INTRODUCTION

Top Abstract Introduction Materials & Methods Results Discussion References

P2X purinoceptors are ligand-gated cation channels that are activated by extracellular ATP and its analogues. These receptors exist in excitable and nonexcitable cells, including neurons, smooth and cardiac muscles, glands, astrocytes, microglia, and B lymphocytes (Nakazawa et al., 1990a; Bean, 1992; Walz et al., 1994; Bretschneider et al., 1995; Capiod, 1998; McQueen et al., 1998). During the past few years, seven P2X purinoceptor subunits (P2X₁-P2X₇) have been cloned (Brake et al., 1994; Valera et al., 1994; Bo et al., 1995; Lewis et al., 1995; Chen et al., 1995; Buell et al., 1996; Seguela et al., 1996; Soto et al., 1996; Surprenant et al., 1996; Wang et al., 1996; Rassendren et al., 1997b). The P2X family has a distinctive motif for ligand-gated ion channels, with each subunit containing two hydrophobic transmembrane domains (M1 and M2) joined by a large intervening hydrophilic extracellular loop (Brake et al., 1994). The cDNA of each receptor is ~2,000 bp in length and has a single open reading frame encoding ~400 amino acids. A comparison of the amino acid sequences of the seven members shows an overall similarity of 35-50% (Collo et al., 1996; North, 1996; Surprenant et al., 1996).

Dose-response analyses of the cloned receptors made with whole cell currents revealed a Hill coefficient larger than 1, suggesting that activation of the channel involves more than one agonist. This is consistent with experiments on the native receptors in PC12 cells and sensory neurons (Friel, 1988; Nakazawa et al., 1991; Bean, 1992; Ugur et al., 1997). Studies aimed at measuring the subunit stoichiometry predict that the naturally assembled form of P2X receptor channels contains three subunits (Nicke et al., 1998).

All of the P2X clones can be expressed in heterologous cells, such as HEK 293 cells and Xenopus oocytes. ATP is a potent agonist for all cloned P2X receptors, and the receptors are highly selective for ATP over most other adenosine derivatives. However, benzyl-ATP is 10-fold more potent than ATP in activating P2X₇ receptors (Surprenant et al., 1996). It is interesting to point out that ,-methyl ATP is a poor agonist for the subtypes that do not show desensitization: P2X₂, P2X₄, P2X₅, P2X₆, and P2X₇, but is a potent agonist for P2X₁ and P2X₃ receptors that do desensitize.

Most studies of cloned P2X receptors have focused on the primary structure and pharmacology based on whole cell currents, while only a small amount of work has been done on the single channel properties. Single channel currents from P2X₁ receptors expressed in Xenopus oocytes were reported to have a mean amplitude of ~2 pA at 140 mV and a chord conductance of 19 pS between 140 and 80 mV (Valera et al., 1994). The conductance for P2X₁, P2X₂, and P2X₄ channels expressed in Chinese hamster ovary cells were ~18, 21, and 9 pS, respectively, at 100 mV with 150 mM extracellular NaCl, but the openings of P2X₃ were not resolved (Evans, 1996).

To provide a firmer basis for further analysis of the P2X family, we have examined P2X₂ receptors at the single channel level. We have characterized the current-voltage (I-V)¹ relationships, cation selectivity of permeation, ATP sensitivity, proton modulation, and gating kinetics.

	MATERIALS AND METHODS

Top Abstract Introduction Materials & Methods Results Discussion References

Expression Systems

P2X₂ receptors were expressed either in stably transfected human embryonic kidney 293 (HEK 293) cells or in Xenopus oocytes by mRNA injection (Rudy and Iverson, 1992). Since receptor expression is generally too high to obtain patches with only a single channel, we decreased the expression of the receptors in Xenopus oocytes by reducing the amount of mRNA to 25 ng, lowering the incubation temperature from 17° to 14°C, and shorting the incubation time to 16 h.

For electrophysiological experiments, HEK 293 cells were cultured at 37°C for 1-2 d after passage. The medium for HEK 293 cells contained 90% DMEM/F12, 10% heat inactivated fetal calf serum, and 300 µg/ml geneticin (G418). The media were adjusted to pH 7.35 with NaOH and sterilized by filtration. The incubation medium (ND96) for Xenopus oocytes contained (mM): 96 NaCl, 2 KCl, 1 MgCl₂, 1.8 CaCl₂, 5 HEPES, titrated to pH 7.5 with NaOH. All chemicals were purchased from Sigma Chemical Co.

Electrophysiology

We made patch clamp recordings from HEK 293 cells 1-2 d after passage and from Xenopus oocytes 16 h after injecting mRNA. Single channel currents from outside-out patches and whole cell currents were recorded at room temperature (Hamill et al., 1981). Recording pipettes, pulled from borosilicate glass (World Precision Instruments, Inc.) and coated with Sylgard, had resistances of 10-20 M.

For recording from HEK 293 cells, the pipette solution contained (mM): 140 NaF, 5 NaCl, 11 EGTA, 10 HEPES, pH 7.4. The bath solution and control perfusion solutions were the same and contained (mM): 145 NaCl, 2 KCl, 1 MgCl₂, 1 CaCl₂, 11 glucose, 10 HEPES, pH 7.4. For Xenopus oocytes, the pipette solution contained 90 mM NaF instead of 140 mM NaF and other components were the same as for HEK 293 cells; the bath and control perfusion solutions were the same as those used for HEK 293 cells except that they contained 100 instead of 145 mM NaCl. The patch perfusion solutions were the same as the bath solutions, except for modified divalent and ATP concentrations. Perfusate was driven by an ALA BPS-4 perfusion system (ALA Scientific Instruments). To investigate the cation selectivity of the channels, we substituted different cations for Na⁺ ion in the perfusate. To investigate the affinity of Na⁺ for the channel pore, we varied the extracellular NaCl concentration without compensation by other ions, while the pipette solution was kept constant. The resulting change of ionic strength caused the development of small liquid junction potentials between the bulk solution and the perfusate. We calculated these potentials according to the Henderson equation (Barry and Lynch, 1991). For solution exchanges from 100 to 150, 125, 100, 75, 50, and 25 mM NaCl, the junction potentials were 2.1, 1.2, 0, 2.5, 3.6, and 7.3 mV, respectively. Because these values are small compared with the holding potentials, we did not correct the membrane potential when we calculated the chord conductances.

Currents were recorded with a patch clamp amplifier (AXOPATCH 200B; Axon Instruments), and stored on videotape using a digital data recorder (VR-10A; Instrutech Corp.). The data were low-pass filtered at 5-20 kHz bandwidth (3 dB) and digitized at sampling intervals of 0.025-0.1 ms using a LabView data acquisition program (National Instruments).

Analysis

Amplitudes and excess channel noise. The mean amplitudes of single channel currents were determined by all-points amplitude histograms that were fit to a sum of two Gaussian distributions. Chord conductances were calculated assuming a reversal potential of 0 mV. The excess open channel noise (_ex) was computed as the root mean square (rms) difference between the variances of the open channel current and the shut channel current (Sivilotti et al., 1997).

The probability of the channel being open. P_o was defined as the ratio of open channel area (A_o) to the total area (A_o + A_c) in the all-points amplitude histogram:

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Power spectra. Power spectra, S(f), were computed using the fast Fourier transform routine in LabView^TM. We used records of 50~100-ms duration associated with open and closed states. The power spectrum of the excess noise was obtained by subtracting the spectrum of the closed state spectrum from that of the open state. The spectra were fit with the sum of a Lorentzian plus a constant:

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Thermal and shot noise. The thermal (or Johnson) and shot noise contributions were calculated according to Defelice (1981). The power spectra of thermal noise is white; i.e., it does not vary with frequency. Its value, S_th, is given by:

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Multiple conductance levels. We tried to see if there were discrete subconductance levels making up the open channel "buzz mode" by using a maximum-point likelihood method (MPL; ) that use the Baum-Welch algorithm (Chung et al., 1990). While we did get convergence at four to six levels, these levels were not consistent among data from different patches, so at the present time we cannot confidently describe the substate structure.

Kinetic analysis. The single channel currents were idealized with a recursive Viterbi algorithm known as the "segmental k-means" algorithm (SKM; ; Qin et al., 1996b). Idealization is dominated by the amplitude distribution, and therefore is essentially model independent. For simplicity, we used a two-state model for idealization: closed  open (C  O). The distributions of closed and open times were displayed as histograms with log distributed bin widths versus the square root of the event frequency (Sigworth and Sine, 1987). The mean open and closed times were simple averages from the idealized currents.

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Simulation. We used Origin (Microcal Software, Inc.) and Scientist (MicroMath Scientific Software, Inc.) software to simulate and fit data.

	RESULTS

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Basic Features of Single Channel Currents

Fig. 1 A shows a typical single channel current, activated by 1.5 µM ATP at a membrane potential of 100 mV from a stably transfected HEK 293 cell. Channel openings appeared as flickery bursts with ill-defined conductance levels. There were a few clear closures and subconductance levels within a burst, but discrete levels could not be resolved from the all-points histogram (see Fig. 1 B). The spread of current levels was reflected by the much larger standard deviation of the open than the closed component, each of which could be fit reasonably well with a single Gaussian. In Fig. 1 B, the mean open current amplitude is 3.2 pA, equivalent to a chord conductance of 32 pS. The standard deviations of the open and closed histograms are 0.95 and 0.24 pA, respectively, so that the excess open channel noise _ex is 0.92 pA; i.e., 29% of the mean current amplitude. Since the mean is clearly less than the peak current, we obtained a closer estimate of the maximal open channel current by measuring the mean of extreme values. Comparing the upper 5% of the two distributions, the peak amplitude and conductance were 4.3 pA (Fig. 1 B, arrow) and 43 pS, respectively, a closer estimate of the maximum ion flux. However, for convenience in discussing later results, unless specified otherwise, "channel current" and "conductance" will refer to the mean rather than the peak values.

View larger version (37K): [in this window] [in a new window]   Fig. 1.   The general features of single channel currents from an outside-out patch of an HEK cell stably transfected with P2X2 receptors. (A) Typical single channel current traces with inward current shown downward. The current was activated by 1.5 µM ATP at 100 mV, in the presence of 1 mM extracellular Mg2+ and Ca2+. The data were low-pass filtered at 5 kHz and digitized at 10 kHz. There are large fluctuations in the open channel current. A distinct substate can be seen occasionally in some bursts (e.g., second trace, second opening burst; bottom trace, third opening burst). Due to their short lifetimes, these substates are not evident in the amplitude histogram (B). (B) The all-points amplitude histogram of single channel currents from A (0.05 pA/bin). The distribution was fit by a sum of two Gaussians (solid lines) with means of 0 and 3.2 pA. The standard deviation in the open state peak (0.95 pA) is much larger than that of the closed state peak (0.20 pA). (C) Comparison of the power spectrum of excess open channel fluctuations (solid line) with the expected thermal (dot line) and shot (short dot line) noises. Note that the amplitude of the open channel fluctuations is much larger than either thermal or shot noise. The solid line is a fit of the data to a Lorentzian with a cutoff at 264 Hz (dash dot line) plus a constant noted S1 (dash dot dot line). The plotted spectrum is the average of three different spectra. (D) A higher time-resolution example of a burst at 5 kHz showing the general absence of easily discernible substates with one possible exception (arrow). The solid line is the mean current (3.2 pA).

To further characterize the open channel noise, we followed the procedures of Sigworth (1985a) for noise analysis using differential power spectra. We compared the power spectra of excess open channel fluctuations with the expected thermal and shot noise (Fig. 1 C). The open channel spectrum was well fit with a Lorentzian with f_c = 264 Hz, equivalent to a relaxation time of 0.62 ms, plus a constant. This noise is much larger than the expected thermal or shot noise, suggesting that the fluctuations most likely arise from rapid conformational changes in the channel.

I-V Curve

Fig. 2 A shows the single channel currents recorded from HEK 293 cells activated by 2 µM ATP at different holding potentials using outside-out patches with symmetrical Na⁺. The currents became small and noisy at positive holding potentials so that the unitary currents were not discernible. The single channel I-V curve (Fig. 2 B) exhibited a strong inward rectification similar to whole cell currents recorded under the same conditions (Fig. 3, A and B). The rapid fluctuation of current in the "open" state was maintained at all holding potentials.

View larger version (20K): [in this window] [in a new window]   Fig. 2.   The current-voltage relationship of single channel currents. (A) Single channel currents of an outside-out patch from HEK 293 cells activated by 2 µM ATP (1 mM extracellular Mg2+ and Ca2+ at different membrane potentials, symmetrical Na+ solutions containing 145 mM extracellular NaCl/145 mM intracellular NaF). The data were filtered at 5 kHz and digitized at 10 kHz. All of the current traces in this figure are from the same patch. (B) Mean I-V relationship of single channel currents. The error bars indicate the standard deviation of the single channel currents from the all-points histograms. The single channel I-V relationship shows strong inward rectification despite exposure to identical Na+ solutions across the patch. The same result was obtained when single channel currents were recorded in the absence of Mg2+ and Ca2+; therefore, divalent cations are not responsible for the rectification.

View larger version (20K): [in this window] [in a new window]   Fig. 3.   The current-voltage relationship of whole cell currents (WCCs). (A) Whole cell currents from an HEK 293 cell at different holding potentials: 100 to +80 mV at 20-mV intervals. Voltage drops from incomplete series resistance compensation were subtracted from the membrane potential. The currents were activated by 10 µM ATP in the presence of 1 mM extracellular Ca2+ with symmetrical Na+ solutions: 145 mM extracellular NaCl/145 mM intracellular NaF. The data were filtered at 2 kHz and digitized at 5 kHz. (B) The mean WCCs (±SD) (, n = 5) and predicted WCCs activated by 10 µM ATP. The I-V curve exhibits strong inward rectification, similar to the single channel currents shown in Fig. 2. The reversal potential was ~0 mV. The predicted WCCs were calculated using Eq. 15 where i (single channel amplitude) was taken from Fig. 2, and Po from the calculations for Model 1-4 () (Fig. 13), and Eq. 16 () as a function of voltage. The number of channels was chosen so that the predicted WCC at 60 mV was equal to the experimental data. The predicted WCCs match reasonably well with the experimental data.

View larger version (19K): [in this window] [in a new window]   Fig. 13.   Simplified and expanded versions of Model 1 from Fig. 11 (1-1, 1-2, 1-3, and 1-4), and other kinetic models (9 and 8-1) that have been used in the literature.

View larger version (18K): [in this window] [in a new window]   Fig. 11.   All models that converged during maximal likelihood estimation in the initial topology screen using the MSEARCH program. The relative likelihoods and AIC rankings of these models are listed in Table IV.

Dose-Response Curve of Single Channel Currents

We were unsuccessful in obtaining outside-out patches containing only a single P2X₂ channel when the receptor was expressed in HEK 293 cells. However, we were able to obtain patches with a single channel from Xenopus oocytes provided we carefully controlled the amount of mRNA, and the time and temperature of incubation. Fig. 4 A shows the single channel currents from an outside-out patch activated by different concentrations of ATP. As expected, increasing the concentration of ATP increased P_o. The all-points histograms (Fig. 4 B) show that the average current and excess noise were independent of ATP concentration (i = 3.5 pA and _ex = 1.6 pA at 120 mV). Thus there is no indication that ATP is blocking the open channel. We calculated the probability of being open at each ATP concentration from the amplitude histograms using ratio of the open area to the total area (Fig. 4 C). The open probability saturated when the ATP concentration reached 30 µM. The dose-response curve was fitted by the Hill equation with a Hill coefficient of 2.3, an EC₅₀ of 11.2 µM, and a maximal open probability of 0.61. The Hill coefficient and EC₅₀ are similar to those obtained from the dose-response curves of whole cell currents of our own data (not shown) and the literature (Brake et al., 1994), indicating that there are at least three subunits in a functional P2X₂ receptor ion channel. The data from this patch were very stable and used later in the comparison of kinetic models.

View larger version (39K): [in this window] [in a new window]   Fig. 4.   The effect of ATP concentration on single channel currents. (A) Single channel currents of P2X2 receptors expressed in Xenopus oocytes activated by different concentrations of ATP in the absence of extracellular Ca2+ (120 mV). The data were filtered at 20 kHz and sampled at 40 kHz. All of the current traces in this figure are from the same patch. (B) All-points amplitude histograms of the currents from A (0.05 pA/bin), with the distributions fit to the sum of two Gaussians. At this bandwidth, the excess channel noise was ~45% of the mean channel amplitude. (C) ATP dose-response curves. The probability of a channel being open is shown from experimental data () and simulated data generated by Fig. 13, Models 1-2 () and 1-4 (), as a function of ATP concentration. Fits of the data sets to the Hill equation are shown as dotted (experimental data), dash dot (Model 1-2), and solid (Model 1-4) lines. The Hill coefficient = 2.3, EC50 = 11.0 µM, and maximum Po = 0.61 for the experimental data, 1.5, 17.4 µM, and 0.74 for simulated data of Model 1-2, and 1.8, 13.3 µM, and 0.64 for simulated data of Model 1-4. All the experimental data were from same patch. The errors in the experimental Po were estimated from the errors in the mean and standard deviation estimates reported by Origin when fitting the amplitude histograms to Gaussians.

Na⁺ Conduction through the Ion Channel

To investigate the affinity of Na⁺ for the open channel, we measured single channel amplitudes at holding potentials of 80, 100, 120, 140 mV for extracellular NaCl concentrations of 10, 25, 50, 75, 100, 125, and 150 mM. Fig. 5 shows single channel currents activated by 15 µM ATP at different extracellular Na⁺ concentrations with a holding potential of 120 mV (Xenopus oocyte). The amplitude increased with the concentration of NaCl but approached saturation at high Na⁺ levels. Because the solutions were asymmetric across the patch, we calculated the conductance with the driving force as the difference between the holding potential and the Nernst potential. The single channel chord conductance, , calculated this way is plotted as a function of Na⁺ concentration in Fig. 6 A. The conductance versus [NaCl] at each potential was well fit with the Michaelis-Menten equation (Hille, 1992):

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View larger version (63K): [in this window] [in a new window]   Fig. 5.   The effect of extracellular NaCl concentration on the single channel current amplitude. Currents activated by 15 µM ATP were recorded from an outside-out patch from a Xenopus oocyte with different concentrations of NaCl without ionic substitution (different ionic strength) in the absence of Ca2+ at 120 mV. The data were digitized at 20 kHz and low pass filtered at 10 kHz.

View larger version (18K): [in this window] [in a new window]   Fig. 6.   The affinity of Na+ for the channels. (A). The relationship between the mean open channel conductance from Fig. 5 and the NaCl concentration at different voltages. The error bars are the standard deviations of the excess open channel noise. The solid line is a fit of Eq. 9. Note that at each concentration the driving force changes because of the change in Nernst potential. We have assumed Ks is dependent only on the holding potential and not the driving force. (B) The dependence of Ks on holding potential. The solid line was fit by the Boltzmann equation with z = 1,  = 0.21, and Ks(0) = 148 mM. A depolarization of 118 mV is required for an e-fold increase of Ks. The error bars are the parameter fitting errors from A. (C) The maximal conductance as a function of holding potential. The error bars are the fitting errors from A. The solid line is simply the connection of data. The conductance is approximately linear with the holding potential supporting the simple approximation of Eq. 9.

yielding K_s and _max at each voltage.

The equilibrium constant, K_s, increased with depolarization (Fig. 6 B). The relationship between K_s and holding potential can be described by a Boltzmann equation for a single binding site:

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where K_s(0) is the dissociation constant at 0 mV,  is the fractional electrical distance of the site from the extracellular surface, z is the valence of the permeating ion (1 in this case), and k_BT is Boltzmann's constant times absolute temperature (~25 mV at room temperature). The fitted values of K_s(0) and  were 148 mM and 0.21, respectively, so that a depolarization of 118 mV is required for an e-fold increase of K_s (Fig. 6 B). The Na⁺ binding site appears to be ~20% of the electrical distance from the extracellular surface, and is half saturated when exposed to 148 mM Na⁺ at 0 mV. The maximal conductance, _max, also increased with the potential as expected in a nearly linear part of the I-V curve (Fig. 6 C).

The Selectivity between Cations

The P2X₂ receptor ion channel is a nonselective cation channel; however, the conductance is different for different cations. We measured the single channel currents at 120 mV from HEK 293 cells using outside-out patches with NaF as the intracellular solution, and LiCl, NaCl, KCl, CsCl, and RbCl as the extracellular solutions (Fig. 7). From the currents obtained at 120 mV (Table I), the selectivity was K⁺ > Rb⁺ > Cs⁺ > Na⁺ > Li⁺. Although currents carried by the different cations had the same flickering behavior, the excess open channel noise, _ex, had a slightly different selectivity K⁺  Rb⁺ > Cs⁺ > Na⁺ > Li⁺. The relative noise, defined as _ex/i, was Rb⁺  Na⁺  Cs⁺  K⁺ > Li⁺. The difference in selectivity of the relative noise for Li⁺ suggests that it can affect the flickery kinetics. We compared _ex with the thermal, _th, and shot, _sh, noise (Table I). Again, _th and _sh were very small compared with _ex, and the ratio (_th + _sh) to _ex ranged from 8 to 14% depending on the ions. The relative noise caused by the open channel fluctuations, when corrected for thermal and shot noise (²_ex  ²_th  ²_sh)^1/2/i, followed the same cation sequence as _ex/i.

View larger version (35K): [in this window] [in a new window]   Fig. 7.   The effect of different permeant ions on the single channel currents. Single channel currents from HEK 293 cells at 120 mV activated by 2 µM ATP in the presence of 1 mM Mg2+ and Ca2+ from an outside-out patch. The data were filtered at 5 kHz and digitized at 10 kHz.

Effect of pH

The effect of pH on channel activation. The effect of extracellular pH on the channel currents is illustrated in Fig. 8 A. Multiple-channel outside-out currents activated by 2 µM ATP increased ~10-fold when pH was decreased from 8.3 to 6.8, and saturated with further decreases in pH (Fig. 8 B). The fluctuations in these multichannel currents at higher pH appeared to be dominated by the overlap of independent channels, so that at pH 8.3, where the mean current is small, single channel events were visible. At pH 6.3, the current saturated and the frequency of fluctuations increased dramatically, apparently dominated by the open channel noise. As is clear from the rise time of the currents, the activation rate decreased with increasing pH, and the fall time remained constant (Fig. 8 C). The potentiation of channel activity by protons is similar to the effect of increasing the ATP concentration, suggesting that protons may increase the affinity of the binding site for ATP. The pK_a was ~7.9 and the Hill coefficient was 2.5, again suggesting that there are more than two subunits in the channel.

View larger version (27K): [in this window] [in a new window]   Fig. 8.   The effect of pH on the affinity of channel for ATP. (A) Multiple-channel currents from an outside-out patch of HEK cells at 120 mV and 2 µM ATP at different values of extracellular pH (0.3 mM extracellular Ca2+). Note the increase in rise time with increasing pH. The data were low pass filtered at 5 kHz and digitized at 10 kHz. The horizontal bar indicates the duration of ATP application. (B) The effect of pH on mean patch current. The data were fitted by the Hill equation with a maximum mean current of 25.1 pA, an EC50 of pH 7.9 (pKa), and a Hill coefficient of 2.5. The error bars are the standard deviation of the data and contain both open channel and gating noise. (C) The pH dependence of the rise and fall times. The time constants for rising () and falling () phase were obtained from fitting single exponential functions (solid lines) to multiple channel currents.

Effect of pH on single channel properties. The results above and published studies on the effect of pH were based on whole cell or multi-channel recordings (Li et al., 1996, 1997; King et al., 1997; Stoop et al., 1997; Wildman et al., 1998). To explore the possible effect of pH on gating and channel conductance, we examined the effect of pH on single channels. To obtain single channel activity from the stable cell lines, we exposed the patch to ATP for long times, so that run down reduced the number of active channels. Fig. 9 A shows these currents recorded at different values of extracellular pH. We measured the single channel amplitude and excess noise from the all-points amplitude histograms. The mean amplitude of the current was independent of pH, but the excess open channel noise increased with decreasing pH (Table II). As visible in Fig. 9 A, the frequency of brief closures within open channel bursts appeared to increase as pH decreased. These interruptions were longer than the normal fast "flickery" behavior. It has been suggested that protons may block an open channel (Yellen, 1984). To further characterize this phenomenon, we computed the power spectra of the open channel fluctuations (Fig. 9 B), and fit them with a Lorentzian plus a constant (Eq. 3). The constant represents relaxations occurring at frequencies beyond our resolution.

View larger version (40K): [in this window] [in a new window]   Fig. 9.   The effect of extracellular pH on single channel currents. (A) Currents recorded from an outside-out patch of an HEK 293 cell under the same experimental conditions as in Fig. 8 A. The data were low-pass filtered at 10 kHz and digitized at 20 kHz. (B) Differential power spectra of the open channel currents at different values of extracellular pH. The spectra were fit with the sum of a Lorentzian function plus a constant (solid line). The corner frequencies are indicated by the arrows. Plotted spectra are averages of three separate data segments.

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View larger version (4K): [in this window] [in a new window]   Scheme I.

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0.33

1

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Kinetic Analysis with the Maximal-Interval Likelihood Method

To understand the kinetics of agonist binding and channel gating, we applied the maximum likelihood method to data from outside-out patches that were stable over time and ATP concentration (Fig. 4 A). We began by fitting simple noncyclic models using the maximum-likelihood interval analysis and used AIC ranking to select a preferred model. The analysis was hierarchical in the sense that we fit portions of the reaction scheme under restricted conditions, and then merged these models to create a full description. The kinetic description required: (a) the number of closed and open states, (b) the connections between states, and (c) the values of the rate constants between the states and their dependence on concentration and voltage.

Mean open and close times. The data was idealized into two classes: open and closed (see Fig. 10 A). We did not attempt to idealize the data making up the bulk of the flickery open channel activity since the amplitudes were uncertain, but instead defined open as a single conductance state possessing a lot of noise.

View larger version (37K): [in this window] [in a new window]   Fig. 10.   Idealization and open- and closed-interval duration histograms of single channel currents activated by different ATP concentrations (from the data in Fig. 4 A). (A) Examples of idealized single channel currents activated by 5 and 15 µM ATP. These data were recorded at 40 kHz and filtered at 20 kHz. Before idealization, the data were further filtered at 5 kHz using a Gaussian digital filter. The idealization was performed with the segmental k-means method based on a two-state model (see MATERIALS AND METHODS). (B) The mean open and closed times of single channel currents as a function of ATP concentration. (C) The open- and closed-time histograms of single channel currents activated by different concentrations of ATP. The solid lines are the predicted probability density functions for Fig. 13, Model 1-4, with rate constants determined by global fitting across concentrations (see Table VIII). Ni/NT on the ordinate is the ratio of the number of events per bin to the total number of events.

Duration histograms. Fig. 10 C shows the open- and closed-time histograms from idealized single channel currents induced by different ATP concentrations (Fig. 10 A). The open-time histograms have two peaks and the closed-time histograms have at least three peaks at low concentration. When the ATP concentration was increased, the intermediate and long time constant peaks of the closed time distribution merged and only two peaks were visible. These results indicate that the channel has at least three closed and two open states.

Kinetic model comparison. We made quantitative comparisons of various kinetic models to determine which model best described the behavior. The models were limited to three closed and two open states (of the same conductance), and at most 10 rate constants. These constraints proved necessary to obtain unique solutions during optimization. There are 98 unique models with that many states. Further constraints were imposed to simplify analysis. (a) We discarded models in which the unliganded states were open because we did not see any spontaneous openings in the absence of ATP. (b) Following traditional models for other ligand-gated channels, the closed states were connected so as to represent the binding of ATP. To evaluate the possible topologies, we used the program MSEARCH () to compare the likelihood of all remaining models. The program evaluates all topologically unique models having a specified number of states of each conductance and optimizes the rate constants for each one. For this stage of the analysis, we used three data sets obtained at 5, 10, and 15 µM ATP. We calculated the likelihood of each model by adding the log-likelihoods from each concentration. This is more a test of the topology of the models than a test of the optimal values of the rate constants since the rate constants will change over concentration, but the connectivity won't. Fig. 11 shows the eight kinetic models that converged on all data sets within 100 iterations. They are listed in the order of AIC rank.

1

1

View larger version (19K): [in this window] [in a new window]   Fig. 12.   The effect of ATP concentration on the rate constants near the open states. The rate constants are based on kinetic Model 1 (shown at bottom), with each data set fit separately. Missed events were corrected by imposing a dead time of 0.05 ms. k12 and k23 are the most sensitive to the concentration of ATP, increasing over the range from 5 to 20 µM, and saturating at higher concentrations. The rate constants are plotted in two panels to avoid overlap (the scales in both plots are identical).

1

1

Model simplification and expansion. As ATP concentration increased, the three peaks in the closed time duration histograms became two (Fig. 10 C), suggesting that at high ATP concentration, Model 1 (Fig. 11) could be simplified by removal of state C₁ (Fig. 13, Model 1-1). When we fit the kinetics of high concentrations of ATP by Model 1 and Model 1-1, the likelihoods were equal. Thus, at high ATP, k₁₂ gets so fast that C₁ is rarely occupied and Model 1-1 is sufficient to describe the kinetics. However, a large difference in maximum likelihoods arose when we fitted Models 1 and 1-1 to the data at low concentrations of ATP. Model 1-1 can well describe the kinetics of single channel currents of high ATP, but not low.

View larger version (13K): [in this window] [in a new window]   Fig. 14.   Representation of the channel activation pathway in terms of energy barriers and wells based on Model 1-4 (Fig. 13). The free energy landscape of the reaction scheme calculated from the transition rates. The relation between kij and free energy is defined by the Eyring equation: (kijs in this case are the rate constants at 120 mV).  is the transmission coefficient (assumed to be 1; Hille, 1992), kB is Boltzmann's constant, h is Planck's constant, and T is the absolute temperature. At 20°C, kBT/h equals 6.11 × 1012 s1. Gij is the free energy at the top of the barrier between states i and j, and Gi is the free energy of state i. The free energies are arbitrarily referenced to a solution of 1 M ATP. The use of kBT/h as the preexponential term of the rates is undoubtedly far off for a macromolecule. However, it is a maximum estimate that will cause the energy barriers to also be maximal estimates. The relationship of the well (state) energies, however, is much more likely to be correct since these energies are determined by ratios of rate constants where the preexponential terms will tend to cancel.

The dependence of P_o and rate constants on membrane potential. We next tried to determine whether the rate constants were dependent on membrane potential using Model 1-4 (Fig. 13). Fig. 15 A shows the single channel currents activated by 30 µM ATP at voltages from 120 to 80 mV. Fig. 15 B shows the voltage dependence of the mean open and closed times obtained from idealized currents, and Fig. 15 C shows P_o as a function of voltage. The mean open time decreased with depolarization, while the mean closed time increased. The closing and opening rates are both voltage dependent, and the overall effect is to reduce the open probability with depolarization. P_o values calculated from the all-points histogram were slightly larger than those calculated from the idealized currents, suggesting that some short lived events were missed, but the trend was the same; i.e., P_o decreased with depolarization.

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