/f component dominates at large depolarizing voltages because of the nonmonotonic voltage dependence of
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
at low pHi. For reference, the sum of the calculated shot noise of current flow and Johnson noise of the 50 GΩ feedback resistor in parallel with the patch resistance (Hainsworth et al., 1994), both of which are white noise, is shown by the dashed lines without symbols in Figs. 10 A and 11. The patch resistance was mainly determined by the H+ conductance. The 1/f spectrum at −80 mV in Fig. 10 A approaches this limiting noise level at ∼20 Hz.

If

$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
represents the only contribution of open/closed transitions to the current variance, then
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
rather than
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
should be used to estimate γH and N (Eqs. 23, Fig. 6). Fig. 12 illustrates y-gH plots at pHi 5.5 (A) or pHi 6.5 (B), using either total H+ current variance
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
(○) or only the integral of the Lorentzian component,
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
(•). Surprisingly, γH and N were little affected when only the Lorentzian component was included. Estimates of γH based on σL2 were reduced by only ∼20% at all pHi, and the estimates of N were, on average, unaffected for pHi 5.0 and 5.5. The reason that estimates based only on
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
are so similar to those based on
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
is that σL2 dominates the total variance at small depolarizations. At large depolarizing voltages where the 1/f component becomes large (Fig. 11), and hence
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
and
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
diverge, the effect on the slope and intercept of the y-gH plot is quite small.

The Lorentzian time constants τL = (2π fc)−1 were smaller than the time constants for H+ current activation (τact) by roughly an order of magnitude (Fig. 13). However, they showed a qualitatively similar dependence on pHi. In contrast to τact (which decreases with V), no consistent voltage dependence could be discerned for τL, although this may have been masked by the considerable scatter. Mean deactivation time constants, τtail, measured during tail currents at voltages just negative to Vrev are plotted in Fig. 13. To compare τtail and τact with τL in the same voltage range, these measured τtail values are extrapolated to the midpoint voltage of the gH-V relationship, assuming an exponential voltage dependence with a slope of 40 mV/e-fold change in τtail, as found in several studies (DeCoursey, 2003). The τL values are closer to τtail than to τact. At pH 7.5//5.5, we determined the mean open time in five patches in which apparently discrete events occurred near Vthreshold (e.g., Fig. 9). The mean open time from these patches is similar to τL.

## Discussion

### Proton Channel Gating Generates H+ Current Noise

Distinct H+ current fluctuations were clearly evident in patches of eosinophil membranes. Compelling evidence indicates that these fluctuations originate in the gating of voltage-gated proton channels. First, at various pHi, σ2 increases precisely at Vthreshold. Second, σ2 increases with voltage to a maximum that occurs near the midpoint of the gH-V relationship at each pHi. At larger depolarizing voltages, σ2 then decreases at pHi ≤ 5.5, but increases again gradually at very large depolarizing voltages. Precisely this behavior is predicted by a simple gating model to occur if Pmax ≥ 0.9 (Fig. 5), but is exceedingly unlikely to result from fluctuations originating in leak current. Finally, no other conductance is evident under the ionic conditions of this study.

Single H+ channel currents were estimated from stationary and quasistationary H+ current variance, and were also measured directly at low pHi. H+ current fluctuations could be resolved with excellent S/N because proton channels in mammalian cells, especially in phagocytes, gate at low frequencies (DeCoursey, 2003), which allows heavy filtering. In contrast, H+ current fluctuations could not be detected in snail neurons (Byerly and Suen, 1989), because these H+ channels open on a time-scale of a few milliseconds (Byerly et al., 1984), requiring ∼100-fold higher bandwidth. Bernheim et al. (1993) reported barely detectable excess H+ current noise in human skeletal myotubes, but they filtered at 5 kHz with S/N < 0.1. We previously detected distinct excess H+ current fluctuations in human neutrophils with 200 Hz but not 2 kHz lowpass filtering (DeCoursey and Cherny, 1993). Due to improved recording conditions and appropriate filtering, S/N is now typically ∼100, and in some patches as high as 2,000. At subthreshold voltages the variance was usually <10−28 A2, and sometimes as low as 2 × 10−29 A2, which is near the theoretical minimum noise level of 6.5 × 10−30 A2 for a patch-clamp recording setup with a 50 GΩ feedback resistor and a bandwidth of 20 Hz (Levis and Rae, 1993). The difference may be accounted for by 1/f noise of unknown origin (e.g., the spectrum at −80 mV in Fig. 10 A).

### Power Spectra

A first order gating process should generate Lorentzian power spectra (Stevens, 1972). Power spectral analysis of voltage-gated proton current indicated a Lorentzian component whose voltage dependence coincided with that of H+ channel activation. Furthermore, the variance obtained as the integral of the Lorentzian component,

$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
⁠, increased to a maximum near the midpoint of the gH-V relationship and then decreased with further depolarization at pHi ≤ 5.5, similar to the behavior of the total variance,
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
. Thus, the Lorentzian component arises from H+ channel gating events. The Lorentzian time constants (τL) defined as τL = (2π fc)−1, were shorter than the time constants for proton-current activation (τact) by roughly an order of magnitude, but were in the range of τtail and the mean open time determined from single channel currents (Fig. 13).

In addition to a Lorentzian component, significant 1/f noise was also often observed. In contrast with Lorentzian spectra, the origin of this noise is unclear; 1/f noise can arise simply from nonstationary processes such as baseline drift (Conti et al., 1980). In the present study, the amplitude of 1/f noise became significant at voltages where IH was activated (Fig. 11). Hence, at least part of the 1/f noise may have been associated with H+ conduction, or possibly even channel gating. Gating with distributed kinetics can generate 1/f noise (Sauvé and Szabo, 1985; Kogan, 1996; Bezrukov and Winterhalter, 2000). Similarly, the roll-off of a low frequency Lorentzian component might contribute low frequency variance that could be mistaken for 1/f noise. Excess white noise evident at high frequencies was also sometimes present (Fig. 11), although this component always represented only a small fraction of the total σ2. White noise may have arisen in the recording system or could reflect an unresolved high frequency Lorentzian component.

It is possible that

$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
underestimates the current variance associated with channel gating. One or more Lorentzian components at low frequencies may not have been detected, or were interpreted as 1/f noise. A Lorentzian with a corner frequency (fc) corresponding to the time constant of H+ current activation (τact) is to be expected (Colquhoun and Hawkes, 1977), but could have been resolved only at low pHi. At pHi 6.5, clear resolution of such a Lorentzian component (i.e., resolution down to fc/10) would require stationary current samples ∼70 min long. Similarly, if all or part of the 1/f noise were associated with channel gating (e.g., if the 1/f spectrum were actually a superposition of Lorentzians) then estimates of γH based on
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
(Fig. 12) will be downwardly biased. The same can be said of the white noise component, although this was very small. On average, however, the estimates of γH based on
$$\mathrm{{\sigma}}_{\mathrm{L}}^{\mathrm{2}}$$
and
$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
differ by only ∼20%.

### Unitary H+ Currents Increase at Low pHi More Than Macroscopic Conductance

The single channel conductance estimated from

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
was 38 fS at pHi 6.5, and 139 fS at pHi 5.5 (Table I). A few measurements at lower pHi (where patches were extremely unstable) indicate similar pHi dependence. Extrapolating γH at pHi 5.5 and 6.5 to pHi 7.2 gives an estimate of 15 fS for the unitary conductance at physiological pH. Corrected to 37°C assuming a Q10 of 2.8 (DeCoursey and Cherny, 1998), γH becomes 78 fS. The most surprising result of this study was that the single channel conductance increased 3.7-fold at pHi 5.5 compared with pHi 6.5, in contrast with the macroscopic conductance, which increased only 1.8-fold. In nearly all existing studies of voltage-gated proton channels, the macroscopic gH increased only ∼2-fold per unit decrease in pHi (DeCoursey, 2003). The relative pH independence of the macroscopic gH has been considered somewhat paradoxical, both for voltage-gated proton channels (DeCoursey and Cherny, 1994) and for the proton channel of ATP synthase (Junge, 1989). In contrast, the H+ conductance of gramicidin channels is almost directly proportional to [H+] over a wide pH range (Eisenman et al., 1980; DeCoursey, 2003). The unitary conductance found here (Table I) is not proportional to [H+], but is closer to proportionality than estimates based on macroscopic gH measurements.

Because lowering pHi increased the estimated single-channel conductance substantially more than the macroscopic gH,max, the total number of H+ channels, N, must decrease. This anomalous behavior has several possible explanations. Although the result might be artifactual, consideration of possible sources of error does not lead to likely candidates. The variance at higher pHi might be underestimated if we did not sample a sufficiently low frequency range, but the variance-versus-record length analysis (materials and methods) gave no indication of this. Progressive rundown (loss of functioning channels) at lower pHi could contribute in experiments in which measurements were first made at higher pHi. However, correction for rundown or reversing the order of pHi measurements did not eliminate the phenomenon. The observed pHi dependence of Pmax does not explain this result, but instead works in the opposite direction. There seems no alternative but to accept that low pHi actually reduces the number of functioning H+ channels. Based on the average values of γH, Pmax, and gH, N is 2.6 greater at pHi 6.5 than 5.5 (or 62% of the channels at pHi 6.5 are unavailable at pHi 5.5).

Single-channel–like events (7–16 fA) could be observed directly in many patches at pHi ≤ 5.5, just above Vthreshold. The amplitude of these events was not well-resolved, but usually was about double the unitary H+ current calculated at the same voltage from

$$\mathrm{{\sigma}}_{\mathrm{H}}^{\mathrm{2}}$$
⁠. It is possible that these events were simultaneous openings of multiple channels, and that the single channels were simply not resolved. Alternatively, H+ channels may have a cooperative gating mechanism. We assume that most H+ current fluctuations occur within the frequency range examined. The adequacy of the bandwidth employed in the low frequency range was demonstrated empirically in Fig. 1, but it is possible that there could be components of gating at higher frequencies than we explored. Of course, it is possible that the discrepancy simply reflects errors in the measurements.

If each channel flickered on a millisecond scale, we would have resolved only the average current. However, from the vantage point of most cellular processes, such as pHi regulation, a channel that conducts 5 fA of continuous H+ current is functionally equivalent to one that conducts 10 fA but flickers rapidly with Popen = 0.5.

Judged solely by their conductance, voltage-gated proton channels cannot be distinguished conclusively from highly efficient carriers. For example, H+ efflux through Na+/H+-antiporters in human fibroblasts at their maximum turnover rate at pHi 6.0 is equivalent to 0.5–1.7 fA (Siczkowski et al., 1994). Present estimates of γH correspond with transport of 2.4 × 104 H+/s (3.8 fA) at pHi 6.5 for a 100-mV driving force, and 9 × 104 H+/s (14 fA) at pHi 5.5. Although the conductance of H+ channels is very small compared with other ion channels, in view of the low concentration of protons at physiological pH, the conductance is, if anything, larger than expected. Gramicidin channels can conduct >2 × 109 H+/s (Cukierman, 2000) at pH < 0, which is a higher rate than any other selective ion channel conducts any ion. The gH of gramicidin channels is directly proportional to [H+] over a wide pH range (DeCoursey, 2003). However, extrapolation of this pH dependence to pHi 6 predicts <1 fA of H+ current at 100 mV. The present demonstration of distinct H+ current fluctuations attributable to voltage- and pH-dependent gating confirms that voltage-gated proton channels behave like genuine ion channels, in spite of their conductance at physiological pH being low enough to approach the range of carriers. Voltage-gated proton channels are simply channels with a small conductance.

## Acknowledgments

The authors thank Wolfgang Nonner for helpful discussions, and Tatiana Iastrebova and Julie Murphy for excellent technical assistance. Many eosinophils were generously provided by Larry L. Thomas.

This work was supported in part by the Heart, Lung and Blood Institute of the National Institutes of Health (research grants HL52671 and HL61437 to Dr. DeCoursey).

Olaf S. Andersen served as editor.

*

Abbreviations used in this paper: HBSS, Hank's balanced salt solution; TMAOH, tetramethylammonium hydroxide.

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