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Figure 1. Slow inactivation rates can become steeply voltage sensitive when high Na+, low K+, internal solutions are used. (A) With 115 mM [Na+] externally and 115 mM [K+] internally, slow inactivation rate is essentially voltage insensitive for test potentials between +20 and +160 mV (traces shown: −20 to +160 mV, 20-mV steps, 5-s interpulse intervals). (B) Despite a marked increase in the rate of slow inactivation in symmetric Na+ solutions, the slow inactivation rate remains insensitive to the test potential (traces shown: +40 to +140 mV, 20-mV steps, 5-s interpulse intervals). (C) Slow inactivation is steeply voltage sensitive when 10 mM of K+ is added to the internal solution used in B (traces shown: −60 to +120 mV, 20-mV steps, 5-s interpulse intervals). (D) Time constants for all three conditions for test potentials from +20 to +160 mV. ▪, 115 Nao//115 Ki as in A (mean data from three to five patches). •, 115 Nao//115 Nai as in B (mean data from two to four patches). ○, 115 Nao//115 Nai + 10 Ki as in C (mean data from three patches, except at +160 mV, where n = 14 patches). Standard deviations are visible only when they exceed the size of the data symbol. All data are from inside-out patches.
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Figure 2. A family of macropatch currents recorded from ShΔ channels expressed in Xenopus oocytes, using a high [Na+], low [K+] internal solution. (A, a–d) Individual current traces are shown for groups of five test potentials to minimize the ambiguity produced by overlapping traces. (B) Peak current magnitudes (○) give an N-shaped peak I-V curve, while end currents (•) fail to increase at potentials greater than +20 mV, indicating steadily increasing slow inactivation in this 500-ms time window at these test potentials. (C) Iend/I peak (□) and the relative increase in magnitude of slow component of the tail current (▪) are plotted against the test potential to give quantitative estimates of steady state slow inactivation at these potentials. Symbols in B and C are connected by straight lines. All data are from the same inside-out patch as in Fig. 1 C. Traces recorded using 5-s interpulse intervals.
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Figure 3. Current families were obtained using a K+-free internal Na+ solution (A) and, in a different patch, following addition of 10 mM internal K+ (B). Holding potential was −80 mV and currents were recorded using on-line −P/n protocols for leak and capacity current subtraction. Test pulse voltages increased by 20-mV increments in A and by 10-mV increments in B. (A) In the absence of internal K+ ions, all outward currents are carried by Na+ ions. Both peak Na+ currents (○) and steady state outward Na+ currents (•) increase steeply at potentials greater than +80 mV. Inactivation becomes readily apparent only at the most positive potentials. (B) In the presence of internal K+ ions, peak currents (○) increase to a maximum at +10 mV, followed by a region of negative slope conductance between +20 and +70 mV. At potentials greater than +80 mV, peak currents rise steeply again, just as in A. However, end currents fall steadily at potentials greater than +10 mV (•). Symbols are connected by straight lines. Data in A and B were obtained from two different inside-out patches. All traces recorded using 5-s interpulse intervals.
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Figure 4. (A and B) Comparison of instantaneous I-V curves and reversal potentials obtained from 1-ms ramps and by the standard tail current method, evaluated in high internal K+ solution (A, top) The pulse protocols illustrate the 1-ms downward ramps from +40 as well as corresponding protocols for the recording of instantaneous tail currents. (Bottom) Ionic currents obtained from an outside-out patch using solutions indicated in B. Data were recorded with a sample interval of 10 μs, digitally low-pass filtered at 20 kHz. (B) Comparison of ramp I-V data from +40 mV to −100 mV (solid line) with instantaneous tail current I-V data (○) from the data shown in A. (C and D) Comparison of instantaneous I-V curves from 1-ms ramps with the N-shaped test pulse I-V curve, evaluated in a high internal Na+ solution with 10 mM added K+. (C, top) The pulse protocols are indicated; note that in low internal K+ concentration, yielding faster inactivation, short (5-ms) depolarizing pulses were used. All records were leak- and capacitative-current subtracted using on-line −P/n pulses. (Bottom) Ionic currents obtained from an inside-out patch using the solutions indicated in D. (D) Comparison of ramp I-V data from +160 to −100 mV (solid line) with test pulse peak current I-V data (○) from the data shown in C. Note the N-shaped I-V curve for both the ramp and the test pulse I-V curves. All data were obtained using 5-s interpulse intervals.
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Figure 5. Effects of increasing test pulse duration on ramp I-V curves recorded following test pulses to +40 mV. Ramp currents are plotted against time (A) and against the ramp potential (B). Solutions were identical to those used in Fig. 4 B. (A, left) Superimposed data traces for 5-, 15-, and 45-ms test-pulse durations. End current levels for 165 and 600 ms are indicated by dots. (Right) The same ramp currents superimposed and aligned with the voltage record (top trace). (B, left) Ramp currents after test pulses shown in A are plotted against ramp voltage (from +40 to −100 mV). (Right) An expanded voltage scale is used to illustrate changes in reversal potential. All data were obtained from one inside-out patch using 5-s interpulse intervals.
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Figure 6. Effects of increasing test pulse duration on ramp I-V curves recorded after test pulses to +160 mV. (A) Ramp currents are plotted against time. (B) Ramp currents are plotted against ramp potential. Same format as in Fig. 5. All data are from the same inside-out patch as in Fig. 5.
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Figure 8. A simple single-site Eyring barrier model can be used to demonstrate voltage-dependent changes in PK/PNa ratio. Parameters of the model used here can be described in relation to a simple kinetic scheme (A) in which N0, N1, and N2 represent the external, intramembrane, and internal energy wells, respectively; where k01 and k10 are the forward and backward rate constants between N0 and N1, and k12 and k21 are the equivalent rate constants between N1 and N2. Values for these rate constants are shown given for both Na+ and K+ ions at 0 mV and the solutions used for the data in Fig. 7 A. Rate constants (s−1): (Na+) k01, 2.77 × 10+8; k10, 1.13 × 10+5; k12, 2.05 × 10+8; k21, 5.01 × 10+11; (K+) k01, 1.84 × 10+11; k10, 4.57 × 10+8; k12, 6.18 × 10+7; k21, 2.49 × 10+11. To calculate the rate constants at other potentials, it is necessary to define the placements of the barriers and wells within the transmembrane field. For the model used here, N0 and N2 were presumed to be at 0 and 100% of the electrical distance from the external side of the membrane, while N1 was set at 45% of this distance. Internal and external energy barriers were placed at 10 and 90% of the transmembrane field, respectively. (B) Simulations of changes in internal K+ concentrations approximate the data shown in Fig. 7 A, when the same internal and external solutions are used. For this simulation, the patch was presumed to contain 1,500 channels. (C) Predicted single-channel Na+ and K+ fluxes were generated by this model for the 10-mM internal K+ condition, suggesting voltage-dependent changes in relative permeabilities. (D) PK/PNa ratios obtained from predicted reversal potentials for this model under different ionic conditions. (○) Simulations with 115 Nao//115 Nai and differing internally, (□) variable external [K+]. ▵ were obtained from simulations using internal 11.5 mM Na+, external 115 mM Na+, and variable K+. Experimental values obtained in this study are shown as filled symbols (mean ± SD): •, Na+o//Na+i + variable K+; ▪, Na+o + 2.5–10 mM K+o//Na+i.
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Figure 7. Effects of changes in K+ concentrations on ramp I-V curves after 5-ms test pulses to +160 mV (A) or +140 mV (B). (A) Effects of changes in internal K+ concentration in one inside-out patch. Note that the outward currents at positive potentials are highest in absence of internal K+ and fall when low K+ concentrations are added to the internal solution. (B) Effects of changes in external K+ in one outside-out patch. Changes in outward currents are small relative to the changes in inward currents at negative potentials. See text for full discussion of these results. Data in A are from one inside-out patch, data in B are from one outside-out patch.
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