pathways of herg inactivation current-voltage relation showed inward recti-ﬁcation, and...

Pathways of HERG inactivation

JOHANN KIEHN, ANTONIO E. LACERDA, AND ARTHUR M. BROWNRammelkamp Center for Research, MetroHealth Campus,Case Western Reserve University, Cleveland, Ohio 44109-1998

Kiehn, Johann, Antonio E. Lacerda, and Arthur M.Brown. Pathways of HERG inactivation. Am. J. Physiol. 277(Heart Circ. Physiol. 46): H199–H210, 1999.—The rapid,repolarizing K1 current in cardiomyocytes (IKr) has uniqueinwardly rectifying properties that contribute importantly tothe downstroke of the cardiac action potential. The humanether-a-go-go-related gene (HERG) expresses a macroscopiccurrent virtually identical to IKr, but a description of thesingle-channel properties that cause rectification is lacking.For this reason we measured single-channel and macropatchcurrents heterologously expressed by HERG in Xenopusoocytes. Our experiments had two main findings. First, thesingle-channel current-voltage relation showed inward recti-fication, and conductance was 9.7 pS at 2100 mV and 3.9 pSat 100 mV when measured in symmetrical 100 mM K1

solutions. Second, single channels frequently showed noopenings during depolarization but nevertheless revealedbursts of openings during repolarization. This type of gatingmay explain the inward rectification of HERG currents. To testthis hypothesis, we used a three-closed state kinetics model andobtained rate constants from fits to macropatch data. Resultsfrom the model are consistent with rapid inactivation from closedstates as a significant source of HERG rectification.

rapid repolarizing cardiac potassium current; kinetics; activation

THE POTASSIUM ION (K1) current expressed heterolo-gously in Xenopus oocytes by the human ether-a-go-go-related gene (HERG) (15, 23) has many properties ofIKr, the rapid component of the repolarizing K1 currentin heart (16). For example HERG current, like IKr,activates slowly and at positive potentials displays theinward rectification so critical to the role of IKr inproducing the downstroke of the cardiac action poten-tial. HERG current, like IKr in human cardiomyocytes(28) and ferret cardiomyocytes (13), has a transientpeak at positive potentials (11, 17). Pharmacologically,HERG is sensitive to block by the class III methanesul-fonanilides (11, 20, 23) that block IKr (8, 12, 16).Mutations in the HERG gene cause one form of heredi-tary long Q-T syndrome (3, 9) that is associated withthe potentially lethal arrhythmia torsade de pointes,and class III methanesulfonanilide blockers of IKr pro-duce similar phenomena.

Recently whole oocyte and macropatch measure-ments have suggested that C-type inactivation is theprimary cause of inward rectification of HERG current(17, 19, 20). To understand further how HERG mightproduce rectification and a peak transient current, wemeasured its elementary currents. We found that singleHERG channels may fail to open on depolarization but

will open on repolarization. We attribute this result toinactivation from a closed state and note that this typeof gating will contribute to inward rectification. Wedemonstrate that single HERG channels accumulate ininactivated states during depolarization and reopen oropen for the first time during repolarization, confirmingthat, once repolarization has been initiated, HERG isuniquely suited to produce the downstroke of thecardiac action potential.

MATERIALS AND METHODS

Electrophysiology. Xenopus oocyte measurements were per-formed using standard two-microelectrode voltage-clamp tech-niques with a Dagan 8500 voltage clamp (Dagan, Minneapo-lis, MN) (11). Macropatch currents were recorded from oocytesusing patch pipettes made from borosilicate glass with tipopenings of 10–15 µm and resistances of 150–250 kV with anAxopatch 1D patch-clamp amplifier (Axon Instruments, Fos-ter City, CA). After a gigaseal was achieved, recordings weremade in the cell-attached mode of the conventional patch-clamp technique (4). Single-channel recordings were per-formed using pipettes pulled from hard borosilicate glasswith resistances of 5–10 MV. The seal resistance was 50–500GV. Pipettes were coated with Sylgard and fire polishedimmediately before use.

Solutions and drug administration. Two-microelectrodevoltage-clamp measurements of Xenopus oocytes were per-formed in a bath solution (low-K1 solution) containing (inmmol/l) 5 KCl, 100 NaCl, 1.5 CaCl2, 2 MgCl2, and 10 HEPES(pH 7.3).

For macropatch and single-channel recordings, the 100mM K1 pipette solution contained (in mM) 100 KCl, 2 MgCl2,and 10 HEPES (pH adjusted to 7.3 with KOH). The 5 mM K1

solution contained (in mM) 5 KCl, 100 NaCl, 1.5 CaCl2, 2MgCl2, and 10 HEPES (pH adjusted to 7.3 with NaOH). Thebath solution in all single-channel and macropatch measure-ments contained (in mM) 100 KCl, 1 MgCl2, and 10 HEPES(pH adjusted to 7.3 with KOH). All measurements were doneat room temperature (22°C).

Data analysis. Data were low-pass filtered at 1–2 kHz (23dB, 4-pole Bessel filter) before digitization at 5–10 kHz.pCLAMP software (Axon Instruments) was used for genera-tion of the voltage-pulse protocols and for data acquisition.The single-channel measurements were corrected for leakand capacitance current by subtracting the average current of5–10 null recordings. Single-channel kinetics were analyzedusing Transit software (24). This resulted in histograms foramplitudes, open time, closed times, and burst duration.Probability density function parameter estimates were ob-tained with the maximum-likelihood method and gave valuesfor the exponential components for open time (topen), closedtimes (tclosed,1, tclosed,2, and tclosed,3), and burst duration (tburst).Transit software uses a statistic based on the maximum-likelihood ratio to determine the minimum number of exponen-tial components in dwell-time distributions. A second, slowopen-time component (29) was not statistically validated inour data. For calculation of burst duration, we used a criticalclosed time calculated so that equal proportions of short andlong closed intervals are misclassified (1). Statistical data are

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0363-6135/99 $5.00 Copyright r 1999 the American Physiological Society H199

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given as means 6 SD. In single-channel data, n refers to thenumber of patches analyzed.

Single-channel detection error. We have calibrated theresponse of our channel-detection system with simulateddata to calculate the error for detection of single channels byTransit under our experimental conditions. Transit idealizeschannels by detecting the instantaneous transitions amongchannel open and closed states rather than the crossing of anamplitude threshold. Transit only requires that the transi-tions have a derivative (slope) that exceeds the standarddeviation of the baseline noise derivative by a user-specifiedmultiple. Details of the algorithm have been published re-cently (24). The maximum likelihood-optimization procedurein Transit is based on the variable metric Davidon-Fletcher-Powell method and includes a correction for intervals shorterthan the minimum and longer than the maximum observableintervals (2). We set the minimum observable time as thefilter rise time and the maximum observable interval as thepulse length for estimation of dwell-time parameters. For ourexperiments these were 0.3 and 398 ms, the closest valuespermitted by Transit.

Single-channel simulation software was provided by Dr.Antonius VanDongen. We simulated data with a simpletwo-state model with a mean open time of 2 ms and a meanclosed time of 8 ms. Under these conditions at a 20-kHzsampling rate without filtering or added noise, the maximum-likelihood parameter estimate for the mean open time was2.004 ms, the average open time was 2.00 ms, and the numberof openings detected was 780. The same simulation sampledat 5 kHz with 1-kHz filtering and the addition of 0.07standard deviation noise resulted in a maximum-likelihoodparameter estimate for the mean open time of 2.042 ms, anaverage open time of 2.30 ms, and 714 detected openings.There was negligible error in estimating the mean open time,and the number of missed openings corresponds to 8% of thenumber of openings detected at 20 kHz in the absence offiltering and noise. With these model parameters, 2% ofopenings should be missed as the result of concatenation ofopen times due to missed brief closures. We conclude that, at5-kHz sampling and 1-kHz filtering, Transit misses 6% ofsingle openings with a true mean of 2 ms because theopenings are too brief. As an aid to channel detection, becausethe HERG channels burst, failure to detect all openings in aburst would require that all the openings in the burst have anopen time less than the detection limit.

Modeling. Nonlinear least-squares fitting of kinetics modeltransition rates to current recordings was accomplished withthe Solver add-in to Microsoft Excel 97 and Windows NT 4.

Experimental current data at each potential were fit to thefunction I(t) 5 N ·Po(t) · i, where I(t) indicates the macroscopiccurrent, N is the number of channels, Po is the probability ofoccupancy of the open state, and i is the single-channelcurrent amplitude. Values of Po(t) were generated in Excel byEuler integration of the kinetics equations for each model.Initial parameter estimates for a model were obtained with astep size of 0.025 ms. When a consistent set of parameterswas obtained that was relatively insensitive to variation ofinitial parameter values, the step size was increased to 0.25ms to permit more rapid exploration of the model. Solutionswere checked by reducing the step size to 0.025 ms. Reportedsolutions were stable when the step size was decreased.Values for N were optimized, and values for i were obtainedfrom experimental data. Initial state occupancies were fixed,with all channels occupying the closed state farthest from theopen state. Allowing the optimization procedure to varyinitial state occupancies produced negligible occupancies ofother closed states in the models evaluated. Currents fromthe deactivating voltage step were used to generate simulta-neous fits to the tail currents. Initial state occupancies for thedeactivating step were set equal to state occupancies atthe end of the activating step. We constrained the sum of thetransition rates for leaving the open state to be equal to thereciprocal of the experimentally determined open time andconstrained the sum of the transitions leaving the proximalclosed state to be equal to the experimentally observed fastclosed time at each potential. Microscopic reversibility wasmaintained in models with transitions among states formingclosed loops by making one of the transition rates in each looptake on appropriate values calculated as a function of all theother independent transition rates in the loop.

Molecular biology. The HERG clone was a gift from Dr.M. T. Keating (3). The pSP64 construct containing HERG waslinearized with EcoR I (Boehringer Mannheim, Indianapolis,IN) and transcribed into cRNA with the mMESSAGEmMACHINE in vitro transcription kit (Ambion, Austin, TX)using SP6 polymerase. RNA (50–500 ng/µl) was injected intoXenopus oocytes, and measurements were performed 2–8days after injection.

RESULTS

Macroscopic currents. In whole oocyte recordingsHERG currents had an activation threshold of 240 mV.The current amplitude became larger at 220 and 0 mVand then decreased at 20-, 40-, and 60-mV membranepotentials because of inward rectification (Fig. 1A). At

Fig. 1. A: double-electrode voltage-clamp measurement of human ether-a-go-go-related gene (HERG) expressedin Xenopus oocytes in 5 mM extracellu-lar K1 concentration ([K1]o). Holdingpotential, 270 mV; test pulse, 2120 to60 mV in 20-mV steps (400 ms); returnpulse, 270 mV (400 ms); bath solu-tion, 5 mM K1. B: cell-attached mac-ropatch measurement in 100 mM[K1]o. Holding potential, 280 mV; testpulse, 2120 to 100 mV in 20-mV (400ms) steps; return pulse, 2120 mV (400ms); bath (internal) solution, 100 mMK1; pipette solution, 100 mM K1. In-set, enlargement of peak transient ob-served at positive potentials.

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40 and 60 mV the currents showed a transient peak.Tail currents were outward at 270 mV and had acharacteristic rising phase (hook), reached a peak, andthen deactivated more slowly. The rising phase in thetails is attributed to recovery from inactivation that isfaster than deactivation (18). The current kinetics incell-attached macropatches were identical to the wholeoocyte measurements [5 mM extracellular K1 concentra-tion ([K]o) cell-attached macropatch currents notshown].

In cell-attached macropatches in 100 mM [K]o, theactivation threshold was also 240 mV and currentswere small and inward at 240 and 220 mV. From 20 to100 mV, outward currents that had transient peakswere observed (Fig. 1, B and inset). During the stepsback to 2120 mV, tail currents were large and inwardand showed the rising phase associated with rapidrecovery from inactivation preceding slower deactiva-tion.

Nature of peak transient current. To investigate thepeak transient at positive potentials, we did single-channel measurements in 100 mM [K]o. The single-channel conductance of HERG depends strongly on [K]oand is 2 pS at 5 mM [K]o and 10 pS at 100 mM [K]o (11).

From a holding potential of 280 mV, we made measure-ments at 0.2 Hz to a test potential of 100 mV for 300 msto activate channels and then stepped back to 2120 mVfor 100 ms to rapidly remove inactivation (voltageprotocol shown in Fig. 2A, bottom). We used 100 mM[K]o to make detection of HERG-channel activity pos-sible at potentials of both 100 and 2120 mV. Figure 2Ashows typical leak and capacitance current-subtractedunitary currents from one HERG channel. A strikingfeature is the occurrence of openings only duringrepolarization (Fig. 2A, 1st through 4th recordings).During the step to 2120 mV, the channel recoveredfrom inactivation, produced bursts of openings with amean burst duration of 15 ms, and finally entered aresting closed state. A possible interpretation of thispattern is that during depolarization the inactivatedstate may be entered directly from a closed state,whereas during repolarization the inactivated channelcloses after visiting an open state. We refer to thisgating pattern as closed-state inactivation. Our esti-mate of one active channel in the patch is based on theabsence of any overlapping openings at 2120 mV fromall recordings, in this case, 160 recordings. We refer torecordings with single-channel openings present at

Fig. 2. Single-channel recordings ofHERG current with only one channelin patch. A: single channels show 3types of activities. First, no openingsduring activation and openings duringdeactivation at 2120 mV (1st-4th re-cordings). Second, early openings pro-ducing transient peak during activa-tion (5th and 6th recordings). Third,late openings (7th and 8th recordings).B: averaged current of 160 recordingsmimics time course of macropatch cur-rent at 100-mV test pulse and 2120-mVreturn pulse to evoke tail currents (cf.Fig. 1B). Holding potential, 280 mV;test pulse, 100 mV (300 ms); returnpulse, 2120 mV (100 ms); bath (inter-nal) solution, 100 mM K1; pipette solu-tion, 100 mM K1. C: cumulative firstlatency from records with single-chan-nel openings at 100 mV was best fitwith a biexponential function (t1 andt2, time constants representing earlyand late single-channel openings). In-cluding records without openings incumulative first latency reduces maximalprobability from 1 to 0.375. D: recoveryfrom inactivation measured as averagecurrent normalized to peak value insecond part of protocol at 2120 mVcould be fit monoexponentially (trecov-

ery, time constant of recovery from inac-tivation). Parameter values in B and Ccorrespond to experiment shown; aver-age values from all experiments arepresented in text.

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2120 mV (84% of all recordings) as ‘‘repolarizationactive’’ (RA) recordings.

We observed three different types of channel activi-ties. In 55% of RA recordings there were no openingsduring the activating pulse (Fig. 2A). Twenty-fourpercent of RA recordings showed early openings(,30-ms latency) during the activating pulse to 1100mV. These openings produce the initial peak transientcurrent observed in the whole oocyte and macropatchrecordings (Fig. 2A, 5th and 6th recordings; Fig. 2B,arrow). In 21% of RA recordings, we observed late firstopenings during the activating pulse (Fig. 2A, 7th and8th recordings). The averaged current of all 160 record-ings had the same kinetics as cell-attached macropatchrecordings (cf. Figs. 2B and 1B). Similar results wereobtained in five patches with only one channel in eachpatch.

We analyzed the latency to first opening of thesingle-channel currents and found that the cumulativedistribution could be best fitted with a biexponentialfunction (n 5 5) (Fig. 2C). The fast time constant of14.3 6 6.3 ms represents early openings that producethe transient peak. The second time constant of 105 622 ms represents late openings that contribute to asmall steady-state current at 100 mV. The weights ofthe rapid and slow components in the cumulativefirst-latency distribution were 46 6 11 and 54 6 11%,respectively. First latencies in Fig. 2C were calculatedonly for recordings with openings resulting in a maxi-mal probability value of 1. Including depolarizationswith no openings makes the maximal probability valueequal to 0.375.

We analyzed recovery from inactivation in the tailcurrents and found that it could be fitted monoexponen-tially with a time constant of 8.9 6 2.1 ms (n 5 5) (Fig.2D). A similar value was obtained from macropatchesat 2120 mV (6.6 6 1.8 ms) (n 5 6).

At 240 mV we observed inward single-channel open-ings (Fig. 3A). Patches with only one channel were notuseful because openings were too rare to collect enoughdata for evaluation. Therefore, we used patches withapproximately 5–10 channels. We analyzed patchesthat, in the majority of recordings, had no overlappingopenings during activation. The averaged single-channel current showed slowly activating inward cur-rent identical to the macropatch recordings (Fig. 3B).HERG channels show bursting behavior (Fig. 3A, 2nd,3rd, 5th, 7th, and 8th recordings).

Resting inactivation at holding potential of 280 mV.If significant channel inactivation exists at a holdingpotential of 280 mV, the number of channels undergo-ing closed-state inactivation could be vanishingly small.We evaluated the amount of steady-state inactivationat a holding potential of 280 mV by monitoring theamplitude of the initial peak transient current at 100mV. Channels producing the peak transient currentactivate directly from resting closed states. The fastcomponent of the first-latency distribution (Fig. 2C) issimilar to the inactivation rate at 100 mV in solutionswith high [K1]o (27), so contributions from channelsrecovering from inactivation during the transient should

be minimal. We used average currents from multichan-nel recordings to obtain sufficient data at severalpotentials in the same patch. Under our solution condi-tions, average peak currents were identical at poten-tials of 2120 to 280 mV, indicating the absence ofinactivation at 280 mV in our recordings (Fig. 4).Inactivation does appear when the patch is held at 260mV (Fig. 4, inset). We obtained similar data from threeother multichannel patches. Therefore, channels thatfail to open at 100 mV but that do open at 2120 mV

Fig. 3. A: single-channel recordings of HERG current in a multichan-nel patch. B: averaged current of 80 recordings mimics time course ofmacropatch current at 240-mV test pulse and 2120-mV return pulseto evoke tail currents. Holding potential, 280 mV; test pulse, 240 mV(300 ms); return pulse, 2120 mV (100 ms); bath (internal) solution,100 mM K1; pipette solution, 100 mM K1.


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may have occupied resting closed states before depolar-ization, entered an inactivated state directly from aclosed state during depolarization, and opened onlyafter recovering from inactivation at 2120 mV.

Comparison of single-channel currents near thresh-old and at 100 mV. The single-channel currents at 100mV (n 5 11) had a mean amplitude of 0.38 6 0.09 pA(Fig. 5A). The open probability (Fig. 5C) showed apattern similar to that of the macropatch measure-ments (Fig. 1B) with a prominent initial transientcomponent. The open-time distribution could be fittedmonoexponentially (Fig. 5E), and we obtained an aver-age open time of 2.5 6 0.49 ms (n 5 11) from all ourdata. The closed-time distribution was fitted by a sumof three exponentials with tclosed,1 5 0.78 6 0.26 ms,tclosed,2 5 6.7 6 4.3 ms, and tclosed,3 5 66 6 28 ms (Fig.5G). The burst-duration distribution gave tburst 5 5.2 61.7 ms (Fig. 5I).

Because we used multichannel patches at 240 mV toincrease the frequency of channel openings, we ana-lyzed burst data with no overlapping openings. Single-channel parameter analysis at 240 mV gave a meanamplitude of 0.32 6 0.07 pA (n 5 5) (Fig. 5B). Theopen-probability distribution at this potential showed aslow sigmoidal rising phase with no peak transient andwas similar to that of macropatch recordings (Fig. 5D).The open-time distribution could be fitted with a mono-exponential function (Fig. 5F), and we obtained anaverage open time of 3.2 6 0.53 ms (n 5 5) from all ourdata. The closed-time distribution was triexponentialwith tclosed,1 5 0.95 6 0.20 ms, tclosed,2 5 3.7 6 0.8 ms,and tclosed,3 5 45 6 14 ms (n 5 5) (Fig. 5H). The valuesfor tclosed,2 and tclosed,3, but not for tclosed,1, depend on thenumber of channels in the patch and underestimate thetrue values of the slower closed times. Nonetheless,

three closed-time components were detected in agree-ment with the data at 100 mV from patches with onlyone active channel. The burst-duration distributiongave tburst 5 14.8 6 2.9 ms (n 5 5) (Fig. 5J).

Single-channel currents between 2120 and 100 mV.We evaluated single-channel openings at several volt-ages in our patches. The analysis includes data frommultichannel patches with few recordings displayingoverlapping openings. By analyzing bursts withoutoverlapping openings, it is possible to evaluate theamplitude, open time, rapid closed time, and burstduration (2). We found that the single-channel current-voltage relation (i-V) is linear in the inward directionand shows inward rectification in the outward direction(Fig. 6A). The calculated slope conductance in theinward direction was 9.7 pS, and the reversal potentialwas 27 mV. The calculated chord conductance at 100mV was 3.5 pS. The open times were nearly voltageindependent (Fig. 6B). The rapid closed time wasvoltage independent (Fig. 6C). Burst duration wasstrongly voltage dependent with a bell shape character-istic (Fig. 6D). tburst became shorter with more depolar-ized potentials. During hyperpolarization, the burstduration in the tail currents was 20.2 6 0.6 ms (n 5 2)at 260 mV, reached a maximum at 280 mV [23.8 6 4.3(n 5 3)] and 2100 mV [24.6 6 3.5 (n 5 5)], and becameshorter at 2120 mV [14.0 6 3.7 (n 5 7)].

When patches (n 5 4) were excised in a solutioncontaining 100 mM KCl, 10 mM EDTA, and 0 mMMg21, the single-channel amplitude at 100 mV was notsignificantly altered (i 5 0.39 6 0.03 pA). In addition,the single-channel kinetics parameters at 100 mV werenot significantly changed [topen 5 3.0 6 0.77 ms, tclosed,1 50.92 6 0.32 ms, tburst 5 5.5 6 0.9 ms].

Fig. 4. Effect of holding potential ontransient current magnitude. Average of$12 depolarizations at each holding po-tential from a multichannel patch. Aver-ages are superimposed and were ob-tained at holding potentials of (insequential order) 280, 2100, and, again,280 mV. Voltage protocol consisted of anactivating step to 100 mV for 300 ms,followed by a deactivation step to 2120mV for 96 ms, repeated at a frequency of0.33 Hz. Currents are not corrected forleak or capacity transients. Inset, tran-sient current averages from main panelsuperimposed with transient current av-erages obtained subsequently with samevoltage protocol from a 2120-mV hold-ing potential followed by a 260-mV hold-ing potential. The only transient currentaverage that does not superimpose ininset is transient current average ob-tained from a 260-mV holding poten-tial.


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Fig. 5. Single-channel amplitude andkinetics parameters at 100 mV (A, C, E,G, and I) and 240 mV (B, D, F, H, andJ). A and B: single-channel amplitudehistogram superimposed with a prob-ability density function generated by aGaussian kernel estimator. C and D:open probability (Po) and open-stateoccupancy of N channels (NPo, where Nis no. of channels); note that open prob-ability mimics whole cell and macro-patch currents at corresponding poten-tials. E and F: open time (topen)histograms displayed on a logarithmictime axis. Distributions are superim-posed with single exponential probabil-ity density functions obtained withmaximum-likelihood method. G and H:closed-time (tclosed,1) histograms dis-played on a logarithmic time axis. Dis-tributions are superimposed with sumof three exponential probability den-sity functions obtained with maximum-likelihood method. I and J: burst dura-tion (tburst) histograms displayed on alogarithmic time axis. Distributions aresuperimposed with single exponentialprobability density functions obtainedwith maximum-likelihood method. Pa-rameter values correspond to experi-ments shown; average values from allexperiments are presented in text.


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Rectification of instantaneous macropatch currents.Inward rectification of the single-channel conductancewas confirmed in macropatch measurements when wemeasured the instantaneous macroscopic current-voltage relation (I-V) after removal of inactivation (19).Measurements were done in a 100 mM [K1]o solution inthe cell-attached mode with a two-step protocol. Westepped first from a holding potential of 0 mV to apotential of 280 mV to remove inactivation and then, ina second step, to various test pulses to measure theinstantaneous I-V curve (Fig. 7A). The instantaneousI-V showed that the conductance in the inward direc-tion is virtually linear but is rectified inwardly in theoutward direction (n 5 7) (Fig. 7B), similar to thesingle-channel measurements (Fig. 6A). With this pro-tocol we could also measure the rate of inactivation thatbecame faster at positive potentials, producing a cross-

over of the currents and indicating that inactivation isvoltage dependent.

Modeling HERG currents. We fitted kinetic models tothe macropatch currents at a 100-mV test pulse poten-tial and 2120-mV tail current potential (Fig. 1B) withthe nonlinear least-squares method. Activating andtail currents could be fitted simultaneously usingappropriate values for i from our single-channel data.Models were constrained to have the experimentallydetermined open time and fast closed time. We foundthat the transient peak at 100 mV was the mostdifficult kinetics property to reproduce with the differ-ent models and could be used to evaluate the models.Therefore, we show best fits of each of the models to thistransient peak (Fig. 8, A–D). All of the models producedvisually indistinguishable fits to the tail current data(Fig. 8E).

Fig. 6. Single-channel parameters ofHERG current as a function of voltage.A: single-channel current-voltage rela-tion (i-V) is linear in inward directionand rectifies inwardly in outward direc-tion. B: open time is nearly voltageindependent. C: rapid closed time isnearly voltage independent as well. D:burst duration has a bell-shaped time-voltage relation.

Fig. 7. A: double-pulse protocol to mea-sure HERG macropatch instantaneous cur-rent-voltage relation (I-V) and inactiva-tion kinetics. Holding potential, 0 mV; 1sttest pulse (recovery from inactivation),280 mV (40 ms); 2nd test pulse (inactiva-tion), 240 to 120 mV in 20-mV steps (50ms); bath (internal) solution, 100 mM K1;pipette solution, 100 mM K1. B: instanta-neous I-V plot of peak current of 2nd testpulse shows inward rectification. Dottedline was extrapolated to current values ininward direction.


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Our single-channel measurements suggest thatHERG channels exhibit closed-state inactivation. There-fore, we tested linear models with an additional transi-tion pathway from the fast closed state to inactivation(C1 = I) to model closed-state inactivation. A four-statemodel with two closed states produced a poor fit of thecurrent data (Fig. 8A). A five-state model with threeclosed states produced a good fit to the transient peakat 100 mV (Fig. 8B). We then tested modified versionsof this model. When we removed the C1 = I transition(Fig. 8C), the fit to the transient peak was poor.However, the five-state model without the transitionpathway from the open state to inactivation (O = I)produced an indistinguishably good fit to the transientpeak (Fig. 8D). This model was tested further atdifferent test-pulse potentials with the experimentallyobtained values for open and rapid closed times and thesingle-channel amplitude i. Initial state occupancieswere specified so that all channels occupied the closedstate farthest from the open state at rest. Modelparameters were most sensitive to scatter in the datafor the fast closed time. Because the fast closed time isvoltage independent (Fig. 6C), we used its averagevalue calculated from data obtained at all potentials.This average value was the constraint for the fastclosed time (duration of a sojourn in C1) at eachpotential. The number of channels was optimized for

the depolarization record for 100 mV and kept constantfor all other potentials. Transition rates for deactiva-tion at 2120 mV were optimized with the depolariza-tion recording for 100 mV and kept constant for allother activation potentials. Figure 9A shows the mac-ropatch recordings overlaid with simulated model cur-rents at 40-, 60-, 80-, and 100-mV test pulses at whichdirect single-channel values were obtained. The transi-tion rates are displayed in Table 1.

Simulated traces and original measurements arevery similar during activation and in the tail currentsat 2120 mV. As an example, the transition rates aregiven in an arrow diagram for the model at 40 mV (Fig.9C). The transition rate for closed-state inactivation(C1 = I; 0.568 ms21) is similar to the opening rate (C1 =O; 0.588 ms21). The probability of the channel leavingC1 to I is 48%, that of leaving C1 to O is 50%, and that ofleaving C1 to C2 is 2%. This agrees with our experimen-tally observed frequency of closed-state inactivation of55%. At the end of the 40-mV, 400-ms test pulse, 94% ofchannels have accumulated in the inactivated state I(Table 2). During repolarization at 2120 mV, the major-ity of channels open before returning to resting closedstates (Fig. 9D). The probability of leaving C1 to O is94%, that of leaving C1 to C2 is 6%, and that of leavingC1 to I is insignificant. Channels accumulate in the C2state during deactivation because the tail current is

Fig. 8. Evaluation of kinetics models forHERG macropatch currents during a testpulse to 100 mV (400 ms; A–D) and a tailpulse to 2120 mV (400 ms; E). C3, C2,and C1, closed states; O, open state; I,inactivated state. Models were con-strained to have the sum of transitionsleaving open state and the sum of transi-tions leaving the fast closed state (C1)equal the experimentally obtained openand fast closed times. A: 4-state modelwith closed-state inactivation could notfit transient peak. B: addition of a closedstate to model in A was sufficient toobtain a good fit to transient peak.C: removal of closed-state inactivationfrom B produced a poor fit. D: removal ofopen-state inactivation produced a fitindistinguishable from fit in B. The5-state model in D is sufficient to producean adequate fit of data with these con-straints. E: tail current data could be fitby all models. Fits from each model areshown superimposed with current mea-surement. Holding potential, 280 mV;test pulse, 100 mV (400 ms); return pulse,2120 mV (400 ms); bath (internal) solu-tion, 100 mM K1; pipette solution, 100mM K1.


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non-zero at the end of the pulse. We examined theability of this model to predict currents with a differentvoltage protocol. The model was used to fit the macro-patch data in Fig. 9B (same as in Fig. 7A). The voltageprotocol (described in legend to Fig. 7) generates aninstantaneous I-V after removal of inactivation. Modelfits to the data are shown superimposed on the originalrecordings in Fig. 9B. At some potentials good fits of thedata to the instantaneous current immediately afterthe voltage step from 280 mV to positive potentialscould not be obtained using mean values from oursingle-channel amplitude measurements. We obtainedsatisfactory fits to the instantaneous current by optimiz-ing the single-channel amplitudes within the standard

deviation of the amplitude measurements at a givenpotential. The values for the channel amplitude i, N,and transition rates for the step to 280 mV wereoptimized for the second voltage step to 100 mV andfixed at these values for second voltage steps to 80, 60,40, and 240 mV. The fits overlay the currents.

DISCUSSION

Efficiency of HERG channels in repolarizing cardiacaction potential. In this paper we provide direct experi-mental evidence that HERG inactivates from a closedstate during depolarization and opens during repolar-ization. A two-step protocol revealed the frequent occur-

Fig. 9. A: measured macropatch currents superimposed with model traces for test pulses to potentials from 40 to100 mV. Model traces and original current records are virtually identical. B: currents from Fig. 7A were fit with5-state model from Fig. 8D. Voltage protocol examines reinduction of inactivation, and model can reproduce thisdistinctive kinetics feature of HERG current. Pulse protocol is described in legend to Fig. 7. Model was used to fitcurrents during removal of inactivation at 280 mV and during reinduction of inactivation at 100-, 80-, 60-, 40-, and240-mV potentials. Parameters for step to 280 mV were optimized only for the reinduction step to 100 mV and heldconstant for all other reinduction steps. C: thickness of arrows in kinetics scheme indicates values of transitionrates for activation at 40 mV: thick arrows, fast transitions; thin arrows, slow transitions, with values in rangesindicated. D: transition rates for corresponding tail currents at 2120 mV. Holding potential, 280 mV; test pulse,40 to 100 mV (400 ms); return pulse, 2120 mV (400 ms); bath (internal) solution, 100 mM K1; pipette solution,100 mM K1.

Table 1. Model transition rates

Potential,mV

Transition Rates, ms21

i NC1=O* O=C1† C1=C2* C2=C1 C1=I* I=C1 C3=C2 C2=C3

100 0.472 0.402 0 0.0997 0.701 0.00167 0.0996 0 0.38 31,33680 0.577 0.370 0 0.0721 0.596 0.00347 0.0721 0 0.3660 0.699 0.370 0 0.0497 0.474 0.00597 0.0497 0 0.2740 0.588 0.323 0.0171 0.0353 0.568 0.0106 0.0340 0 0.27

2120 1.102 0.353 0.0713 0.000245 0 0.111 0.00162 0 21.10

Values for transition rates are expressed for model currents at 40-, 60-, 80-, and 100-mV test pulses, with deactivation at 2120 mV; an entryof 0 indicates a value ,0.0001. No. of channels (N ) was optimized at depolarization at 100 mV and kept constant for all other activationpotentials. Single-channel amplitude (i) was fixed at measured values for use in model. C1, C2, and C3, three closed states; O, open state; I,inactivation state. *Constrained to experimental average fast closed time (duration in C1); †constrained to experimental open time at eachpotential.


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rence of failures during the test pulse at positivepotentials followed by openings during the tail pulse atnegative potentials. To make this statement, it isimportant to determine precisely the number of missedevents under our recording conditions. We calculatedthat we missed only 8% of single openings during the100-mV pulse when we simulated single-channel cur-rents with a 2-ms mean open time. Moreover, there isno significant steady-state inactivation of HERG at280 mV. This indicates that many of the channels usedthe closed-to-inactivated state transition. In the data inFig. 2A, 55% of recordings showed no openings duringthe depolarization but did show openings during thefollowing repolarization. We estimate that 92% of theserecordings were produced by failure of the channel toopen during the depolarization because it inactivatedfrom a closed state. Cloned neuronal A-type potassiumchannels are also known to reopen during recoveryfrom inactivation (14). Closed-state inactivation andopening during recovery from inactivation make HERGthe ideal channel to perform repolarization withoutshortening the plateau phase of the cardiac actionpotential. If inactivation were strongly coupled to open-ing (linear model in Fig. 8C), outward current wouldmarkedly affect early repolarization and the plateauphase of the cardiac action potential.

The trigger to begin repolarization is probably notHERG, because the outward current it contributes issmall and relatively steady at this phase of the plateau.It is likely that the sum of all outward currents triggersrepolarization, and once the process has been initiated,HERG performs it efficiently.

Basis of peak transient current. HERG currentsproduced a small, peak transient at positive potentials,which has also been reported for IKr recorded in humanatrial (28) and ferret cardiomyocytes (13). The peakprobably arises from the fraction of channels with brieffirst latencies that transit the open state before theyinactivate. The persistent, small current (Figs. 1B and8) may result from a fraction of slowly activating HERGchannels at 100 mV or incomplete inactivation, or acombination of both. In support of incomplete inactiva-tion of HERG-channel activity, on rare occasions weobserved second openings during depolarizations afterpauses too long to be associated with bursting, suggest-ing that the channel inactivated and then reopened (seeFig. 2A, 8th recording).

Steady-state inactivation of HERG channels. We useda holding potential of 280 mV for our single-channelstudies. Because channels already inactivated at 280

mV will fail to open during the step to 100 mV but willrecover in the step to 2120 mV, they will be indistin-guishable from channels that inactivated before open-ing during activation. This will result in an overestima-tion of the frequency of closed-to-inactivated transitions.In our analysis, we assume that channels are notinactivated at the holding potential of 280 mV. Previ-ous measurements of HERG and IKr steady-state inacti-vation in 98 mM K1 are consistent with no significantsteady-state inactivation at 280 mV (27), but othermeasurements have found a much more negative mid-point for steady-state inactivation (19). In fact, most ofour evidence for 55% probability of closed-state inacti-vation could be accounted for by steady-state inactiva-tion at the holding potential of 280 mV in the vicinity of50%. This possibility has to be considered, becauseSmith at al. (19) obtained a midpoint for inactivation ofHERG channels expressed in HEK293 cells of 290 mV.

However, the observations made by Smith et al. (19)are not directly comparable to our measurements,because they used 10 mM [K1]o and we used 100 mM[K1]o. High [K1]o shifts the midpoint of the inactivation-voltage relation ,20–30 mV (27, 30), which is consis-tent with our results. In addition, measurements ofHERG inactivation-voltage relations are complicatedby rapid channel closing at potentials less than about260 mV, requiring short-duration voltage steps. Twoprotocols have been used to measure steady-state inac-tivation (19, 27). Because of the small conditioning-pulse durations employed and HERG-inactivation timeconstants that can be similar to the pulse duration insolutions with high [K1]o, the inactivation-voltage rela-tions may deviate significantly from steady state.

The presence of inactivation at 280 mV can becritically tested by measuring availability at morenegative conditioning potentials. We focused on theinitial peak transient current at 100 mV as an index ofchannel availability because long (many seconds) hold-ing potentials can be used and because the experimentsare the same as those for our single-channel recordings,except for the holding potential. Although the currentat 100 mV is small in amplitude, it is generatedprimarily by channels that occupied resting closedstates before the step to 100 mV (see Resting inactiva-tion at holding potential of 280 mV). These channelsopen for the first time and then inactivate during thetime of the transient (,30 ms). At 100 mV, channels areunlikely to reopen from inactivated states during thetime of the peak transient, so peak current amplitudeshould be proportional to the number of resting chan-nels available for activation at a particular potential.We found that the peak transient was unchanged byvarying holding potential from 2120 to 280 mV but didbecome reduced at a holding potential of 260 mV. Thisresult is in agreement with the steady-state inactiva-tion-voltage relation described by Wang et al. (27) forHERG channels measured with 98 mM [K1]o in oocytes.Kiehn et al. (10) measured the steady-state inactivation-voltage relation with a protocol similar to that of Smithet al. (19) and found with 5 mM [K1]o that the midpointof inactivation was 268 mV. At the same [K1]o used bySmith et al. (19), Taglialatela et al. (22) obtained a

Table 2. Model state occupancies at end of step

Potential,mV

Occupancy, %

C3 C2 C1 O I

100 0 0 0.002 0.003 0.99580 0 0 0.006 0.009 0.98560 0 0 0.012 0.023 0.96540 0 0.008 0.018 0.032 0.942

2120 0 0.985 0.004 0.011 0

Values indicate percentage of channel occupancy in various modelstates at end of step to each potential.


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midpoint of 262 mV for HERG channels expressed inoocytes. Because we expect a positive shift of theinactivation-voltage relation at higher [K1]o, in oursolutions the midpoint of the inactivation-voltage rela-tion will be positive to these values by at least 10–20mV. The difference in the midpoint values measuredwith similar protocols suggests that HERG channelsexpressed in oocytes are not equivalent to HERGchannels expressed in HEK293 cells.

HERG and IKr have similar properties. Single-channel kinetics parameters and conductance of HERGwere similar to reported values for IKr. IKr unitarycurrents measured in sinoatrial nodal cells of the rabbitheart have (in 150 mM [K]o) an inward single-channelconductance of 11.1 pS (18) or inward/outward conduc-tances of 10.8/7.8 pS (7), with values of 10/3 pS inguinea pig atrial myocytes (5) and 10.8 pS (inward) inrabbit ventricular myocytes (25). IKr in human ventricu-lar myocytes has an inward single-channel conduc-tance of 12.9 pS in 140 mM [K]o (26). Measurements ofsingle HERG channels expressed in oocytes found aninward/outward conductance of 12.1/5.1 pS in 120 mM[K]o (29). Our value for HERG unitary inward/outwardcurrent was 9.7/3.5 pS in 100 mM [K]o. The conduc-tance properties for HERG and IKr are in good agree-ment.

IKr single-channel kinetics analysis shows evidencefor a single open state and two closed states in rabbitsinoatrial nodal cells (18) and guinea pig atrial myo-cytes (5). The open state in 150 mM [K]o in sinoatrialnodal cells is short lived (topen 5 2.5 ms at 260 mV)relative to the value for guinea pig atrial myocytes(topen 5 9 ms at 2100 mV). In guinea pig atrialmyocytes the relatively large value of topen reported forIKr may actually represent a mean burst duration(tburst), because the authors describe the distributionused to generate topen as the distribution of burstdurations and used a relatively slow sampling rate fordata acquisition (5).

HERG channels expressed in oocytes are reported tohave open dwell-time constants similar to those for IKr.However, one report has found kinetics evidence fromHERG recordings for two open states. HERG open-timedistributions in 120 mM [K]o were best fit with biexpo-nential distributions with mean values at 290 mV of2.9 and 11.8 ms for the fast and slow components,respectively (29). We did not find evidence for a statisti-cally significant second, kinetically distinct open statein our HERG data and obtained topen 5 2.8 ms at 2120mV and topen 5 2.5 ms at 100 mV. Mean open times inour data were weakly voltage dependent, becomingshorter with increasing depolarization as reported pre-viously for HERG (29) and IKr (18).

IKr values in 150 mM [K]o for mean fast and slowclosed times in rabbit sinoatrial nodal cells are biexpo-nential with values of 0.7 and 17.6 ms at 260 mV (18),and comparable values of 1.2 and 37 ms at 2100 mVwere obtained from guinea pig atrial myocytes (5).Closed-time distributions from HERG expressed inoocytes are also biexponential and yield estimates forthe mean fast and slow closed times of 0.54 and 14.5ms, respectively, at 290 mV that are similar to the

values for IKr (29). Our closed-time distributions aredistinguished from previous measurements in observ-ing three closed-time distribution components. Theadditional closed-time component in our data has avalue (6.7 ms at 100 mV) intermediate to the fast andslow components reported for HERG and IKr. Theslowest component in our closed-time data has a timeconstant (66 ms at 100 mV) that is larger than that inprevious reports. The mean fast closed time was volt-age independent in our data, as in data for IKr (18), andwas not significantly voltage dependent for HERG (29).Previous data from HERG and IKr unitary currents areconsistent with burst gating of the channels. Our datashows that burst duration has a bell-shaped voltagedependence and suggests that bursts may be organizedinto clusters.

Inward rectification of HERG conductance. Thesingle-channel conductance of HERG rectifies inwardly(Fig. 6A), as does the instantaneous tail current I-V(Fig. 7B) in our macropatch recordings. When patcheswere excised in a solution containing zero Mg21 andzero Na1, the single-channel rectification was notchanged, similar to that for IKr (7). This rectification istherefore not produced by soluble internal blockingparticles (30) and may be intrinsic to the ion-conduc-tion pathway itself. However, rectification of macro-scopic currents appears to be due primarily to voltage-dependent gating of the channel, resulting in reducedopen probability at depolarized potentials (19, 21).Rectification of the single-channel conductance onlyappears at much more positive potentials. Therefore,rectification produced by HERG pore structures ap-pears to be more of biophysical than of physiologicalinterest. Our instantaneous tail current measurementsare similar to other results (19, 21) that showed a linearinstantaneous I-V up to 40 mV. These authors haveinvoked C-type inactivation as an explanation.

A model of HERG kinetics. Others have successfullyused a linear five-state kinetics scheme to quantita-tively model macroscopic HERG currents expressed inoocytes without single-channel constraints (27). Fromour data a minimum five-state constrained model wasalso required to adequately fit all our experimentaldata (Figs. 8 and 9). Variations of this model showedthat inactivation exclusively from the proximal closedstate (Fig. 8D) was better able to fit the data thaninactivation exclusively from the open state (Fig. 8C).This supports a role for closed-state inactivation duringchannel activation and is consistent with our single-channel data. We chose to analyze data with the modelwithout open-state inactivation (Fig. 8D) because it fitthe data as well as the more general model (Fig. 8B)with fewer parameters. We have no experimental datademonstrating the absence of open-state inactivation,so we cannot exclude the more complex general model(Fig. 8B), especially at potentials that fail to produce atransient current. All of the tested models can producegood fits to noninactivating plateau currents duringdepolarization and the large tail current on repolariza-tion. In the absence of experimental constraints, sim-pler four-state models can also produce good fits of thedata. The open time and the rapid closed time of HERG


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are nearly voltage independent (Fig. 6, B and C). Thesame has been reported for cloned Shaker K1 channelsin the absence of N-type inactivation (6). However, inthe models with closed-state inactivation, there is aninverse relationship in the voltage dependence of therates from the fast closed state to the inactivated stateand the open state such that their sum is voltageindependent, as required by the voltage independenceof the fast closed time constraint. In these models thisis the mechanism responsible for strong inward rectifi-cation of HERG currents.

In summary, our data provide more evidence thatHERG encodes IKr in cardiomyocytes. Its exceptionalkinetic features make HERG an efficient channel forproducing the downstroke of the cardiac action poten-tial (21). Because IKr in cardiomyocytes is difficult toseparate from other currents, HERG expressed inXenopus oocytes is a satisfactory system in which tostudy the kinetics of IKr.

J. Kiehn and A. E. Lacerda contributed equally to this work.We thank Dr. G. Kirsch for comments on the manuscript, P. Kiehn

and Dr. W. Q. Dong for technical assistance, and Dr. M. Keating forproviding the HERG clone.

This study was supported by a Deutsche ForschungsgemeinschaftGrant (to J. Kiehn) and National Heart, Lung, and Blood InstituteGrants HL-37044 and HL-36930 (to A. M. Brown).

Present address of J. Kiehn: Dept. of Cardiology, Medical Univ.Hospital, Bergheimerstr. 58, 69115 Heidelberg, Germany.

Address for reprint requests and other correspondence: A. E.Lacerda, Rammelkamp Center, 2500 MetroHealth Drive, Cleveland,OH 44109-1998 (E-mail: [email protected]).

Received 10 April 1998; accepted in final form 16 February 1999.

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