## Abstract

The single channel properties of cloned P2X_{2} purinoceptors expressed
in human embryonic kidney (HEK) 293 cells and *Xenopus* oocytes
were studied in outside-out patches. The mean single channel
current–voltage relationship exhibited inward rectification in symmetric
solutions with a chord conductance of ∼30 pS at −100 mV in 145
mM NaCl. The channel open state exhibited fast flickering with significant power
beyond 10 kHz. Conformational changes, not ionic blockade, appeared responsible
for the flickering. The equilibrium constant of Na^{+} binding
in the pore was ∼150 mM at 0 mV and voltage dependent. The binding site
appeared to be ∼0.2 of the electrical distance from the extracellular
surface. The mean channel current and the excess noise had the selectivity:
K^{+} > Rb^{+} >
Cs^{+} > Na^{+} >
Li^{+}. ATP increased the probability of being open
(*P*_{o}) to a maximum of 0.6 with an EC_{50}
of 11.2 μM and a Hill coefficient of 2.3. Lowering extracellular pH
enhanced the apparent affinity of the channel for ATP with a pK_{a} of
∼7.9, but did not cause a proton block of the open channel. High pH
slowed the rise time to steps of ATP without affecting the fall time. The mean
single channel amplitude was independent of pH, but the excess noise increased
with decreasing pH. Kinetic analysis showed that ATP shortened the mean closed
time but did not affect the mean open time. Maximum likelihood kinetic fitting
of idealized single channel currents at different ATP concentrations produced a
model with four sequential closed states (three binding steps) branching to two
open states that converged on a final closed state. The ATP association rates
increased with the sequential binding of ATP showing that the binding sites are
not independent, but positively cooperative. Partially liganded channels do not
appear to open. The predicted *P*_{o} vs. ATP
concentration closely matches the single channel current dose–response
curve.

## Introduction

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
(P2X_{1}–P2X_{7}) 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
P2X_{7} receptors (Surprenant et al.,
1996). It is interesting to point out that α,β-methyl ATP
is a poor agonist for the subtypes that do not show desensitization:
P2X_{2}, P2X_{4}, P2X_{5}, P2X_{6}, and
P2X_{7}, but is a potent agonist for P2X_{1} and P2X_{3}
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
P2X_{1} 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 P2X_{1},
P2X_{2}, and P2X_{4} 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 P2X_{3} were not resolved (Evans, 1996).

To provide a firmer basis for further analysis of the P2X family, we have examined
P2X_{2} 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

### Expression Systems

P2X_{2} 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 MgCl_{2}, 1.8 CaCl_{2}, 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 MΩ.

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 MgCl_{2},
1 CaCl_{2}, 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 (σ_{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:
1

This calculation is insensitive to short events. In our initial analysis, we treated the channel as having two amplitude classes, open and closed. All rapid gating events associated with the open channel were treated as noise. Essentially we defined open as “not closed.”

#### Power spectra.

Power spectra, *S*(*f*), were computed using
the fast Fourier transform routine in LabView™. 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: 2

The rms noise, σ_{L}, from the Lorentzian component is:
3

#### 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:
4

where *k*_{B}*T* is Boltzmann's
constant times the absolute temperature, and *R* is the
equivalent resistance of the open channel. The rms noise in a bandwidth
*f* is given by: 5

The power spectrum of shot noise, *S*_{sh}, is also
white and given by: 6

where *q* is the charge of an elementary charge carrier, and
*i* is the single channel current amplitude. The rms
amplitude of shot noise over bandwidth *f* is: 7

#### 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; www.qub.buffalo.edu) 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; www.qub.buffalo.edu; 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.

The rate constants of state models were obtained by using the maximal
interval likelihood method with corrections for missed events (MIL;
www.qub.buffalo.edu; Qin et
al., 1996a). We used two strategies to fit the data: (a)
individual fitting (i.e., fitting the data sets from each experimental
condition individually), and (b) global fitting (i.e., fitting a group of
data sets obtained under different experimental conditions). The first
method produces an independent set of rate constants for each condition, but
suffers from poor identifiability: a given model may not have unique rate
constants. Global fitting improves identifiability by using a model with
fewer parameters. We did both kinds of analysis of the data, and the results
were consistent between the two methods of analysis, but global fitting
permitted fitting more complicated models. For simplicity, we will emphasize
the results of global fitting across ATP concentrations at the same voltage,
or across voltages at the same ATP concentration. When we globally fit data
from different ATP concentrations, we assumed that the association rates
were proportional to concentration [i.e., *k*_{ij}
= *k*_{ij}(0)[ATP], where
*k*_{ij}(0) is an intrinsic rate constant at the
specified voltage], while the other rates were assumed to be independent of
ATP. When we performed global fitting on data from different voltages at
same ATP concentration, the rates were assumed to be exponential functions
of voltage; i.e., *k*_{ij} =
*k*_{ij}(0)exp(−*z*δ_{ij}V/*k*_{B}*T*),
where *k*_{ij}(0) is the apparent rate constant at 0
mV and the specified ATP concentration, and
*z*δ_{ij} is the effective sensing
charge.

We used Akaike's asymptotic information criterion (AIC) to rank different kinetic models (Vandenberg and Horn, 1984; Horn, 1987): 8

where *j* is the number of the data set. The model with a
higher AIC is considered a better fit.

#### Simulation.

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

## Results

### 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 σ_{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.

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.

### Dose–Response Curve of Single Channel Currents

We were unsuccessful in obtaining outside-out patches containing only a single
P2X_{2} 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 σ_{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 EC_{50} of 11.2 μM, and a maximal open
probability of 0.61. The Hill coefficient and EC_{50} 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 P2X_{2} receptor ion channel. The data from
this patch were very stable and used later in the comparison of kinetic models.

### 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,
γ, 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): 9

yielding *K*_{s} and γ_{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: 10

where *K*_{s}(0) is the dissociation constant at 0 mV,
δ 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*_{B}*T* is
Boltzmann's constant times absolute temperature (∼25 mV at room
temperature). The fitted values of *K*_{s}(0) and
δ 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, γ_{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 P2X_{2} 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,
σ_{ex}, had a slightly different selectivity
K^{+} ≅ Rb^{+} >
Cs^{+} > Na^{+} >
Li^{+}. The relative noise, defined as
σ_{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 σ_{ex} with the
thermal, σ_{th}, and shot, σ_{sh}, noise (Table
I). Again, σ_{th} and
σ_{sh} were very small compared with σ_{ex},
and the ratio (σ_{th }+ σ_{sh}) to
σ_{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 (σ^{2}_{ex} −
σ^{2}_{th} −
σ^{2}_{sh})^{1/2}/*i*,
followed the same cation sequence as σ_{ex}/*i*.

### 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.

#### 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.

The fits are illustrated in Fig. 9 B as
solid lines. The Lorentzian represents a two-state relaxation process whose
characteristic time constant τ is related to the corner frequency,
*f*_{c}, by: 11

Diffusional block of the open channel can be described as a two-state model
(Scheme I), where O is the open state and C_{b} is the
protonated-blocked state.
(Scheme I)

α and β are the blocking and unblocking rate constants. The relaxation time for this two-state process is related to the rate constants by: 12

The prediction of proton block is that *f*_{c}
increases linearly with increasing proton concentration. However, our data
show that *f*_{c} decreased with increasing proton
concentration (Fig. 9 B). To further
examine the possibility of proton block, we analyzed bursts kinetically
using the maximum likelihood method with a two-state model. We fit the
extracted α's and β's at different pH to an equation of the
form: 13

where α_{0} = 224
μM^{−0.33}s^{−1},
*n*_{α} = 0.33,
β_{0} = 1,493
μM^{−0.16}s^{−1}, and
*n*_{β} = 0.16. Since α
and β are not directly proportional to the proton concentration, a
single site model appears to be inappropriate. We speculate that we may be
titrating several sites that display negative cooperativity. The effect of
pH on the open channel is to modify the conformation of the channel rather
than to provide a simple proton block. Table II summarizes the open channel properties at different
pH. Remarkably, the effect of pH on the mean open channel current is
negligible.

### 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.

The probability of a channel being open increased with ATP, as shown in Fig. 4 C. This could result from an increase in mean open time, a decrease in mean closed time, or a combination. Fig. 10 B shows the mean open and closed times calculated from idealized single channel currents, and plotted as a function of ATP concentration. The mean closed time dramatically decreased with the increase in ATP and saturated at 30 μM, while the mean open time was not affected by ATP. The results indicate that ATP controls the rate at which the channel opens, but not the rate at which it closes.

#### 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 (www.qub.buffalo.edu) 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.

To determine which model was best, we compared the log(maximum likelihood)s
and AIC rankings (Table III). The
likelihoods of Models 1, 2, and 3 (Fig. 11) are the same, but Model 3 has two more parameters and,
hence, a lower AIC rank. Models 1 and 2 have the same number of parameters,
likelihood, and AIC rank, so we can not tell the difference between them.
Model 7 (Fig. 11) has a larger
likelihood than Models 1 and 2; however, its AIC ranking is much lower
because of the increased number of parameters. Model 8 (Fig. 11), which has a partially liganded open
state, has the smallest likelihood and lowest AIC rank. When Models 1 and 2
were compared across concentration, they were indistinguishable and, for
simplicity in what follows, we arbitrarily selected Model 1. In both models,
state C_{1} is unliganded, C_{2} and C_{3} are
liganded, and O_{4} and O_{5} are open. k_{12} and
k_{23 }are the agonist association rates, k_{21} and
k_{32 }are the agonist dissociation rates, k_{34 }and
k_{35} are the channel opening rates, and k_{43} and
k_{53} are the channel closing rates.

The rate constants governing ATP binding and gating were solved by fitting
across a range of ATP concentrations. Fig. 12 shows the rates from the model at bottom (from Fig. 11, Model 1) as a function of ATP
concentration when the data from each concentration were fit independently.
The association rates k_{12} and k_{23} showed a strong
dependence on ATP concentration in the 5–20 μM range.
However, when the ATP concentration was >20 μM, the rate
constants appeared to saturate and the error limits on the parameters
increased. A concentration-driven rate should not saturate, but there are a
few explanations. First, there may be a concentration-independent state not
contained in the model. Second, k_{12} and k_{23} approach
k_{35} at high ATP concentration, making k_{35} rate
limiting and rendering the optimizer incapable of properly solving the
model. Third, if k_{12} and k_{23} are linearly proportional
to concentration, then the intrinsic rate constants of both k_{12}
an k_{23} are ∼2 × 10^{7}
M^{−1}s^{−1}, which is approaching the
diffusion limit.

We tested the first possibility by adding concentration-independent states to the model in Fig. 12, but that did not prevent the association rates from saturating. We tested the identifiability of the model by simulating the model across concentrations (SIMU; www.qub.buffalo.edu) and attempting to extract the rate constants using maximal interval likelihood. Fitting the simulated data, we found that the estimated rate constants also saturated (see below) so that the correct model is not identifiable with data from a single concentration. As far as the diffusion limit providing a true saturation, further experiments are required to test that prediction. However, we currently believe that the apparent saturation is an artifact caused by the lack of identifiability of the model at high concentrations.

(Details of the test on the artifactual origin of saturating rates. We
simulated data using Model 1 [Fig. 11], with the rate constants k_{12} and k_{23}
increasing linearly with ATP in the 5–50 μM range. The
intrinsic rate constants k_{12}(0) and k_{23}(0), obtained
from the slope of k_{12} and k_{23} versus ATP from
5–30 μM (Fig. 12),
were 14 and 22 μM^{−1}s^{−1},
respectively. All other rate constants were made independent of ATP and set
to values averaged across the data sets. We then analyzed the simulated data
as if it were experimental data. The recovered rate constants were similar
to the values used to simulate the data for ATP <20 μM. At
higher ATP levels, however, the estimated values of k_{12} saturated
and k_{21} even decreased. Large error limits also occurred in
k_{12} and k_{21} at the high concentrations [Table
IV]. Thus, Model 1 [Fig. 11] cannot uniquely fit data at single
high ATP concentration.)

To improve identifiability, we fit the data simultaneously across all
concentrations. Such global fitting makes the likelihood surface steeper
(Qin et al., 1996a). We assumed
that the association rate constants were proportional to the ATP
concentration, and the other rate constants were independent of ATP (see
materials and methods). This time, the rate constants derived
from global fitting of simulated data were very close to the values used for
simulation (Table V). The results of
global fitting to the experimental data are listed in Table VI. It is worth noting that the second
ATP association rate constant, k_{23}(0), is larger than the first,
k_{12}(0). This result shows that the binding sites are not
independent, but that binding to one site modifies binding to the other.
With independent sites, the association rate should decrease as the number
of free sites decreases. The conclusion is quite model independent; for
every model we tested, the association rates increased with proximity to the
open state (see below).

#### 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 C_{1} (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, k_{12}
gets so fast that C_{1} 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.

Our model has only two binding steps. The fact that the
*P*_{o} curve has a Hill coefficient of 2.3
suggests that there are at least three binding sites in the P2X_{2}
channel. Since it is a homomer, this implies that three or more subunits are
needed to form the channel. A more realistic model should have at least one
additional partially liganded closed state (Fig. 13, Model 1-2).

The rate constants from Model 1-2 (Fig. 13) are shown in Table VI. Again in this model, the first ATP binding step speeds up
the second one. The transition rates near the open state are similar between
Model 1 (Fig. 11) and Model 1-2. While
Model 1-2 has two more free parameters than Model 1, it has 5.4 units higher
likelihood so that Model 1-2 is preferred (see Table VIII). The predicted *P*_{o}
as a function of ATP concentration is plotted in Fig. 4 C (⋄) and fit with the Hill equation with a
Hill coefficient of 1.5, an EC_{50} of 17.4 μM, and maximal
*P*_{o} of 0.74. However, compared with the
experimental data, the EC_{50} and maximal
*P*_{o} are too large and the Hill coefficient
too small. These discrepancies can be reduced by connecting an
ATP-independent closed state to the open states. Additional evidence for
this closed state comes from the closed time histogram that has two
components at saturating ATP (Fig. 10
C). Adding a closed state to the right of the open states in Model 1-2
produces Model 1-4 (Fig. 13). This
modification corrects the prediction of the dose– response curve.
Similarly, adding one more closed state to Model 1 produces Model 1-3 (Fig.
13).

Constraining Models 1-3 and 1-4 (Fig. 13) with detailed balance in the loops, and globally fitting the
data from 5 to 50 μM ATP, we obtained rate constants with small
error limits (Table VII). The
relative likelihoods and the AIC ranking of Model 1 (Fig. 11) and its expanded versions, Models
1-2, 1-3, and 1-4 (Fig. 13) are listed
in Table VIII. Models 1-3 and 1-4,
which contain loops, have much higher likelihoods than Model 1 or 1-2. Model
1-4 has the highest AIC rank, and therefore is the preferred model. The rate
constants are listed in Table VI and
VII. The transition rates near the open states for Models 1 and 1-2, and
Models 1-3 and 1-4 are very similar, supporting the hierarchical approach.
The predicted probability densities for the open and closed lifetimes of
Model 1-4 are shown in Fig. 10 C and
match the histograms reasonably well. Again, we found that the ATP
association rate constants increased with proximity to the open states:
k_{12}(0) < k_{23}(0) <
k_{34}(0). This is opposite to what would be expected from
independent subunits. Each binding step makes the next faster. This
cooperativity of binding appears model independent since all models tested
had the same trend. From the Eyring model for the rates, the energy
landscape for the whole reaction is shown in Fig. 14.

The kinetic model fits the single channel data quite well. In Fig. 4 C, the predicted
*P*_{o} (□) from Model 1-4 (Fig. 13) and its fit to the Hill equation
(solid line) are plotted as a function of ATP. The maximal
*P*_{o} (0.64) and EC_{50} (13.3
μM) are close to those of the experimental data, although the Hill
coefficient (1.8) is slightly smaller. These values are much closer to
experimental data than that from Model 1-2 (Fig. 13), again suggesting that Model 1-4 is better than
Model 1-2.

#### 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.

To examine which rate constants vary with voltage, we globally fit the data between −80 and −120 mV with Model 1-4 (Fig. 13). Each rate constant was taken to be of the form: 14

where *k*_{ij}(0) is the rate constant at 0 mV,
*k*_{B}*T* is Boltzmann's constant
times absolute temperature, and *z*δ_{ij} is
the effective charge (in a lumped parameter model, a product of the sensing
charge and the fraction of the total electric field felt at the location of
the sensor). However, this model has many parameters and did not converge
[with a detailed balance constraint in loop, there are 30 parameters,
including 15 *k*_{ij}(0) and 15
*z*δ_{ij}]. We had to apply further
constraints to reduce the number of parameters. Since it is presumed that
the ATP binding site is located in the extracellular loop (Brake et al., 1994), it is reasonable
to assume that it is outside the electric field, and therefore the
association and dissociation rates are voltage independent. We fixed them to
the values obtained by global fitting based on Model 1-4 (Table VII). The likelihood estimator
converged, but with large error limits for *k*_{ij}
and *z*δ_{ij} (Table IX). Therefore, we could not make a firm conclusion
regarding the voltage dependence for any individual rate constant. However,
the predicted *P*_{o} using the mean values of rate
constants does decrease with depolarization and is similar to the
*P*_{o} from idealized currents (Fig. 15 C). Fig. 15 D shows the open and closed interval histogram and
the predicted probability densities (solid lines) from the rate constants.

We predicted the shape of the whole cell I–V relationship by
combining *P*_{o} from outside-out patches and the
single channel conductance. The whole cell current *I* is
determined by the product of single channel current, *i*, the
number of channels, *n*, and the open probability,
*P*_{o}: 15

*P*_{o} obtained from histograms can be fit with the
Boltzmann equation: 16

where *P*_{o}(0) is *P*_{o} at
0 mV, and is equal to 0.11. *z*δ is equal to 0.34,
indicating that a hyperpolarization of 74 mV is needed for an e-fold
increase of *P*_{o}. If we presume that the voltage
dependence of *P*_{o} at different ATP concentrations
is the same, we can use this result, together with the dose–response
curve (Fig. 4 C), to estimate
*P*_{o}(V) of a single channel. Multiplying
*P*_{o}(V) by the single channel current (Fig.
2) predicts the shape of the
whole-cell I–V relationship. It is close to that predicted by Fig.
13, Model 1-4 (Fig. 3 B).

## Discussion

In this study, we have characterized the single channel properties of cloned
P2X_{2} receptor ion channels. The characterization included general
gating features, permeation properties, ATP concentration dependence, effects of pH,
and kinetic analysis.

### Single Channel Current Behavior and Excess Open Channel Noise

The typical single channel Na^{+} current has a chord conductance
of ∼30 pS at −100 mV (Fig. 1). The open channel current shows high frequency, high amplitude
flickering with some apparent full closures. Because of the difficulty in
resolving the fluctuations comprising this “buzz mode,” rather
than build a substate model to characterize the open channel behavior, we
characterized it as a single conductance with noise. The standard deviation of
the excess open channel current is ∼30% of the mean. This is much larger
than that of the acetylcholine receptor, for example, where the noise is only
2∼5% of the mean (Auerbach and Sachs,
1984; Sigworth, 1985, 1986). The excess noise does not arise from
thermal or shot noise nor from the voltage noise of the amplifier (in the worst
case, this is 10^{−8}× the thermal noise of the channel;
Sigworth, 1985). The fluctuations
appear to represent rapid conformational changes that modulate the open channel
conductance. Occasionally, we saw relatively long-lived subconductance levels
(see Fig. 1 D), but these were too
infrequent to be evident in the all-points histograms. We attempted to estimate
whether the fluctuations were to a discrete number of conducting states using a
maximum-point likelihood approach. However, we could not find a consistent set
of substate amplitudes between records from different patches, although it is
clear that the flickers do not represent simple band-limited full closures of
the channel. It is possible that there are actually a large number of states
better described by a noise rather than a state model. The presence of these
rapid fluctuations means that attempts to estimate the unitary channel current
with noise analysis are prone to large, bandwidth-dependent errors.

We do not think that the flickers arise from channel block by a diffusible agent,
a mechanism that is often seen in other channels.
Ca^{2+}-activated K^{+} channels can be blocked
in a flickery manner by Na^{+} (Yellen, 1984), and cardiac Ca^{2+} channels are
discretely blocked by divalent ions (Lansman et
al., 1986). Since our currents were equally noisy with (Fig. 1 A) and without (Figs. 4 A and 5) extracellular divalent ions, we do not believe
that the excess noise comes from the block of divalent ions. ATP is not a
candidate for blocking the channels since the mean amplitude and the excess
noise are independent of ATP concentration (Fig. 4 A). The voltage dependence of the excess noise is also not
significant, suggesting that the flickers do not involve processes that sense
the electric field. The simplest interpretation is that the excess noise arises
from conformational transitions of the channel itself.

The general features of the cloned P2X_{2} receptors we have discussed
are similar to data recorded from native receptors in rat sensory neurons and
PC12 cells (Krishtal et al., 1988; Nakazawa and Hess, 1993). In rat dorsal
root ganglion (DRG) cells, single channel currents flickered much more rapidly
than in PC12 cells—so rapidly that the lifetime of both states was
almost always too short to be resolved by the recording system (Bean et al., 1990). The mean amplitude of
the open state with 150 mM extracellular Na^{+} was only 0.9 pA
at −130 mV with an equivalent chord conductance of 7 pS and no obvious
substates. In contrast, we observed a mean single channel current of 3.2 pA,
much larger than in the rat DRG cells, with 145 mM extracellular
Na^{+} at −100 mV with an equivalent mean chord
conductance of 32 pS. The true maximum conductance is even larger since the
difference in amplitude of the upper 5% of closed and open distributions is 4.3
pA, ∼34% larger than the mean current.

### I–V Relationship

The single channel I–V relationship of the cloned P2X_{2}
receptors exhibited strong inward rectification (Fig. 2). This result is consistent with the whole cell
I–V relationship (Fig. 3) (Brake et al., 1994; Valera et al., 1994). Zhou
and Hume (1998) studied the mechanisms of inward rectification of
P2X_{2} receptors. In their data, both gating and single channel
conductance contributed to the inward rectification. They also reported that
inward rectification did not require intracellular Mg^{2+} or
polyamines, and was present when the same solution was used on both sides of the
patch. Our data supports these results. The currents in Fig. 2 were recorded in the presence of 1 mM
extracellular Ca^{2+} and Mg^{2+}; however, the
single channel current I–V relation showed similar inward rectification
when currents were recorded in the absence of divalent cations (data not
shown).

Since the mean open and closed times vary with voltage (Fig. 15 B), the opening and closing rate constants are voltage
dependent. Although our kinetic analysis was unable make a firm assignment of
the voltage dependence to particular rate constants,
*P*_{o} did decrease with depolarization (Fig. 15 C). The predicted whole cell currents
(Fig. 3 B) based on Model 1-4 (Fig. 13) and single channel I–V curve
matched reasonably well with the data. These results also suggest that both the
instantaneous conductance and voltage-dependent gating contribute to the inward
rectification. The dual mechanisms of inward rectification in this receptor are
similar to the neuronal nicotinic acetylcholine receptor (Sands and Barish, 1992). The most important feature of the
voltage dependence of P2X_{2} kinetics is that it is minor.

### Probability of Being Open

ATP is a potent agonist for cloned P2X receptors, except P2X_{7}, and the
receptors are highly selective for ATP over most other adenosine derivatives.
Dose–response studies of whole cell currents reveal a Hill coefficient
larger than 1 (Brake et al., 1994),
suggesting that activation requires more than one agonist. This is reasonable
since the channels are composed of multiple homomeric subunits. We studied
*P*_{o} over a wide range of ATP concentrations with
outside-out patches (Fig. 4) and showed
that the *P*_{o} curve has a Hill coefficient of 2.3, an
EC_{50} of 11.2 μM, and a maximum of 0.61. A Hill
coefficient of 2.3 suggests that there are at least three binding sites in the
receptor. (That the Hill coefficient is only a lower estimate of the
stoichiometry is emphasized in Fig. 4 C,
where data from a simulation of Model 1-4 [Fig. 13] with three binding steps could be well fit with a Hill
coefficient of 1.8). Presumably, the cooperativity arises from the multimeric
structure of the channel. Based on refolding studies of the P2X_{2}
extracellular domain (P2X_{2}-ECD), Kim
et al. (1997) predicted that the naturally assembled form of
P2X_{2} receptors may be tetrameric. Lewis et al. (1995) found that coexpression of P2X_{2} and
P2X_{3} can form a new channel type by subunit heteropolymerization,
providing further evidence that the P2X receptors are multimers. Recent
experiments with chemical cross-linking of P2X_{1} and P2X_{3}
receptors (Nicke et al., 1998) indicate
that P2X receptor channels are trimeric. Since these results were obtained from
native P2X receptors expressed in *Xenopus* oocytes, we expect
that they are more representative than the studies on the isolated extracellular
domains.

The maximum *P*_{o} of ∼0.6 indicates that the
mean opening rates are slower than the closing rates. Our kinetic analysis based
on Model 1-4 (Fig. 13) shows that the two
opening rates k_{46} and k_{76} are much slower than
corresponding closing rates k_{64} and k_{67}. The opening rate
k_{45} is faster than closing rate k_{54}, while the opening
rate k_{75} is similar to the closing rate k_{57}, so the
overall opening rate is slower than the closing rate.

### Affinity of the Pore for Na^{+}

The theory of independent ion passage predicts that the flux of a permeating ion
should increase linearly with the ion concentration (Hille, 1992). However, most channels do not exhibit this
behavior due to the competition for binding sites in the channel. Ion flux
saturates when the binding–unbinding steps of permeation become rate
limiting. This occurs at high ion concentrations when the rate of ion entry
approaches the rate of unbinding. Conductances in the P2X_{2} channels
show clear deviations from independence (Fig. 6 A). When the concentration of extracellular NaCl is raised, the
single channel conductance saturates. In our data, the mean conductance versus
Na^{+} concentration was well fit by the Michaelis-Menten
(MM) equation, with one binding site, X, in the pore (Scheme II).
Scheme II

The rate constants are, in general, dependent on membrane potential. We tried to
fit our conductance data with Scheme II, but could not obtain a unique set of
rate constants: Scheme II is over
determined because the data does not have enough distinguishing features. If we
assume that at high potentials the reverse flux is negligible, only the two
forward rates are necessary and we can obtain solutions. We found that the
equilibrium constant *K*_{s} is voltage dependent (Fig.
6 B), with the binding site located
∼20% of the way through the field relative to the extracellular face. It
is interesting to speculate as to where the site may be relative to the primary
sequence if one assumes that side chains form the selectivity filter rather than
the backbone carbonyls (Doyle et al.,
1998). In their study of the ionic pores of P2X_{2} receptors
using the substituted cysteine accessibility method (SCAM), Rassendren et al. (1997a) identified three
residues: I328, N333, and T336 in the M2 domain that were located in the outer
vestibule of the pore. Two of these are polar and might be part of a binding
site for Na^{+}. When the channel was open, D349C could be
inhibited only by the small, positively charged MTSEA
(2-aminoethyl-methanethiosulfonate), but not by MTSET
{[2-(trimethylammonium) ethyl]methanethiosulfonate} or MTSES
[sodium (2-sulfonatoethyl)methanethiosulfonate], implying that D349 is located
near the middle of the channel. D349 is a negatively charged amino acid and is
conserved among all seven P2X receptors. It is possible that D349 could be the
site of permeant cation binding and is responsible for ionic selectivity.

### Cation Selectivity

Our data shows P2X_{2} is a nonselective cation channel. The ionic
selectivity based on the conductance is: K^{+} >
Rb^{+} > Cs^{+} >
Na^{+} > Li^{+}, Eisenman sequence
IV (Hille, 1992). This sequence is
different from free solution mobility and from the sequence of high field sites.
This suggests the pore may be smaller than the nicotinic acetylcholine receptor
with an interior having little charge in the selectivity filter. This is
consistent with the results from substituted cysteine accessibility method
experiments (Rassendren et al., 1997a)
where only I328C, N333C, T336C, L338C, and D349C in the M2 domain were
accessible to MTS reagents**.** Only D349 is negatively charged among
these residues, and it may not be part of the selectivity filter.

Based on whole cell currents of P2X_{2} receptors, Brake et al. (1994) reported that the replacement of
extracellular Na^{+} by K^{+} did not affect the
reversal potential, suggesting that Na^{+} and
K^{+} have a similar permeability near 0 mV. In our
experiments, the currents carried by Na^{+} were larger than the
currents carried by K^{+} at negative potentials. Similar
results were reported for PC12 cells (Nakazawa
et al., 1990b). The origin of the discrepancy between our results and
theirs is masked by the lack of knowledge of the interplay between permeation
and gating in the whole cell current. Different ionic environments may change
the agonist binding and/or gating. In the nicotinic acetylcholine receptor
(Akk and Auerbach, 1996), external
monovalent ions compete with agonists for binding, changing the
dose–response curves for reasons that have nothing to do with the
permeation process itself. If the kinetics of ATP binding and/or gating is
different for Na^{+} and K^{+} in the
extracellular solution, *P*_{o} will be different,
changing the maximum conductance at a fixed agonist concentration.

The excess open channel noise sequence is the same as the cation selectivity
(i.e., K^{+} ≅ Rb^{+} >
Cs^{+} > Na^{+} >
Li^{+} (Table I),
indicating that it is proportional to the single channel current amplitude, as
expected if the noise arises from modulation of the normal flow. If the excess
noise arose completely from simple conformational modulation of the pore, all
ions would have the same relative selectivity. This is true for all alkali ions
with the exception of Li^{+}, which had ∼20% smaller
relative fluctuations. This suggests a more specific interaction between
Li^{+} and the channel than for other permeant ions.

### pH Potentiation

The sensitivity of cloned P2X_{2} receptors to ATP was affected by
extracellular pH. King reported (King et al.,
1996) that with acidification, the ATP dose–response curve of
whole cell currents shifted to the left without altering the maximal response.
The effective receptor affinity for ATP was enhanced 5–10-fold by
acidifying the bath solution (to pH 6.5), but was diminished four- to fivefold
in an alkaline solution (pH 8.0). Different P2X receptors have different
sensitivities to pH. Unlike P2X_{2} receptors, P2X_{1},
P2X_{3}, and P2X_{4} receptors decrease their apparent
affinity with acidification (Stoop et al.,
1997). Our studies on outside-out patches showed that the mean
current increased about an order of magnitude when the extracellular pH changed
from 8.3 to 6.8, exhibiting a pK_{a} of ∼7.9 (Fig. 8 B). The Hill coefficient of 2.5 suggests
that the channel has at least three binding sites, which is consistent with the
stoichiometry study by Nicke et al.
(1998). In related experiments, extracellular protons potentiated
adenosine binding to A_{2A} receptors, and this effect could be modified
by mutagenesis or by chemically altering the strategic residues (Allende et al., 1993). In the extracellular
loop of P2X_{2} receptors, there are 9 histidine residues interspersed
between 10 cysteine residues, the latter being conserved throughout the
P2X_{1–7} proteins. Both cysteine and histidine residues
have been shown to be important for agonist and antagonist binding at the
A_{1} receptor, which is pH sensitive (Allende et al., 1993). It is reasonable to speculate that
these two amino acids may play a similar role in ATP binding to P2X_{2}
receptors. Protonation of the histidine residues may account for the increase in
P2X_{2} current at low pH, but this seems unlikely because
diethylpyrocarbonate, which irreversibly denatures histidyl residues, has no
effect on the magnitude of the currents (Wildman
et al., 1998).

The major effect of pH was on the kinetics of activation. The rate of activation increased as pH decreased (Fig. 8 C), while the deactivation time constant was independent of pH. This suggests that the closing rates and the dissociation rates are not affected by protons. The simplest interpretation of the data is that in acidic environments, the binding site becomes more positive, increasing its affinity for ATP. However, since macroscopic kinetics is a function of all of the rate constants, many of which are not associated with binding, such an interpretation is not reliable.

The single channel current amplitudes at different pH were similar, but the excess open channel noise increased when pH was lowered (Table II). Comparing the single channel currents at different values of pH, as shown in Fig. 9 A, more brief closings can be seen at lower pH. The fluctuations caused by protons are slower than the fluctuations of the intrinsic channel flicker. While these results suggest that protons served as blockers, analysis of the power spectra and single channel kinetics contradict this interpretation. The blocking and unblocking rates were only weakly dependent on proton concentration (see Eq. 13). Power spectral analysis also showed that the corner frequency decreased with an increase in pH, opposite to the prediction for proton block. It appears that the brief closings at low pH are due to conformational changes produced by the titration of several sites.

### Kinetics

#### Preferred model.

We used the maximum interval likelihood method to statistically compare
kinetic models (Vandenberg and Horn,
1984; Horn, 1987; Qin et al., 1996a). The models were
built hierarchically, beginning with one that described the transitions near
the open states (Vandenberg and Bezanilla,
1991). The first model we chose (Model 1 or, equivalently, Model
2; Figure 11) had three closed states,
C_{1}, C_{2}, and C_{3}, representing
unliganded, monoliganded, and biliganded closed states, and two open states
O_{4} and O_{5}.

Starting with this model, we expanded to Models 1-2, 1-3, and 1-4 (Fig. 13) to account for the ATP titration
data. Comparing Model 1 (Fig. 11) with
Model 1-2, and Model 1-3 with Model 1-4, we found that the opening and
closing rate constants were surprisingly close (see Tables VI and VII), suggesting that the transitions near the open
state were well defined. This result supports our strategy of model
development. Among the four models, Model 1-4 had the highest likelihood and
AIC rank, and therefore is our preferred model (Table VIII). In this model, there are five closed states,
C_{1}, C_{2}, C_{3}, C_{4}, and
C_{7}, representing unliganded, monoliganded, biliganded, and
triliganded closed states, and two open states, O_{5} and
O_{6}. The three ATP binding steps require the channel to be at
least a trimer. By constraining the ATP association rates to be proportional
to concentration, reliable rate constants were obtained from global fitting
with this model (Table VII). The
predicted probability density functions match reasonably well the open- and
closed-time histograms at all concentrations, and the predicted
*P*_{o} is close to the experimental data so that
our final preferred model is Model 1-4.

#### ATP binding sites and cooperativity.

From the results of the basic model (Fig. 11, Model 1) and its expanded versions (Fig. 13, Models 1-2, 1-3, and 1-4), we found that association and dissociation rate constants increased as they approached the open states (Table VI and VII). This means that the subunits are not independent and that the association rate for an incoming ATP is increased by the presence of bound ATPs. This trend was consistent among all models examined.

The increase in association rates with consecutive binding is most surprising when one thinks about the opposing electrostatic factors. Bound ATP with a charge of −4 should repel the next incoming ATP (note: the actual valence of bound ATP is not known and is probably less than −4). Since the energy is proportional to the product of the charges, if the sites were independent, the second ATP would be repelled by a resident ATP with an energy proportional to 4*4 = 16, and the third by 8*4 = 32. We would thus expect the later binding rates to decrease by more than just the number of available sites. The trend of increasing association rates with occupancy must be caused by conformational changes in the channel that mask the electrostatic contribution. While the increasing rates of dissociation with occupancy fit the predicted electrostatic trend, given the conformational changes associated with binding, this trend may be coincidental. The binding of ATP causes the remaining unoccupied sites to open up in such a manner so as to increase the rates of ATP entry and exit without having a large effect on the equilibrium affinity of the site (Fig. 14).

If the channel were a tetramer, as predicted by Kim et al. (1997), we might add one closed state to the
left of C_{1} as in Model 1-5 (Fig. 13). We attempted to fit this model, but could not obtain unique
rates. This may be because we had insufficient data at very low ATP
concentrations, or because the channel really is a trimer (Nicke et al., 1998). The predicted
*P*_{o} vs. ATP concentration from Model 1-4
(Fig. 13) fits well the
*P*_{o}, EC_{50}, and Hill coefficient
obtained from the dose–response curve (Fig. 4 C), supporting the consistency of the model and the
necessity of the last ATP-independent closed state.

#### Other kinetic models.

There have been only a few studies on the kinetics of P2X receptor ion
channels based on single channel currents (Krishtal et al., 1988). Kinetic studies using whole cell
currents showed that the rise time of current elicited by ATP was strongly
concentration dependent, but the decay time was not (Surprenant, 1996). This is in accord with the pH
experiments discussed above. There is some variability among reports
regarding the rise and fall times. In rat sensory neurons, using fast
solution exchange, the rise time was ∼10 ms at saturating ATP and
the decay time was ∼100 ms (Bean et
al., 1990). In smooth muscle and cloned P2X_{1}
receptors, the rise time was ∼5 ms, while in PC12 cells, cloned
P2X_{2} receptors, and rat superior cervical ganglion (SCG)
cells, the rise time was ∼25 ms (Surprenant, 1996). In rat SCG cells, nodose, and guinea-pig
coeliac neurons, the latency to the onset of whole cell currents was
estimated to be ∼0.8–4 ms, and the 10–90% rise time
at high ATP concentrations ranged from 5 to 20 ms (Khakh et al., 1995). Since these experiments were done
in the whole cell configuration, the rate of rise was likely limited by the
speed of the solution exchange around the cells. Hess (1993) reported that the time resolution for
solution exchange around a whole cell of this size is 2∼10 ms under
maximal flow velocities and even slower for lower velocities. With
outside-out patches, the rise times can be ∼250 μs (Colquhoun et al., 1992). Moreover,
because in the whole cell experiments there was no marker for the start of
solution exchange, the latency to the onset of the currents could not be
estimated accurately.

Preliminary kinetic analysis of single channel currents from rat sensory neurons showed that the distribution of the open times could be approximately fit by two exponentials with time constants of 0.35 and 3.4 ms (Krishtal et al., 1988). The ratio between the fast component amplitude and the slow one varied between patches, with ratios of 47.4:1 to 4.8:1.

Using the rise and fall time constants from whole cell currents at different
concentrations of ATP, and based on kinetic models of the ACh receptor
channel, Bean (1990) proposed a linear
kinetic model with independent subunits for ATP activation (Fig. 13, Model 9). The association and
dissociation rate constants *k*_{+} =
1.2 × 10^{7} M^{−1}s^{−1}
and *k*_{− }= 4
s^{−1} were chosen so that the simulations mimicked the
kinetics seen in the bullfrog sensory neurons. Agreement between the model
and the data suggested that the ATP binding sites could be independent.

We applied the independent binding site assumption to Model 1-2; i.e.,
k_{34} = 1/2k_{23} = 1/3k_{12}
= 1/3k_{10} = k_{+}, and
k_{21} = 1/2k_{32} = 1/3k_{43}
= k_{−}. Although the estimation converged, the
likelihood was much lower than our favored models. We also fit our data with
Bean's (1990) model, which has only one open state (Fig. 13, Model 9), and again the fits were
poor.

In other ligand-gated channels, such as the Ca^{2+}-activated
potassium channel and ACh receptors (Magleby
and Song, 1992; Auerbach et al.,
1996), partially liganded channels can open. To explore whether
these states were visible in our data, we compared the maximum likelihood of
Model 8-1 (Fig. 13) that has partially
liganded openings with Model 1-2 (Fig. 13). Global fitting of Model 8-1 with data from 5, 10, 15, 20,
30, and 50 μM ATP produced a maximum likelihood 664 units lower than
Model 1-2, suggesting the model is e^{664}× less likely to
produce the data. Apparently, P2X_{2} channels do not open for a
significant fraction of time in partially liganded states.

In summary, Model 1-4 (Fig. 13) can
well represent the channel gating processes. It is adequate to explain the
behavior across concentration and is physically reasonable. Fig. 14 shows the calculated free energy
barriers and wells at −120 mV referenced to 1 M ATP. The energies
were calculated from the rate constants assuming an Eyring model. The free
energies of all wells decreased with the reaction coordinate. State
C_{4} could go to either open state O_{5} or
O_{6} with state O_{5} being slightly more stable.
O_{5} and O_{6} go to the same closed state
C_{7} that is the most stable in the reaction pathway.

#### Voltage dependence of P_{o} and rate constants.

Although *P*_{o} is not strongly dependent on membrane
potential, it did decrease with depolarization (Fig. 15 C), indicating that some of the rate constants are
voltage dependent. To reduce the free parameters, we limited the voltage
sensitivity to only the rate constants in the final loop and ended up with
very large errors limits for *k*_{ij}(0) and
*z*δ_{ij}. We have no confidence in the
voltage dependence of any of the individual rate constants. Data from a
wider voltage range will be required to adequately address this
question.

Despite the wide error limits, by lumping the kinetics into an equilibrium
model to predict the probabilities of occupancy, the predicted
*P*_{o} and whole cell currents calculated from
the mean values of *k*_{ij}(0) and
*z*δ_{ij} were consistent with those
obtained by idealization (Fig. 15 C)
and with experimental data (Fig. 3 B).
The probability density functions match reasonably well with duration
histograms (Fig. 15 D).

In conclusion, the currently optimal model, Model 1-4 (Fig. 13), can be summarized as follows: (a) the channel proceeds through three ATP binding steps before opening; (b) the three ATP binding sites are not independent, but positively cooperative; (c) There are two open states, which connect to a common ATP-independent closed state; (d) activation and deactivation proceed along the same pathway; and (e) channels only open after being fully liganded.

## Acknowledgments

We thank Drs. David Julius and Tony Brake (University of California, San Francisco)
for providing P2X_{2} DNA, Dr. Annmarie Surprenant (Glaxo Welcome and
University of Sheffield, Sheffield, UK) for providing stably transfected cell lines,
Dr. Tao Zeng (Department of Physiology and Biophysics, State University of New York,
Buffalo) for assistance with the LabView™ programs. We also thank Drs. Tony
Auerbach, Feng Qin, Alan North, and Annmarie Surprenant for many helpful
discussions.

This study was supported in part by the National Institutes of Health.

## Footnotes

- Submitted: 10 December 1998
- Accepted: 9 March 1999