Fineberg JD et al. (2012), Modeling-independent elucidation of inactivatio...

XB-ART-46904

J Gen Physiol 2012 Nov 01;1405:513-27. doi: 10.1085/jgp.201210869.

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Modeling-independent elucidation of inactivation pathways in recombinant and native A-type Kv channels.

Fineberg JD , Ritter DM , Covarrubias M .

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A-type voltage-gated K(+) (Kv) channels self-regulate their activity by inactivating directly from the open state (open-state inactivation [OSI]) or by inactivating before they open (closed-state inactivation [CSI]). To determine the inactivation pathways, it is often necessary to apply several pulse protocols, pore blockers, single-channel recording, and kinetic modeling. However, intrinsic hurdles may preclude the standardized application of these methods. Here, we implemented a simple method inspired by earlier studies of Na(+) channels to analyze macroscopic inactivation and conclusively deduce the pathways of inactivation of recombinant and native A-type Kv channels. We investigated two distinct A-type Kv channels expressed heterologously (Kv3.4 and Kv4.2 with accessory subunits) and their native counterparts in dorsal root ganglion and cerebellar granule neurons. This approach applies two conventional pulse protocols to examine inactivation induced by (a) a simple step (single-pulse inactivation) and (b) a conditioning step (double-pulse inactivation). Consistent with OSI, the rate of Kv3.4 inactivation (i.e., the negative first derivative of double-pulse inactivation) precisely superimposes on the profile of the Kv3.4 current evoked by a single pulse because the channels must open to inactivate. In contrast, the rate of Kv4.2 inactivation is asynchronous, already changing at earlier times relative to the profile of the Kv4.2 current evoked by a single pulse. Thus, Kv4.2 inactivation occurs uncoupled from channel opening, indicating CSI. Furthermore, the inactivation time constant versus voltage relation of Kv3.4 decreases monotonically with depolarization and levels off, whereas that of Kv4.2 exhibits a J-shape profile. We also manipulated the inactivation phenotype by changing the subunit composition and show how CSI and CSI combined with OSI might affect spiking properties in a full computational model of the hippocampal CA1 neuron. This work unambiguously elucidates contrasting inactivation pathways in neuronal A-type Kv channels and demonstrates how distinct pathways might impact neurophysiological activity.

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Species referenced: Xenopus
Genes referenced: drg1 kcnc4 kcnd2 sh2b2 tbx2

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	Figure 1. Inactivation pathways of voltage-gated ion channels. Inactivation may occur strictly from the open state (OSI) or pre-open closed states (CSI). A hybrid scenario allowing inactivation from both open and closed states is also likely (OSI + CSI). Gray arrows indicate a subset of this scheme in which interconversion between closed-inactivated and open-inactivated is allowed. For proof-of-principle simulations, the detailed versions of these schemes are shown in Fig. S1.
	Figure 2. The effect of recovery from OSI on the simulated relationship between the GP-V and the steady-state inactivation curves. The GP-V and steady-state inactivation curves were simulated assuming OSI (Fig. S1 and Table S1) in three conditions that compare the effect of varying the rate constant of recovery from inactivation (λ1). Note that the steady-state inactivation curve shifts to the left as λ1 is slowed. In contrast, the GP-V curves superimpose exactly on each other.
	Figure 3. OSI simulation. (A) Family of outward currents evoked by a series of voltage steps (inset). (B) Normalized GP-V and steady-state inactivation curves. The simulation of steady-state inactivation assumed 10-s conditioning pulses and a test pulse of +70 mV. (C) Voltage dependence of the time constant of inactivation. Time constants were determined by fitting an exponential function to the decay phase of the simulated outward currents. For comparison, the red symbol indicates the time constant determined from the double-pulse protocol. (D) Outward currents evoked by a double-pulse protocol with a 5-ms resetting gap between the two pulses (inset). This gap eliminates a Cole–Moore effect on the test current and is not long enough to cause significant recovery from inactivation (the time constant of recovery at −100 mV is ∼2,000 ms). The conditioning pulse activated 19% of the peak conductance. (E) Kinetics of double-pulse inactivation. The simulated normalized peak current evoked by the test pulse of the protocol in D plotted against the duration of the conditioning pulse. (F) Overlay of the outward current (black) evoked by a single pulse (−100 to 0 mV) and the rate of inactivation (red) at 0 mV. The rate of inactivation is the scaled negative first derivative of the plot in E. The simulations were performed at 24°C, and the model parameters are given in Table S1.
	Figure 4. CSI simulation. Details of A–F are as described in the Fig. 3 legend. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. The conditioning pulse in D activated 14% of the peak conductance. Recovery from inactivation at −100 mV was significant within 5 ms and, therefore, we used no gap between the two pulses. These simulations were performed at 34°C to assess the predictions of the model on spiking properties at the temperature used to study the excitability of hippocampal neurons (Materials and methods; Fig. 11). Simulation parameters are given in Table S1. G and H are analogous to E and F, with simulation parameters as reported by Amarillo et al. (2008; Table S1), except the allosteric factor f = 0.45 (red symbols). The blue symbols demonstrate the result of further increasing the allosteric factor f to 0.67 and setting the allosteric factor g to 4.
	Figure 5. The recombinant Kv3.4 channel expressed in Xenopus oocytes undergoes strict OSI. (A) Family of whole oocyte outward currents evoked by a series of voltage steps (inset). (B) Normalized GP-V and steady-state inactivation curves (closed and open circles, respectively). The steady-state inactivation protocol used 10-s conditioning pulses and a test pulse to +70 mV. Red solid lines are the best-fit fourth-order Boltzmann (GP-V curve) and a Boltzmann (steady-state inactivation) function (best-fit parameters and descriptive statistics are summarized in Table 1). (C) Voltage dependence of the time constant of inactivation. Time constants or weighted time constants were determined from the best-fit exponential or sum of two exponentials that describes the decay phase of the currents, respectively. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. (D) Outward currents evoked by a double-pulse protocol with a 5-ms resetting gap between the two pulses (inset). The conditioning pulse activated 12% of the peak conductance. (E) Kinetics of double-pulse inactivation. The normalized peak current evoked by the test pulse of the protocol in D plotted against the duration of the conditioning pulse (closed circles). The solid red line represents the following empirical best-fit sum of exponential terms: I/I0 (t) = 0.52 − 0.38(1 − e−t/88)1.3 + 0.48e−t/280. (F) Overlay of the average outward current (mean ± SEM; black and gray, respectively) evoked by a single pulse (−100 to 0 mV) and the rate of inactivation (red) at 0 mV. The rate of inactivation is the scaled negative first derivative of the red solid line in E. The blue solid line is the exponential function that best describes the decay phase of the current trace (black). The scaled negative first derivative of the observed time course of double-pulse inactivation is also plotted (open black circles) for comparison.
	Figure 6. The native Kv3.4 channel expressed in DRG neurons undergoes strict OSI. Currents were recorded under cell-attached patch-clamping conditions (Materials and methods). Details of A–F are as described in the Fig. 5 legend. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. The conditioning pulse in D activated 16% of the peak conductance. The complex steady-state inactivation curve reflects the complexity of the native system including a dominant Kv3.4 component and two minor components corresponding to a low voltage–activated A-type K+ current described previously and a sustained outward current (Ritter et al., 2012). The best-fit parameters describing the small voltage-dependent component of the double Boltzmann were V1/2 = −98 mV and k = 3 mV. The solid red line in E represents the following empirical best-fit sum of exponential terms: I/I0 (t) = 0.79 − 0.16(1 − e−t/16)3 + 0.2e−t/177.
	Figure 7. The recombinant Kv4.2 ternary channel complex expressed in tsA-201 cells undergoes preferential CSI. Currents were recorded under cell-attached patch-clamping conditions (Materials and methods). Details of A–F are as described in the Fig. 5 legend. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. The conditioning pulse in D activated 15% of the peak conductance. The solid red line in E represents the following empirical best-fit sum of exponential terms: I/I0 (t) = 0.36e−t/6.5 + 0.54e−t/34 − 0.11. The negative first derivative of the observed time course of double-pulse inactivation is also plotted (open black circles) for comparison.
	Figure 8. The native Kv4.2 ternary channel complex expressed in CGNs exhibits preferential CSI. Currents were recorded under cell-attached patch-clamping conditions (Materials and methods). Details of A–F are as described in the Fig. 5 legend. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. The conditioning pulse in D activated 14% of the peak conductance. The solid red line in E represents the following empirical best-fit sum of exponential terms: I/I0 (t) = 0.38e−t/6.6 + 0.38e−t/76 + 0.23.
	Figure 9. The recombinant Kv4.2–DPP6-S binary channel complex expressed in tsA-201 cells exhibits a hybrid inactivation phenotype. Currents were recorded under cell-attached patch-clamping conditions (Materials and methods). Details of A–F are as described in the Fig. 5 legend. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. The conditioning pulse in D activated 11% of the peak conductance. The solid red line in E represents the following empirical best-fit sum of exponential terms: I/I0 (t) = 0.42e−t/65 + 0.58e−t/12.28 − 0.01.
	Figure 10. The recombinant Kv4.2–KChIP1-DPP10a ternary channel complex expressed in tsA-201 cells exhibits a hybrid inactivation phenotype. Currents were recorded under cell-attached patch-clamping conditions (Materials and methods). Details of A–F are as described in the Fig. 5 legend. For comparison, the red symbol in C indicates the time constant determined from the double-pulse protocol. The conditioning pulse in D activated 15% of the peak conductance. The solid red line in E represents the following empirical best-fit sum of exponential terms: I/I0 = .5 − .52(1 − exp(−t/10))^1.4 + .5*exp(−t/120).
	Figure 11. The pathways of Kv4 channel inactivation influence spiking properties in a computational model of the CA1 pyramidal neuron. (A) NEURON simulation of current families evoked by depolarizations from −60 to +80 mV (20-mV steps). Holding potential was −100 mV. (B) Gp-V and steady-state inactivation curves of CSI (black) and CSI + OSI (red). (C) Somatic (dim traces) and the corresponding dendritic (solid; 400 µm from the soma) APs from a 90-ms stimulation of 150 pA at the soma. (D) Latency to the first somatic spike with a 40-pA stimulation for 200 ms (rheobase for CSI model at 200 ms). (E) Simulated somatic AP trains assuming specific Markov schemes: CSI (black) and CSI + OSI (red). AP firing was elicited by injecting 250 pA over a period of 200 ms. (F) Overlay of the first (thick) and the last (thin) AP in the trains shown in A. (G) Summary of somatic AP properties. Each point corresponds to an AP, and the shape of the symbol denotes the pathway of inactivation (diamond, CSI; triangle, CSI + OSI). The color gradient represents the fraction of available Kv4.2 channels at the AHP before the spike (i.e., maximal availability preceding the spike).

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