![Figure 4. An elements-based kinetic model of the GABAA receptor. (A) Three binary elements model representations for the GABAA receptor (schemes I–III) incorporating two agonist binding sites A that are either unoccupied (A0) or occupied (A1), each of which interacts with a main channel gate m and fast and slow desensitization gates df and ds that are either closed (m0, df1, ds1) or open (m1, df0, ds0). The channel is conducting when all three gates are open. Elements are depicted as labeled circles, and interactions as lines connecting the pair of interacting elements (e.g., see Fig. 3). All model parameters are referenced with respect to the symbol of their associated elements such that αi and βi are the rate constants for element i, and Θij, Λij, and Λji are the interaction factors between elements i and j (see Materials and methods and Eqs. 7–12). Model parameters reflect simulations at a temperature of 298.15 K. Optimized rate constants ([M−1]s−1) across patches for scheme I: αA = 2.3 ± 0.2 × 106, βA = 91 ± 9, αdf = 0.40 ± 0.03, βdf = 86 ± 9, αds = 0.021 ± 0.008, βds = 2.6 ± 0.9. For scheme II: αA = 1.9 ± 0.2 × 106, βA = 86 ± 4, αdf = 0.50 ± 0.04, βdf = 82 ± 7, αds = 0.020 ± 0.005, βds = 1.2 ± 0.5. For scheme III: αA = 2.0 ± 0.2 × 106, βA = 81 ± 6, αdf = 0.65 ± 0.07, βdf = 62 ± 6, αds = 0.027 ± 0.006, βds = 1.3 ± 0.5. All other model parameters were constrained as described in the Materials and methods. (B–E) Simulated open probability (red) overlaid on an outside-out patch current recording (gray) in response to rapid application of GABA (top trace is the solution exchange time course at the pipet tip after the experiment; see Materials and methods). Simulations in B–J are shown for scheme I, although nearly indistinguishable simulations were obtained for schemes II and III. (B) Simulated and observed current response to a 4-ms pulse of 10 mM GABA. The same responses are shown to the right on an expanded time scale. (C) Simulated and observed current response to a 500-ms pulse of either 30 µM or 10 mM GABA (pulses were interleaved on the same patch). (D) Simulated and observed current response to a 3-s pulse of 10 mM GABA. (E) Simulated and observed current responses to pairs of 5-ms pulses of 10 mM GABA separated by a variable recovery period (responses to six separate pulse pairs for a single patch are shown overlaid). One of the pulse pairs is shown to the right on an expanded time scale. (F) Simulated responses to a family of 500-ms pulses of varying GABA concentrations from 10 nM to 100 mM. (G) Peak current dose–response relationship for the simulated currents in F. The median ligand concentration (see Chowdhury and Chanda, 2013) was 50.3 µM GABA. (H) Simulated responses to varying duration pulses of 10 mM GABA (left, individual responses overlaid) illustrate the prolongation of deactivation by desensitization (right, deactivation after 1 ms–3 s pulses of 10 mM GABA are aligned to their onset and normalized). (I) Open and closed dwell time histograms from Monte Carlo simulations of a single channel in 10 mM GABA. Exponential time constants (and relative areas) from maximum likelihood fits (solid red) to the dwell time distributions (solid black) are labeled (individual exponential components of the fit are shown as broken black lines). (J) Agonist dependence of single channel burst lengths separated by closures longer than 15 ms.](https://cdn.rupress.org/rup/content_public/journal/jgp/144/1/10.1085_jgp.201411183/4/jgp_201411183_fig4.jpeg?Expires=1767805544&Signature=BmQojbSlFlLxDn22afEhl2pZPWjQlDt0qKIEAHBZ0UxfkKNOXiALiYAHbpwZ74SNaFVxeVQs67LBPd3paSIrGhhbcdOHSneDWp-tYh35Dx0wY9ppVv5knc1kQy9SCVb1z~5L0DPHq~rBjcehtj5xPs0ayHx2vljU7tC1FohviT3CDE7thGI2ydm0yK2jynaEI-fMyFqUda4NXkJp1hGTY3bCMe1bfANLdDkfaT1B6TMdTY12~r39TsD8sxOuauNivnr~u-hi8PxRQ49ds5KdPVvvtElPVjyg-mDpnEg805lIs2DvG1Djm8uGlsqbTV-hhtlJ8iK4~Dcx7jMAuKYoTA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
An elements-based kinetic model of the GABAA receptor. (A) Three binary elements model representations for the GABAA receptor (schemes I–III) incorporating two agonist binding sites A that are either unoccupied (A0) or occupied (A1), each of which interacts with a main channel gate m and fast and slow desensitization gates df and ds that are either closed (m0, df1, ds1) or open (m1, df0, ds0). The channel is conducting when all three gates are open. Elements are depicted as labeled circles, and interactions as lines connecting the pair of interacting elements (e.g., see Fig. 3). All model parameters are referenced with respect to the symbol of their associated elements such that αi and βi are the rate constants for element i, and Θij, Λij, and Λji are the interaction factors between elements i and j (see Materials and methods and Eqs. 7–12). Model parameters reflect simulations at a temperature of 298.15 K. Optimized rate constants ([M−1]s−1) across patches for scheme I: αA = 2.3 ± 0.2 × 106, βA = 91 ± 9, αdf = 0.40 ± 0.03, βdf = 86 ± 9, αds = 0.021 ± 0.008, βds = 2.6 ± 0.9. For scheme II: αA = 1.9 ± 0.2 × 106, βA = 86 ± 4, αdf = 0.50 ± 0.04, βdf = 82 ± 7, αds = 0.020 ± 0.005, βds = 1.2 ± 0.5. For scheme III: αA = 2.0 ± 0.2 × 106, βA = 81 ± 6, αdf = 0.65 ± 0.07, βdf = 62 ± 6, αds = 0.027 ± 0.006, βds = 1.3 ± 0.5. All other model parameters were constrained as described in the Materials and methods. (B–E) Simulated open probability (red) overlaid on an outside-out patch current recording (gray) in response to rapid application of GABA (top trace is the solution exchange time course at the pipet tip after the experiment; see Materials and methods). Simulations in B–J are shown for scheme I, although nearly indistinguishable simulations were obtained for schemes II and III. (B) Simulated and observed current response to a 4-ms pulse of 10 mM GABA. The same responses are shown to the right on an expanded time scale. (C) Simulated and observed current response to a 500-ms pulse of either 30 µM or 10 mM GABA (pulses were interleaved on the same patch). (D) Simulated and observed current response to a 3-s pulse of 10 mM GABA. (E) Simulated and observed current responses to pairs of 5-ms pulses of 10 mM GABA separated by a variable recovery period (responses to six separate pulse pairs for a single patch are shown overlaid). One of the pulse pairs is shown to the right on an expanded time scale. (F) Simulated responses to a family of 500-ms pulses of varying GABA concentrations from 10 nM to 100 mM. (G) Peak current dose–response relationship for the simulated currents in F. The median ligand concentration (see Chowdhury and Chanda, 2013) was 50.3 µM GABA. (H) Simulated responses to varying duration pulses of 10 mM GABA (left, individual responses overlaid) illustrate the prolongation of deactivation by desensitization (right, deactivation after 1 ms–3 s pulses of 10 mM GABA are aligned to their onset and normalized). (I) Open and closed dwell time histograms from Monte Carlo simulations of a single channel in 10 mM GABA. Exponential time constants (and relative areas) from maximum likelihood fits (solid red) to the dwell time distributions (solid black) are labeled (individual exponential components of the fit are shown as broken black lines). (J) Agonist dependence of single channel burst lengths separated by closures longer than 15 ms.
