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Figure 4. Estimates of α1, αp, and β1 for V2. (A) The voltage dependence of α1 was estimated by fitting an exponential to τon values derived from the on gating currents at voltages between −13 and +47 mV. From the data in the patch shown in Fig. 3 A, estimates were obtained α1(0) = 1,410 s−1 and qα1 = 0.31 e0, which are similar to WT's (dotted curve). (B) The voltage dependence of V2's αp was estimated by fitting an exponential to V2's τa values taken from macroscopic ionic current time courses measured between +87 and +147 mV. From the data in the patch shown in Fig. 2 A, estimates were obtained (αp(0) = 2,000 s−1 and qα1 = 0.15 e0) that are similar to WT's (dotted curve). (C) The voltage dependence of β1 was estimated from gating currents induced by voltage steps between −93 and −153 mV. These gating currents for V2 (solid curves, top) are nearly superimposable with WT's (dotted curves). Patches v240 and w249. The bottom plot shows that the time constants of the single exponentials fitted to the decay of V2's currents in this patch yielded estimates (β1(0) = 200 s−1 and qβ1 = −0.56 e0) that are similar to the mean estimates obtained for WT's β1 (dotted curve).
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Figure 8. V2's off gating currents yield other information about intermediate transitions. (A) V2's off gating currents measured after a prepulse to −3 mV were used to estimate the partial charge qβd of the backward rates of intermediate transitions. The off currents measured at test voltages between −63 and −113 mV were fitted to an exponential, yielding a decay time constant τoff. The τoff values from this and two other patches were then fitted with an exponential function of voltage (solid curves, right), yielding values for qβd = −0.44, −0.54, and −0.61 e0. For one of the displayed experiments, the prepulse voltage was −43 mV. (B) Close examination of V2's off gating current at −63 mV (from this and one other patch) indicates the presence of a fast component (arrows) that is poorly accounted for by a fit of a single exponential, consistent with some intermediate transitions having more rapid backward kinetics than the first transition at this voltage.
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Figure 3. V2's effects on gating currents. (A) WT (left) and V2's (right) gating currents induced by voltage steps from −93 mV to test voltages between −73 and +47 mV. WT and V2 have roughly similar on current time courses at most voltages, but V2 displays markedly faster off current kinetics after the larger depolarizations. The upward deflections at the end of the test pulses at depolarized voltages reflect a leak subtraction artifact arising from charge movement that occurs during the −133- to −153-mV voltage pulse used to calculate the leak and capacitive currents (Stühmer et al., 1991). Patches w212 and v219. (B) The time constant τon fitted to the decay of WT and V2's on gating currents have similar values at most voltages, but are nearly two times faster at some intermediate voltages near −40 mV. Each value reflects three to seven experiments, except WT's value at +67 mV (n = 1). (C) V2's faster decaying on gating current at −43 mV in A reflects the absence of a slow component that is present in WT's currents, associated with WT's channel opening. WT's trace (top) has been fitted to a sum of two exponentials with time constants equal to 1.2 and 4.8 ms (dashed curves). The bottom trace shows that a scaled version of the fast component (τ = 1.2 ms) accounts for V2's current very well. Horizontal lines reflect the estimated baseline of the current, taken from the mean current during the last 2 ms of the test pulse.
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Figure 2. V2's effects on activation kinetics. (A) At both low and high voltages, V2 has slower channel opening kinetics, reflected here in a comparison of WT and V2 currents at +7 and +147 mV. Patches w312 and v096. V2's ionic current at +7 mV was fitted to a single exponential to estimate the activation time constant τa and an activation delay δa. The current at +147 mV was fitted to the sum of two exponentials, I(t) = (Af + As) − Afe−(t−δa)/τa +Ase−(t−δa)/τs. The faster time constant is τa, which is taken to reflect the kinetics of the main activation path (Schoppa and Sigworth, 1998a). (B) The derived values for τa for V2 are larger than WT at V < +67 mV, but are similar at higher voltages. Individual values reflect two to seven experiments. Error bars are smaller than the symbols in many cases. (C) WT and V2 have similar, though not identical, values for the activation delay δa (from the same experiments as in B). (D) Comparison of the sigmoidicity of WT and V2 ionic currents at voltages where the two channels have Po ≅ 0.2. The current traces have normalized amplitudes and have their time axes scaled to yield the same rising phase kinetics of the current. Patches w312 and v142.
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Figure 1. WT and V2's voltage dependence of charge movement and channel opening. (A) Voltage dependence of channel opening Po for WT (▪) and V2 (▵). The Po values were evaluated from macroscopic ionic currents as described in Fig. 1 of Schoppa and Sigworth (1998a) and were normalized to unity. Each value reflects one to nine experiments. Superimposed curves are fits of Scheme SI to the averaged data with V1/2 values for k1 equal to −59 and −54 mV, and V1/2 values for k2 equal to −54 and +14 mV, for WT and V2 respectively. (B) Voltage dependence of charge movement for WT (▪) and V2 (▵) scaled to match the maximal single-channel charge movement, qmax = 12.3 e0 (Schoppa et al., 1992). Each value reflects one to seven experiments. Superimposed curves are fits to Scheme SI to the averaged WT and V2 data with parameter estimates given in A. (C) The derivative Δq/ΔV of V2's q-V relation was calculated from the difference in q measured between different voltages (in 10-mV increments, except 20-mV increments at V ≤ −93 and V > +7 mV). Each value reflects measurements in four patches. Besides the main peak centered near −50 mV, a second smaller peak is seen at depolarized voltages near +10 mV. The smooth curve is the derivative of the simulated q-V curve shown in B for V2.
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Scheme II.
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Figure 5. Failure to estimate αN from V2's reactivation time courses. (A) V2's ionic currents elicited by a triple-pulse stimulus, using a pair of depolarizations to +67 mV separated by a voltage step to a hyperpolarized voltage Vh = −93 mV. The displayed currents correspond to hyperpolarizations of different durations th between 100 and 2,000 μs. Tail currents during the second pulse were inward since the pipette solution contained 5.4 mM K+ replacing an equivalent amount of the N-methyl- d-glucamine+ (NMDG+). Data were filtered at 12 kHz. Patch v165. (B) No fast-reactivating component is evident in the same traces that have been expanded and time shifted to align the start of the test pulses. Only traces corresponding to th = 100, 200, 300, and 500 μs are shown. The current for th = 500 μs has been fitted to a single exponential (with τa = 0.52 ms), and the current for th = 100 μs is shown to be reasonably described by an exponential with the same time constant. (C) The negligible effect of prepulses of different th on V2's reactivation time course compares with the strong dependence for WT, reflected in the nearly fourfold decrease in the derived τa values for shorter th. Patches w448 and v165. (D) V2's reactivation time course at +67 mV in a different patch (v162) for Vh = −13 mV and th = 100 μs. To demonstrate that we have not missed a fast reactivating component that may have been obscured in the instantaneous current change, the reactivation time course has been fitted to Eq. 7 from Schoppa and Sigworth (1998a), which explicitly takes into account the delays in the recording system. It was assumed that the change in current due to gating is described by a function x(t) with a time constant (τ = 0.41 ms) that matches the τa value derived from V2's ionic current at +67 mV, measured in the absence of any conditioning pulses. The amplitude (−15 pA) was taken from the amount of decay of V2's tail current in the same patch at 100 μs. Data were filtered at 12 kHz.
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Figure 6. Estimate of βN. (A) Across a range of test voltages, WT's tail currents decay much more rapidly than V2's (taking into account the different time scales). The tail currents were measured after prepulses to +7 and +67 mV, respectively, for WT and V2; they were outward since measurements were made with 0 mM pipette K+. Estimates of the tail current decay time constant τtail were obtained by fitting the deactivation phase of the tail current to a single exponential. (B) The τtail values obtained from four WT (closed symbols) and five V2 (open symbols) patches were fitted to an exponential function of voltage yielding estimates of τtail(0) and qtail. Fits were made only to the τtail values at voltages at which the time constant values become faster with increasingly negative voltages (V ≤ −63 mV for WT and V ≤ −23 mV for V2). For most of the patches, currents were measured in 0 mM pipette K+, but for one patch each for WT and V2, currents were measured with 14 mM pipette K+ (▴ and □, respectively). For comparison, the value of 1/βN derived for WT in Schoppa and Sigworth (1998a) is plotted as a straight dashed line, indicating that V2's tail current decay has a similar voltage sensitivity as the channel closing rate.
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Figure 7. V2 has little effect on αd and βd gating currents. (A) WT (dotted curves) and V2 have nearly superimposable on gating currents at −13 and +27 mV, including similar time courses near the peak of the current. The current amplitudes were scaled slightly so that the peaks match. Patches w212 and v219. (B) Comparison of WT's and V2's off gating currents, following voltage steps that preload channels into late closed states but not the open state. For WT, the current was measured after a 2-ms pulse to −33 mV, and V2's current was measured after a 20-ms pulse to the same voltage. WT and V2's off currents have been fitted to a single exponential, yielding similar time constants τoff. The slightly slower time course for WT probably reflects the contribution of the small fraction of channels that are open at that end of the prepulse, which contribute a small slow component to the off current. Patches w217 and v219.
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Figure 9. V2 single channel activity at voltages between −13 and +107 mV. (A) Single channel activity induced by steps from −93 mV to the indicated voltages. The data displayed at voltages between −3 and +67 mV reflect measurements in one patch (v433) and are plotted on the same scale. The data at the two extreme voltages reflect two additional patches (v428 and v344). The dashed vertical line reflects the beginning of the test pulse, and, for all but the currents at +107 mV, the currents measured after the test pulse are not shown. In our measurements, V2's single channel conductance was usually ∼30% smaller than WT's (corresponding to a change in conductance from 11 to 8 pS). (B) Closed time histograms derived from the experiments shown in A. Superimposed solid curves on histograms are fits to mixtures of two or three exponentials; dashed curves illustrate each component. Each histogram contains at least 630 events. (C) Open time histograms, each fitted with a single exponential.
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Scheme III.
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Figure 10. V2's effects on transitions to closed states outside of the main activation path. (A) WT (dotted curves) and V2 have nearly superimposable closed dwell-time histograms at very large depolarizations, indicating that the V2 has little effect on the transitions from C iN, C f1, and C f2 that correspond to each of the three components in these histograms. The time constants and amplitudes of the three exponentials fitted to 5 WT and 22 V2 closed time histograms at V ≥ +47 mV were averaged, and the curves reflect the derived means. (B) The measured open times for V2 at large depolarizations (▵) are approximately one-third as long as WT's (▪), indicating that V2 destabilizes the open state relative to C iN, C f1, and C f2. Open times are uncorrected for missed events, but may be compared since WT and V2 display the same closed time distributions at these voltages (from A), and the analysis filtering bandwidths were set to be equal for WT and V2. Each value reflects a single experiment. (C) WT (top) and V2 (bottom) cumulative first latency histograms at +107 mV were fitted to the sum of two exponentials (see legend for Fig. 2 A), starting at the time when P = 0.5. The dashed curves reflect the fast component in the same fits. The main difference between the fits for WT and V2 is the amplitude of the slow component with time constant τs, indicating that V2 increases the probability that a channel enters Ci states from closed states in the activation path. In the fitting, the values for τs for WT and V2 were 1.9 and 1.3 ms, respectively; values for the fast time constant τa were 0.21 and 0.29 ms. The values for Af and As in the fits were adjusted for the delay in the fitted function. The two histograms reflect 182 and 258 sweeps, respectively. Patches w266 and v344.
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Figure 11. Estimates of βN-1 from V2's single-channel burst durations. (A) V2's cumulative first latency histograms at V2's activation voltages were well-fitted by a single exponential; an example is shown at top. As shown in the plot at the bottom, the time constant τl of the fitted exponential is similar to the time constant τlong of the longest duration exponential component in V2's closed time histograms. The τlong values at V ≤ +27 mV always reflect the longer of two fitted exponentials, and all but one of the τlong values at V ≥ +47 mV reflects the longest of three fitted exponentials. At high voltages, τlong reflects closures in Ci states and is generally longer than the latency time constant. Values reflect data obtained from five patches. (B) The mean duration mB of the bursts of openings separated by long closures had values similar to the reciprocal of V2's channel closing rate (bold dotted curve), defined by the parameters βN(0) = 580 s−1 and qβN = −0.53 e0. The mB values at V ≤ +27 mV were calculated by normalizing the measured channel open time by the fraction of the measured closures that correspond to the longer duration exponential component in fits of the closed time histograms to the sum of two exponentials. Solid curves reflect fits of the mB values obtained in each of the patches to an exponential, yielding estimates of mB(0) and qmB. Data reflect the same experiments as in A. (C) The same mB values as in B have been superimposed with the predictions of Eq. 5 for different values of βN-1(0). In the calculations, αN(0) was assumed to be 1,900 s−1. The charges qαN = 0.18 e0 and qβN-1 = −0.30 e0 were the WT values.
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Scheme IV.
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Scheme V.
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Scheme VI.
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