Experimental Characterization and Mathematical Modeling of P2X7 Receptor Channel Gating

Activation kinetics of P2X7R. A, Single exponential fitting of the I₁ activation phase. Notice a progressive decrease in the time constant (τ₁) derived from monoexponential fittings with elevation in BzATP concentration. B, The four parameters logistic curve fitting of the I₂ rising phase. Vertical dotted lines indicate the calculated half-time constants (τ₂). C, Mono- and biexponential fitting of deactivation of P2X7R after washout of BzATP. τ_f, fast deactivation time constants; τ_s, slow deactivation time constants. In A–C, representative traces are shown; gray traces indicate experimental records and black lines the fitted curves. D, E, Concentration-dependent effects of BzATP on the activation time constants (D) and on the I_s and I_f amplitudes derived from deactivation fittings (E); mean ± SEM values from at least 5 records per dose.

Effects of substitution of bath sodium with NMDG and addition of a P2X7R-specific antagonist on the pattern of agonist-induced current responses. A–C, Permeability of the P2X7R pore to NMDG during the sustained agonist application. Pattern of 100 μm BzATP-induced current (A) and reversal potential (B) in cells bathed in sodium-deficient/NMDG-containing Krebs–Ringer buffer during the initial agonist application. Voltage-ramps from −80 mV to +80 mV twice per second during 40 s application were used to generate voltage-current curves. Only selected traces are shown. C, Comparison of kinetics of the secondary current growth (black trace) and changes in the reversal potential (RP, gray trace) during 40 s application of BzATP. D–G, Concentration-dependent effect of Az10606120 (Az) on 100 μm BzATP-induced current response in cells bathed in Krebs–Ringer buffer. D, Time course of activation and deactivation of receptors in the presence (left) and absence (right) of 100 nm Az10606120. E, G, Repetitive stimulation of cells with 100 μm BzATP in the presence and absence of 1 μm Az10606120. Inset shows the magnified first current response; notice the presence of the residual current during sustained application of agonist and antagonist. F, Abolition of both I₁ and I₂ by 10 μm Az10606120, with kinetics comparable to that observed during the washout of agonist (E, second application). In all panels, horizontal bars indicate duration of treatments.

Receptors sensitize during repetitive agonist application. A–C, Time-dependent increase in the peak amplitude of current and a decrease in the rate of receptor deactivation in cells stimulated repeatedly with 10 μm (A) 32 μm (B), and 100 μm (C) BzATP for 40 s. For clarity, every second trace is shown as gray. D, A difference in the rate of receptor deactivation caused by short (1 s) and prolonged (40 s) stimulation with BzATP. E, A decrease in the rate of receptor deactivation was induced by repetitive short (1 s) application of BzATP followed by 2 min washout periods. F, Sensitized receptors respond with monophasic currents during the subsequent application of BzATP, with the peak amplitude of current determined by agonist concentration. G, Duration of the sensitized state after the washout of agonist. Intact cells ready to be patched were initially stimulated with 100 μm BzATP for 40 s (left) followed by washout period of variable times. Before the secondary agonist application, the whole-cell patch clamp was established and current response was recorded. The response of cells after the washout period of 10 min (top) and 30 min (bottom) are shown.

Sensitization of receptors is independent of bath sodium and calcium. A–C, Cells were bathed in KR buffer containing Na⁺, K⁺, Mg²⁺ and Ca²⁺ (A), and in KR buffer in which 90% (B) or 100% (C) of Na⁺ was replaced by NMDG, with a pipette solution containing 10 mm EGTA. Left, Biphasic responses observed during the initial agonist application. Right, High amplitude monophasic responses were always observed during the second application of 100 μm BzATP after 2 min washout periods. D, E, Transition from biphasic to high amplitude monophasic current responses was observed in cells bathed in Ca²⁺-deficient KR buffer with the pipette medium containing 10 mm EGTA (D) or 5 mm BAPTA (E). In both experiments cells were clamped at −60 mV. F, G, Sensitization of receptors was also observed in cells bathed in medium in which Ca²⁺ was substituted with Mg²⁺ (F), as well as in cells containing 1 mm Mg²⁺ and clamped at +60 mV (G). In both experiments, the pipette medium contained 10 mm EGTA. H, In Ca²⁺-deficient medium and with pipette medium containing 10 mm EGTA, transition from biphasic to high amplitude monophasic currents was also accompanied with slower rate of deactivation. Because of the drop in the divalent cation concentrations in experiments shown in D, E, and G, 10 μm BzATP was used.

Dependence of P2X7R sensitization on the N-terminal structure. A–C, Characterization of the K17A (A), T15K (B), and T15E (C) mutants. The T15K and T15E mutants instantaneously opened with the dilated state, as indicated by the value of the reversal potential and the lack of a positive shift during prolonged agonist application. In contrast, the K17A mutant dilates gradually during the initial agonist application, as indicated by the rightward shift in the reversal potential (left). Similar records have been shown previously (Yan et al., 2008). Three mutants differed in their deactivation time kinetics during the short (1 s) and prolonged (2× 40 s) stimulation. Notice the slow deactivation of T15K and T15E mutants and the lack of changes in the rate of receptor deactivation after secondary agonist application, in contrast to the K17A mutant. D, Concentration-dependent effects of BzATP on the rate of T15E mutant receptor activation, which shows the lack of the secondary current growth in all BzATP concentrations.

Markov state cell model describing the sequence of binding/unbinding and sensitization/loss-of-sensitization events of P2X7Rs in a cell. The states C_i (closed channel pore) and Q_i (open channel pore), i = 1, 2, 3, 4, represent the fraction of receptors in a given state. White (black) circles on each state indicate unoccupied (occupied) binding sites (3 in total) on the receptors of that state. The upper row corresponds to the unsensitized (undilated channel pore) states, while the bottom row corresponds to the sensitized states (open ones are dilated). k_i, i = 1, 2,… , 6 and L_i, i = 1, 2, 3, are the transition rates between the different states and A is the agonist concentration (BzATP or ATP). The gating variables and reversal potentials of Q₁ (Q₃) and Q₂ (Q₄) are the same (Table 1).

Current responses to increasing doses of agonist concentration according to the Markov state cell model, Equations 1–9. A, Current simulations obtained from the cell model upon 3.2, 10, 32, 100, and 320 μm/2 min BzATP stimulation. B, Average amplitudes of the fast, I₁, and slow, I₂, currents in response to 40 s agonist (BzATP) stimulation of a heterogeneous population of n = 10 cell models, randomly generated using the normal and uniform distributions according to Table 1. Notice the monodirectional dose dependence of I₁ and bidirectional dose dependence of I₂ on BzATP. Inset, Dose–response curve of the total current I (= I₁ + I₂) after 40 s stimulation with 3.2, 10, 32, 100, and 320 μm BzATP; mean ± SEM values from 10 model cells per dose. The estimated EC₅₀ obtained from these stimulations is 45 μm. C, D, The time evolution of the states Q₁ + Q₂ (solid, top), C₄ (dashed, top), Q₃ (solid, bottom) and Q₄ (dashed, bottom) are shown during 40 s stimulation with 32 μm (C) and 320 μm (D) BzATP.