Activation of shaker potassium channels. I. Characterization of voltage-dependent transitions

Abstract

The conformational changes associated with activation gating in Shaker potassium channels are functionally characterized in patch-clamp recordings made from Xenopus laevis oocytes expressing Shaker channels with fast inactivation removed. Estimates of the forward and backward rates for transitions are obtained by fitting exponentials to macroscopic ionic and gating current relaxations at voltage extremes, where we assume that transitions are unidirectional. The assignment of different rates is facilitated by using voltage protocols that incorporate prepulses to preload channels into different distributions of states, yielding test currents that reflect different subsets of transitions. These data yield direct estimates of the rate constants and partial charges associated with three forward and three backward transitions, as well as estimates of the partial charges associated with other transitions. The partial charges correspond to an average charge movement of 0.5 e0 during each transition in the activation process. This value implies that activation gating involves a large number of transitions to account for the total gating charge displacement of 13 e0. The characterization of the gating transitions here forms the basis for constraining a detailed gating model to be described in a subsequent paper of this series.

Figure 7

Estimate of β_N. (A, top) Inward macroscopic ionic currents elicited by a fixed prepulse to +7 mV followed by test pulses to various hyperpolarizations between −93 and −193 mV. Filtering at 15 kHz. Patch w448. (bottom) A single exponential (dashed curves) poorly accounts for the decay of the tail currents at −153 and −193 mV. (B) An estimate of β_N was obtained from the faster time constant τ_f in fits of the tail currents at V ≤ −153 mV to the sum of two exponentials (Eq. 8). Values reflect five different experiments, and estimates for β_N(0) and q _βN were derived from each of the patches (solid lines). These estimates are similar to β_N (dashed line) derived from fits of Scheme SIII to the tail current and C_N-1 occupancies in Fig. 8. (C) Voltage dependence of the relative amplitude of the τ_f component in fits of the tail currents in the same five patches to Eq. 8. The superimposed dashed curve reflects the amplitude A _f(III) of the faster of two tail current relaxation components predicted by Scheme SIII, assuming values for β_N and β_N-1 derived from the fits in Fig. 8. For α_N–1 = 0, the amplitude is given by Here, λ_f is the faster relaxation eigenvalue that approaches −β_N at very negative voltages.

Figure 8

Estimate of β_N-1. (A) Separation of the reactivation time course into fast and slow components. Selected current traces in Fig. 5 A are shown for t _h between 100 μs and 1 ms. The time course of the fast component, reflecting channels reopening from C_N-1, and the slow component, reflecting channels reopening from all closed states that precede C_N-1, were approximated by fits of Eq. 9 (smooth curves). In the fitting, the value for α_N was fixed to the mean value derived from the reactivation time courses in Fig. 5 D. From the slow component, we derived an estimate of the delay δ_a (shown for t _h = 1 ms; dashed curve). (B) The occupancies in C_N-1 derived from the reactivation time courses, as well as tail currents (C), were fitted to Scheme SIII (superimposed smooth curves) to obtain estimates of β_N-1 and β_N. The occupancy p _N-1 in C_N-1 for different amplitude V _h and duration t _h was obtained from fits of Eq. 9 to the reactivation time course as p _N−1 = A _f/ (I _inst + A _f + A _s); that is, taking A _f to reflect the amplitude of current due to the return of channels from C_N-1 to the open state. This expression for p _N-1 is approximate, but is expected to hold in this case. Each of the data points reflects one to four experiments. The parameter estimates obtained were: β_N(0) = 150 s⁻¹, q _αN = −0.57 e₀, and β_N-1 (0) = 320 s⁻¹, q _βN-1 = −0.30 e₀. In the fitting, α_N was fixed to mean estimate value for α_N (Fig. 5 D); all channels were assumed to reside in the open state at the beginning of the test pulse.

Figure 5

Estimate of α_N from a fast reactivation component. (A, top) WT's macroscopic ionic currents elicited by a triple-pulse stimulus, using a pair of depolarizations to +47 mV separated by a voltage step to a hyperpolarized voltage V _h = −153 mV. The displayed currents correspond to different hyperpolarization durations t _h between 70 and 1,000 μs. Tail currents during the second pulse were inward since the pipette solution contained 14 mM K⁺. Data were filtered at 15 kHz. Patch w448. (bottom) The same traces are shown, but expanded and time shifted to align the start of the test pulses. The “upper half” of the reactivating current relaxations for t _h = 70 μs and 1 ms have been fitted to a single exponential to estimate τ_a (smooth curves). (B) The dependence of the derived values for τ_a on the hyperpolarization duration t _h, shown for different hyperpolarization amplitudes V _h. Note that for each V _h, the fastest τ_a values appear to approach 100 μs. All data reflect the patch in A. (C) To demonstrate that the fast reactivating component is not a recording artifact, we compare the apparent fast reactivating current in A for t _h = 100 μs with two different simulated current traces reflecting Eq. 7. The solid and dashed smooth curves, respectively, correspond to x(t) being a single exponential with a fast time constant τ = 100 μs (the good fit) or a slower τ = 430 μs (the poor fit). The total amplitude (−39 pA) associated with x(t) was constrained by fitting the tail current at −153 mV in the same patch to the sum of two exponentials and determining the amount of decrease in current by 100 μs after the beginning of the pulse. The impulse response h(i) was determined by differentiating the step response measured at the 15-kHz bandwidth (see methods). (D) The fast reactivation time constant (τ_f) values at different voltages were fitted to an exponential (solid curves) to estimate the voltage dependence of α_N, yielding estimates for α_N(0) and q _αN for each of three patches (α_N(0) = 7,600, 6,800, and 6,500 s⁻¹ and q _αN = 0.19, 0.16, and 0.18 e₀). For each patch, τ_f was obtained from currents measured after a 150-μs hyperpolarization to −153 mV. The reactivation time course for t _h = 150 μs includes a small slow component (accounting for, on average, 14% of the time course) as well as the dominant fast component; the τ_f values reflect the fast time constant in fits of the reactivation time course to the sum of two exponentials:

Figure 6

Estimates of β₁ and β_d. (A) Gating currents elicited by voltage steps between −93 and −153 mV. The current recorded at −93 mV (top) reflects the on current measured after a voltage step from −133 mV; the currents recorded at the −153-, −133-, and −113-mV test voltages reflect the off current measured after voltage steps from −93 mV. Currents were fitted to a single exponential (smooth curves) to estimate a decay time constant τ. Patch w249. (B) To estimate β₁, the τ values derived from the currents in A were fitted to an exponential (solid curve), yielding β₁(0) = 200 s⁻¹ and q _β1 = −0.48 e₀. (C) The off gating current measured at −93 mV after a 2-ms depolarization to −33 mV was fitted to a single exponential with τ = 0.82 ms. This time constant is similar to the reciprocal of the value of β₁ at −93 mV (0.77 ms) estimated in B, consistent with β_d being similar to β₁ at −93 mV.

Scheme I

Figure 1

Voltage dependence of relative channel open probability P _o and charge movement Q. Relative P _o estimates (▪) at V ≤ +67 mV were derived from measurements of ionic currents made using a double pulse protocol, in which currents were measured at a fixed amplitude voltage pulse (at −13 or +7 mV) that followed different test pulses. The values at +107 and +147 mV were obtained by measuring the magnitude of the current relaxation elicited by voltage jumps from +67 mV (in experiments similar to those illustrated in Fig. 12 A). Each plotted value reflects one to eight experiments. Relative Q estimates (○) were obtained as described previously (Schoppa et al., 1992), by numerically integrating the on gating current at each voltage. Each value reflects three to five experiments. The vertical dashed lines at −20 and −90 mV mark the boundaries of the defined hyperpolarized (V ≤ 90 mV), activation (−90 mV < V < −20 mV), and depolarized (V ≥ −20 mV) voltage ranges.

Figure 12

Characterization of the transitions to C_f1 and C_f2. (A, top) Macroscopic ionic currents elicited by voltage steps between pairs of depolarized voltages. The smaller current (at both the prepulse and test voltages) reflects a voltage step from +7 to +127 mV, and the larger current reflects a voltage step from +47 to +147 mV. Data were filtered at 15 kHz. Patch w447. (bottom) The same traces are expanded to show just the current relaxation during the test pulse; zero time is the start of the test pulse. The current relaxations are fitted to a single exponential to estimate the time constant τ_r (solid curves). At +127 and +147 mV, the time constants are τ_r = 230 and 180 μs, respectively, and the amplitudes of the fitted exponentials are −32 and −21 pA. These amplitudes can be compared with the size of the rest of the test current (278 and 323 pA, respectively) to yield estimates of the change in P _o induced by these voltage steps (10 and 6%). (B) The rate f ₁ from C_f1 to the open state was estimated by fitting an exponential (solid curve) to the τ_r values (▪) taken from the current relaxations measured in the experiment in A and from similar measurements made in one other patch. (C) Estimates of absolute P _o at voltages between +47 and +147 mV were derived from the mean measured channel closed and open dwell times in the equilibrium single channel activity. The data points reflect measurements made in four patches. Absolute P _o apparently saturates near 0.9.

Figure 2

Fits of a single exponential function and delay (Eq. 4) to the time course of open probability P _o predicted by different models. (A) Fits to the time course of P _o (solid curve) from the n ⁴ scheme Note that the order of rate constants in this scheme does not influence the time course. A fit of Eq. 4, taking only points where P _o ≥ 0.5, is shown as the dotted curve; it yields τ⁻¹ = 0.89 and δ = 1.09. The values expected from the approximate theory, τ⁻¹ = 1 and δ = 1.083, yield the dashed curve. (B) Fits to the time course from the same scheme but with all four rate constants equal to 1. The fit (dotted curve, fitted for P _o ≥ 0.5) yielded τ⁻¹ = 0.53 and δ = 2.45; the expected values are τ⁻¹ = 1 and δ = 3 (dashed curve). (C) Fits to the time course of P _o from Scheme SII, in which each of four independent subunits undergoes two transitions, with the forward rate constants a ₁ and a ₂ equal to 1 and 4, respectively. The fit (dotted curve, fitted for P _o ≥ 0.5) yielded τ⁻¹ = 0.89 and δ = 1.38. The expected values are τ⁻¹ = 1 and δ = 1.37 (dashed curve); these were obtained from the mean latency to opening t _l that was computed by use of a recursive subroutine as the expectation value over all possible paths in Scheme SII of the sum of dwell times in states in each path. (D) Fits to the time course from Scheme SII with a ₁ and a ₂ both equal to 1. The fit (dotted curve) yielded τ⁻¹ = 0.71 and δ = 2.38; the expected values are τ⁻¹ = 1 and δ = 2.55 (dashed curve).

Scheme II

Figure 3

Estimate of α₁. (A) Macroscopic ionic currents at −13 and +37 mV were fitted to a single exponential (smooth curves) to estimate an activation time constant τ_a. Extrapolating the fitted exponential to zero current yielded an estimate of the activation delay δ_a. Patch w312. (B) The decay of WT's on gating currents at the same voltages was fitted to a single exponential (smooth curves) to estimate the decay time constant τ_on . Patch w212. For the fitting, a baseline was first calculated from the mean current measured at the end of the voltage pulse (horizontal lines); the fitting began at the time point at which the current had decayed by 20% from the peak value. (C) The values of τ_a (▪) and τ_on (○) derived from the fitting have nearly equal values at voltages between −13 and +67 mV. Each data point reflects the average from two to eight experiments. Superimposed curve reflects the average voltage dependence of α₁, obtained by fitting the τ_a values between −13 and +67 mV in seven different patches. (D) Exponential fits of the activation time courses and on gating currents for a five-state sequential scheme, as depicted in the legend for Fig. 2 A. For these simulations, the rates for all but one of the transitions was set to be 4; the slowest transition had a rate constant equal to 1. The position of the slowest transition was varied to yield the different curves. The activation time courses (top) were identical for each of the conditions; these were fitted to an exponential (dotted curve), yielding an activation time constant τ_a = 1.04. The gating current time courses for each of the conditions (bottom), however, differed. For C₁ → C₂, C₂ → C₃ = 1, the decay of the currents (dashed curves) was not well described by a single exponential. For C₃ → C₄ = 1, the decay of the current (solid curve) was well described by a single exponential (dotted curve), but the fitted time constant τ_on = 0.69 was faster than τ_a. For C₀ → C₁ = 1, the decay time constant τ_on = 1.09 was similar to τ_a . (E) Exponential fits of the activation time courses and on gating currents for Scheme SII, with the forward rate constants a ₁ and a ₂ equal to 1 and 4, respectively, or with a ₁ = 4 and a ₂ = 1. The two cases yielded identical activation time courses (top), which were fitted to an exponential with τ_a = 1.12 (dotted curve). The two cases, however, yielded different gating currents (bottom). The decay of the current for the case of a ₁ = 1 and a ₂ = 4 (solid curve) was well described by a single exponential with a time constant τ_on = 1.05, similar to τ_a. The case of a ₁ = 4 and a ₂ = 1, however, yielded a more complex gating current decay time course, which, when approximated by a single exponential (dotted curve), yielded a decay time constant τ_on = 0.51 that was much faster than τ_a. In all simulations, each transition carried an equivalent charge movement.

Figure 4

Estimate of α_p. (A) The upper half of the macroscopic ionic current time course at +87 and +147 mV was fitted to one or two exponentials (Eq. 6), respectively, to estimate τ_a and δ_a (smooth curves). Two exponentials were required at +147 mV to account for a slow relaxation that corresponds to an alternate activation path. Patch w312. (B) Voltage dependence of τ_a and δ_a taken from current measurements in two different patches (left and right). The τ_a values display shallower voltage sensitivities at high voltages. The voltage dependence of the rate α_p was estimated from the τ_a values at V ≥ +87 mV (solid lines at V ≥ +87 mV). The δ_a values between −13 and +147 mV also become less voltage sensitive at high voltages. Estimates of the charge q that determines the voltage sensitivity of the delay at low and high depolarized voltages, respectively, were obtained by fitting an exponential to the δ_a values at V ≤ +67 and ≥ +87 mV (dashed lines). These charge values will be used in a following paper (Schoppa and Sigworth, 1998b ).

Scheme III

Figure 9

Estimate of q _βd. (A) Values of δ_a taken from the slow component in the reactivation time courses (shown in Fig. 8 A), for hyperpolarizations of different amplitude V _h and duration t _h. For each V _h, the time course of the accumulation of the delay for increasing t _h was approximated by a fit of the δ_a values to a single exponential (solid curves), yielding τ_acc. The fitted exponential was constrained to begin at zero. The amplitude was fixed to have the value of δ_a measured from the current elicited by the first of the three voltage pulses in the triple pulse protocol (starting from a −93-mV holding potential). For V _h = −113, −153, and −193 mV, the amplitude was multiplied by a scaling factor to account for the fact that prepulses to voltages more negative than −93 mV yield a slightly longer delay in the channel opening time course. All data except for V _h = −93 mV come from the same patch (w448). (B) Values of τ_acc for different V _h were fitted to an exponential (solid curve) to estimate a charge q _βd = −0.24 e₀. Values reflect pooled measurements made in four different patches.

Figure 10

Single channel activity at depolarized voltages. (A) Traces of single channel currents elicited by voltage pulses from −93 mV to different test voltages. The beginning of the voltage pulse is indicated by the vertical dashed line. Patches w265 and w276. (B) Closed dwell-time histograms from depolarizations in 40-mV increments between −13 and +147 mV. The histograms were fitted to the sum of three exponentials; dashed curves correspond to each of the fitted exponential components. The number of events in each histogram is ≥605. (C) The open dwell-time histograms at the same voltages were well fitted by a single exponential. (D) The time constants (τ₁, τ₂, and τ₃) of the fast, intermediate, and slow exponential components of the closed-time histograms have nearly voltage-independent values near 0.1, 0.3, and 2 ms. The τ₃ values were fitted to an exponential (solid line) to estimate the rate d from C_iN to the open state. Data points reflect pooled results from several patches. Time constant values from the fits of the histograms shown in B are indicated by the filled symbols. (E) The time constants τ₀ of the single exponentials fitted to the open times display little voltage dependence. Also, the large discrepancy between τ₀ and the reciprocal of the channel closing rate β_N (solid line) indicates that nearly all of the closures at depolarized voltages are to states that are not in the activation path. The τ₀ values from the fits of the histograms shown in C are indicated by the filled symbols. (F) An estimate for the rate c from the open state to C_iN was derived by fitting an exponential (solid curve) to estimates of the frequency of C_i closures, corresponding to the τ₃ component in the closed dwell-time distributions. Frequency estimates were obtained from the measured channel open times normalized by the relative contribution of the C_i closures to the total number of measured closures. Values obtained from the histograms in B and C are indicated by the filled symbols. For the closed dwell-time histograms shown in B, the relative amplitudes A ₁, A ₂, and A ₃ of the fast, intermediate, and slow exponential components are as follows: at −13 mV, 0.74, 0.24, and 0.02; at +27 mV, 0.83, 0.16, and 0.01; at +67 mV, 0.79, 0.20, 0.02; at +107 mV, 0.83, 0.16, and 0.01; and at +147 mV, 0.85, 0.14, and 0.01.

Figure 11

C_i states can be entered from closed states in the activation path. (A) The upper half of the cumulative first latency histogram at +67 mV was fitted to the sum of two exponentials (Eq. 6; solid curve), yielding the indicated τ_a, τ_s, and relative A _s values. The dashed curve reflects just the fast component in Eq. 6. The difference in the amplitude of the two curves reflects A _s. Patch w265. (B) The time constants τ_s obtained in the fits of Eq. 6 to first latency distributions (▪) and macroscopic ionic currents (○) at V ≥ +67 mV have values of 1–3 ms. Only two of the single channel experiments had enough traces that a slow component could be convincingly discerned in the latency histogram. However, 21 of 28 relatively smooth macroscopic ionic current time courses at V ≥ +67 mV (measured in seven patches) displayed an unambiguous slow component. The τ_s values were fitted to single exponential (solid curve). The derived charge estimate q = −0.14 e₀ indicates that the time constant of the slow component is nearly voltage independent. (C) The relative magnitude of the slow exponential component A _s/(A _f + A _s) is also nearly voltage independent. These values were fitted to an exponential, yielding q = 0.07 e₀.

Scheme IV

Scheme V

Scheme VI