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	Figure 1. Homology modeling of the structure of rat P2X2 from zebra fish P2X4 in closed and open states with localization of the residues K308, D315, and T339S, which are critical in the homotrimer for voltage- and [ATP]–dependent gating. (A and E) Homology model of the rat P2X2 structure based on the closed- (A) and open-state (E) structures of zebra fish P2X4 (Kawate et al., 2009; Hattori and Gouaux, 2012). The critical residues at the ATP-binding site (K308), linker (D315), and pore (T339) are shown in pink, magenta, and orange spheres, respectively. (B and F) Only the TM helices and their connections to ATP-binding sites are shown for a better view of critical residues in closed (B) and open (F) states. (C and G) Bottom views of the pore in closed (C) and open (G) states showing T339 residues. (D and H) Top view just above the level of the intersubunit ATP-binding site in closed (D) and open (H) states. K308 and K69 form a groove for the intersubunit ATP docking.
	Figure 2. Analysis of voltage- and ATP-dependent gating for WT, WT–WT–WT, and WT–K308A–WT. Voltage- and [ATP]-dependent gating is intact when one ATP-binding site is disrupted. (A) Normalized voltage-induced activation traces for WT, WT–WT–WT, and WT–K308A–WT from the representative data shown in Fig. S2 at −160 mV at various concentrations of ATP. (B) Mean (± SEM) of activation time constants at various [ATP] and membrane potentials for WT (n = 7–9), WT–WT–WT (n = 12–18), and WT–K308A–WT (n = 8–25) at various [ATP]. (C) Mean (± SEM) normalized G-V relationship for WT (n = 9), WT–WT–WT (n = 26), and WT–K308A–WT (n = 12) derived from the maximum tail current responses by fitting with the two-state Boltzmann equation as described in Materials and methods. (D) Mean (± SEM) [ATP] dose–response relationships at −160 mV for K308A–WT–WT (n = 6), WT–K308A–WT (n = 13), and WT–WT–K308A (n = 11), together with WT (n = 16) and WT–WT–WT (n = 10). (E) Mean (± SEM) EC50 values and (F) Hill coefficients are derived from the fitting of the normalized maximum [ATP] dose–response relationships in D with the Hill equation. Mean (± SEM) EC50 values for WT (n = 16), WT–WT–WT (n = 10), K308A–WT–WT (n = 5), WT–K308A–WT (n = 12), and WT–WT–K308A (n = 11) are 14.5 ± 1.2 µM, 19.1 ± 2.0 µM, 42.3 ± 2.2 µM, 22.9 ± 1.8 µM, and 33.3 ± 1.65 µM, respectively. Mean (± SEM) Hill coefficients for WT (n = 16), WT–WT–WT (n = 10), K308A–WT–WT (n = 5), WT–K308A–WT (n = 13), and WT–WT–K308A (n = 11) are 1.7 ± 0.2, 1.8 ± 0.2, 1.7 ± 0.18, 1.8 ± 0.18, and 1.6 ± 1.4, respectively. *, P < 0.05.
	Figure 3. Analysis of voltage- and [ATP]-dependent gating of the P2X2 receptor channel with the D315A mutation in the linker region. The D315A mutation reveals two different gating modes. (A) Mean (± SEM) [ATP] dose–response relationships for WT and D315A at −160 mV are shown in red and blue, respectively. EC50 (1) and EC50 (2) for D315A are 1.2 ± 0.6 µM and 89.1 ± 1.48 µM, with Hill coefficients of Hill (1) = 2.4 ± 0.7 and Hill (2) = 1.0 ± 0.2 (n = 10). EC50 for WT is 14.5 ± 1.2 µM with a Hill coefficient of 1.7 ± 0.2 (n = 16). (B) [ATP] dose–response relationship from a single representative experiment for WT (red) and D315A (blue). A dose–response shift by voltage is observed for WT and only for the second phase of D315A at high [ATP]. (C) Mean (± SEM) normalized G-V relationship at various [ATP] for D315A (n = 8) derived from the maximum tail current responses by fitting with the two-state Boltzmann equation, as described in Materials and methods. (D) Normalized voltage-induced activation traces for D315A at −160 mV at various concentrations of ATP from the representative traces shown in Fig. S5.
	Figure 4. Analysis of voltage- and [ATP]-dependent gating of tandem trimers having three, two, and one D315A mutant subunits. Two subunits with D315 are necessary for normal gating. (A) [ATP] dose–response relationships at −160 mV for WT, D315A, and tandem trimers with three, two, and one D315A at various membrane potentials. Mean (± SEM) EC50 values and Hill coefficients are as follows: WT: EC50, 14.5 ± 1.2 µM, and Hill, 1.7 ± 0.2 (n = 16); D315A–D315A–D315A: EC50 (1), 1.5 ± 0.8 µM; EC50 (2), 130 ± 5.0 µM; Hill (1), 3.7 ± 0.6; and Hill (2), 1 ± 0.2 (n = 13); D315A–D315A–WT: EC50 (1), 3.15 ± 0.9 µM; EC50 (2), 794 ± 12 µM; Hill (1), 1.8 ± 0.2; and Hill (2), 1.06 ± 0.2 (n = 22); and D315A–WT–WT: EC50, 6.02 ± 1.1 µM, and Hill, 1.4 ± 0.1 (n = 24). (B) One representative experiment from tandems of D315A and WT to show the shift of dose–response relationships by voltage in between −60 to −160 mV. (C) Cumulative data for normalized G-V relationships at various [ATP] for tandem trimers with three (n = 8), two (n = 8), and one (n = 6) D315A mutant subunit, derived from the maximum tail current responses by fitting with the two-state Boltzmann equation, as described in Materials and methods. Data points are mean ± SEM. (D) Normalized voltage-induced activation traces for tandem trimers with three, two, and one D315A mutant subunit at −160 mV at various concentrations of ATP from the representative traces shown in Fig. S6.
	Figure 5. Analysis of voltage- and [ATP]-dependent gating of tandem trimers with three, two, and one T339S mutant subunit in the pore region of the P2X2 receptor channel together with WT–WT–WT. An increase in the number of T339S in the trimer had a gradual and additive effect on voltage-dependent gating. (A) Representative macroscopic current recordings from tandem trimers with three, two, and one T339S, evoked by step pulses during the steady state after the application of saturating concentrations of [ATP]. The holding potential was −40 mV. Step pulses from 40 to −160 mV were applied in 20-mV decrements. Tail currents were recorded at −60 mV, and their enlarged images are shown next to the main activation traces. (B) Normalized G-V relationships derived from maximum tail currents at −60 mV fitted with the two-state Boltzmann equation are shown as mean ± SEM at 100 µM [ATP] for WT–WT–WT (red; n = 12), WT–T339S–WT (blue; n = 9), WT–T339S–T339S (magenta; n = 11), and T339S–T339S–T339S (black; n = 6). (C) Ratio of conductance at −60 and −160 mV at 100 µM [ATP] for tandems having three, two, and one T339S mutant subunit and WT–WT–WT is shown by a boxplot using the same color code as in B. Means are shown by a plus sign. The bottom of each box is the 25th percentile, the top is the 75th percentile, and the line in the middle is the median. Whiskers show the minimum and maximum data. *, P < 0.05. (D) Normalized voltage-induced activation traces for tandem trimers with one, two, and three T339S mutation(s) and WT–WT–WT at −160 mV at various concentrations of ATP from the representative traces shown in A (color code is the same as in C). (E) Comparisons of activation time constants at saturating concentrations of ATP for WT–WT–WT (n = 20) and tandem trimers with two (n = 35) and one (n = 25) T339S mutations by fitting the voltage-induced activation phase to a single-exponential function, as explained in Materials and methods. Data are shown by boxplot as in C, using the same color code. *, P < 0.05. As there is no voltage-induced activation for the tandem trimer with three T339S subunits, it was not analyzed. (F) [ATP] dose–response relationships for tandem trimers at −160 mV. EC50 and Hill coefficients are as follows: T339S–T339S–T339S: EC50, 2.4 ± 0.4 µM, and Hill, 1.5 ± 0.3 (n = 7); WT–T339S–T339S: EC50, 6.0 ± 0.4 µM, and Hill, 1.5 ± 0.2 (n = 10); and WT–T339S–WT: EC50, 12.2 ± 1.2 µM, and Hill, 1.5 ± 0.9 (n = 6; color code is the same as in B).
	Figure 6. Voltage- and [ATP]-dependent gating differs depending on the location of one D315A relative to the location of K308A in a trimer with two intact ATP-binding sites. Analysis of trans (K308A–D315A–WT) and cis (WT–K308A&D315A–WT) constructs shows different voltage- and [ATP]-dependent gating. (A and B) Voltage-induced normalized activation traces at −160 mV of trans (K308A–D315A–WT; A) and cis (WT–K308A&D315A–WT; B) at various [ATP] from the representative data shown in Fig. S7. (C and D) Dependence of the activation time constants on voltage and [ATP] for trans (C) and cis (D) constructs. Mean (± SEM) activation time constants for trans (C; n = 8–15) and cis (D; n = 14–19) constructs at various [ATP] and membrane potentials are shown. (E and F) Normalized G-V relationship at various [ATP] for tandem trimer trans (n = 9–20; E) and cis (n = 8–11; F) derived from the maximum tail current responses at −60 mV by fitting with the two-state Boltzmann equation, as described in Materials and methods from the same oocytes. (G and H) Mean ± SEM of V1/2 (mV) (G) and Z (H) values for the trans (n = 9–20) and cis (n = 8–11) constructs. *, P < 0.05.
	Figure 7. The D315A linker mutation in one subunit shows different voltage- and [ATP]-dependent activation depending on the location relative to one ATP-binding site mutation (K69A) in the tandem trimer molecule. Analysis of D315A&K69A–WT–WT and WT–D315A–K69A shows different voltage- and [ATP]-dependent gating. (A) Normalized Voltage-induced activation traces at −160 mV for D315A&K69A–WT–WT (left) and WT–D315A–K69A (right) at various [ATP] from the representative data shown in Fig. S9. (B) Dependence of the activation time constants on voltage and [ATP] for D315A&K69A–WT–WT (left) and WT–D315A–K69A (right). Mean (± SEM) activation time constants for D315A&K69A–WT–WT (n = 6–10) and WT–D315A–K69A (n = 7–12) at various [ATP] and membrane potentials are shown. (C) Mean (± SEM) normalized G-V relationships at various [ATP] for tandem trimers D315A&K69A–WT–WT (n = 6–10) and WT–D315A–K69A (n = 6–16) derived from the maximum tail current responses at −60 mV by fitting with the two-state Boltzmann equation, as described in Materials and methods from the same oocytes. (D) Mean (± SEM) V1/2 (mV) and Z values for the D315A&K69A–WT–WT (n = 6–10) and WT–D315A–K69A (n = 6–16). *, P < 0.05.
	Figure 8. Voltage- and [ATP]-dependent gating does not change depending on the location of one T339S relative to K308A in the trimer with two intact ATP-binding sites; trans (K308A–T339S–WT) and cis (WT–K308A&T339S–WT) showed similar voltage- and [ATP]-dependent gating. (A and B) Voltage-induced normalized activation traces of trans (K308A–T339S–WT; A) and cis (WT–K308A&T339S–WT; B) at various [ATP] from the representative traces shown in Fig. S10. (C and D) Dependence of the activation kinetics on voltage and [ATP] for trans (C) and cis (D) constructs. Mean (± SEM) activation time constants for trans (C; n = 5–18) and cis (D; n = 6–9) constructs at various [ATP] and membrane potentials are shown. (E and F) Normalized G-V relationships at various [ATP] for trans (E) and cis (F) constructs derived from the maximum tail current responses by fitting with the two-state Boltzmann equation, as described in Materials and methods. (G and H) Mean (± SEM) V1/2 (mV) (G) and Z (H) values for trans (C; n = 5–18) and cis (D; n = 6–9) constructs.
	Figure 9. Voltage- and [ATP]-dependent gating does not change depending on the location of one T339S relative to D315A in the trimer; trans (D315A–T339S–WT) and cis (WT–D315A&T339S–WT) showed similar voltage- and [ATP]-dependent gating. (A and B) Normalized voltage-induced activation traces of trans (A) and cis constructs (B) at various [ATP] from the representative traces shown in Fig. S11. (C and D) Dependence of the activation kinetics on voltage and [ATP] for trans (C) and cis (D) constructs. Mean (± SEM) activation time constants for trans (C; n = 12–16) and cis (D; n = 9–14) constructs at various [ATP] and membrane potentials are shown. (E and F) Mean (± SEM) normalized G-V relationships at various [ATP] for trans (C; n = 7–14) and cis (D; n = 6–10) constructs derived from the maximum tail current responses by fitting with the two-state Boltzmann equation, as described in Materials and methods. (G and H) Mean (± SEM) V1/2 (mV) (G) and Z (H) values for the trans (C; n = 7–14) and cis (D; n = 6–10) constructs.
	Figure 10. Evaluation of how the binding of two ATP molecules for channel activation and the independent contribution of three subunits to the final pore opening can converge using Markov models. The voltage-induced activation phase of the simulation was compared with experimental data for the lowest activating [ATP]. State diagrams for different Markov models (A–C), which were based on the assumption that each subunit is independent and passes through two transitions, C⇄CA⇄OA, with a fast ATP-binding and a rate-limiting voltage-dependent step. (Details of the model are given in Materials and methods.) (A) 10-step model with three intact ATP-binding sites, which requires the binding of three ATP molecules for full activation. (B) 10-step model with three intact ATP-binding sites that can be activated by the binding of two ATP molecules. (C) Six-step model with only two intact ATP-binding sites, which can be activated by the binding of two ATP molecules. Next to each model diagram, simulation traces for voltage-induced activation at various [ATP] are shown (traces for 3, 10, 30, 100, and 300 µM ATP are shaded in red, orange, blue, green, and black, respectively). Dashed black lines show single-exponential fittings of the voltage-induced activation phase at 3 µM ATP. Note the apparent sigmoidicity of voltage-induced activation for model A, which could not be fitted by a single-exponential function (shown by the arrow). Simulation traces of the models in B and C were almost successfully fitted by a single-exponential function.
	Figure 11. Schematic presentation of the activation signal transmission from two ATP-binding sites to the pore upon voltage- and [ATP]-dependent activation. For simplicity, two subunits are illustrated in red and blue. Colored spheres mark the K308 (orange) and K69 (blue) residues in the ATP-binding region, D315 (yellow) in the linker, and T339 (green) at the pore level. Arrows with the same color of borderlines with the subunits depict the signal transmission on each subunit. The activation signal from one intersubunit ATP binding flows directly on the corresponding β-14 strand of the ATP-binding site down to the D315 level, and then spreads to other subunits at the pore level.

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