Activation of Shaker potassium channels. II. Kinetics of the V2 mutant channel

Abstract

This second of three papers, in which we functionally characterize activation gating in Shaker potassium channels, focuses on the properties of a mutant channel (called V2), in which the leucine at position 382 (in the Shaker B sequence) is mutated to valine. The general properties of V2's ionic and gating currents are consistent with changes in late gating transitions, in particular, with V2 disrupting the positively cooperative gating process of the normally activating wild type (WT) channel. An analysis of forward and backward rate constants, analogous to that used for WT in the previous paper, indicates that V2 causes little change in the rates for most of the transitions in the activation path, but causes large changes in the backward rates of the final two transitions. Single channel data indicate that the V2 mutation causes moderate changes in the rates of transitions to states that are not in the activation path, but little change in the rates from these states. V2's data also yield insights into the general properties of the activation gating process that could not be readily obtained from the WT channel, including evidence that intermediate transitions have rapid backward rates, and an estimate of a total charge 2 e0 for the final two transitions. Taken together, these data will help constrain an activation gating model in the third paper of this series, while also providing an explanation for V2's effects.

Scheme I

Figure 4

Estimates of α₁, α_p, and β₁ for V2. (A) The voltage dependence of α₁ was estimated by fitting an exponential to τ_on 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 q _α1 = 0.31 e₀, which are similar to WT's (dotted curve). (B) The voltage dependence of V2's α_p was estimated by fitting an exponential to V2's τ_a 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 (α_p(0) = 2,000 s⁻¹ and q _α1 = 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 q _β1 = −0.56 e₀) that are similar to the mean estimates obtained for WT's β₁ (dotted curve).

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 q _βd 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 τ_off. The τ_off values from this and two other patches were then fitted with an exponential function of voltage (solid curves, right), yielding values for q _βd = −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.

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 τ_on 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.

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 τ_a and an activation delay δ_a. The current at +147 mV was fitted to the sum of two exponentials, I(t) = (A _f + A _s) − A _f e ^{−(t−δa)/τa} +A _s e ^{−(t−δa)/τs}. The faster time constant is τ_a, which is taken to reflect the kinetics of the main activation path (Schoppa and Sigworth, 1998a ). (B) The derived values for τ_a 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 δ_a (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 P _o ≅ 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.

Figure 1

WT and V2's voltage dependence of charge movement and channel opening. (A) Voltage dependence of channel opening P _o for WT (▪) and V2 (▵). The P _o 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 V _1/2 values for k ₁ equal to −59 and −54 mV, and V _1/2 values for k ₂ 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, q _max = 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.

Scheme II

Figure 5

Failure to estimate α_N 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 V _h = −93 mV. The displayed currents correspond to hyperpolarizations of different durations t _h 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 t _h = 100, 200, 300, and 500 μs are shown. The current for t _h = 500 μs has been fitted to a single exponential (with τ_a = 0.52 ms), and the current for t _h = 100 μs is shown to be reasonably described by an exponential with the same time constant. (C) The negligible effect of prepulses of different t _h on V2's reactivation time course compares with the strong dependence for WT, reflected in the nearly fourfold decrease in the derived τ_a values for shorter t _h. Patches w448 and v165. (D) V2's reactivation time course at +67 mV in a different patch (v162) for V _h = −13 mV and t _h = 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 τ_a 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.

Figure 6

Estimate of β_N. (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 τ_tail were obtained by fitting the deactivation phase of the tail current to a single exponential. (B) The τ_tail values obtained from four WT (closed symbols) and five V2 (open symbols) patches were fitted to an exponential function of voltage yielding estimates of τ_tail(0) and q _tail. Fits were made only to the τ_tail 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/β_N 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.

Figure 7

V2 has little effect on α_d and β_d 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 τ_off. 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.

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.

Scheme III

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 τ_s, indicating that V2 increases the probability that a channel enters C_i states from closed states in the activation path. In the fitting, the values for τ_s for WT and V2 were 1.9 and 1.3 ms, respectively; values for the fast time constant τ_a were 0.21 and 0.29 ms. The values for A _f and A _s 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.

Figure 11

Estimates of β_N-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 τ_l of the fitted exponential is similar to the time constant τ_long of the longest duration exponential component in V2's closed time histograms. The τ_long values at V ≤ +27 mV always reflect the longer of two fitted exponentials, and all but one of the τ_long values at V ≥ +47 mV reflects the longest of three fitted exponentials. At high voltages, τ_long reflects closures in C_i states and is generally longer than the latency time constant. Values reflect data obtained from five patches. (B) The mean duration m _B 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 β_N(0) = 580 s⁻¹ and q _βN = −0.53 e₀. The m _B 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 m _B values obtained in each of the patches to an exponential, yielding estimates of m _B(0) and q _mB. Data reflect the same experiments as in A. (C) The same m _B values as in B have been superimposed with the predictions of Eq. 5 for different values of β_N-1(0). In the calculations, α_N(0) was assumed to be 1,900 s⁻¹. The charges q _αN = 0.18 e₀ and q _βN-1 = −0.30 e₀ were the WT values.

Scheme IV

Scheme V

Scheme VI