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Modeling of the adrenergic response of the human I_Ks current (hKCNQ1/hKCNE1) stably expressed in HEK-293 cells

Safety and Exploratory Pharmacology, Safety Assessment, Merck Research Laboratories, West Point, Pennsylvania

Submitted 24 April 2008 ; accepted in final form 28 July 2008

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX: THE HODGKIN-HUXLEY... REFERENCES

 
Stable coexpression of human (h)KCNQ1 and hKCNE1 in human embryonic kidney (HEK)-293 cells reconstitutes a nativelike slowly activating delayed rectifier K⁺ current (HEK-I_Ks), allowing β-adrenergic modulation of the current by stimulation of endogenous receptors in the host cell line. HEK-I_Ks was enhanced two- to fourfold by isoproterenol (EC₅₀ = 13 nM), forskolin (10 µM), or 8-(4-chlorophenylthio)adenosine 3',5'-cyclic monophosphate (50 µM), indicating an intact cAMP-dependent ion channel-regulating pathway analogous to the PKA-dependent regulation observed in native cardiac myocytes. Activation kinetics of HEK-I_Ks were accurately fit with a novel modified second-order Hodgkin-Huxley (H-H) gating model incorporating a fast and a slow gate, each independent of each other in scale and adrenergic response, or a "heterodimer" model. Macroscopically, β-adrenergic enhancement shifted the current activation threshold to more negative potentials and accelerated activation kinetics while leaving deactivation kinetics relatively unaffected. Modeling of the current response using the H-H model indicated that observed changes in gating could be explained by modulation of the opening rate of the fast gate. Under control conditions at nearly physiological temperatures (35°C), rate-dependent accumulation of HEK-I_Ks was observed only at pulse frequencies exceeding 3 Hz. Rate-dependent accumulation of I_Ks at high pulsing rate had two phases, an initial staircaselike effect followed by a slower, incremental accumulation phase. These phases are readily interpreted in the context of a heterodimeric H-H model with two independent gates with differing closing rates. In the presence of isoproterenol after normalizing for its tonic effects, rate-dependent accumulation of HEK-I_Ks appeared at lower pulse frequencies and was slightly enhanced (25%) over control.

slowly activating cardiac delayed rectifer potassium current; human embryonic kidney-293 cells; β-adrenergic modulation; KCNQ1; KCNE1

The role that I_Ks plays in cardiac repolarization is particularly important for its ability to counterbalance the depolarizing effect of enhanced L-type Ca²⁺ current during sympathetic stimulation of the heart (4, 5, 12, 23). This is highlighted by the finding that LQT1 mutations are usually symptomatically silent in many carriers until sudden exertion or emotional upset triggers cardiac events (7, 54). I_Ks is distinguished from the rapidly activating delayed rectifier K⁺ current (I_Kr) by its gating kinetics, pharmacological sensitivity, and other properties, notably its considerable enhancement by β-adrenergic stimulation (20, 42). The properties of I_Ks constitute an important cardiac repolarization reserve invoked especially during elevated sympathetic tone (33).

Modeling of the effect of direct β-adrenergic modulation of I_Ks (e.g., by isoproterenol) has traditionally been limited to native cardiac myocytes. Electrophysiological study of native I_Ks is complicated by the technical difficulty of isolating I_Ks due to the presence of other cardiac K⁺ currents, such as I_Kr, whose kinetics overlap those of I_Ks, as well as the relatively small size of native I_Ks, especially at lower temperatures. The difficulty of obtaining healthy human cardiac myocytes for native I_Ks studies has limited studies of β-adrenergic modulation of human I_Ks (23).

Until recently, modulation of recombinant I_Ks in heterologous expression systems has relied on addition of second messengers such as cAMP and phosphatase inhibitors to the intracellular recording solution (47) rather than β-adrenoceptor-mediated activation of endogenous G protein-coupled signaling pathways that are present in the host background. In this context, we stably expressed hKCNQ1 and hKCNE1 in human embryonic kidney (HEK)-293 cells. Expression of hKCNQ1 and hKCNE1 in HEK-293 cells reconstitutes not only the voltage- and temperature-dependent gating characteristics and pharmacological responses but also the β-adrenergic modulation of native I_Ks (11). We have taken advantage of this isolated I_Ks expression system to derive an accurate mathematical model of I_Ks gating that allows the effects of β-adrenergic stimulation to be easily quantified. The accuracy and simplicity of this model of I_Ks lends itself to incorporation into mathematical models of the cardiac action potential as well as to differentiation of the effects of pharmacological modulation or genetic alteration of I_Ks. These studies validate the stable expression of hKCNQ1/hKCNE1 in the HEK-293 background as a highly useful model of native I_Ks.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX: THE HODGKIN-HUXLEY... REFERENCES

 
Establishment and maintenance of the HEK-I_Ks cell line. hKCNQ1 (hKvLQT1) and hKCNE1 (hminK) (licensed and obtained from the University of Utah) were respectively cloned into pZeoSV2+ and pcDNA1neo vectors (Invitrogen) and stably transfected into HEK-293 cells (ATCC). Cells were grown in Dulbecco's modified Eagle's medium supplemented with 10% fetal bovine serum, 2 mM L-glutamine, 10 U/ml penicillin, 50 µg/ml streptomycin, 0.5 mg/ml Zeocin, and 0.4 mg/ml G418 antibiotics (Invitrogen Life Technologies). Cells were incubated at 37°C in 5% CO₂ and grown in T75 tissue culture flasks (Corning Costar) to near confluence, at which time they were passaged and plated in six-well plates. Before electrophysiological recording, cells were gently trypsinized in 0.05% trypsin-EDTA solution (Invitrogen Life Technologies), dislodged from the growth substrate, and then resuspended and maintained in the culture medium until electrophysiological recording.

Electrophysiological recordings. A small aliquot of HEK-293 cells stably expressing hKCNQ1/hKCNE1 was placed into a glass-bottom perfusion chamber containing a HEPES-buffered solution (HBS). Single HEK-I_Ks cells were studied using the whole cell configuration of the patch-clamp technique with glass microelectrodes (Warner Instruments G150F-4) with tip resistances of 1.5–3 M containing (in mM) 119 K-gluconate, 15 KCl, 3.2 MgCl₂, 5 HEPES, 5 EGTA, and 5 K₂ATP, adjusted to pH 7.35 with KOH. Cells were continuously superfused with HBS containing (in mM) 132 NaCl, 4 KCl, 1.8 CaCl₂, 1.2 MgCl₂, 10 HEPES, and 11.1 glucose, adjusted to pH 7.35 with NaOH. HEK-I_Ks was recorded at monitored temperatures ranging from 19 to 36°C and was quantified as the peak tail current amplitude during repolarization to the holding potential (V_h) following a step depolarization (V_step). The temperature of the bath perfusate was measured with a calibrated thermistor positioned near the cell and was maintained at desired settings with a temperature controller (Warner Instruments TC-344B). For cardiac ventricular myocyte recordings, the bath solution was nominally Ca²⁺-free HBS with 0.4 µM nisoldipine to block L-type Ca²⁺ channels. The pipette solution contained (in mM) 500 K-gluconate, 25 KCl, and 5 K₂ATP, adjusted to pH 7.35 with KOH. Guinea pig ventricular myocytes were isolated by enzymatic digestion of the heart using the Langendorff perfusion method (38). Guinea pig myocyte isolations were conducted according to study protocols reviewed and approved by the Institutional Animal Care and Use Committee. In myocytes, cardiac I_Ks was quantified as the amplitude of the time-dependent activating outward current at the end of a 1-s V_step to +50 mV from a V_h of –50 mV.

The benzodiazepine-selective I_Ks inhibitors L-768,673 and L-735,821 were prepared as 2 mM stock solutions in DMSO. Forskolin (Sigma F-6886) was prepared as a 100 mM stock solution in DMSO. The cAMP analog 8-(4-chlorophenylthio)cAMP sodium (CPT-cAMP; Sigma C-3912) was prepared as a 50 mM stock solution in distilled water. Isoproterenol (Sigma I-6504) was prepared as a 10 mM stock solution in 0.1% ascorbic acid in distilled water. Working dilutions were made fresh before each recording by diluting stock solutions directly into bath solution. Final DMSO concentrations did not exceed 0.1%.

Whole cell currents were elicited with a voltage-clamp amplifier (Axopatch 200B; Axon Instruments) and recorded through a Digidata 1322a interface (Axon Instruments) to an IBM-compatible computer (Compaq). Voltage-clamp protocols and data acquisition and analyses were performed using Clampex v8.2 software (Axon Instruments). The voltage drop across the access resistance was dynamically compensated 80%, while the whole cell capacitance current was subtracted from the clamp current before acquisition using the existing Axopatch 200B circuitry. The resulting whole cell currents were amplified, low-pass filtered with a cutoff at 1 kHz, digitally sampled at 2–5 kHz, and stored to disk. The bath temperature was synchronously recorded for off-line analysis and to monitor temperature-induced changes in current amplitude.

Fitting of whole cell currents. Activating outward currents elicited with depolarizations to activating potentials, V_step, were fitted with Hodgkin-Huxley (H-H) model-derived equations in the form of products of single exponentials,

where the order of the H-H model, n, designates the number of independent, first-order gates that must transition from a closed to an open state before ions can flux through the channel (21), and _Ai is the time constant of the reequilibration of each independently activating gate with index i = 1, 2,... n. In contrast to standard H-H models, where _Ai values are identical, we allowed each _Ai value to vary independently. Least-squares fits to the data, with n ranging from 1 to 4, were evaluated.

Deactivating HEK-I_Ks tail currents on repolarization to the tail potential, V_tail, were fit with either a single exponential or the sum of two decaying exponentials of the form

where Ai is the amplitude of each exponential component with deactivating time constant _Di and B is the steady-state current, if any. If V_tail was below the activation threshold of the current, B became negligible and the deactivating tail currents were accurately fit with a single decaying exponential.

Calculation of Q₁₀: temperature dependence. Time constants () derived from fits of activation or deactivation kinetics were plotted as a function of temperature and fit with the Arrhenius equation: 1/ = k = A·exp(–Ea/RT), where k is a rate constant at the absolute temperature T, Ea is the activation energy, R is the gas constant, and A is a constant factor. Rearranging this equation as ln = (Ea/R)/T – ln A indicates that the logarithm of varies linearly as a function of 1/T with the ratio Ea/R defining the slope of this linear relationship. Thus Q₁₀ values were calculated from the slope of the Arrhenius plot.

For evaluating the voltage dependence of activation and deactivation, values were derived from fitting of the activation and deactivation time courses. It was assumed that voltage-sensitive gating transition rates followed the relation 1/ exp[(zF/RT)(V)], where z is the gating charge, F is Faraday's constant, R and T are as defined above for the Arrhenius equation, and V is the transmembrane potential. According to this relation, at a fixed temperature, the logarithm of varies as a linear function of the membrane potential, and the slope of this relation yields the span of voltage over which an e-fold change in can be expected. To fully define the relation between and voltage, the value of at a given membrane potential was averaged for all cells and reported with the averaged slope for all cells. For determination of V_mid, the potential of half-maximal activation of HEK-I_Ks, normalized I_Ks tail amplitudes were fit with the Boltzmann relation, {1/(1 + exp[(z_dF/RT)(V – V_mid)])}, where constants are as defined above and (z_dF/RT) is the slope factor k.

Statistics. The reported significance of observed changes in selected parameters was calculated using the two-tailed paired Student's t-test. The P values obtained are indicated.

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX: THE HODGKIN-HUXLEY... REFERENCES

 
Pharmacological isolation and characterization of HEK-I_Ks. The pharmacological sensitivity of the outward currents resulting from the stable coexpression of hKCNQ1 and hKCNE1 in HEK-293 cells (HEK-I_Ks) was probed using potent and selective small molecule inhibitors of native I_Ks. L-768,673 and L-735,821 are benzodiazepines that have been shown to selectively inhibit native I_Ks of guinea pig ventricular myocytes at nanomolar concentrations (39). Figure 1A illustrates the concentration dependence of inhibition by L-768,673 and L-735,821 of HEK-I_Ks outward time-dependent activating and deactivating tail currents recorded at 35°C. An initial variable instantaneous HEK-293 background current (58) was insensitive to these I_Ks inhibitors at concentrations (100 nM) that completely inhibited HEK-I_Ks. Thus the time-independent kinetics of a background current, I_const, was effectively revealed. Figure 1B illustrates a comparable effect of L-768,673 on native I_Ks in guinea pig ventricular myocytes at 35°C. The recording of native myocyte current illustrates the difficulty of isolating the I_Ks current in myocytes given that other K⁺ currents, notably the inward rectifier current I_K1 as well as I_Kr, can introduce considerable instantaneous and holding current offsets as well as contribute to the time-dependent activating and deactivating tail currents. Figure 1C illustrates the concentration dependence and reversibility of the effect of L-768,673 on the amplitude of the HEK-I_Ks tail current. L-768,673 was applied at increasing concentrations of 3, 10, and 100 nM, separated by an intervening washout period (3 to 10 nM) that revealed the reversibility of the HEK-I_Ks inhibition. The average fraction of control tail current amplitude remaining after equilibration at various inhibitor concentrations is plotted in Fig. 1D, and fitting of the Hill equation to these data yielded IC₅₀ values of 2.4 and 0.8 nM for inhibition of HEK-I_Ks by L-768,673 and L-735,821, respectively. The IC₅₀ value for L-768,673 inhibition of HEK-I_Ks (2.4 nM) was comparable to that (within 3-fold) for native I_Ks (7.3 nM) of guinea pig ventricular myocytes, whereas L-735,821 was 10 times more potent on HEK-I_Ks (0.8 nM) compared with native I_Ks (8 nM).

View larger version (19K): [in this window] [in a new window]   Fig. 1. Pharmacological isolation and characterization of slowly activating delayed rectifier currents in HEK-293 cells (HEK-IKs). A: inhibition of HEK-IKs time-dependent outward currents by L-768,673 and L-735,821. Voltage steps were applied for 1 or 2 s to +50 mV from a holding potential (Vh) of –50 mV at interpulse intervals of 10–15 s. Superimposed currents are shown from before (control, ctl) and after equilibration with IKs inhibitors at the indicated concentrations (nM). Slowly activating outward and deactivating tail currents were blocked to similar degrees and were completely inhibited by saturating concentrations of IKs inhibitors. The instantaneous time-independent current during a step to +50 mV was insensitive to IKs inhibitors. B: inhibition of native IKs of a guinea pig ventricular myocyte by L-768,673. The large offset in the holding current (arrow) is due largely to the inward rectifier current, IK1, and a small steady-state activation of the rapidly activating current, IKr, and illustrates one difficulty of isolating native IKs. C: determination of potency of L-768,673 on HEK-IKs peak deactivating tail currents at –50 mV. Voltage steps were applied at 10-s interpulse intervals during application of L-768,673 at 3, 10, and 100 nM with a washout interposed between 3 and 10 nM. D: concentration dependence of IKs inhibition. Averaged effects (means ± SE) as a fraction of control value are plotted for HEK-IKs and native IKs of guinea pig ventricular myocytes as a function of the concentration of L-768,673 (circles) and L-735,821 (triangles), respectively. Dotted lines are fits of the Hill equation {1/[1 + ([Conc]/IC50)p], where [Conc] is inhibitor concentration and p is the Hill coefficient} to the data, and derived IC50 values are listed (n = 3–10).

View larger version (21K): [in this window] [in a new window]   Fig. 2. Temperature sensitivity of HEK-IKs and its activation and deactivation kinetics. A: superimposed whole cell HEK-IKs in response to voltage steps to +50 mV from a Vh of –50 mV obtained from a single cell while varying temperature. The outward currents during the step to +50 mV were fitted with the equation IKs amp[1 – exp(–t/A1)][1 – exp(–t/A2)] + Iconst at each temperature (see text for details). Fits of the model are the red lines superimposed over the activating currents. The deactivating tail currents during repolarization to –50 mV (inset, currents plotted on semilogarithmic scale) were fitted with a single decaying exponential with the time constant D. B: effect of temperature on the time constants of activation and deactivation for the cell shown in A. The log-linear dependence of the time constants on temperature allowed fitting of the Arrhenius equation, which yielded the Q10 value, the fold increase in the parameter over a change of 10°C, for each time constant. C: summary of the averaged Q10 (means ± SE, n = 8) for each time constant and tail amplitude.

(1)

was fitted to the outward current during the voltage step, I_step, where I_{Ks amp} is the peak amplitude of the time-dependent slowly activating current and I_const is the time-independent instantaneous constant background current (Fig. 1). The fitted model currents are superimposed over the actual currents obtained at the indicated temperatures (Fig. 2A). The activating time constants for the currents, _A1 and _A2, at each temperature are plotted in Fig. 2B.

The tail current deactivation kinetics at –50 mV were analyzed and fit with the following monoexponential decaying function:

(2)

where I_{Ks peaktail} is the peak amplitude of the tail current on repolarization to –50 mV, which varies with temperature, and _D is the deactivation time constant at a given temperature. In Fig. 2A, inset, the tail currents at –50 mV are plotted on a logarithmic ordinate axis to demonstrate the linear time course expected for a monoexponential decay of the tail current. Figure 2B plots the deactivation time constants _D for the currents in Fig. 2A as a function of temperature.

At 20°C, there is only a minimal amount of time-dependent activating current in response to the 1-s pulse to +50 mV, and the activation and deactivation is relatively very slow with time constants _A1, _A2, and _D in the range of 1–1.5 s. Raising the temperature to 25°C substantially speeded activation (_A1 and _A2 = 0.39 s), increased the magnitude of the time-dependent activating and deactivating tail currents, and speeded deactivation (_D = 0.74 s). At a nearly physiological temperature of 35°C, the HEK-I_Ks apparently activated fully within the 1-s step with rapid time constants of activation (_A1 = 0.13 s, _A2 = 0.04 s), and the tail current deactivated rapidly (_D = 0.2 s). On average, the peak tail current at –50 mV following a 1-s step to +50 mV was 0.17 ± 0.01 nA at room temperature (19–20°C) and increased 6.5-fold to 1.1 ± 0.4 nA at 35–36°C (n = 6). At potentials where the current could be fitted along a trajectory to a near steady-state level by the end of the 1-s pulse, a faster and slower component of activation with different temperature sensitivities emerged (Fig. 2B, 29°C). The temperature dependence of the two activation time constants was determined for eight cells, and the Q₁₀ for each time constant was averaged and is shown in Fig. 2C. Q₁₀ values of 3.2 ± 0.3 and 9.5 ± 1.2 were determined for the slow and fast activation time constants _A1 and _A2, respectively, as shown in Fig. 2C.

A Q₁₀ of 4.3 ± 0.9 was calculated for the temperature sensitivity of deactivation. The deactivation Q₁₀ values obtained with HEK-I_Ks compare favorably with those of I_Ks studies in cardiac myocytes. For example, Walsh et al. (52) demonstrated a Q₁₀ of 3.8 for I_Ks recorded in guinea pig ventricular myocytes based on the change in the time constant for deactivation of I_Ks tail current at –30 mV when the temperature was increased from 22 to 32°C.

Effect of temperature on voltage-dependent activation of HEK-I_Ks. Experiments to gauge the effect of temperature on the gating kinetics above used a limited-duration 1-s depolarizing step to a single activating potential of +50 mV. Although this step duration was adequate to resolve activation time courses at higher temperatures, longer step durations were required for more complete saturation of the activating current at lower temperatures and examination of the effect of changing the step potential on the activation time constants of the model (Eq. 1). Figure 3 illustrates the voltage and temperature dependence of the activation time course of HEK-I_Ks at 25 and 35°C. Voltage-dependent activation of the current was measured at increasing V_step with a longer duration of 3 s. The peak amplitude of the ensuing tail current following repolarization to –50 mV was used to quantify the extent of isochronal activation of the HEK-I_Ks current during the 3-s steps (Fig. 3C, circles). At nearly physiological temperature (35°C), the tail current activated at V_step greater than –40 mV and saturated as V_step exceeded +40 mV. HEK-I_Ks activation was faster at more positive potentials, and eventually the currents saturated during the 3-s V_step. As shown by fits of Eq. 1, the time constants of the two first-order activation processes, _A1 and _A2, varied in an apparently log-linear fashion with V_step (Fig. 3C). Figure 3D shows the averaged time constants from six cells. The straight line fits of the time constants on the log-linear plot yielded e-fold changes of the time constants every –55 ± 8 mV for the faster activation process, _A2, and every –63 ± 4 mV for the slower activation process, _A1 (Table 1). The averaged time constants of activation at 35°C with a V_step of +20 mV were 0.12 ± 0.02 s for _A2 and 0.38 ± 0.04 s for _A1. The midpoint of activation, V_mid, was +3.1 ± 4.6 mV from fits of the Boltzmann equation to the normalized tail currents with an average slope factor, k, of 12.2 ± 1.4 mV, which translates to an equivalent of 2.2 elementary gating charges per channel. By comparison with native I_Ks, Li et al. (26) determined a V_mid of +9.4 mV and a k of 11.8 mV for the I_Ks current in human ventricular myocytes at 35°C.

View larger version (29K): [in this window] [in a new window]   Fig. 3. Effect of temperature on the voltage-dependent activation time course of HEK-IKs. Superimposed whole cell HEK-IKs currents were recorded at temperatures of 25 (A) and 35°C (B) from the same cell. HEK-IKs traces are shown in response to successive 3-s step depolarizations ranging between –50 and +60 mV in +10-mV increments applied every 15 s from a Vh of –80 mV. Tail current was obtained during a 5-s repolarization to –50 mV. The outward currents during each depolarizing voltage step were fitted with the expression IKs amp[1 – exp(–t/A1)][1 – exp(–t/A2)] + Iconst. The fits to the data are plotted as lines superimposed over the current traces and are extended in time to show the incomplete activation at the end of the 3-s step at 25°C and/or lower step potentials. C: the fast (A2, triangles) and slow (A1, squares) time constants of activation and the peak tail currents (circles) are plotted as a function of step potential at 25 (filled symbols) and 35°C (open symbols) for the currents of the cell shown in A and B. D: averaged fast and slow time constants of activation (means ± SE, n = 6) from fits of the equation to the activating currents recorded at 25 and 35°C. The straight lines are log-linear fits of the A, whose slopes yield the average voltage-dependent changes in the A (see Table 1).

Effect of external K⁺ concentration on reversal potential and deactivation kinetics of HEK-I_Ks. Two separate studies in human ventricular myocytes (26, 50) have measured the reversal potential (E_rev) of native I_Ks (Ref. 26, at –70 mV, or Ref. 50, at –82 mV). To examine the K⁺ selectivity of HEK-I_Ks and to reveal possible changes in gating kinetics with altering the K⁺ driving force, we lowered the external K⁺ concentration ([K⁺]_e) from 4 to 1 mM (Fig. 4). The E_rev of the HEK-I_Ks tail current with a [K⁺]_e of 4 mM was –70 ± 1.6 mV (n = 4), considerably less negative than the expected Nernst potential for K⁺ if I_Ks were exclusively K⁺ selective. This finding is consistent with various studies of native I_Ks, which have established E_rev for I_Ks in the range of –60 to –80 mV. The E_rev of the HEK-I_Ks current shifted from –70 ± 1.6 to –102 ± 1.2 mV when [K⁺]_e was lowered from 4 to 1 mM (Fig. 4C), demonstrating the primarily K⁺-selective property of HEK-I_Ks and consistent with findings in native guinea pig I_Ks (43). Peak activating and deactivating tail current amplitudes scaled with membrane potentials V_m, according to the expected E_rev-dependent change in current driving force, V_m – E_rev, indicating that changes in tail current amplitude result simply from the shift in E_rev (E_rev). Monoexponential fits (Eq. 2) of the decaying tail currents at potentials 30 mV revealed little or no change in the deactivation time constants with lowered [K⁺]_e (Fig. 4D). The V_mid of activation of HEK-I_Ks was insensitive to lowering of [K⁺]_e (not shown). Together, these results indicate that altering [K⁺]_e affects HEK-I_Ks only insofar as it shifts E_rev of the channel but has little or no effect on gating kinetics.

View larger version (15K): [in this window] [in a new window]   Fig. 4. Effect of reduced external K+ concentration ([K+]e) on HEK-IKs reversal potential (Erev) and deactivation. A: superimposed voltage protocols applied at an interval of 15 s. A 2-s activation step to +50 mV from a Vh of –80 mV was followed by repolarization to tail potentials ranging from –50 to –120 mV in –10-mV decrements. B: superimposed HEK-IKs tail currents in response to and aligned with the tail potentials shown in A. The tail currents were recorded from the same cell at 4 and 1 mM [K+]e. C: amplitudes of the deactivating current at each tail potential were averaged [means ± SE, n = 4, temperature (T) = 25°C] at 4 and 1 mM [K+]e. The Erev shifted from –70 ± 1.6 to –102 ± 1.2 mV when [K+]e was lowered from 4 to 1 mM. D: tail currents were fitted with a monoexponential function of the form A·exp(–t/D) + C to yield D at each tail potential. Averaged D (means ± SE, n = 4) at 1 and 4 mM [K+]e are plotted on a log-linear scale. Fits of D are shown as dashed lines and reveal e-fold changes in time constants every 36 ± 2.6 or 35 ± 1.8 mV at 4 or 1 mM [K+]e, respectively.

View larger version (19K): [in this window] [in a new window]   Fig. 5. Effect of modulators of the β-adrenergic signaling pathway on HEK-IKs amplitude and gating kinetics. A: HEK-IKs tail current amplitudes following application of 10 and 100 nM isoproterenol (Iso) and after a brief washout. HEK-IKs was elicited with a 2-s step to +50 mV, and tail current amplitudes were measured during return to the Vh of –50 mV. B: HEK-IKs representative traces from the cell in A are superimposed from before (ctl) and after equilibration with 10 and 100 nM Iso. C: concentration-response relationship for Iso (means ± SE, n = 8, T = 24°C). The Hill equation was fitted to the data to determine the EC50 of Iso. Tail current amplitudes were normalized to the control amplitude to obtain the fold increase. The average fold increases (means ± SE) by 10 µM forskolin (n = 4, T = 24°C) and 50 µM 8-(4-chlorophenylthio)cAMP (CPT-cAMP; n = 5, T = 30°C) are also shown. D: a decaying monoexponential function with time constant D was fitted to the deactivating tail current at –50 mV during control and after equilibration with the indicated modulator (0.1 µM Iso, 10 µM forskolin, or 50 µM CPT-cAMP). Comparison of the effects of the β-adrenergic modulators on D is expressed as percent change from control. E and F: a modified second-order Hodgkin-Huxley (H-H) model (Eq. 1) was fitted to the rising phase of the activating current. Effects of the β-adrenergic activators on the fast (A2) and slow (A1) activating time constants are expressed as percent change from control. *P 0.01.

Given that the effects on the kinetics of activation by the different agonists were comparable and reproducible, we next examined the effects of isoproterenol on the voltage dependence of activation. Figure 6 shows the effect on voltage-sensitive activation kinetics of isoproterenol from a single cell at a temperature of 24°C together with the fits of the activation time course at each potential. Isoproterenol shifted the V_mid of activation to more negative potentials. Application of 10 nM and 1 µM isoproterenol at 24°C resulted in average shifts in the V_mid of activation of –5.3 ± 1.0 and –13.4 ± 2.9 mV (n = 3), respectively (not shown). Moreover, isoproterenol speeded the activation kinetics as revealed by fits of the second-order modified H-H model (Eq. 1). Figure 6D shows the effects of isoproterenol on the step current amplitude as well as the activation time constants _A2 and _A1 from a single cell at 24°C. At activating V_step below +50 mV, the fitting algorithm yielded identical time constants for _A1 and _A2, presumably due to incomplete definition of a fast and slow component as a result of incomplete saturation of HEK-I_Ks during the 2-s V_step, analogous to the low temperature fits of Fig. 2. However, at potentials of +50 mV or higher, the fitting algorithm was able to discriminate a faster and slower time constant. Again, the fits were highly correlated with the data, regularly exceeding correlation coefficients of 0.99. Together, these results indicate that the increase in HEK-I_Ks in response to adrenergic stimulation results from lowering of the activation voltage and speeding of activation kinetics, as well as increasing the overall open probability of the channel.

View larger version (32K): [in this window] [in a new window]   Fig. 6. Effect of Iso on HEK-IKs. A: superimposed whole cell HEK-IKs in response to successive 2-s step depolarizations ranging between –50 and +140 mV applied at +10-mV increments from a Vh of –80 mV applied at a 15-s interpulse interval. Tail currents were obtained during a 3-s repolarization to –50 mV. HEK-IKs for the same cell is shown before (ctl; A) and after application of 100 nM Iso (B). Activating currents were fitted with a modified second-order H-H model (Eq. 1). The fits are plotted as lines superimposed over the current traces and are extended in time to show the incomplete saturation of currents at the end of the 2-s step. C: amplitudes of the tail currents at –50 mV shown as a function of preceding step potential are plotted for control and 100 nM Iso. The amplitudes were fitted with the Boltzmann equation (see MATERIALS AND METHODS) to yield the midpoint of activation (Vmid) and the equivalent gating charge moved, zd, for each condition. D: fast (A2) and slow (A1) time constants of activation are plotted along with peak activating current amplitude during control and after application of 100 nM Iso. T = 24°C.

View larger version (18K): [in this window] [in a new window]   Fig. 7. Effect of forskolin on voltage dependence and gating kinetics of HEK-IKs activation. HEK-IKs traces are shown for 2-s activating voltage steps (Vstep) between –50 and +20 mV during control (A) and after application of 10 µM forskolin (B), a direct activator of the endogenous adenylate cyclase. Vstep ranging from –50 to +50 mV were applied in 10-mV increments at a 15-s interpulse interval from a Vh of –50 mV. Vstep are labeled next to current traces for comparison. HEK-IKs tail current amplitudes were recorded during repolarization to the Vh of –50 mV, following Vstep of –40 to +50 mV. C: tail currents were normalized to the maximum tail current amplitude following the Vstep to + 50 mV, averaged (means ± SE), and plotted as a function of Vstep during control and after application of 10 µM forskolin. Forskolin treatment shifted Vmid as determined by the fits with a Boltzmann relation (dashed lines), Vmid = –10.0 ± 0.94 mV (n = 5), without affecting the slope factor (k). D: the kinetics of current activation were fit with a second-order modified H-H model (Eq. 1, RESULTS) yielding a slow (A1) and a fast (A2) activation time constant at each step potential. The time constants were averaged (means ± SE, n = 4) for control and 10 µM forskolin and plotted on a log-ordinate scale. The slope of the straight line fits of the time constants on the log-ordinate scale yields the e-fold changes of the two time constants as a function of membrane potential for each condition (see Table 2). T = 30°C.

View larger version (19K): [in this window] [in a new window]   Fig. 8. Effects of forskolin on Erev and deactivation kinetics of HEK-IKs. A: HEK-IKs tail currents during control conditions are superimposed at successively more negative potentials following 2-s depolarizations to +50 mV from a Vh of –80 mV. Tail potential steps were decreased by –10 mV with successive sweeps applied at 15-s intervals. B: HEK-IKs tail currents were obtained from the same cell as in A during application of 10 µM forskolin. (Scale is the same as in A). C: plot of the averaged IKs tail current amplitudes (means ± SE), normalized to the control tail amplitude at +40 mV, during control and after application of 10 µM forskolin at 30°C. The averaged values for control Erev and shift of the reversal potential (Erev) by forskolin (means ± SE, n = 5) are listed. There was a small but significant shift in Erev with forskolin (2-tailed paired Student's t-test; P < 0.0005). D: deactivation time constants (D) are plotted at each potential during control and after application of 10 µM forskolin at 20 and 30°C. Tail currents at –70 mV at 30°C were too small to be fitted. There was little or no change in D below –30 mV with 10 µM forskolin at either temperature. Dashed lines are log-linear fits of the D as a function of voltage and are superimposed for control and forskolin at each temperature. The voltage sensitivities of D, expressed as e-fold changes, were 31 mV at 30°C and 48 mV at 20°C.

Figure 8D quantifies the effects of 10 µM forskolin on deactivation kinetics. To examine effects of forskolin at potentials below the activation threshold of HEK-I_Ks, we averaged and compared the time constants _D from monoexponential fits of the decaying tail currents obtained at potentials less than or equal to –30 mV (Fig. 8D, 30°C). Although forskolin increased tail current amplitudes two- to threefold at all potentials (Fig. 8C), it had little or no effect on deactivation kinetics. This result confirmed those obtained with isoproterenol, forskolin, and cAMP at a single potential (Fig. 5). The voltage-dependent changes in deactivation were also examined at 20°C, where the constants are significantly slower (see Fig. 2), and minimal changes in _D were observed (Fig. 8D). Log-linear fits of the averaged _D time constants revealed that _D increased e-fold over a change in potential of 31 mV at 30°C and over a change in potential of 48 mV at 20°C.

Rate-dependent accumulation of HEK-I_Ks at 35°C and the effect of isoproterenol. An important physiological function of I_Ks is its potential enhanced role during elevated sympathetic tone and, consequently, at faster heart rates. In addition to the scaling and more rapid activation of I_Ks observed above, an unresolved question is whether or not I_Ks "accumulates" at faster heart rates as a consequence of incomplete deactivation. Given the speeding of deactivation kinetics observed with increases in temperature, we examined whether HEK-I_Ks could accumulate appreciably at near-physiological temperatures (35°C), where the _D constants are <50 ms at a ventricular resting potential of –90 mV (Figs. 2 and 4). If the deactivation of I_Ks were the primary determinant for accumulation, then it would be expected to occur at pulse rates and interpulse intervals where deactivation is incomplete between successive action potentials. To test this hypothesis, we applied trains of simulated action potential voltage-clamp pulses consisting of a 200-ms V_step to +40 mV followed by a 17-ms repolarizing ramp to the V_h of –90 mV at pulse rates of 0.5, 2, 3, and 4 Hz (Fig. 9A). Figure 9B illustrates the relatively small amount of outward time-dependent I_Ks that is activated over such a short voltage pulse. Large rate-dependent accumulation of I_Ks over a pulse train of 10-s duration was evident only at the highest pulse rate of 4 Hz as shown in Fig. 9, B and C. At 4 Hz, a pulse repeat interval of 250 ms leaves only a short 33-ms rest interval at –90 mV for deactivation of the current before reactivation by the subsequent pulse. This allows for a rapid staircaselike accumulation at 4 Hz of the I_Ks from pulse to pulse, leading to a fourfold (4.0 ± 0.5, n = 7) rate-dependent enhancement of the current by the end of the 10-s pulse train. In contrast, at the pulse rate of 3 Hz, where the interpulse interval increases from 33 to 116 ms, much less rate-dependent accumulation of current was observed (1.4 ± 0.2-fold increase, n = 7).

View larger version (23K): [in this window] [in a new window]   Fig. 9. Rate dependence of HEK-IKs current and effect of Iso. A: action potential-like voltage pulse protocol used to elicit HEK-IKs current during repetitive voltage-clamp pulsing at rates of 0.5, 2, 3, and 4 Hz from a Vh of –90 mV. B: whole cell current responses at pulse rates of 2, 3, and 4 Hz from a single cell before (control, left) and after application of 1 µM isoproterenol (right). The HEK-IKs current responses during the first and last voltage pulses of a 10-sec continuous pulsing regimen are superimposed at left of each panel, and the concatenated whole cell current responses during the entire 10-s train of pulses are shown at right; interpulse currents are omitted. Time and current scales are indicated at top right. Solid horizontal lines indicate zero current line; dashed lines indicate the baseline of the outward time-dependent IKs current. C: plot of the rate-dependent fold increase (last pulse/1st pulse, means ± SE, n = 7) of the peak outward IKs after pulsing for 10 s at the indicated pulse rate (Hz = 1/s). D: HEK-IKs last pulse currents (after 10 s of pulsing) in the presence of 1 µM Iso were normalized to the control last pulse currents and are plotted (means ± SE, n = 7) against the pulse repeat interval (1/Hz). *P 0.01. T = 35°C.

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX: THE HODGKIN-HUXLEY... REFERENCES

 
Study implications. This study presents a systematic characterization and quantification of the gating kinetics of the human KCNQ1/KCNE1 K⁺ channels stably expressed in HEK-293 cells in response to β-adrenergic, temperature-dependent, and pharmacological modulation. These findings validate a recent report that the expression of hKCNQ1/hKCNE1 in the HEK-293 background (HEK-I_Ks) provides a unique model of native human I_Ks because β-adrenergic modulation with isoproterenol is achievable without recourse to cotransfection of other accessory proteins (11). This model of the human I_Ks provides an alternate means to study the role of I_Ks in ventricular repolarization and its modulation in response to β-adrenergic receptor and adenylate cyclase activating pharmacological agents, which has not been demonstrated in other expression backgrounds.

Modeling of the hKCNQ1/hKCNE1 current activation and deactivation kinetics. A modified second-order H-H model postulating two independent but nonidentical gates, each of which follows first-order kinetics, was able to describe with high fidelity (R 0.99) the biophysical characteristics of the HEK-I_Ks at varying potentials and temperatures and during modulation with agents in the β-adrenergic stimulatory pathway. Conventional second-order H-H models with two identical gates or processes have been used to model slow delayed rectifier current activation in both amphibian (18) and mammalian cardiac cells (30). Our results demonstrate that under conditions where the slow gate is not at steady state by the end of the activating voltage pulse, i.e., under conditions of lower temperature, lower stepping potentials, or shorter step durations, the activating current kinetics are well fit with identical time constants for the two gates (see Figs. 2 and 6). Our results further demonstrate that a second-order H-H model with nonidentical gates best defines activation when the current reaches a steady state during the activating step and the time course is fully resolved, i.e., using longer pulses, higher temperatures, or more depolarized potentials.

A second-order H-H model using two nonidentical gates (termed a heterodimeric H-H model to distinguish it from a homodimeric H-H model) was first proposed for native I_Ks gating in action potential simulation studies by Viswanathan et al. (51) based on activation kinetics obtained in guinea pig ventricular myocytes at the physiological temperature of 34–36° (48). This model proposed two gates with first-order kinetics that are strictly scaled versions of one another. In our fits of the activation kinetics of HEK-I_Ks, _A2 and _A1 differ by a relatively constant ratio of 3–5 across the span of activating voltages (Figs. 3, 6, and 7). Although our observed activation kinetics at first glance are in accord with the model of Viswanathan et al., where a factor of four was adopted, the congruence between our model and the Viswanathan group's model does not hold across the entire voltage range, because the closing rates at negative potentials are not scalar multiples of one another.

Figure 10 shows the overall fit of the second-order H-H model (see APPENDIX for the mathematical formulation of the heterodimeric model) with two nonidentical independent gates for the forskolin data presented in Figs. 7 and 8 obtained at 30°C. This model of I_Ks gating allows direct interpretation of the time constants obtained in our fits of activation and deactivation current kinetics under limiting membrane potential conditions (see APPENDIX). Table 3 presents the parameter values obtained by the fit of the model to the HEK-I_Ks current at a temperature of 30°C. Comparison of the individual parameters determined for each gate indicates that the kinetics of the two gates are not simply scaled versions of one another but, rather, independently deterministic. Figure 10 shows the model fit superimposed over the constraining data under control and forskolin-stimulated conditions.

View larger version (14K): [in this window] [in a new window]   Fig. 10. Heterodimeric H-H gating model fitted to the HEK-IKs current during control and after treatment with forskolin. A: plot of the inverse time constants from experiments shown in Figs. 7 and 8 (1/A1, 1/A2, 1/D). Inverse time constants are shown for both control condition and after application of 10 µM forskolin (T = 30°C). A second-order H-H model with nonidentical gates ("heterodimeric" model) was fitted to the plot according to constraints presented in the APPENDIX. Dotted lines superimposed over the plots are the sums of the opening and closing rate constants, 1(V) +β1(V) and 2(V) + β2(V) (see Eq. 5b), for each of 2 independent H-H gates after fitting of the data (see Table 3). An increase in the opening rate, 2(V), of the faster gate is the primary effect required to model the observed changes in gating on stimulation of the current by forskolin. CTL, control; FSK, forskolin. B: plotted averaged HEK-IKs activation normalized to the maximum tail current amplitude from Fig. 7C for both the control condition and after application of 10 µM forskolin. Dotted lines are the superposition of the calculated steady-state open probability of the heterodimeric H-H model given by 1(V)2(V)/{[1(V) + β1(V)][2(V) + β2(V)]}. The leftward shift in the steady-state activation curve during stimulation of the current by forskolin is the result of the increase in the opening rate, 2(V), of the faster gate (see Table 3).

In contrast to the speeding of the activation kinetics of HEK-I_Ks, we found little or no effect of β-adrenergic modulation on the deactivation kinetics of HEK-I_Ks with repolarization to potentials below –40 mV (Fig. 8). We limited our analysis of deactivation to potentials less than or equal to –30 mV (approximate activation threshold), such that deactivation reflected primarily the transitioning of the channel to the fully closed state [i.e., where the opening rates are small, _i(V) 0] rather than reequilibration among closed and open states.

Interpreted through the heterodimeric H-H gating model in Fig. 10, the data presented in Figs. 7 and 8 show that β-adrenergic modulation primarily affects the opening rates of the HEK-I_Ks channel, leaving the closing rates unchanged. Fitting of the data with forskolin required only two adjustments to the opening rate of the fast gate: 1) a change in the constant ₂ from 78 to 65 and 2) a 18 mV negative shift in the voltage offset from 21 to 3 mV (Table 3). Such a shift could arise presumably as a result of the phosphorylation of an intracellular residue, such as occurs with Ser²⁷ of KCNQ1 during cAMP-dependent modulation of the channel (29). Because deactivation kinetics are relatively unaffected, no changes were required to the closing rates to model β-adrenergic modulation of HEK-I_Ks. Studies of native I_Ks deactivation in response to β-adrenergic modulation are equivocal in mammalian myocytes, reporting no changes (56), a slight increase (52), or a reduction (2) of the time constant of deactivation. A slowing of deactivation has been reported in amphibian preparations (13, 17). Bearing in mind the difficulties in specifically isolating I_Ks from I_Kr tail currents in native preparations, the disparities reported in the relatively minor effects of β-adrenergic modulation on deactivation kinetics could potentially arise from experimental variation. For example, such variation could arise from small temperature fluctuations during experimentation if temperature were not actively monitored and controlled. Alternatively, an apparent speeding of deactivation could occur if the deactivation potential were insufficiently negative to rule out the effects of enhanced opening rates on overall rates of deactivation.

β-Adrenergic modulation of rate-dependent facilitation of I_Ks. We examined rate-dependent facilitation of HEK-I_Ks at 35°C using fixed-duration (217 ms) pulses, roughly mimicking action potentials, from a physiological holding potential of –90 mV (Fig. 9). A large rate-dependent facilitation of I_Ks under control conditions was evident only at the highest pulse rate of 4 Hz, where the pulses repeated every 250 ms, leaving only a short interpulse (or diastolic) interval of 33 ms, during which the current can deactivate. At –90 mV, given a deactivation time constant, _D, of 84 ms at 30°C (Fig. 8) with a Q₁₀ for tail deactivation of 4 (Fig. 2), the calculated _D of HEK-I_Ks at 35°C would be 40 ms. Thus, the strong initial rate-dependent facilitation of I_Ks arises from beat-to-beat accumulation of I_Ks as a result of incomplete deactivation during the 33-ms "diastolic" interval between action potential pulses at 4 Hz (Fig. 9C). Human diastolic intervals, measured as the time between the electrocardiographic T wave and subsequent QRS complex, scale nonlinearly with cardiac cycle length (or RR interval). Consequently, even at the heart rate of 180 beats/min (3 Hz, RR interval = 333 ms) in humans, the diastolic interval would normally exceed 100 ms (28). This suggests that the observed initial staircase accumulation of HEK-I_Ks observed under control conditions used in this study at 4 Hz would likely not occur under physiological conditions (46).

In the presence of isoproterenol, a small enhancement of rate-dependent facilitation of I_Ks over that which occurred under control conditions was observed (Fig. 9D). This rate-dependent enhancement of the isoproterenol effect peaked at 25% at the pulse frequency of 3 Hz, where the diastolic interval is 116 ms (Fig. 9C). This type of rate-dependent enhancement of I_Ks during β-adrenergic stimulation with isoproterenol has been demonstrated in studies of native I_Ks from guinea pig (36) and dog (46) ventricular myocytes. Studies of native I_Ks have shown that deactivation time constants in human ventricular myocytes stimulated by 1 µM forskolin at physiological temperature are comparable to those observed in this study (100 ms at –50 mV at 37°C; Ref. 50) and that rate-dependent enhancement of I_Ks in the absence of β-adrenergic stimulation is dependent on species as well as experimental conditions (27, 35). For example, rate-dependent accumulation of native I_Ks is increased with repolarization to more positive potential (46) or at a lower temperature, both of which slow deactivation (see Figs. 2 and 8).

During β-adrenergic stimulation, two apparently paradoxical findings in this study are the slight enhancement of rate-dependent facilitation of I_Ks at higher pulsing rates (Fig. 9C) and the lack of significant slowing of current deactivation (Fig. 5D). Besides tonic current amplification, the main effects of β-adrenergic modulation of HEK-I_Ks are a negative shift in the voltage dependence of activation and acceleration of the activation kinetics (Figs. 6, 7, and 10). These two effects lead to enhanced rate-dependent facilitation due to the net effect of cycling rapidly between the holding potential of –90 mV and the test pulse plateau of +40 mV. This is illustrated by comparing the time course of activation for control vs. isoproterenol-enhanced I_Ks during the last pulse in a train (Fig. 9B, 3 Hz). By speeding the channel opening kinetics, β-adrenergic enhancement reduces the activating current delay that is evident upon depolarization under control conditions.

Further insight into the ability of the heterodimeric gating model of I_Ks to correctly predict the observed characteristics of rate-dependent accumulation of I_Ks current arises from the nature of the H-H gating model: channels are conducting only when all gates are open but become nonconducting when any of the gates are closed. If two gates are nonidentical, as in the heterodimeric model presently proposed for I_Ks, current activation kinetics is dominated by the slowest opening gate, whereas current deactivation kinetics is dominated by the fastest closing gate. Understanding this key concept allows us to explain the observation in Fig. 9B at 4 Hz, where, after an initial staircase accumulation of current during the first few seconds of pulsing, a slower accumulation of peak current amplitude becomes evident that spans the entire 10-s pulsing duration, even in the absence of a significant effect of β-adrenergic stimulation on current deactivation (Fig. 5D) as shown in Table 3, where neither closing rate is affected. However, the basal closing rate of the fast gate closing rate (parameter β₂) is about nine times faster than the slower gate closing rate (parameter β₁). The rapid cycling of the channel at the higher pulsing rates allows accumulation of open probability in the slow gate due to its slower closing rate. This accumulation remains "hidden" during deactivation, since deactivation is dominated by the fast gate. The hidden accumulation of the open probability of the slow gate persists beyond observable current deactivation and is evident as the growing near-instantaneous component of subsequent test pulses, as illustrated in the last pulse of the train of pulses (Fig. 9B, 4 Hz). The hidden rate-dependent reserve of I_Ks that we observe is dependent on the slow closing rate of the slow H-H gate of our model and is unmasked under the physiological conditions of limited duration action potentials only when pulsing rates are rapid.

Because the heterodimeric H-H model fits both single-pulse activation gating as well as β-adrenergic modulation on temperature-controlled recordings within a human-derived background cell line, we did not attempt kinetic analyses using more complex Markov models of voltage-gated K⁺ channels (57). Silva and Rudy (44) utilized such Markov modeling of I_Ks gating to fit experimental data obtained by a variety of investigators using both native cardiac and expressed I_Ks currents (29). Their model is a significantly more complex one that builds on gating at the microscopic level, starting with observations of activation gating of KCNQ1 expressed in isolation and then expanding to incorporate coexpression of KCNE1 (or native I_Ks results). Our model attempts to primarily explain macroscopically observed whole cell currents on a multisecond time scale. Compared with the model of Silva and Rudy, our model is computationally more tractable and would allow incorporation into more large-scale simulation of the action potential in response to β-adrenergic modulation. Interestingly, Silva and Rudy observed that interaction between KCNQ1 and KCNE1 confers kinetic properties on I_Ks that make it suitable for adaptation to rate changes; in particular, the channel develops an available reserve of closed states near the open state that can open rapidly on demand. This mechanism would be provided by the slow closing rate of the slow gate of the heterodimeric model.

Our model also differs from another recently proposed model of I_Ks adrenergic modulation based on expression of KCNQ1/KCNE1 together with the PKA-anchoring protein (AKAP) yotiao in Chinese hamster ovary (CHO) cells and simulation of PKA-dependent stimulation of the current by addition of intracellular cAMP and okadaic acid (47). Under such experimental conditions, a slowing of deactivation was observed. A gating model incorporating these effects proposed that β-adrenergic stimulation causes both speeding of activation, as in our model, as well as slowing of deactivation. A slowing of I_Ks deactivation would likely result in a shortening of action potential duration (APD) and could increase postrepolarization refractoriness. However, this potential latter effect should be outweighed by the overriding shortening of APD by I_Ks enhancement during β-adrenergic stimulation. Overall, any changes in gating of I_Ks need to support the dynamic rapid cycling of the membrane potential underlying the increased heart rate, decreased APD, and decreased refractory period that are associated with ventricular electrophysiology during β-adrenergic stimulation (15). It is not known whether the combined action of cAMP and okadaic acid, which blocks dephosphorylation of the channel, is the equivalent of receptor-mediated β-adrenergic stimulation with isoproterenol or forskolin, as used in our studies. We did not investigate how cotransfection of yotiao, an AKAP that has been shown to be necessary for the adrenergic modulation of I_Ks in the CHO cell expression system, may potentially affect the deactivation kinetics of the KCNE1/KCNQ1 current in the HEK expression system. The identity of the endogenous AKAP that presumably facilitates the adrenergic modulation of HEK-I_Ks is not known. Thus the model of human I_Ks presented in this study should help extend our current understanding of I_Ks gating and its contribution to cardiac repolarization in response to β-adrenergic stimulation of the heart.

The HEK-293 cell line (19) has served extensively as a host for both transient and stable expression of receptors and ion channels for pharmacological, biophysical, and modulator characterization. The endogenous G protein-coupled pathways in HEK-293 cells have been used to examine receptor and ion channel coupling to second messenger cascades. HEK-293 cells have a documented endogenous second messenger pathway that incorporates the hallmarks of the prototypical β adrenergic receptor cascade involving β-adrenergic receptors, which couple via G_s to adenylate cyclase and cAMP-dependent PKA (9). Daaka et al. (9) have shown, for example, that treatment of HEK-293 cells with isoproterenol or forskolin increases intracellular cAMP levels 17- and 45-fold, respectively. The endogenous adenylate cyclase activating pathway in HEK-293 cells has been harnessed previously to test whether expressed L-type Ca²⁺ (Ca_V1.2) channels can be modulated by the cAMP-dependent β-adrenergic pathway (14), but nativelike enhancement of Ca_V1.2 current has been found only on cotransfection of AKAPs (16, 22). Recent studies have shown that multiple AKAPs are endogenously present in HEK-293 cells (55), but it is unknown whether the AKAP yotiao (29), shown to be involved in PKA-dependent I_Ks modulation, is endogenously present.

Possible structural interpretations of a heterodimeric H-H gating model. It is generally accepted that the native I_Ks channel consists of a core of four KCNQ1 subunits. Although it is not certain whether two or four KNCE1 subunits are contained within an I_Ks channel, recent evidence favors the belief that two KCNE1 subunits are expressed per channel (6, 32). Depending on whether two or four KNCE1 subunits are expressed per channel, the resulting channel would possess a physical two- or fourfold symmetry. The simplicity of the proposed heterodimeric H-H formalism and its straightforward biophysical interpretation suggest structural changes that may underlie β-adrenergic modulation of I_Ks gating. As a H-H model, the heterodimeric model places strong constraints on how the channel may function.

In a H-H model with two gating processes with two time scales, current activation is dominated by the slower opening gate, whereas current deactivation is dominated by the faster closing gate. With the assumption that like subunits behave in a concerted, limited two-state gating scheme, it is attractive to speculate that the faster gate in the heterodimeric model is constituted by the cooperative movement of the KCNQ1 subunits. This hypothesis is supported by the faster activation kinetics of KCNQ1 expressed in isolation and the observation that current deactivation of KCNQ1 expressed in isolation shows deactivation time scales similar to those of I_Ks.

The collapsing of the gating transitions of the KCNQ1 subunit into two states, closed and open, is a simplification given what is known about KCNQ1 gating in isolation (34), but it is one that can be made based on the goodness of fit at time scales on which our fits are based. A cooperative single functional transition of the KCNQ1 tetramer as a consequence of association with KCNE1 can be envisioned based on the allosteric models of function proposed by Monod et al. (31) for symmetric heterooligomeric enzyme structures. The assignment of the fast gating process to KCNQ1 also correlates the finding that PKA-dependent I_Ks channel phosphorylation targets the KCNQ1 subunit (29). The primary effect of adrenergic modulation in our model of I_Ks gating is the increase of the opening rate of the fast gate via a shift in its voltage sensitivity and voltage offset (Table 3).

The concerted movements of the KCNE1 subunits, whether two or four, would in this interpretation constitute the functional slow activation gate and thus would dominate the time scale of current activation once KCNE1 coassembles with the KCNQ1 channel. Bearing in mind that the model parameter fits of Table 3 were obtained using a set of limited test conditions, additional aspects of the slow gate need to be further refined. Specifically, incorporation of the kinetics of the second phase of pulsing-dependent current accumulation (Fig. 9, 4-Hz pulsing rates) would yield a more accurate estimate of the closing rate of the slow gate. Despite the limited conditions of model testing and validation used presently, however, the lack of a strong effect of adrenergic stimulation on rate-dependent accumulation of HEK-I_Ks (Fig. 9, C and D) suggests limited involvement of the slow gate in the adrenergic response.

An alternate possibility arising from a potential twofold symmetry of the channel complex is to interpret I_Ks gating as that of a structural dimer, with each protomer consisting of one KCNE1 and two KCNQ1 subunits. In our model the two time scales could no longer be reconciled with independent movements of each half of a channel dimer, because each half would be structurally identical and thus would be expected to gate identically in a H-H model. To reconcile structural movements of a dimer with our findings, the H-H model requirement of the independent action of the two gates would have to be abandoned.

Conclusion. The demonstration of the enhancement of the hKCNQ1/hKCNE1 current, HEK-I_Ks, in HEK-293 cells in the presence of isoproterenol validate the recent finding that the molecular constituents necessary for β-adrenergic modulation of I_Ks are present in this host line (11). The ability to isolate and modulate the I_Ks current in the HEK-293 background has allowed us to derive a simple yet precise model of human I_Ks gating on the time scales of seconds, termed the heterodimeric Hodgkin-Huxley model of I_Ks gating. The effect of β-adrenergic modulation on I_Ks is incorporated in this model, which can explain two observed rates of rate-dependent accumulation of I_Ks at high pulsing rates. The quantitative model presented in this study may further refine the mathematical model of human I_Ks in the cardiac myocyte. These results indicate that the HEK-293 line would be very attractive for molecular biology studies of the genetic mutations of I_Ks with respect to their effect on β-adrenergic modulation, since it would require only the transfection of the mutated channel subunits themselves.

	APPENDIX: THE HODGKIN-HUXLEY FORMALISM APPLIED TO IKs GATING

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX: THE HODGKIN-HUXLEY... REFERENCES

 
The heterodimeric gating model uses the mathematical formalism introduced by Hodgkin and Huxley (21), who proposed that the potassium conductance they studied in the squid giant axon could be modeled by a set of four identical, independently operating voltage-sensitive gates. Each gate is denoted by a time- and voltage-dependent state variable, n(t, V), denoting the open probability of each gate. The overall open probability of a channel in the original H-H model is given by the product of the open probabilities of all of the four identical gates, n⁴(t, V). Because voltage-gated potassium channels of the type that Hodgkin and Huxley studied are based on the structurally homotetrameric Kv family potassium channel, the original H-H model could be called a homotetrameric fourth-order H-H gating model, because there are four identical gates to each channel. By analogy, a heterodimeric second-order H-H gating model proposes two nonidentical gates, n₁ and n₂, with the overall open probability of the channel given by the product of the open probabilities of each of the two nonidentical gates at any given time, t, and membrane potential, V. All other aspects of the heterodimeric model are the same as in the original H-H formalism.

Each I_Ks gate in the heterodimeric model is characterized by an opening rate, _i, and a closing rate, β_i, which are voltage sensitive, with i = 1, 2. Equations 3a and 3b formulate the voltage dependence of the opening and closing rates of each gate as a function of membrane potential, V:

where k_i, k_βi, _i, and _βi are constants (see Eqs. 12 and 13 of Ref. 21). We attempted to use an expression of the form of Eq. 3b for fitting the activation time constant data, but this expression was poor at fitting the 1/_A values across the depolarized voltage range.

The steady-state open probability of each gate at a given membrane potential, n_i(, V), is given by the equation

(4)

The product of the open probabilities of the two gates at steady state determines the steady-state voltage-dependent open probability of the channel, for which the isochronal activation curve of Fig. 7C is an approximation (since true steady state would require the step duration to be of infinite duration).

The time-dependent relaxation of the open probability of each gate from an initial condition at potential V₀ to a new steady state at the potential V is given by

The open probability of the channel at any time t is thus the product of n₁(t, V) and n₂(t, V).

In our studies of the HEK-I_Ks current, two special cases of Eq. 5a are used to constrain the values of _i(V) and β_i(V) for a given voltage. In the first case, current activation from resting potential, the variable V₀ is negative enough that the initial condition, n_i,(V₀) 0 such that Eq. 5a is simplified to n_i,(V)[1 – exp(–t/_i)]. Equation 1 is the implementation of this special case, and the time constants derived from fits of Eq. 1 are used to place constraints on _i(V) and β_i(V) during activating voltage steps. A second special case of Eq. 5a is encountered when repolarizing the HEK-I_Ks current from an activated state to resting potentials where _i(V) 0, such that n_i,(V) 0. In this case, the time-dependent open probability of each gate is described by n_i,(V₀)exp(–t/_i), and the overall open probability of the channel is thus given by n_1,(V₀)n_2,(V₀)exp[–t(β₁ + β₂)], which is the same form as Eq. 2.

Summarizing from the previous paragraphs, the following constraints were placed on the opening and closing rates of each gate to obtain the fitting constants in Eqs. 3a and 3b:

(6)

where _Ai is as defined in Eq. 1 and i = 1, 2;

(7)

where _D is as defined in Eq. 2; and

(8)

the normalized tail current-voltage relation.

By limiting the fits of the model to the limiting cases of membrane potentials, the constraints imposed by Eqs. 6–8 yielded the parameter constants shown in Table 3.

	ACKNOWLEDGMENTS

 
We thank Armando Lagrutta for critical reading of the manuscript and David T. Yue for insightful discussion.

Present address of W. D. Irving: Beth Israel Medical Center, New York, NY 10003.

	FOOTNOTES

 

Address for reprint requests and other correspondence: J. Imredy, Merck & Co., WP 81-207, PO Box 4, West Point, PA 19486 (e-mail: john_imredy{at}merck.com)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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