Figure 1A shows typical multiple channel currents activated by 10 μM ATP at -120 mV recorded from an Xenopus oocyte. 10 μM ATP is about equal to EC₅₀ value. Since we did not see open level more than 3 channels from entirely record, we think the patch contained at least three channels. As indicated by arrows, there are many simultaneous closing and open transitions. These concurrences of openings and closings are highly suggestive of channel interactions since independent channels would have less clustering 20. We observed this phenomenon in all seven multiple-channel patches.

We estimated the channel amplitude by fitting amplitude histograms (Figure 1B) with four Gaussians representing the closed, 1^st, 2^nd, and 3^rd open level. The mean current of the states was 4.0, 7.9 and 11.9 pA, respectively. The mean open channel noise/channel was ~1.2 pA with a 5 kHz bandwidth (estimated from the standard deviation of the Gaussians), a value ~30 % of the mean open channel current amplitude (also see Figure 3D). Since the amplitude and open channel noise of the different open levels are essentially the same, the conductance properties appear identical.

The probability that k channels are open out of a total of N should follow a binomial distribution if the channels are identical and independent (Eq. 6). A deviation from this distribution would indicate that at least one of the assumptions is not true. Using p_o obtained from the single channel dose-response curve shown in Fig. 2, we have plotted in Figure 1C the ratio of the observed open probability at each level, P(k)_exp, to the predicted distribution obtained from the binomial distribution, P(k)_binomial. If channel behaviors are the same in patches containing a single and multiple channels, P(k)_exp/P(k)_binomial should be ~1 regardless of k. The results show here that P(k)_exp/P(k)_binomial increases with increasing k, suggesting a positive deviation from the binomial distribution. However, p_o = 0.4 is a more accurate value estimated from the optimization, indicating the increase in open probability of channel in multiple-channel patches. These analysis strongly suggest that the gating mechanism is different between single channel and multiple channels

However, the binomial test is not a stringent test of cooperativity, especially for relatively small deviations. Binomial tests do not contain any kinetic information, only equilibrium information. As Horn 21 pointed out, the binomial distribution is no better a statistical predictor for the number of active channels in a patch than is the maximum observed level. A better test of independence is to ask whether events are correlated in time, since that utilizes both amplitude and duration information. That analysis is discussed later in the paper.

Figure 2 shows multiple channel currents activated at different concentrations of ATP (A) and the peak-current dose-response curve (B, Circles). In order to compute the mean response from multiple channel currents, the dose-response curves were normalized to the current activated by 50 μM ATP and fit with the Hill equation. This yielded an EC₅₀ of 9.8 ± 0.8 μM and a Hill coefficient of 1.9 ± 0.29. Figure 2B also shows the dose-response curve of single channel currents (Diamonds), fit with a Hill coefficient, EC₅₀ and p_o,max of 2.3 ± 0.44, 11.2 ± 1.0 μM and 0.61 respectively 19. These parameters depend on the molecular rate constants in the reaction pathway. The similar values of EC₅₀ and Hill coefficient of multiple channel currents and single channel currents suggest that the rate constants along the activation pathway had changed in a compensatory way. However, we do not know the absolute value of p_o in multiple channel currents and had to normalize the data of a single channel.

We might assume that rate constants in the activation pathway are similar in single channel currents and multiple channel currents since both have a similar EC₅₀ and Hill coefficient. Because we saw clusters of openings, we presumed the dominant effect might be on the closing rates associated with aggregation. Earlier kinetic analyses of single channel currents suggested that there were at least three binding sites (four closed states) in the activation pathway 19. Although the presence of aggregated closed states complicates the kinetics of multiple-channel currents, the mean open channel lifetime can be computed without explicitly considering the four closed states. By comparing the mean open lifetime of single channel currents and mean open lifetime of each level in multiple channel currents, we can determine whether the mean closing rate (i.e. the inverse of the mean open time) is affected by channel interactions. We obtained the lifetimes of different current levels from idealization of the currents using the program SKM http://www.qub.buffalo.edu. Our previous study demonstrated that the mean open lifetime was independent of ATP concentration 19.

Figures 3A and 3B show currents from a single-channel and a two-channel patch (upper panel) with the idealized currents shown above the raw data, and their amplitude histograms below. From visual inspection we can see that the open times of the currents from the two-channel patch are much longer than those from the single channel patch. We analyzed the mean open times of currents containing one, two, or three channels in the patch and these are plotted in Figure 3C. The mean open time of a single channel patch is 2.50 ± 0.67 ms (n = 6), while in the multiple channel patches mean open time of each level is longer; opposite to the behavior expected for independent channels. With independent channels, a given state lifetime should decrease when more channels are available to change state. The increase in mean open lifetime with channel number in the patches is consistent with our observation of a trend toward positive deviations from the binomial distribution (Fig 1C).

Consider a simple two-state model:

where C and O represent the closed and open states; α and β are opening and closing rate constants that give the mean open and closed times of τ_o = 1/β and τ_c = 1/α. If there are two independent channels in the patch, the model could be formulated as follows 22:

C represents both channels closed, O₁ one channel open, and O₂ both channels open. Then, the lifetimes of C, O₁ and O₂ (designated as τ_c, τ_o1 and τ_o2) are 1/2α, 1/(α+β), 1/2β, respectively. This indicates that the lifetimes of O₁ and O₂ for two independent channels should be smaller than O in a one channel patch (Scheme 1) due to the multiple channel openings. This prediction is opposite to our observations.

We further tested this conclusion with simulations. We simulated currents assuming α = 250 s^-1, and β = 400 s^-1 in Scheme 1. The theoretical lifetimes of the closed and open states are 4 and 2.5 ms, respectively. We simulated the currents with one, two, and three independent channels and calculated the mean lifetime of each level (program MIL, http://www.qub.buffalo.edu) (Figure 4). The mean closed and open lifetimes calculated for a single channel are 3.92 and 2.51 ms, close to theoretical values. For simulations with two independent channels, the recovered lifetimes of closed level, 1^st and 2^nd open level were 2.09, 1.60, and 1.28 ms respectively, for levels 1, 2 and 3, close to the theoretical values of 2.00, 1.54, and 1.25 ms. The mean open times decreased with the number of channels (Figure 4B). The simulation results for independent channels are those expected from theory, but opposite to our observations with multiple channel currents (compare Figures 3C and 4B). Although Scheme 1 is the simplest possible kinetic model, the same general behavior applies to more complicated kinetics 23. The dramatic increase in mean open time of channel with multiple channel patches indicates that some kinetic property is different from single-channel patches.

We did a more global test of cooperativity by directly comparing cooperative and independent models using a maximum likelihood technique. If two binary channels were active, there would be three distinct current levels. We can model this with Scheme 2 with the constraints imposed by independence (above), or Scheme 2 without any constraints on the rates. If one assumes the number of channels is known, the unconstrained version of Scheme 2 has two extra parameters. If the unconstrained version of Scheme 2 is more likely to explain the data than the constrained one, the cooperative model is more likely.

We fit several data sets with the two models using the maximum interval likelihood program MIL http://www.qub.buffalo.edu, and in all cases the likelihood ratio of the cooperative/independent model was >140, far in excess of the amount expected for the extra degrees of freedom. This strongly favors the cooperative model. In other words, the likelihood of observing multiple level events occurring so close in time is unlikely to occur with independent channels.

We have observed an interesting phenomenon that relates to channels having different properties. When there is more than one channel in a patch, as expected, the open channel noise is higher than in single-channel patches. However, the open channel noise of each level in multiple channel currents is the same (c.f., Figure 1 and Figure 3D)! The relative open channel noise (σ_ex,n/i, where i is the amplitude of a single channel) at the 1^st and the 2^nd level is 0.29 ± 0.01 and 0.30 ± 0.04 (n = 4) (Figure 3D), the 3^rd open level has a similar value in multiple-channel patches (see Figure 1), while in the single channel patch, it is ~0.67 ± 0.01 (n = 6) (Figure 3D and Table 1). The differences in relative fluctuations may be the consequence of faster closing rates in single channel currents than in multiple channel currents, so that some short events are missed and end up being classed as open channel noise 24.

The increase in open channel noise of single channel currents relative to multiple channel currents with equivalent mean conductances at the same bandwidth suggests the basic channel permeability properties are comparable. Apparently the interaction of the channels affects not only the main-state gating rates, but the substate transition rates that create the open channel noise.

In some ligand-gated ion channels, such as ACh receptors, the agonist not only activates the receptors, but also blocks the pore as well 2526. In order to test if ATP blocks the P2X₂ receptors and affects open channel noise, we recorded single channel currents activated by different concentrations of ATP. Figure 5 shows the currents recorded from a single channel patch activated by different ATP concentrations and the corresponding amplitude histograms. The currents activated by different ATP concentrations have a similar mean amplitude i of ~3.5 pA and σ_ex of 65~70% (from the all-points histograms, see parameters in Table 1). Therefore, there is no indication that ATP blocks the channel or influences the open channel noise. This is consistent with the idea that ATP, a strongly charged anion, would be excluded from a pore selective for monovalent cations 718.

P2X₂ receptors were expressed in Xenopus oocytes by mRNA injection 35. In order to obtain outside-out patches with a single channel from Xenopus oocytes, we decreased expression by reducing the amount of mRNA from 50 ng to 25 ng, lowering the incubation temperature from 17 to 14°C, and shortening the incubation time to 16 hours.

For electrophysiological experiments, Xenopus oocytes were cultured in the medium (ND96) contained (in mM): NaCl 96, KCl 2, MgCl₂ 1, CaCl₂ 1.8, HEPES 5, and was titrated to pH 7.5 with NaOH and sterilized by filtration. All chemicals were purchased from Sigma Chemical Co. (St. Louis, MO).

Patch clamp recordings were made from Xenopus oocytes 16 hr after injecting mRNA at room temperature 10. Recording pipettes were pulled from borosilicate glass (World Precision Instruments, Sarasota, FL), coated with Sylgard, and had resistances of about 10 MΩ.

The pipette solution for recording from Xenopus oocytes contained (in mM): 90 NaF, 5 NaCl, 11 EGTA, 10 HEPES at pH 7.4. The bath and control perfusion solutions were the same and contained (in mM): 100 NaCl, 2 KCl, 1 MgCl₂, 1 CaCl₂, 11 glucose, 10 HEPES at pH 7.4. The patch perfusion solutions were the same as the bath solutions, except for modified divalent and ATP concentrations as indicated for particular experiments. The perfusate was driven by an ALA BPS-4 perfusion system (ALA Scientific Instruments, NY).

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