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Figure 2. The current–voltage relationship of single channel currents. (A) Single channel currents of an outside-out patch from HEK 293 cells activated by 2 μM ATP (1 mM extracellular Mg2+ and Ca2+ at different membrane potentials, symmetrical Na+ solutions containing 145 mM extracellular NaCl/145 mM intracellular NaF). The data were filtered at 5 kHz and digitized at 10 kHz. All of the current traces in this figure are from the same patch. (B) Mean I–V relationship of single channel currents. The error bars indicate the standard deviation of the single channel currents from the all-points histograms. The single channel I–V relationship shows strong inward rectification despite exposure to identical Na+ solutions across the patch. The same result was obtained when single channel currents were recorded in the absence of Mg2+ and Ca2+; therefore, divalent cations are not responsible for the rectification.
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Figure 3. The current–voltage relationship of whole cell currents (WCCs). (A) Whole cell currents from an HEK 293 cell at different holding potentials: −100 to +80 mV at 20-mV intervals. Voltage drops from incomplete series resistance compensation were subtracted from the membrane potential. The currents were activated by 10 μM ATP in the presence of 1 mM extracellular Ca2+ with symmetrical Na+ solutions: 145 mM extracellular NaCl/145 mM intracellular NaF. The data were filtered at 2 kHz and digitized at 5 kHz. (B) The mean WCCs (±SD) (○, n = 5) and predicted WCCs activated by 10 μM ATP. The I–V curve exhibits strong inward rectification, similar to the single channel currents shown in Fig. 2. The reversal potential was ∼0 mV. The predicted WCCs were calculated using Eq. 15 where i (single channel amplitude) was taken from Fig. 2, and Po from the calculations for Model 1-4 (▵) (Fig. 13), and Eq. 16 (□) as a function of voltage. The number of channels was chosen so that the predicted WCC at −60 mV was equal to the experimental data. The predicted WCCs match reasonably well with the experimental data.
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Figure 13. Simplified and expanded versions of Model 1 from Fig. 11 (1-1, 1-2, 1-3, and 1-4), and other kinetic models (9 and 8-1) that have been used in the literature.
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Figure 11. All models that converged during maximal likelihood estimation in the initial topology screen using the MSEARCH program. The relative likelihoods and AIC rankings of these models are listed in Table IV.
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Figure 4. The effect of ATP concentration on single channel currents. (A) Single channel currents of P2X2 receptors expressed in Xenopus oocytes activated by different concentrations of ATP in the absence of extracellular Ca2+ (−120 mV). The data were filtered at 20 kHz and sampled at 40 kHz. All of the current traces in this figure are from the same patch. (B) All-points amplitude histograms of the currents from A (0.05 pA/bin), with the distributions fit to the sum of two Gaussians. At this bandwidth, the excess channel noise was ∼45% of the mean channel amplitude. (C) ATP dose–response curves. The probability of a channel being open is shown from experimental data (○) and simulated data generated by Fig. 13, Models 1-2 (⋄) and 1-4 (□), as a function of ATP concentration. Fits of the data sets to the Hill equation are shown as dotted (experimental data), dash dot (Model 1-2), and solid (Model 1-4) lines. The Hill coefficient = 2.3, EC50 = 11.0 μM, and maximum Po = 0.61 for the experimental data, 1.5, 17.4 μM, and 0.74 for simulated data of Model 1-2, and 1.8, 13.3 μM, and 0.64 for simulated data of Model 1-4. All the experimental data were from same patch. The errors in the experimental Po were estimated from the errors in the mean and standard deviation estimates reported by Origin when fitting the amplitude histograms to Gaussians.
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Figure 5. The effect of extracellular NaCl concentration on the single channel current amplitude. Currents activated by 15 μM ATP were recorded from an outside-out patch from a Xenopus oocyte with different concentrations of NaCl without ionic substitution (different ionic strength) in the absence of Ca2+ at −120 mV. The data were digitized at 20 kHz and low pass filtered at 10 kHz.
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Figure 6. The affinity of Na+ for the channels. (A). The relationship between the mean open channel conductance from Fig. 5 and the NaCl concentration at different voltages. The error bars are the standard deviations of the excess open channel noise. The solid line is a fit of Eq. 9. Note that at each concentration the driving force changes because of the change in Nernst potential. We have assumed Ks is dependent only on the holding potential and not the driving force. (B) The dependence of Ks on holding potential. The solid line was fit by the Boltzmann equation with z = 1, δ = 0.21, and Ks(0) = 148 mM. A depolarization of 118 mV is required for an e-fold increase of Ks. The error bars are the parameter fitting errors from A. (C) The maximal conductance as a function of holding potential. The error bars are the fitting errors from A. The solid line is simply the connection of data. The conductance is approximately linear with the holding potential supporting the simple approximation of Eq. 9.
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Figure 7. The effect of different permeant ions on the single channel currents. Single channel currents from HEK 293 cells at −120 mV activated by 2 μM ATP in the presence of 1 mM Mg2+ and Ca2+ from an outside-out patch. The data were filtered at 5 kHz and digitized at 10 kHz.
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Figure 8. The effect of pH on the affinity of channel for ATP. (A) Multiple-channel currents from an outside-out patch of HEK cells at −120 mV and 2 μM ATP at different values of extracellular pH (0.3 mM extracellular Ca2+). Note the increase in rise time with increasing pH. The data were low pass filtered at 5 kHz and digitized at 10 kHz. The horizontal bar indicates the duration of ATP application. (B) The effect of pH on mean patch current. The data were fitted by the Hill equation with a maximum mean current of 25.1 pA, an EC50 of pH 7.9 (pKa), and a Hill coefficient of 2.5. The error bars are the standard deviation of the data and contain both open channel and gating noise. (C) The pH dependence of the rise and fall times. The time constants for rising (•) and falling (▪) phase were obtained from fitting single exponential functions (solid lines) to multiple channel currents.
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Figure 9. The effect of extracellular pH on single channel currents. (A) Currents recorded from an outside-out patch of an HEK 293 cell under the same experimental conditions as in Fig. 8 A. The data were low-pass filtered at 10 kHz and digitized at 20 kHz. (B) Differential power spectra of the open channel currents at different values of extracellular pH. The spectra were fit with the sum of a Lorentzian function plus a constant (solid line). The corner frequencies are indicated by the arrows. Plotted spectra are averages of three separate data segments.
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Scheme I.
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Figure 10. Idealization and open- and closed-interval duration histograms of single channel currents activated by different ATP concentrations (from the data in Fig. 4 A). (A) Examples of idealized single channel currents activated by 5 and 15 μM ATP. These data were recorded at 40 kHz and filtered at 20 kHz. Before idealization, the data were further filtered at 5 kHz using a Gaussian digital filter. The idealization was performed with the segmental k-means method based on a two-state model (see materials and methods). (B) The mean open and closed times of single channel currents as a function of ATP concentration. (C) The open- and closed-time histograms of single channel currents activated by different concentrations of ATP. The solid lines are the predicted probability density functions for Fig. 13, Model 1-4, with rate constants determined by global fitting across concentrations (see Table VIII). Ni/NT on the ordinate is the ratio of the number of events per bin to the total number of events.
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Figure 12. The effect of ATP concentration on the rate constants near the open states. The rate constants are based on kinetic Model 1 (shown at bottom), with each data set fit separately. Missed events were corrected by imposing a dead time of 0.05 ms. k12 and k23 are the most sensitive to the concentration of ATP, increasing over the range from 5 to 20 μM, and saturating at higher concentrations. The rate constants are plotted in two panels to avoid overlap (the scales in both plots are identical).
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Figure 14. Representation of the channel activation pathway in terms of energy barriers and wells based on Model 1-4 (Fig. 13). The free energy landscape of the reaction scheme calculated from the transition rates. The relation between kij and free energy is defined by the Eyring equation: \documentclass[10pt]{article}
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\begin{equation*}k_{ij}={\kappa}\frac{k_{B}T}{h}exp\hspace{.167em} \left( -\frac{G_{ij}-G_{i}}{RT} \right) ,\end{equation*}\end{document} (kijs in this case are the rate constants at −120 mV). κ is the transmission coefficient (assumed to be 1; Hille, 1992), kB is Boltzmann's constant, h is Planck's constant, and T is the absolute temperature. At 20°C, kBT/h equals 6.11 × 1012 s−1. Gij is the free energy at the top of the barrier between states i and j, and Gi is the free energy of state i. The free energies are arbitrarily referenced to a solution of 1 M ATP. The use of kBT/h as the preexponential term of the rates is undoubtedly far off for a macromolecule. However, it is a maximum estimate that will cause the energy barriers to also be maximal estimates. The relationship of the well (state) energies, however, is much more likely to be correct since these energies are determined by ratios of rate constants where the preexponential terms will tend to cancel.
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Figure 15. The effect of voltage on the single channel currents, mean open and closed times, and Po. (A) Single-channel currents activated by 30 μM ATP were recorded at different membrane potentials. Other conditions were the same as in Fig. 4. All the current traces in this figure are from the same patch. The currents were idealized for further kinetic analysis after filtering at 5 kHz using a Gaussian digital filter. (B) Mean open and closed times extracted from the idealized currents as a function of voltage. (C) The probability of being open, Po, as function of voltage calculated from idealized currents (▪), all-points histograms (•), and the prediction by Fig. 13, Model 1-4 (♦). Po from the histogram is slightly larger than that from idealized currents, indicating that some short-lived openings were missed during idealization. Po predicted by Model 1-4 is close to Po from idealized currents. (D) The closed and open time histograms at different voltages. The solid lines in the histograms are predicted probability density functions based on Model 1-4. Ni/NT has the same meaning as in Fig. 10 C.
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Scheme II.
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