Regulation of Kv4.3 voltage-dependent gating kinetics by KChIP2 isoforms

Abstract

We conducted a kinetic analysis of the voltage dependence of macroscopic inactivation (τ_fast, τ_slow), closed-state inactivation (τ_closed,inact), recovery (τ_rec), activation (τ_act), and deactivation (τ_deact) of Kv4.3 channels expressed alone in Xenopus oocytes and in the presence of the calcium-binding ancillary subunits KChIP2b and KChIP2d. We demonstrate that for all expression conditions, τ_rec, τ_closed,inact and τ_fast are components of closed-state inactivation transitions. The values of τ_closed,inact and τ_fast monotonically merge from −30 to −20 mV while the values of τ_closed,inact and τ_rec approach each other from −60 to −50 mV. These data generate classic bell-shaped time-constant–potential curves. With the KChIPs, these curves are distinct from that of Kv4.3 expressed alone due to acceleration of τ_rec and slowing of τ_closed,inact and τ_fast. Only at depolarized potentials where channels open is τ_slow detectable suggesting that it represents an open-state inactivation mechanism. With increasing depolarization, KChIPs favour this open-state inactivation mechanism, supported by the observation of larger transient reopening currents upon membrane hyperpolarization compared to Kv4.3 expressed alone. We propose a Kv4.3 gating model wherein KChIP2 isoforms accelerate recovery, slow closed-state inactivation, and promote open-state inactivation. This model supports the observations that with KChIPs, closed-state inactivation transitions are [Ca²⁺]_i-independent, while open-state inactivation is [Ca²⁺]_i-dependent. The selective KChIP- and Ca²⁺-dependent modulation of Kv4.3 inactivation mechanisms predicted by this model provides a basis for dynamic modulation of the native cardiac transient outward current by intracellular Ca²⁺ fluxes during the action potential.

Myocytes isolated from subepicardial and subendocardial surfaces of the free wall of the left ventricle (LV) display significant differences in action potential amplitude, plateau duration, and frequency-dependent characteristics (Antzelevitch & Dumaine, 2002; Carmeliet & Vereecke, 2002). Nonetheless, the action potentials of both myocyte types display a characteristic early repolarization (‘phase 1’ or ‘notch’) occurring immediately after the upstroke and preceding the plateau. This early repolarization is primarily governed by a rapidly activating and inactivating K⁺ current phenotype designated ‘I_to’ (Campbell et al. 1995; Archer & Rusch, 2001; Oudit et al. 2001; Nerbonne, 2002). Since the kinetics of I_to closely overlap those of the L-type calcium current, it is not only a significant regulator of ventricular repolarization but also the excitation–contraction coupling process, and thus overall cardiac performance (Heppner et al. 1966; Morad & Trautwein, 1968; Giles & van Ginnecken, 1985; Campbell et al. 1995; Bers, 2001; Carmeliet & Vereecke, 2002; Sah et al. 2003).

Prominent I_to phenotypes have been recorded in ventricular myocytes of many species, including mice, rats, rabbits, cows, cats, dogs, ferrets and humans (Campbell et al. 1995; Oudit et al. 2001; Carmeliet & Vereecke, 2002; Nerbonne, 2002; Sah et al. 2003). The designation ‘I_to’ has thus become synonymous with any rapidly activating and inactivating K⁺ current present in a given ventricular myocyte. However, depending upon both species and anatomical region, there may be at least two functionally distinct I_to phenotypes, ‘I_to,slow’ and ‘I_to,fast’. I_to,slow displays very slow kinetics of recovery from inactivation (time constants on the order of seconds) with marked cumulative inactivation, is not blocked by Heteropoda toxin, and is likely generated by Kv1.4 α subunits (Nabauer et al. 1996; Brahmajothi et al. 1999; Nerbonne, 2002). I_to,slow is prominent in ferret and human LV subendocardial myocytes, and appears to be the predominant I_to phenotype in rabbit ventricle (Giles & Imaizumi, 1988; Nabauer et al. 1996; Brahmajothi et al. 1999). In contrast, I_to,fast displays rapid recovery kinetics (time constants on the order of tens of milliseconds) with little to no cumulative inactivation, is blocked by Heteropoda toxin, and is most likely due to either Kv4.2 or Kv4.3 α subunits or a heteromeric combination of the two (Nabauer et al. 1996; Brahmajothi et al. 1999; Guo et al. 2002a; Nerbonne, 2002; Sah et al. 2003). I_to,fast is prominent in ferret and human LV subepicardial myocytes, and appears to be the predominant I_to phenotype in the canine LV (Nabauer et al. 1996; Brahmajothi et al. 1999; Rosati et al. 2001, 2003).

Although the properties of heterologously expressed Kv4.2 and/or Kv4.3 closely resemble the native LV I_to,fast, these clones fail to fully reconstitute the gating kinetics of the native current, thus suggesting involvement of additional regulatory subunits. Many auxiliary subunits have been shown to modulate Kv4 channels, and some still remain to be identified (Nadal et al. 2001; Deschenes & Tomaselli, 2002). One family of regulatory subunits that appears to be of physiological significance is the KChIPs (Kv Channel Interacting Proteins; An et al. 2000). KChIPs are Ca²⁺-binding proteins containing EF-hand domains that selectively interact with the N-termini of Kv4 channels, most notably Kv4.2 and Kv4.3. Members of the KChIP2 family are the predominant isoforms expressed in the heart (Rosati et al. 2001, 2003; Patel et al. 2002a,b). When heterologously coexpressed with Kv4 α subunits, KChIPs increase cell surface expression, slow inactivation kinetics, and accelerate recovery kinetics to rates approaching that of native ventricular I_to,fast (An et al. 2000; Bahring et al. 2001a,b; Beck et al. 2002; Patel et al. 2002a,b). While the mechanisms underlying these regulatory effects are unclear, the functional importance of KChIPs in ventricular function is emphasized by the fact that I_to,fast, normally present in mouse LV myocytes, is absent in transgenic mice lacking the KChIP2 gene, a condition which results in increased susceptibility to ventricular arrhythmias (Kuo et al. 2001). KChIPs have also been demonstrated to be involved in trafficking of Kv4.2 protein from the endoplasmic reticulum to the cell membrane (Shibata et al. 2003). In addition, variations in myoplasmic [Ca²⁺]_i during the normal excitation—contraction coupling cycle may dynamically modulate the kinetics of I_to,fast through interactions with EF-hands of KChIP2 isoforms. Thus, Ca²⁺-dependent regulatory effects of KChIP2 isoforms on I_to,fast inactivation kinetics may provide an important negative feedback system allowing changes in [Ca²⁺]_i to regulate repolarization of specific ventricular myocyte types under different physiological conditions.

To ultimately decipher the electrophysiological role of Kv4 and KChIP2 isoforms in generating ventricular I_to,fast and modulating the action potential requires knowledge of both molecular and biophysical mechanisms governing voltage-dependent gating characteristics. Unfortunately, unlike inactivating K⁺ channels of the Shaker (Kv1) family, which display rapid N-type and slow C-type inactivation, the molecular and biophysical mechanisms governing Kv4 channel inactivation and its regulation are unclear (Zagotta et al. 1990; Hoshi et al. 1990, 1991; Choi et al. 1991; Rasmusson et al. 1995, 1998; Yellen, 1998). Most studies indicate that Kv4 inactivation is multiexponential, thereby implying at least two underlying inactivation mechanisms. However, these two mechanisms do not conform to basic criteria established for characterization of classic N- and C-type inactivation. For example, for Kv4: (i) N-terminal deletion does not slow the kinetics of closed-state inactivation or alter the kinetics of recovery (Bahring et al. 2001a); (ii) neither extracellular nor intracellular tetraethylammonium alters inactivation (Jerng & Covarrubias, 1997); and (iii) increasing [K⁺]_o accelerates inactivation and slows recovery (Jerng & Covarrubias, 1997; Bahring et al. 2001a). In combination, these studies suggest that inactivation from Kv4 closed states is a predominant mechanism (Jerng & Covarrubias, 1997; Jerng et al. 1999; Bahring et al. 2001a; Beck & Covarrubias, 2001; Beck et al. 2002). In addition, in contrast to Shaker and Kv3 (Demo & Yellen, 1991; Ruppersberg et al. 1991), Kv4.2 has been reported not to reopen upon membrane hyperpolarization (Bahring et al. 2001a). Rather, it has been proposed that Kv4.2 accumulates in the closed inactivated state(s) from which it directly recovers via an ‘electrically silent’ mechanism (Bahring et al. 2001a).

Beck et al. (2002) have also proposed a mechanistic model for the effects of KChIP1 on Kv4·1 and Kv4.3. This model is based upon their experimental observations that KChIP1 accelerated closed-state inactivation at −50 mV, slowed the initial phase of macroscopic inactivation, and accelerated recovery kinetics. However, two major assumptions were also made in this model: (i) inactivation from the open-state, mediated by the N-terminus, kinetically corresponds to the fast time constant of inactivation (τ_fast); while (ii) inactivation from the closed-state, mediated by conformational changes near the internal mouth of the pore, kinetically corresponds to the slow time constant(s) of inactivation (τ_slow). With these two assumptions, this model predicts that KChIP1 binds to and immobilizes the Kv4 N-terminus leading to a direct slowing of open-state inactivation. This results in less steric hindrance around the internal mouth of the channel pore, thus favouring closed-state inactivation and lowering the energy barrier for recovery from inactivation.

Assignment of time constants to kinetic processes associated with specific channel conformational states requires an overall analysis of their voltage dependence (Bezanilla, 2000; Hille, 2001b). Since such an analysis has not previously been conducted for any Kv4 channel, the underlying assumptions of previous Kv4 gating models (Bahring et al. 2001a; Beck et al. 2002), and thus their applicability as biophysical and molecular descriptors of I_to,fast, have yet to be verified. In addition, kinetic analysis of Kv4 inactivation and recovery is not only of biophysical modelling interest, but is also required for understanding how endogenous regulatory channel subunits, neurotransmitters, and drugs modulate Kv4 function, and thus the electrophysiological activity and pharmacological responses of the specific cell types in which these channels are expressed (Archer & Rusch, 2001; Nadal et al. 2001; Hille, 2001a; Nerbonne, 2002).

In this study we quantitatively analyse the voltage dependence of inactivation, recovery, activation, and deactivation kinetics of Kv4.3 expressed alone and in the presence of KChIP2b or KChIP2d (Patel et al. 2002a,b). We selected Kv4.3, KChIP2b and KChIP2d because all are abundantly expressed isoforms in the ferret heart. In particular, KChIP2b (4 EF-hands) represents the largest expressed KChIP2 isoform (270 amino acids), while KChIP2d (1 EF hand) represents a minimal isoform corresponding to only the last 70 amino acids of the common C-termini of the larger KChIP2 isoforms (Patel et al. 2002a,b). Our results demonstrate that both KChIP2b and 2d slow Kv4.3 closed-state inactivation kinetics and accelerate open-state inactivation kinetics, with significant quantitative differences in the effects of the two isoforms on these processes. These regulatory effects of KChIP2b and 2d on Kv4.3 result in a shift from a prominent closed-state inactivation mechanism to a much more prominent open-state inactivation mechanism at depolarized potentials. We also present evidence that the fraction of Kv4.3 channels that inactivate by the open-state mechanism reopen upon hyperpolarization, and that these reopening currents are proportionally greater in the presence of KChIP2b and 2d. Based upon our results, we propose a model for Kv4.3/KChIP2 interactions and gating.

An initial account of this work has appeared in abstract form (Patel et al. 2003).

Methods

Animal protocols

All animal protocols were conducted according to NIH approved guidelines of the Institutional Animal Care and Use Committee, UB, SUNY. Female Xenopus laevis were anaesthetized by soaking in 0.75 g l⁻¹ aminobenzoic acid ethyl ester for 30–45 min followed by surgical removal of the oocytes through a lateral incision in the lower abdomen. Oocytes were rocked gently to defolliculate in OR2 solution (mm: 82.5 NaCl, 2 KCl, 1 MgCl₂, 5 Hepes, pH 7.40) with 2 mg ml⁻¹ collagenase (Type II, Sigma, St Louis, MO, USA) 2 × 45−60 min. The oocytes were then rinsed 3 times in OR2 solution, incubated for 15 min in OR2 solution with 1 mg ml⁻¹ bovine serum albumin, and rinsed 3 times in OR2 solution. The oocytes were then incubated at 18°C in Barth's solution (mm: 88 NaCl, 1 KCl, 2.4 NaHCO₃, 0.82 MgSO₄, 0.33 Ca(NO₃)₂, 0.41 CaCl₂, 10 Hepes, pH 7.40) with 2% antibiotic-antimycotic (v/v of 100 × stock, GibcoBRL) until use. Stage V–VI oocytes were used for electrophysiology experiments. After 4–5 surgeries (6 weeks apart) frogs were killed by lethal overdose of anaesthetic.

Cloning of ferret Kv4.3, KChIP2b, and KChIP2d

The specific protocols used for cloning of ferret Kv4.3 (long form), KChIP2b and KChIP2d (GenBank AF454388, AF454387 and AF538875, respectively) have previously been described in detail (Patel et al. 2002a,b).

In vitro transcribed cRNA and Xenopus oocyte injection

Kv4.3, KChIP2b and KChIP2d clones (Patel et al. 2002a,b) were maintained in the pGEM-HE5 oocyte expression vector. Plasmids were linearized with restriction endonucleases and cRNA was transcribed using the mMessage mMachine Kit (Ambion, Austin, TX, USA). cRNA quality was checked by glyoxal–agarose gel electrophoresis and concentration was determined by spectrophotometry. Oocytes were injected with 20–50 fmol of each cRNA of interest. For coexpression experiments, the cRNAs were mixed in a 1 : 1 molar ratio.

Electrophysiology

Two-microelectrode voltage clamp recordings (GeneClamp 500B, Axon Instruments, Union City, CA, USA) were performed on Xenopus oocytes 3–10 days after cRNA injection. Microelectrodes were filled with 3 m KCl and 10 mm Hepes, pH 7.40, with resistances of 0.8–3.0 MΩ. Recordings (22 ± 2°C) were conducted in ND 96 (mm: 96 NaCl, 2 KCl, 1 MgSO₄, 1.8 CaCl₂, 5 Hepes, pH 7.40) or in low chloride ND 96 to minimize the endogenous chloride current present in some batches of oocytes (same composition as above with 96 mm sodium aspartate or glutamate in place of NaCl and 2 mm potassium aspartate or glutamate in place of KCl). The effects of 100 μm BAPTA/AM (Calbiochem, La Jolla, CA, USA) were analysed using protocols previously described (Patel et al. 2002b). All voltage clamp recordings were conducted at the maximal gain of the amplifier (10 000 ×) and clamp rise time stability settings of 50–120 μs. Currents were acquired (filtered at 1 kHz, digitized at 5 kHz) with a Digidata 1320A 16-bit acquisition system under pCLAMP 8 software control (Axon Instruments).

Analysis

To account for potential variability among different batches of oocytes, currents were recorded from a minimum of three independently isolated batches of oocytes obtained from different frogs. Oocytes from each independent batch were injected for all experimental conditions (Kv4.3 alone, Kv4.3 + KChIP2b, Kv4.3 + KChIP2d) and samples of currents for each expression condition were recorded on the same day. All recordings were then pooled to derive overall statistical values for each condition.

Currents were analysed using pCLAMP 8.0 (Axon Instruments) and Origin (OriginLab Corp., Northampton, MA, USA). For analysis of steady-state gating relationships (activation, inactivation) and kinetics of macroscopic inactivation, closed-state inactivation, recovery, and deactivation, no direct ‘leakage correction’ protocols were applied. Rather, peak transient current at any given potential was defined as the difference between peak current minus the residual current at the end of 500–2000 ms voltage clamp step pulses. Mean data points obtained from the steady-state inactivation and activation protocols were best fitted (Origin) to standard single Boltzmann relationships of the general form 1/(1 + exp([V_m − V_½]/k)), where V_½ is the potential for either half-maximal steady-state inactivation or activation, and k is the slope factor. Inactivation kinetics were analysed (pCLAMP 8) by best fit analysis to either single or double exponential functions of the general form:

where t is time, τ the associated inactivation time constant(s), and A_n the initial amplitude of each component. Recovery kinetics were analysed (pCLAMP 8) by best fit analysis to a single exponential saturating growth equation of the general form:

where τ_rec is the associated recovery time constant at any given fixed holding potential. Finally, depending upon results and specific protocols applied, the mean data points for the overall voltage dependence of any given time constant were fitted to either: (i) single exponential growing (Aexp[t/τ] + offset) or declining (Aexp[−t/τ] + offset) functions (pCLAMP 8); or (ii) Boltzmann relationships of the general form (A₁ − A₂)/(1 + exp [(V_m − V_½)/k]) + A₂, where A₁ is the initial value at −∞ and A₂ is the final value at +∞ (Origin).

For analysis of activation kinetics, appropriately scaled linear background and capacitive transient currents were subtracted from net current recordings elicited by depolarizing voltage clamp pulses to −40 mV and more depolarized (Campbell et al. 1993). Analysis of activation kinetics was then conducted on such subtracted records using an assumed independent a⁴ sigmoidal activation model (Hodgkin & Huxley, 1952) and the 90% rise time protocol previously applied for analysis of native I_to,fast activation kinetics in ferret right ventricular myocytes (Campbell et al. 1993). Using this protocol, the mean value of Δt_90% was 1.85 ± 0.08 ms (n = 22 oocytes). The initial rising phases of subtracted currents were then best fitted (pCLAMP 8) beginning at Δt_90% to a sigmoidal equation of the general form:

where τ_act was the associated activation time constant (ms). In the present analysis, at each potential fits were restricted to only the early rising phases of the currents (i.e. before significant inactivation was evident), and no attempts were made to correct for potential overlapping effects of inactivation. Although such complicating effects should have been minimal, this is one potential limitation of our activation analysis.

Determination of statistical significance (BAPTA-AM experiments) was conducted using paired t test analysis, with statistical significance taken at P < 0.05.

With the exception of the representative currents illustrated in Fig. 9 (fits to activation kinetics), all current recordings are illustrated with no leakage correction protocols applied. Experimental data points are plotted as means ± s.e.m.

Figure 9. Voltage dependence of Kv4.3 activation kinetics.

A, representative Kv4.3 current activation waveforms after scaled capacitive transient subtraction. First 12 ms illustrated. Voltage clamp pulses applied from −40 mV to +50 mV in 10 mV increments. Rising phases of current waveforms fitted (beginning at Δt = 90%; see Methods) with a sigmoid a⁴ activation relationship. Best-fit time constants (−40 to +50 mV, respectively) 7.2, 5.7, 4.7, 4.1, 3.7, 3.4, 3.4, 3.0, 2.8 and 2.6 ms. For the oocyte illustrated Δt_90% = 1.4 ms. Calibration bar: 2 ms, 0.3 μA. B, voltage dependence of mean values of τ_act for Kv4.3 (black squares, n = 7), Kv4.3 + KChIP2b (blue triangles, n = 8), and Kv4.3 + KChIP2d (green circles, n = 8). Fits: Kv4.3 (black), τ_act = 6.99853exp−([V_m + 40]/21.74328) + 1.60518 ms; Kv4.3 + KChIP2b (blue), τ_act = 10.30906 exp−([V_m + 40]/25.39266) + 1.23242 ms; and Kv4.3 + KChIP2d (green), τ_act = 9.05399 exp−([V_m + 40]/22.3671) + 1.17165 ms.

Results

Compared to uninjected controls, KChIP2b or 2d injected alone into Xenopus oocytes produce no effect on background currents. They also do not affect Kv1.4 inactivation or recovery kinetics (Patel et al. 2002a,b). For reference, the predicted sequence alignment of these two KChIP2 isoforms is illustrated in Fig. 1.

Figure 1. Predicted amino acid sequence comparison of ferret heart KChIP2b and KChIP2d.

EF-hand sequences are boxed. Asterisks at the top of the sequence mark every 10th amino acid.

Effects of KChIPs on Kv4.3 peak current–voltage (I–V) relationship

A common regulatory characteristic of KChIPs on Kv4 channels is to increase cell surface expression, as manifested by an increase in peak macroscopic current amplitude with no effect on single channel conductance (Beck et al. 2002). The mean peak transient I–V relationship for Kv4.3 is illustrated in Fig. 2A. Coinjection of KChIP2b or 2d with Kv4.3 consistently increased the peak current at all potentials (Fig. 2B). Under our injection and recording conditions the effects of the two KChIPs on increasing current amplitude were not different (+50 mV: KChIP2b, 2.40-fold increase; KChIP2d, 2.34-fold increase) nor were the reversal potentials altered (Kv4.3, E_rev = − 70.7 ± 3.1 mV, n = 21; Kv4.3 + KChIP2d, E_rev = − 70.2 ± 2.7 mV, n = 18; Kv4.3 + KChIP2d, E_rev = − 71.8 ± 2.7 mV, n = 22). When mean peak currents for each expression condition were normalized to their values at +50 mV, there was very little difference between the voltage-dependencies of the normalized peak I–V curves (Fig. 2B, inset). This suggests that KChIP2b and 2d exert minimal effects on the voltage dependence of Kv4.3 activation.

Figure 2. Kv4.3 peak current—voltage (I—V) relationships.

A, mean peak transient I—V relationship of Kv4.3 (n = 8 oocytes). Currents elicited during 2000 ms depolarizing voltage clamp pulses from HP = − 100 mV, frequency 0.1 Hz. Peak transient currents were defined as the maximal outward current at any given potential minus the residual current at the end of the 2000 ms pulse. Inset, representative Kv4.3 current recordings. First 1000 ms of currents illustrated for depolarizing clamp pulses applied in 10 mV increments from −30 to +50 mV. Calibration bars: 0.4 μA, 200 ms. B, overlay of mean peak I–V relationships of Kv4.3 alone (black squares) and in the presence of KChIP2b (blue triangles; n = 8) or KChIP2d (green circles; n = 8). Inset, overlay of normalized peak I–V relationships for Kv4.3 alone (black squares) and in the presence of KChIP2b (blue triangles) or KChIP2d (green circles). Currents normalized to mean peak values at +50 mV for each expression condition.

Steady-state activation and inactivation relationships

Steady-state activation (aⁿ, where we have assumed a value of n = 4) was measured using a conventional double-pulse saturating tail current protocol (Fig. 3A, inset). For all expression conditions, the mean activation curves were approximated with single Boltzmann relationships (mean fit parameters in Fig. 3 legend). Consistent with the normalized peak I—V relationships, the activation curves for both KChIP2b and 2d were virtually identical and displayed only modest (approximately +5 mV) depolarizing shifts in mean V_½ values compared to Kv4.3 alone (Fig. 3B).

Figure 3. Voltage dependence of Kv4.3 steady-state activation and inactivation relationships.

Mean steady-state gating relationships fitted with single Boltzmann relationships. Voltage clamp protocols schematically illustrated in inset. Frequency: one pulse protocol per 8 s. A, Kv4.3. activation (aⁿ, assumed value of n = 4), V_½ = −7.9 mV, slope factor k = 12.34 mV (n = 14). Inactivation, V_½ = −68.9 mV, k = 6.31 mV (n = 8). B, overlay of mean steady state activation and inactivation relationships for Kv4.3 (black squares), Kv4.3 + KChIP2b (blue triangles), and Kv4.3 + KChIP2d (green circles). Kv4.3 + KChIP2b : activation, V_½ = −2.97 mV, k = 12.64 mV (n = 14); inactivation, V_½ = −57.4 mV, k = 4.78 mV (n = 10). Kv4.3 + KChIP2d: activation, V_½ = −2.3 mV, k = 12.49 mV (n = 9); inactivation, V_½ = −61.1 mV, k = 5.0 mV (n = 9).

Steady-state inactivation relationships ‘i’ were determined using a conventional double-pulse protocol (Fig. 3A, inset). For all cases, the mean inactivation curves were well described by single Boltzmann relationships. Compared to Kv4.3 alone, expression with KChIP2b or 2d resulted in +12 and +7 mV depolarizing shifts, respectively, in mean V_½ values of inactivation (Fig. 3B). For all expression conditions, an overlay of the steady-state activation a⁴ and inactivation i relationships demonstrated very little overlap in their potential dependence. Kv4.3 channels therefore possess a prominent closed-state inactivation mechanism both in the absence and presence of KChIPs (Bahring et al. 2001a; Beck et al. 2002).

Kinetic analysis of inactivation and recovery

To quantitatively characterize the kinetics of inactivation and recovery over the potential range −100 to +50 mV, three different voltage-clamp protocols were employed for Kv4.3 channels expressed alone and in the presence of either KChIP2b or 2d.

Macroscopic inactivation.

Macroscopic inactivation kinetics were examined over the voltage range from minimal to nearly maximal current activation (−30 to +50 mV). Inactivation kinetics at each potential were quantified by fitting the time course of activated current decay to exponential functions. Previous studies on Kv4 channels have suggested that macroscopic inactivation is best described by three exponential components (Beck et al. 2002; Bahring et al. 2001a). However, under all of our expression and recording conditions, attempts to fit inactivation to three exponential components repeatedly resulted in a negative initial amplitude of the slowest (third) component. We therefore utilized the best fits with either single or double exponential functions.

For Kv4.3, inactivation was well described as a double exponential process over the entire voltage range analysed (Fig. 4.A). The fast time constants of inactivation, τ_fast, declined exponentially with progressive depolarization (e-fold decrease per 12.8 mV), until they became essentially independent of voltage (Fig. 4B). The slower time constants of inactivation, τ_slow, also declined exponentially with depolarization (e-fold decrease per 18.5 mV) and became independent of voltage at depolarized potentials (Fig. 4C). In contrast, the initial fractional amplitude of the fast component of inactivation, A_fast/(A_fast + A_slow), showed only an ∼15% decline in its mean value over this same potential range (Fig. 4D). Thus, at depolarized potentials where Kv4.3 channels approach maximal activation, the fast component accounts for ∼75% of the total inactivation process and proceeds at a rate approximately 5 times faster than the slower component.

Figure 4. Voltage dependence of Kv4.3 macroscopic inactivation kinetics (−30 to +50 mV).

A, representative double exponential fits (unless indicated otherwise) to macroscopic inactivation at −10, +10, +30 and +50 mV for Kv4.3 (black curves), Kv4.3 + KChIP2b (blue curves), and Kv4.3 + KChIP2d (green curves). Fast (τ_fast) and slow (τ_slow) time constants and A_fast/(A_fast + A_slow) ratio (A_f) for each recording as indicated. Calibration bars: 1 μA, 200 ms. B, voltage dependence of τ_fast for Kv4.3 (black squares, n = 13), Kv4.3 + KChIP2b (blue triangles, n = 10), and Kv4.3 + KChIP2d (green circles, n = 16). Fits: Kv4.3 (black), τ_fast = 30.154exp−([V_m + 30]/12.789) + 39.788 ms; Kv4.3 + KChIP2b (blue), τ_fast = 58.837exp−([V_m + 30]/34.315) + 54.539 ms; and Kv4.3 + KChIP2d (blue), τ_fast = 39.972exp−([V_m + 30]/17.747) + 54.6 ms. C, voltage dependence of τ_slow for Kv4.3 (black squares), Kv4.3 + KChIP2b (blue triangles), and Kv4.3 + KChIP2d (green circles). Fits: Kv4.3 (black), τ_slow = 141.674 exp−([V_m + 30]/18.486) + 208.939 ms; Kv4.3 + KChIP2b (blue), τ_slow = 710.337exp−([V_m + 30]/28.328) + 92.093 ms; and Kv4.3 + KChIP2d (green), τ_slow = 30.145exp−([V_m − 10]/5.862) + 114.3025 ms. D, voltage dependence of the initial fractional amplitude of the fast component of inactivation A_fast/(A_fast + A_slow) for Kv4.3 (black squares), Kv4.3 + KChIP2b (blue triangles), and Kv4.3 + KChIP2d (green circles). Mean data points for each expression condition fit with Boltzmann functions as follows: Kv4.3 (black), A_fast/(A_fast + A_slow) = (0.79954)/(1 + exp([V_m − 89.022]/27.838)) + 0.10405; Kv4.3 + KChIP2b (blue), A_fast/(A_fast + A_slow) = (0.62856)/(1 + exp([V_m − 19.308]/8.5044)) + 0.62856; and Kv4.3 + KChIP2d (green), A_fast/(A_fast + A_slow) = (0.825602)/(1 + exp([V_m − 33.982]/4.3065)) + 0.080498.

The time constants of Kv4.3 inactivation kinetics and the relative contributions of the fast and slow components of inactivation were significantly altered in the presence of either KChIP2b or 2d (Fig. 4A–D). Compared to Kv4.3 expressed alone, both KChIPs produced: (i) a slowing of τ_fast; (ii) a much larger fractional contribution of the slower component of inactivation at depolarized potentials; and (iii) a marked voltage dependence to the initial amplitude of the fast component of inactivation (A_fast/(A_fast + A_slow)). These effects resulted in well-defined biexponential inactivation kinetics at more depolarized potentials. However, from −30 mV to ∼0 mV the slower component of inactivation could not be resolved reliably. Thus inactivation kinetics were fitted with single exponential functions at those voltages.

Despite the overall similarities in the effects of KChIP2b and 2d on Kv4.3 inactivation, there were notable quantitative differences between the two isoforms. In the presence of KChIPs, depolarization accelerated τ_slow to values approximately twice as fast as those of Kv4.3, while at more hyperpolarized potentials τ_slow values were slower than those of Kv4.3 (Fig. 4C). While both KChIPs caused the slower component of inactivation to become dominant at depolarized potentials, at +50 mV this effect was more pronounced for KChIP2b than KChIP2d (Fig. 4D). In the presence of KChIP2d the slow component of inactivation accounted for ∼65% of inactivation at +50 mV, while in the presence of KChIP2b it accounted for ∼90% of inactivation. Thus, at more depolarized potentials inactivation kinetics of Kv4.3 + KChIP2b began to closely approach single exponential behaviour, consistent with our previous kinetic results obtained at +50 mV (Patel et al. 2002a). However, when we attempted single exponential fits to Kv4.3 + KChIP2b inactivation over the range of voltages from −30 to +50 mV the extracted time constants consistently displayed an anomalous voltage dependence in that they progressively increased in value with progressive depolarization.

Closed-state inactivation.

Since steady-state inactivation of Kv4.3 channels occurs predominantly from the closed state(s), we next determined the kinetics of development of closed-state inactivation over a voltage range where there was significant inactivation but minimal activation (−70 to −20 mV). Closed-state inactivation kinetics were measured using a P2 pulse to +50 mV (holding potential, HP = −100 mV) preceded by a P1 pulse of progressively increasing duration applied at the voltage under examination (protocol Fig. 5A, inset; Campbell et al. 1993).

Figure 5. Voltage dependence of Kv4.3 closed-state inactivation kinetics (−70 to −20 mV).

A, representative Kv4.3 closed-state inactivation protocol current waveforms for P1 = −50 mV. Peak P2 currents fit with single exponential relationship with indicated τ_closed,inact. Inset, voltage clamp protocol. B, overlay of mean time constants (τ_closed,inact) of closed-state inactivation over the potential range −70 to −20 mV. Fits: Kv4.3 (black squares, n = 8), τ_{closed,inact, −60 to −20mV} = 1236.742exp–([V_m + 60]/8.447) + 51.9 ms; Kv4.3 + KChIP2b (blue triangles, n = 12), τ_{closed,inact, −50 to −20mV} = 1218.467exp−([V_m + 50]/10.084) + 37.9 ms; and Kv4.3 + KChIP2d (green circles), τ_{closed,inact, −50 to −20mV} = 1022.911exp−([V_m + 50]/7.657) + 68.8 ms. Note that the mean time constants deviate significantly from the exponential fits at −70 mV for Kv4.3 and −60 mV for Kv4.3 coexpressed with either KChIP2b or KChIP2d.

At any given P1 potential, closed-state inactivation kinetics were well described as single exponential processes for all expression conditions (Fig. 5A). For Kv4.3, from −60 to −20 mV closed-state inactivation time constants, τ_closed,inact, declined exponentially with depolarization (e-fold decrease per 8.5 mV). From −50 to −20 mV, there was also a voltage-dependent exponential decline in τ_closed,inact for Kv4.3 + KChIP2b (e-fold decrease per 10.1 mV) and Kv4.3 + KChIP2d (e-fold decrease per 7.7 mV). Over this potential range, values of τ_closed,inact for Kv4.3 in the presence of either KChIP2 isoform were slower than Kv4.3 alone (Fig. 5.B).

The mean values of τ_closed,inact at −70 mV for Kv4.3 and −60 mV for Kv4.3 in the presence of either KChIP deviated from the exponential functions which well described the voltage dependence of closed-state inactivation kinetics at more depolarized potentials. We hypothesized that at these more hyperpolarized potentials, closed-state inactivation kinetics were influenced by the kinetics of recovery from inactivation.

Kinetics of recovery from inactivation

To measure the voltage dependence of recovery kinetics at holding potentials ranging from −100 to −60 mV, a conventional double-pulse protocol was applied (Fig. 6A, inset). For all three expression conditions: (i) at any given fixed HP, recovery kinetics could be well approximated as a single exponential process with a corresponding time constant of recovery, τ_rec; and (ii) over the potential range analysed, the mean values of τ_rec progressively increased with depolarization (Fig. 6B). While the voltage dependencies of τ_rec for all conditions were adequately fitted with exponential relations, better fits were obtained using saturating Boltzmann functions (fits in Fig. 6 legend). At all holding potentials, the presence of KChIP2b or 2d led to faster recovery kinetics than those observed for Kv4.3 alone and KChIP2b accelerated recovery more than KChIP2d.

Figure 6. Voltage dependence of Kv4.3 recovery kinetics.

A, representative Kv4.3 recovery waveforms at HP = −80 mV fitted with indicated τ_rec. Inset, recovery protocol. B, overlay of mean values of τ_rec for Kv4.3 (black squares), Kv4.3 + KChIP2b (blue triangles, n = 9), and Kv4.3 + KChIP2d (green circles, n = 7) over the holding potential range −100 to −60 mV. Fits: Kv4.3 (black), τ_rec = (1926.07)/(1 + exp([−70.008 − V_m]/7.3096)) +274.63 ms; Kv4.3 + KChIP2b (blue), τ_rec = (1168.523)/(1 + exp([−50.840 − V_m]/9.8463)) + 45.977 ms; and Kv4.3 + KChIP2d (green), τ_rec = (1541.707)/(1 + exp([−59.693 − V_m]/7.6011)) + 61.793 ms. Inset, data plotted on an expanded scale to better illustrate the voltage dependence of τ_rec values for Kv4.3 + KChIP2b (blue triangles) and Kv4.3 + KChIP2d (green circles).

Rate constant analysis of closed-state inactivation

Both in the absence and presence of KChIPs the values of τ_closed,inact monotonically approached and overlapped the values of τ_fast measured from direct fit analysis of activated current decay (see Fig. 8 for overlays of all mean time constant values for each expression condition). These results suggest that τ_closed,inact and τ_fast correspond to a voltage-dependent continuum of a single kinetic process, and are consistent with the hypothesis that τ_fast corresponds to an inactivation mechanism that can be reached from preactivated closed state(s) (‘closed-state inactivation’). In contrast, in the presence of KChIP2b or 2d, values of τ_slow and the corresponding initial A_fast/(A_fast + A_slow) ratios could only be consistently resolved at potentials depolarized above ∼0 mV. However, once resolved the magnitudes and voltage dependence of τ_slow were clearly distinct from τ_closed,inact and τ_fast suggesting that τ_slow corresponds to an inactivation mechanism that is available only upon entering the open state (‘open-state inactivation’).

Figure 8. Comparative summary of voltage dependence of derived closed-state inactivation and recovery kinetics.

Overlays of derived time constants of closed-state inactivation for Kv4.3 (black), Kv4.3 + KChIP2b (blue), and Kv4.3 + KChIP2d (green). Also illustrated are the corresponding exponential fits to the values of open-state τ_slow for each expression condition.

To derive theoretical forward (α_V) and backward (β_V) rate constants of the closed-state inactivation process, the inverse time constants 1/τ_fast, 1/τ_closed,inact, and 1/τ_rec were analysed as a function of potential (Fig. 7Ai–Ci). For each expression condition, the mean data points were then best fitted to the sum of two saturating Boltzmann equations for α_V and β_V (equation fits in Fig. 7 legend). Overlays of the theoretically predicted closed-state inactivation time constants and the experimentally measured mean time constants for each expression condition are illustrated in Fig. 7Aii–Cii.

Figure 7. Closed-state inactivation: voltage dependence of Kv4.3 forward (α_V) and backward (β_V) rate constants and theoretically predicted time constants.

Ai, Bi and Ci, mean data points for inverse time constants 1/τ_fast, 1/τ_closed,inact, and 1/τ_rec fitted with Boltzmann functions. Ai, Kv4.3. Fits (black): α_V = 8.839507(1/(1 + exp([V_m + 104.17])/12.761)) s⁻¹; β_V = 24.83537(1/(1 + exp−([V_m + 30.970])/9.117)) s⁻¹. B, Kv4.3 + KChIP2b. Fits (blue): α_V = 16.46443 (1/1 + exp−([V_m + 19.597]/14.879)) s⁻¹; β_V = 23.0838(1/1 + exp[V_m +84.130]/9.8974) s⁻¹. (C) Kv4.3 + KChIP2d; Fits (green): α_V = 17.9337(1/(1 + exp[−V_m − 24.3]/11.55) s⁻¹; β_V = 7.833 (1/1 + exp[V_m + 86.381]/8.4748) s⁻¹. Aii, Bii and Cii, overlay of theoretically predicted time constants ( = 1/[α +β]) with measured time constant values for Kv4.3 (Aii) Kv4.3 + KChIP2b (Bii), and Kv4.3 + KChIP2d (Cii). Note that for all expression conditions the values of τ_closed,inact monotonically merge into and overlap the values of τ_fast at −30 to −20 mV.

Summary: voltage dependence of Kv4.3 inactivation and recovery kinetics and effects of KChIP2b and 2d

A summarized overlay of the theoretically predicted time-constant–potential curves for each expression condition is illustrated in Fig. 8. The predicted time constant–potential curves of closed-state inactivation show an apparent depolarizing shift in the presence of KChIP2b and 2d. A portion of these shifts may be accounted for by +12 and +7 mV depolarizing shifts in V_½ values of steady-state inactivation produced by KChIP2b and 2d, respectively. However, such shifts cannot solely account for the large differences in inactivation and recovery kinetics produced by the two isoforms. To generate such regulatory effects, KChIP2b and 2d must also be altering inherent inactivation gating properties of Kv4.3 channels.

Ca²⁺ -independent kinetics of closed-state inactivation

For Kv4.3 + KChIP2d, we have previously demonstrated that τ_fast and τ_rec are Ca²⁺ -independent processes, while τ_slow is Ca²⁺ -dependent (Patel et al. 2002b). We thus hypothesized that if τ_rec, τ_closed,inact and τ_fast correspond to transitions of closed-state inactivation, then in the presence of KChIP2b or KChIP2d, τ_closed,inact should also be Ca²⁺ -independent. To test this hypothesis we analysed the effects of 100 μm BAPTA/AM on closed state inactivation kinetics at −50 mV. As anticipated, BAPTA/AM had no significant effects (P < 0.05) on τ_closed,inact for Kv4.3 alone or when expressed with KChIP2b or 2d (Kv4.3: control τ_closed,inact = 633.3 ± 66.6 ms, BAPTA τ_closed,inact = 710.2 ± 74.7 ms [n = 5]; Kv4.3 + KChIP2b: control τ_closed,inact = 870.7 51.2 ms, BAPTA τ_closed,inact = 928.6 ± 52.0 ms [n = 4]; and Kv4.3 + KChIP2d: control τ_closed,inact = 999.9 ± 157.8 ms, BAPTA τ_closed,inact = 1035.9 ± 191.5 ms [n = 4]). These results further support the hypothesis that τ_rec, τ_closed,inact and τ_fast correspond to Ca²⁺ -independent transitions associated with the closed-state inactivation mechanism.

Kinetic analysis of activation and deactivation

To quantitatively characterize the kinetics of activation and deactivation over the potential range −100 to +50 mV, two different voltage-clamp protocols were employed.

Activation

Activation kinetics (−40 to +50 mV) were quantified by fitting the time course of the rising phase of currents after subtraction of linearly scaled capacitive transients (using the 90% rise-time criterion; Campbell et al. 1993). Activation time constants, τ_act, were extracted by fitting currents to an assumed a⁴ sigmoid kinetic relationship (Fig. 9A). For all expression conditions, τ_act values displayed an exponential dependence upon membrane potential, progressively decreasing with depolarization (Fig. 9B). Consistent with the slight depolarization in the steady-state activation relationships produced by the KChIP2 isoforms (Fig. 3B), the τ_act–potential relationships in the presence of KChIP2b and 2d were slightly depolarized to that of Kv4.3 alone. However, in contrast to the effects of the two KChIPs on inactivation kinetics over the same voltage range, there was very little difference in the τ_act–potential relationships, with all three curves approaching essentially the same voltage-independent values by +50 mV (fits in Fig. 9 legend).

Deactivation

The time constants of deactivation, τ_deact, were determined by fitting the time course of tail current decay from −50 to −100 mV generated after a brief 10–15 ms depolarizing voltage clamp pulse to +50 mV (protocol in Fig. 10A, inset). Using this brief pulse protocol, tail currents could be fit with single exponential functions (Fig. 10A). However, in contrast to the minimal effects that KChIP2b and 2d exerted upon activation kinetics, both isoforms significantly altered deactivation kinetics, as manifested by an ∼2-fold decrease in the mean value of the deactivation time constant, τ_deact, at any given potential (fits given in Fig. 10B legend).

Figure 10. Voltage dependence of Kv4.3 deactivation kinetics.

A, representative Kv4.3 deactivation kinetics from −50 to −100 mV (10 mV increments). Curves fitted (except at −70 mV) with single exponential functions with following time constants: 31.8, 29.4, 12.3, 11.9 and 10.5 ms for −50, −60, −80, −90 and −100 mV, respectively. Extrapolated reversal potential E_rev = −72 mV. Calibration bar: 20 ms, 40 nA. B, overlay of the mean values of τ_deact for Kv4.3 (black squares, n = 9), Kv4.3 + KChIP2b (blue triangles, n = 13), and Kv4.3 + KChIP2d (green circles, n = 11). Mean data points fitted with the following Boltzmann functions: Kv4.3 (black), τ_deact = (25.121)/(1 + exp([−71.662 − V_m]/13.658)) + 36.342 ms; Kv4.3 + KChIP2b (blue), τ_deact = (25.681)/(1 + exp([−62.199 + V_m]/5.9925)) + 2.868 ms; and Kv4.3 + KChIP2d (green), τ_deact = (360.0973)/(1 + exp([8.8384 − V_m]/24.604)) + 361.78 ms.

Summary: theoretical voltage dependence of Kv4.3 activation and deactivation kinetics and effects of KChIP2b and 2d

To derive theoretical forward (α_V) and backward (β_V) rate constants of the activation and deactivation processes, the inverse time constants 1/τ_act and 1/τ_deact were analysed as a function of potential assuming a sigmoid a⁴ activation model. For each expression condition, the derived mean data points were then best fit to the sum of two saturating Boltzmann equations for α_V and β_V (equation fits and details in Fig. 11 legend). Overlays of the theoretically predicted time constants and the experimentally measured mean time constants for each expression condition are illustrated in Fig. 11A–C. For comparative purposes, the three theoretical τ_act/deact–potential curves are overlaid in Fig. 11D.

Figure 11. Theoretically predicted time constants of Kv4.3 activation, τ_act, and deactivation, τ_deact, and the effects of KChIP2b and 2d.

A, B and C, experimentally measured mean τ_act and τ_deact values overlaid with predicted fits for an a⁴ activation/deactivation scheme (τ_measured = 1/[α +4β]) for Kv4.3 (circles, black curve) (A) Kv4.3 + KChIP2b (triangles, blue curve) (B), and Kv4.3 + KChIP2d (squares, green curve) (C). Fits: Kv4.3: α = (−626.18)/(1 + exp([4.25813 + V_m]/19.97808)) + 637.28034 s⁻¹, 4β= (97.94299)/(1 + exp([89.22373 + V_m]/23.08609)) ms; Kv4.3 + KChIP2b, α = (−819.0252798)/(1 + exp([V_m − 14.63613]/23.40209)) + 819.02528 s⁻¹, 4β = (185.10174)/(1 + exp([74.23462 + V_m]/13.21161)) s⁻¹; and Kv4.3 + KChIP2d, α = (−1044.633789)/(1 + exp([V_m − 17.30539]/24.01797)) + 1044.63379 s⁻¹, 4β = (240.9402199)/(1 + exp([87.65039 +V_m]/16.36294) ms. D, overlay of theoretically predicted τ_act/deact curves. Kv4.3 (black), Kv4.3 + KChIP2b (blue), Kv4.3 + KChIP2d (green).

The τ_act/deact–potential curves display an apparent depolarizing shift in the presence of KChIP2b and 2d. As per our inactivation results (Fig. 8), a portion of these effects may be accounted for by the slight depolarizing shifts in V_½ values of steady-state activation produced by KChIP2b and 2d. However, again as was the case for inactivation, such shifts cannot solely account for the significant acceleration in deactivation kinetics produced by the two isoforms over the hyperpolarized range of potentials. Thus, while KChIP2b and 2d have minimal effects upon activation kinetics of Kv4.3 channels, they alter inherent deactivation kinetics.

Kv4.3 reopening currents and the effects of KChIP2 isoforms

Both Shaker and Kv3 channels have been reported to reopen upon membrane hyperpolarization (Demo & Yellen, 1991; Ruppersberg et al. 1991). In contrast, Bahring et al. (2001a) have reported that Kv4.2 channels expressed in HEK 293 cells do not reopen upon membrane hyperpolarization, but rather accumulate in a closed inactivated state(s) from which they directly recover via an ‘electrically silent’ pathway.

To determine if Kv4.3 channels reopen upon membrane hyperpolarization, modified long duration tail current protocols were applied first in 2 mm and then 98 mm [K⁺]_o (protocol in Fig. 12A, inset). Following a 1000 ms depolarizing pulse to +50 mV, for all three expression conditions non-conventional tail currents were generated upon repolarization (Fig. 12A–C). In contrast to the results obtained using the brief pulse protocol (Fig. 10), the tail currents generated using the longer pulse protocol displayed an initial rising phase (or ‘hook’) followed by a slower conventional deactivating phase. Importantly, for all expression conditions the amplitude of these hooked tail currents increased when [K⁺]_o was increased from 2 to 98 mm. These results contrast with the general predictions of the Kv4.2 gating model proposed by Bahring et al. (2001a).

Figure 12. ‘Hooked’ Kv4.3 reopening currents generated upon hyperpolarization and effects of KChIP2b and 2d.

Voltage clamp protocol schematically illustrated in A, inset. A, B and C, representative current recordings obtained first in 2 and then 98 mm[K⁺]_o for Kv4.3 alone (A) Kv4.3 + KChIP2b (B) and Kv4.3 + KChIP2d (C). To account for differences in driving force, currents have been normalized to their peak values at +50 mV. D, comparative overlay of normalized peak currents recorded in 98 mm[K⁺]_o for Kv4.3 alone (black), Kv4.3 + KChIP2b (blue), and Kv4.3 + KChIP2d (green). The relative amplitudes of reopening currents (−120 mV) are smallest for Kv4.3, intermediate for Kv4.3 + KChIP2d, and largest for Kv4.3 + KChIP2b. Calibration bar: 250 ms.

If KChIP2 isoforms promote gating shifts such that the open-state inactivation mechanism becomes more prominent at depolarized potentials, then (i) hooked reopening currents should become more prominent in their presence; and (ii) the relative amplitudes of the reopening currents should be KChIP2 isoform specific. Representative results consistent with this hypothesis are illustrated in Fig. 12D. When the amplitudes of the peak outward currents elicited at +50 mV were normalized, the relative peak amplitudes of the inward hooked tail currents generated upon hyperpolarization were smallest for Kv4.3, intermediate for Kv4.3 + KChIP2d, and greatest for Kv4.3 + KChIP2b. These observations support our hypothesis that Kv4.3 has an obligatorily coupled open-state inactivation mechanism that is enhanced in the presence of KChIPs.

Discussion

Kv4.3 displays two separate and distinct mechanisms of inactivation – one that occurs from preactivated closed states, and a second that appears to proceed exclusively from the open state. The closed-state mechanism is prominent and appears to account for steady-state inactivation. Our analysis also clearly indicates that the values of τ_closed,inact monotonically merge into and overlap τ_fast. We thus conclude that τ_closed,inact and τ_fast both correspond to voltage-dependent transitions involved in the closed-state inactivation pathway. In contrast, we were only able to resolve values of τ_slow at depolarized potentials. The distinct voltage dependence and magnitudes of τ_slow suggest it corresponds to an inactivation mechanism that may only be reached when the channel enters the open state.

KChIP2b and 2d significantly modified all of the kinetic processes associated with these inactivation transitions in that both isoforms: (i) accelerated the time constants of recovery; (ii) slowed the time constants of closed-state inactivation; (iii) accelerated the slow time constant of inactivation at depolarized potentials; (iv) slowed the fast time constant of inactivation; and (v) increased the fractional contribution of the slow component of inactivation at depolarized potentials. Although the effects of KChIP2b and 2d on Kv4.3 inactivation and recovery differed in magnitude, the voltage dependence of the respective τ_closed,inact and τ_fast values still monotonically merged into each other. Thus, similar to Kv4.3 expressed alone, we conclude that in the presence of KChIP2b and 2d closed-state inactivation and the fast component of macroscopic inactivation both correspond to voltage-dependent transitions involved in the closed-state inactivation pathway, while the slow component of macroscopic inactivation corresponds to transitions of the open-state inactivation pathway.

We have previously demonstrated that, in the presence of KChIP2d, both τ_fast and τ_rec are Ca²⁺ -independent, while τ_slow is Ca²⁺ -dependent (Patel et al. 2002b). Our present results indicate that in the presence of KChIP2b and 2d τ_closed,inact is also Ca²⁺ -independent. The shared Ca²⁺-independency of recovery, closed-state inactivation, and fast macroscopic inactivation further supports our hypothesis that these three mechanisms correspond to transitions regulating closed-state inactivation. In contrast, in the presence of KChIP2d, τ_slow is Ca²⁺ -dependent (Patel et al. 2002b). These results support the proposal that Kv4.3 inactivation is regulated by two distinct mechanistic pathways selectively regulated by KChIP2 isoforms.

In contrast to inactivation and recovery kinetics, the effects of either KChIP2b or 2d on Kv4.3 activation kinetics were minimal. Nonetheless, both isoforms significantly accelerated (∼2-fold) the kinetics of Kv4.3 deactivation measured using the short pulse (10–15 ms) protocol. Similar to the effects on inactivation and recovery, these regulatory effects cannot be solely explained by simple shifts in the voltage dependence of the steady-state activation curves. KChIP2b and 2d therefore alter the inherent kinetics of the open to closed (O → C) state gating transition (see Fig. 13). Whether this indicates that this transition is allosterically coupled to other transitions governing slower open-state inactivation and/or recovery is presently unclear.

Figure 13. Proposed Kv4.3 gating model.

C_n, closed-state(s); I_C, inactivated closed-state(s); O, open state; and I_O, open inactivated state. Forward (α) and backward (β) rate constants for each transition as indicated. In the presence of KChIP2 isoforms closed-state inactivation is slowed, recovery is accelerated, and open-state inactivation is promoted. Of all of the inactivation processes, only open-state inactivation is Ca²⁺ -dependent.

Proposed gating model for Kv4.3

The simplest state diagram for Kv4.3 channel gating which is consistent with all of our present data is illustrated in Fig. 13. In this model we have assumed that each of the four Kv4.3 α subunits gate independently between closed and open states. This portion of the gating pathway would thus correspond to a Hodgkin–Huxley-like independent activation/inactivation gating mechanism (Hodgkin & Huxley, 1952; Hille, 2001b). Upon reaching the open-state, we propose that inactivation can proceed through either (i) a closed-state mechanism or (ii) an obligatorily coupled open-state mechanism. However, recovery kinetics would be dominated by the closed-state pathway, as manifested by our observation that recovery could be well described as a single exponential process.

As anticipated from this model, KChIPs would slow closed-state inactivation, accelerate recovery, and produce overall shifts in Kv4.3 gating kinetics favouring the slower open-state inactivation pathway. This model also predicts that the fraction of Kv4.3 channels that inactivate by the proposed obligatorily coupled open-state mechanism must reopen upon hyperpolarization before reentering the closed-state inactivation pathway. Thus, for short duration depolarizing pulses ‘conventional’ tail current deactivation kinetics would be observed (very few channels will have entered the open inactivated state), while for long duration depolarizing pulses hooked reopening currents would be predicted (a greater percentage of channels must return through the open-state before recovering via the closed-state pathway). These predictions are consistent with our experimental results on reopening currents (Fig. 12). In addition, the model also predicts that not only are the relative magnitudes of reopening currents KChIP2 isoform specific (Fig. 12D), but they should also scale according to the voltage dependence of the A_fast/(A_fast + A_slow) ratios. If reopening currents fail to appropriately scale as predicted, then this would suggest an additional recovery pathway existing between the closed- and open-state inactivation mechanisms. Finally, this model also predicts that in the presence of KChIP2 isoforms, reopening currents would be minimized with decreased [Ca²⁺]_i and maximized under conditions of elevated [Ca²⁺]_i levels. These specific predictions will be tested in detail in future studies. In combination with our present kinetic results under ‘basal’ conditions, these future studies will allow quantitative mathematical analysis of the applicability of the proposed kinetic model under varying [Ca²⁺]_i levels, as might be seen in cardiac myocytes.

Interestingly, in the presence of KChIP2b and 2d, increasing [K⁺]_o from 2 to 98 mm significantly altered Kv4.3 inactivation kinetics at +50 mV (Fig. 12). Our proposed model does not account for this observation. We are presently analysing this effect and attempting to determine the underlying mechanism(s). A final generalized Kv4.3/KChIP2 gating model will need to include the effects of varying [Ca²⁺]_i as well as the effects of varying [K⁺]_o. The fact that [K⁺]_o is a regulator of Kv4.3 gating has not been adequately addressed in most studies, and may provide one basis for the common observation that KChIP isoforms coexpressed with Kv4 channels fail to completely reconstitute all of the kinetic characteristics of native I_to,fast.

Comparison to previous studies and Kv4 gating models

Our general results are consistent with previous studies indicating the importance of preactivated closed-state inactivation transitions in regulation of Kv4 function (Jerng & Covarrubias, 1997; Bahring et al. 2001a; Beck et al. 2002). However, our analysis yields results that are incompatible with predictions of previously proposed models of Kv4 channel gating and regulation.

Our data indicate that a fraction of Kv4.3 channels reopen upon membrane repolarization (Demo & Yellen, 1991; Ruppersberg et al. 1991), with the relative sizes of these reopening currents being largest in the presence of KChIP2b and 2d. The Kv4.2 gating model proposed by Bahring et al. (2001a) cannot account for these results. Whether this discrepancy is due to differences in expression systems, recording conditions, and/or differences in gating mechanisms between Kv4.2 versus Kv4.3 is at present unclear. The latter is a distinct possibility, since there are clear quantitative and biophysical differences in the inactivation characteristics of Kv4.1 versus Kv4.3 channels (Beck et al. 2002; Wang et al. 2002). This suggests that a generalized gating model may not be appropriate for all Kv4 channels and KChIP isoforms.

Our results also clearly indicate that: (i) τ_closed,inact and τ_fast correspond to Kv4.3 closed-state inactivation; (ii) τ_slow corresponds to open-state inactivation; and (iii) KChIP2b and 2d slow closed-state inactivation. The slowing of closed-state inactivation by KChIP2b and 2d cannot be solely attributed to simple depolarizing shifts in the steady-state inactivation curve but is rather due to alteration of inherent Kv4.3 inactivation gating kinetics. The Kv4/KChIP1 gating model proposed by Beck et al. (2002) cannot explain our Kv4.3/KChIP2 findings.

We suggest two possible explanations for the differences between our results and those of Beck et al. (2002). First, there may be differences in the regulatory effects of KChIP1 versus KChIP2 isoforms on Kv4.3 function. This is a very plausible suggestion, considering the marked heterogeneity in the regulatory effects of KChIP2 isoforms upon Kv4.3 function (Patel et al. 2002a). Since KChIP1 isoforms are not expressed in cardiac myocytes we have not pursued this possibility further. Second, the proposal that KChIPs accelerate Kv4 closed-state inactivation was based upon kinetic measurements conducted solely at −50 mV (Beck et al. 2002). However, the effects that KChIP1 exerts on the overall voltage dependence of Kv4 closed-state inactivation and recovery are unclear. If KChIP1 alters the voltage dependence and kinetics of recovery in a manner similar to that produced by KChIP2b and 2d, then it is possible that measurements of closed-state inactivation kinetics conducted at −50 mV may be significantly influenced by altered recovery kinetics. The net effect would be an apparent acceleration of ‘closed-state inactivation’ similar to the apparent acceleration we observed at more hyperpolarized potentials where recovery becomes the predominant process (Fig. 5).

Proposed structure–function relationships of Kv4.3–KChIP2 isoform interactions

Here we propose a model of KChIP2b/2d regulation of Kv4.3 function based on our present and previous observations, previous studies on Kv4 channel function, and comparison of the potential KChIP2 isoform structure to the known crystal structure of human frequenin. The fact that KChIP2d (minimal isoform with 1 EF hand) is functional indicates that the common C-terminal domain of KChIP2 isoforms is sufficient for inducing regulation of Kv4.3 channel function (Patel et al. 2002b). Nonetheless, KChIP2b (largest isoform with 4 EF hands) produced effects on inactivation and recovery that were quantitatively different from those produced by KChIP2d. Therefore, to begin to differentiate which regulatory effects result from physical interactions of KChIP2 isoform binding to the Kv4.3 N-terminus and which result from Ca²⁺ -mediated interactions with the KChIP EF-hands, we divide our results into Ca²⁺ -independent and Ca²⁺ -dependent effects of KChIP2b and 2d on Kv4.3 function.

Ca²⁺ -independent effects

Human frequenin (HuFrq), also known as neuronal calcium sensor-1, slows inactivation kinetics of Kv4.2 and Kv4.3 channels but only exerts minimal effects on recovery (Nakamura et al. 2001; Guo et al. 2002b). HuFrq also immunoprecipitates with mouse ventricular Kv4.3, suggesting that the two molecules may associate in native cardiac tissue (Guo et al. 2002b). Alignment of amino acid sequences indicates that HuFrq shares ∼59% similarity (44% identity) with the C-terminal sequence of ferret KChIP2b (Fig. 14). Based upon these functional similarities, and the fact that the crystal structure of KChIP2 isoforms has not yet been determined, we will use the crystal structure of HuFrq as a potential model for KChIP2 isoforms (Bourne et al. 2001).

Figure 14. Amino acid sequence alignment of KChIP2b and human frequenin (HuFrq).

HuFrq GenBank number AF186409. Identical amino acids are highlighted in black. Amino acids present in the hydrophobic crevice in HuFrq are indicated by: below the sequence. Asterisks at the top mark every 10th amino acid.

As we have previously suggested (Patel et al. 2002b), the crystal structure of HuFrq displays three characteristics that may be critical for comparison to KChIP2 isoform structure – function relationships: (i) a hydrophobic crevice on one face of the molecule; (ii) four EF-hands aligned on the face opposite the hydrophobic crevice (Bourne et al. 2001; Ren et al. 2003); and (iii) a prominent loop protruding from the periphery of the molecule. These characteristics are illustrated in Fig. 15.

Figure 15. Proposed key features in the structure of human frequenin with potential applications to KChIP2 function.

NCBI structure IG8I. The two opposing faces of the HuFrq structure are labelled ‘crevice face’ and ‘EF-hand face’. A, view of the hydrophobic crevice of HuFrq. Amino acids present in the hydrophobic crevice are shaded dark grey. Note that the amino acids in the crevice are not as apparent on the EF-hand face. B, amino acids that bind Ca²⁺ in EF-hands 2, 3 and 4 are shaded dark grey. Note that these amino acids contribute to the EF-hand face but are not as apparent on the crevice face. C, amino acids shaded grey at the peripheral ‘loop’ of HuFrq that correspond to amino acids mutated in KChIP2d shown to be involved in Ca²⁺ -independent regulation of recovery (Patel et al. 2002b).

It has been suggested that a hydrophobic crevice similar to that in HuFrq may exist in KChIPs and acts as the site involved in binding to the Kv4 N-terminus (Bourne et al. 2001). In the hydrophobic crevice of HuFrq, 48 amino acids are exposed. In ferret KChIP2b, 29 of these amino acids are identical and 11 are conservative substitutions (refer to Fig. 14). Because of this sequence similarity, we propose that a similar hydrophobic crevice exists in KChIP2b. The corresponding sequence region in KChIP2d also suggests that it may contain a modified hydrophobic crevice structure.

A region of ∼10 amino acids is necessary for KChIP binding to the N-terminus of Kv4.2 channels (Bahring et al. 2001a). The stretch of amino acids identified, FARAAAVGWL, is composed of mainly hydrophobic residues. We thus propose that the crevice of the KChIP2 structure binds to the corresponding N-terminal hydrophobic residues in ferret Kv4.3, FARAAAIGWM (Fig. 16).

Figure 16. Proposed model for KChIP2—Kv4.3 interactions.

KChIPs bind to the N-termini of Kv4.3 channels (sequence of ferret Kv4.3 as indicated) via a hydrophobic crevice. Hydrophobic surfaces of the KChIP molecules are shaded, hydrophilic surfaces are crosshatched. Ca²⁺ ions are indicated as black dots. The steric effects of KChIP binding to the Kv4.3 N-terminus leads to slower closed-state inactivation kinetics and faster recovery kinetics. The majority of KChIPs have 4 EF-hands, only three of which bind Ca²⁺. All of the EF-hands are on the face of the molecule opposite the hydrophobic crevice. A, in the Ca ²⁺ – bound state the EF-hands expose a hydrophobic surface on the KChIP molecule. B, in the Ca²⁺ -unbound state a hydrophilic surface is presented on the KChIP molecule. Conformational changes in KChIP structure mediated by Ca²⁺ binding to EF-hands will thus govern shifts toward Ca²⁺ -dependent processes, namely open-state macroscopic inactivation.

Since both inactivation time constants τ_closed,inact and τ_fast are Ca²⁺ -independent, we assign changes in these properties in the presence of KChIP2b or 2d to the effects of N-terminus binding. However, it is unclear if the resultant regulatory effects (slowing of closed-state inactivation, acceleration of recovery) are due to simple steric constraint of the N-terminus. This uncertainty arises from the observation that deletion of the N-terminus of Kv4.2 channels does not slow closed-state inactivation or alter recovery kinetics (Bahring et al. 2001a). It is thus possible that the Kv4.3 N-terminus may not function as an ‘inactivation gate’ at all, but rather as a scaffold network for KChIP-mediated effects on inactivation and recovery. Such N-terminus mediated binding may allow for proper orientation of the putative loop domain of KChIP2 isoforms, a region that we have demonstrated is involved in regulation of Kv4.3 recovery kinetics by KChIP2d (Patel et al. 2002b). Resolution of these issues will require further combined site-directed mutagenesis and kinetic studies of Kv4.3 channels.

Ca²⁺ -dependent effects

We propose that the Ca²⁺ -dependent regulatory effects of KChIP2 isoforms are based upon structural changes mediated by Ca²⁺ in the EF-hand region. This proposal is appealing since it would allow Ca²⁺ binding to the EF-hands to produce localized conformational changes without altering N-terminus binding effects on the opposite face of the KChIP molecule (Fig. 16). In general, Ca²⁺ binding to EF-hands results in sequestration of hydrophilic amino acids and exposure of hydrophobic amino acids (Ikura, 1996; Lewit-Bentley & Rety, 2000). Such localized changes in hydrophilicity and hydrophobicity may alter the interactions of KChIPs with other parts of the channel molecule involved in the slower open-state inactivation mechanism. Since KChIP2d is a functional KChIP, the single EF-hand in the C-terminus (corresponding to the fourth EF-hand of the larger KChIP2 isoforms) is sufficient for mediating Ca²⁺ -dependent regulation of open-state inactivation. In this regard, it is very interesting to note that a recent study has indicated that the fourth EF-hand of KChIP1 displays the highest Ca²⁺ affinity and appears to be largely responsible for the Ca²⁺ -dependent functional properties of KChIP1 (Chang et al. 2003).

In summary, our previous analysis of the effects of the calcium chelator BAPTA on Kv4.3 + KChIP2d indicated that acceleration of recovery kinetics is a Ca²⁺ -independent process, while regulation of the slower component of inactivation is Ca²⁺ -dependent (Patel et al. 2002b). Our present model is compatible with these previous observations in that it separates KChIP2-mediated regulation of Kv4.3 inactivation into distinct Ca²⁺ -independent closed-state and Ca²⁺ -dependent open-state mechanisms, thus allowing KChIP2 isoforms to regulate recovery and closed-state inactivation kinetics independently of slower open-state inactivation kinetics.

Our model also has interesting implications for the results reported by Schrader et al. (2002) on the potential role(s) of phosphorylation in KChIP-mediated regulation of Kv4 function. These investigators reported that phosphorylation of Kv4.2 only produced regulatory effects in the presence of KChIP3. Interestingly, the regulatory effects of phosphorylation were manifested as a slowing of inactivation kinetics (particularly the slow time constant), with no effects on recovery kinetics. This regulatory pattern is comparable to our previous results on the effects of BAPTA on Kv4.3 + KChIP2d (Patel et al. 2002b). At present we cannot assign a role for phosphorylation in Kv4.3/KChIP2 interactions. However, based upon our proposed model, a reasonable hypothesis would be that the effects of localized charge added by phosphorylation of Kv4.2 are similar to the effects exerted by charges exposed on the hydrophilic KChIP EF-hand face in the calcium-unbound state. If, when expressed alone, Kv4.2 favours the fast component of inactivation via predominance of a closed-state inactivation mechanism, then phosphorylation would have minimal regulatory effects since the new charge distribution affects mainly the slower open-state inactivation mechanism. Only when KChIPs and Kv4.2 are coexpressed is the slower open-state inactivation mechanism more prominent, thus allowing the regulatory effects of phosphorylation to be more fully manifested. It will be interesting to see if this hypothesis is verified by future studies.

Based upon our current data we cannot assign specific parts of Kv4.3 to Ca²⁺ -dependent interactions with the EF-hands of KChIP2 isoforms, and therefore open-state inactivation. However, a previous study has suggested involvement of a region located near the inner pore domain of Kv4.3 in governing slow inactivation (Wang et al. 2002). Mutation of two valines to isoleucines in this region produced only modest slowing of inactivation when the mutant channel was expressed alone, but when coexpressed with KChIPs inactivation was significantly slowed. These results suggest that a region in the inner pore domain of Kv4.3 is involved in open-state inactivation and gating transitions in this domain are allosterically promoted by KChIP2 isoforms.

Potential physiological and therapeutic implications

If our results are applicable to native I_to,fast in cardiac myocytes, then the inherent kinetic behaviour of this current will be much more complex than predicted by current models based upon conventional patch clamp results. Specifically, (i) due to increased [Ca²⁺]_i during the normal excitation–contraction coupling cycle in cardiac myocytes, inactivation kinetics of I_to,fast will be altered such that it will be a much more prominent repolarizing current during all phases of the action potential plateau than is presently believed; and (ii) reopening of channels from the obligatorily coupled inactivated open-state may be a significant contributor to final (‘phase 3’) repolarization. Our data indicate that the voltage dependencies and magnitudes of each of these regulatory effects are KChIP2 isoform specific. Differences in the regulatory effects of KChIP2 isoforms on Kv4.3 gating kinetics may therefore provide a mechanism for generating further heterogeneity of native I_to,fast current phenotypes in cardiac myocytes.

The fact that KChIP2 isoforms slow closed-state and promote open-state inactivation has important pharmacological and therapeutic implications, in that the state- and use-dependent effectiveness of any given Kv4.3/I_to,fast blocker will depend upon the presence of both KChIP2 isoforms and the level of [Ca²⁺]_i. These regulatory effects have not been accounted for in previous pharmacological studies of Kv4.3 channels and their relationship to native I_to,fast. KChIP2 isoforms may thus provide an important and much needed alternative substrate for development of specific, effective and safe antiarrhythmic agents and/or genetic approaches aimed at modulating ventricular repolarization under various disease states.