New Aspects of HERG K+ Channel Function Depending upon Cardiac Spatial Heterogeneity

HERG K+ channel, the genetic counterpart of rapid delayed rectifier K+ current in cardiac cells, is responsible for many cases of inherited and drug-induced long QT syndromes. HERG has unusual biophysical properties distinct from those of other K+ channels. While the conventional pulse protocols in patch-clamp studies have helped us elucidate these properties, their limitations in assessing HERG function have also been progressively noticed. We employed AP-clamp techniques using physiological action potential waveforms recorded from various regions of canine heart to study HERG function in HEK293 cells and identified several novel aspects of HERG function. We showed that under AP-clamp IHERG increased gradually with membrane repolarization, peaked at potentials around 20–30 mV more negative than revealed by pulse protocols and at action potential duration (APD) to 60%-70% full repolarization, and fell rapidly at the terminal phase of repolarization. We found that the rising phase of IHERG was conferred by removal of inactivation and the decaying phase resulted from a fall in driving force, which were all determined by the rate of membrane repolarization. We identified regional heterogeneity and transmural gradient of IHERG when quantified with the area covered by IHERG trace. In addition, we observed regional and transmural differences of IHERG in response to dofetilide blockade. Finally, we characterized the influence of HERG function by selective inhibition of other ion currents. Based on our results, we conclude that the distinct biophysical properties of HERG reported by AP-clamp confer its unique function in cardiac repolarization thereby in antiarrhythmia and arrhythmogenesis.


Introduction
Cardiac function, in particular the cardiac electrical activity, is controlled by an array of ion channels that activate in a wellorganized manner with a delicate balance between inward and outward ion movements. Upon receiving an incoming impulse, cardiac cells excite with a rapid membrane depolarization followed by a relatively slow repolarization process. Repolarization abnormalities, either excessive slowing or accelerating of the rate of repolarization, can cause cardiac electrical perturbations or arrhythmias. The rate of repolarization is determined by a team effort of several ion currents, of which the rapid delayed rectifier K + current (I Kr ) is a crucial player, particularly to the plateau phase of an action potential [1][2][3]. The major molecular component of native I Kr has been identified as the human ethera-go-go-related gene (HERG) which when expressed in heterologous systems generates I Kr -like current [4]. Impairment of I Kr /HERG can cause excessive prolongation of action potential duration (APD). Indeed, HERG has been implicated as a molecular target for mutations leading to induction of chromasome-7 linked type 2 familial long QT syndrome and as a pharmacological target for drug actions that induce acquired long QT syndrome, a lethal ventricular tachyarrhythmia often leading to sudden cardiac death [4].
HERG possesses unique biophysical characteristics and pharmacological properties distinct from other K + channels. During membrane depolarization, HERG K + channel simultaneously activates and inactivates; but its inactivation kinetics is faster than its activation kinetics, with inactivation time constants (in the order of ms) some 1-2 orders of magnitude smaller than the activation time constants (in a range up to hundreds of ms) at the same potential. Upon membrane repolarization or hyperpolarization, HERG channel rapidly reactivates from inactivated state and slowly deactivates; the reactivation kinetics is similar to the inactivation time course whereas the deactivation process is approximately two orders of magnitude slower than the inactivation, at the same membrane potential. These biophysical characteristics confer HERG a strong inward rectification and a bell-shaped current-voltage relationship (I-V relationship). Presumably due to its wide-opened pore architecture, HERG channel is susceptible to blockade by a variety of drugs and compounds of various categories with heterogeneous structures [5]. This high pharmacological sensitivity renders HERG the most frequent cause of drug-induced long QT syndrome. In addition, HERG might also be involved in pathological QT prolongation. Heart failure is electrophysiologically characterized by abnormal QT prolongation and early afterdepolarization (EAD) [6]. Indeed, depression of I Kr has been documented in failing hearts of both animal models [7,8] and theoretical simulation [9]. Tumor necrosis factor-a (TNF-a), a critical factor causing heart failure and when overexpressed prolonging APD and promoting ventricular arrhythmias, suppresses HERG function [10]. Recent studies further suggest that decreasing I Kr increases rate-related APD alternants that can dispose to ventricular tachyarrhythmias [11,12]. On the other hand, enhancement of HERG function might also be proarrhythmic. A study demonstrated that I Kr -like current is increased in cells from acute myocardial infarction that is associated with arrhythmias [13,14]. And it has been shown that HERG function is enhanced by phospholipid metabolites that are known to accumulate during the early phase of acute myocardial ischemia and to cause ischemic arrhythmias by shortening APD [10,[15][16][17]. These data indicate that I Kr /HERG plays an important role in determining propensity of arrhythmias. Understanding HERG function is therefore crucial to understanding mechanisms of arrhythmias of various types under different pathological conditions or induced by drug toxicity.
A cardiac action potential (AP) is typically divided into phase 0 depolarization, phase 1 repolarization, phase 2 plateau, and phase 3 repolarization, with magnitude, length and rate of these phases varying in cells from different regions of the heart. The key feature of cardiac AP is its relatively long repolarization process, ranging from decades of to hundreds of mille-seconds depending on species and regions from which the cells are investigated, compared to its rapid and brief phase 0 depolarization (within 2 ms). This implies that during each excitation a cardiac cell spends a majority of time in the repolarization process after its peak depolarization. Another important note about the cardiac APs is the variability of AP waveforms; the regional differences (such as sinus-atrial nodal (SAN), atrial and ventricular cells) and transmural heterogeneity (such as endocardium, midmyocardium and epicardium of ventricular walls) [18][19][20]. Noticeably, given the unique features of voltage-and time-dependence of HERG channel and the characteristics of cardiac APs, HERG channel activities are expected to differ during membrane repolarization from during depolarization, and HERG function assessed with repolarizing waveforms (or AP configurations) should be of more physiological relevance. However, HERG function has been studied primarily by conventional voltage step protocols with long rectangular depolarizing pulses of usually $2-s in duration-non-physiological voltage waveforms. This view raises a serious doubt about the fidelity of depolarizing pulses to reflect the true physiological function and pharmacological sensitivity of HERG K + channels. Some efforts have been made in previous studies to address this apparent problem by using either authentic AP waveforms or simulated AP configurations in assessing HERG function [11,12,[21][22][23]. These studies indeed revealed some important features of HERG channels, which are otherwise masked by conventional square pulse protocols. Nonetheless, precise understanding of HERG activity under more physiological conditions during an AP is still lacking. Specifically, several unanswered questions await more detailed investigation. First, what are the biophysical attributes that determine HERG function during an AP in cardiac cells? Or conversely, how do changes of HERG function influence cardiac repolarization? Second, whether there exist regional differences in terms of HERG function and if yes how do these differences contribute to the highly organized cardiac repolarization? Finally, how does I Kr /HERG change in response to inhibition of ion currents that activate before I Kr / HERG does? The present study was designed to delineate these points with the use of AP-clamp techniques.

Myocyte Isolation
For action potential clamp (AP-clamp) experiments, APs were obtained from myocytes isolated from different regions of canine hearts. The procedure for canine myocyte isolation was essentially the same as described in detail elsewhere [25]. Briefly, adult male mongrel dogs were anesthetized with morphine (2 mg/kg SC) and a-chloralose (120 mg/kg IV load, 29.25 mg/kg/h infusion), and a median sternotomy was performed. The hearts were removed and mounted to a Langendorff perfusion system. The preparation was perfused with Ca 2+ -containing Tyrode solution at 37uC until the effluent was clear of blood, and the perfusate was then switched to Ca 2+ -free Tyrode solution for 20 min at a constant rate of 25 ml/ min, followed by perfusion with the same solution containing collagenase and 0.1% BSA for 35 min. The right atrium was dissected out in Kraftbrühe (KB) medium and cells were dispersed by agitation. Dissection of different layers of left ventricular wall was carried out according to the method established by Liu et al [26]. Briefly, after perfusion, thin slices of tissues were dissected from epicardium (,1.5 mm from epicardial surface), M region (3 to 5 mm from epicardial surface), and endocardium (,2 mm from the endocardial surface). Shavings were made parallel to the surface of the left ventricular free wall midway along the apicobasal axis. The SAN region was dissected out and cut into small pieces in the enzyme solution for continuous digestion for another 20 min. Cells were then stored in KB medium for later use. A total of six adult male mongrel dogs (22,27 kg) were used in this study. The protocols for the use of dogs in this study were approved by the Animal Use and Care Committee of the Minhang Central Hospital.

Whole-Cell Patch-Clamp Recording
Patch-clamp recording of HERG K + currents (I HERG ) was conducted with the whole-cell voltage-clamp methods in the voltage-clamp mode, and single cell action potential was recorded in the current-clamp mode, using an Axopatch 200B amplifier (Axon Instruments, Burlingame, CA). Borosilicate glass electrodes (1 mm) had tip resistances of 1 to 3 MV when filled with pipette solution containing (mM) 130 KCl, 1 MgCl 2 , 5 Mg-ATP, 10 EGTA, and 10 HEPES (pH 7.3). Junction potentials were zeroed before formation of the membrane-pipette seal in the extracellular (Tyrode) solution containing (mM) 136 NaCl, 5.4 KCl, 1 CaCl 2 , 1 MgCl 2 , 10 glucose, and 10 HEPES (pH 7.4). Single cell action potentials (APs) in myocytes isolated from various regions of canine hearts were revoked by 10 consecutive stimuli of 3-ms duration and twice threshold strength at a frequency of 1 Hz (or a cycle length of 1 s). The APs recorded by the 10 th pulse reached the steady state and were converted to pCLAMP 6 format for use as voltage-clamp waveforms using the DacFile command in pCLAMP 6. For current recordings in HERG-expressing HEK293 cells, the capacitance and series resistance were electrically compensated to minimize the duration of the capacitative surge on the current recording and the voltage drop across the clamped cell membrane. Cells with changing leak current (indicated by .10 pA changes in holding current at 250 mV) were rejected. Experiments were conducted at 3661uC. All chemicals were purchased from Sigma Chemical Co.

Data Analysis
Group data are expressed as mean 6 S.E. Statistical comparisons (performed using ANOVA followed by Dunnett's method) were carried out, and paired or unpaired t-test was used, as appropriate, for single comparisons, using Microsoft Excel. A two-tailed p,0.05 was taken to indicate a statistically significant difference. Nonlinear least square curve fitting was performed with CLAMPFIT in pCLAMP 8.0 or GraphPad Prism and integration was performed to calculate the area under I HERG trace using GraphPad Prism.

Characteristics of Action Potentials from Various Regions of the Heart
Action potentials (APs) were recorded in cardiomyocytes isolated from various regions of canine hearts, including endocardium, midmyocardium and epicardium of left ventricular wall, right atrium and SAN. APs from different regions had different morphology ( Fig. 1) and characteristics ( Table 1).
The AP from epicardium (Epi-AP) was characterized by prominent spike-and-dome morphology, with an initial rapid and pronounced repolarization followed by a secondary depolarization. Midmyocardial AP (Mid-AP) demonstrated a moderate phase 1 spike and a long flat phase 2 plateau. The AP of endocardial cells (Endo-AP) has a noticeable phase 1 repolarization and steeper phase 2 repolarization. The APs from three layers of left ventricular wall all had a rapid and regenerative phase 4 repolarization. By comparison, typical atrial AP (A-AP) was characterized by a short plateau phase and a slow final repolarization, approximating triangular configuration. The AP from sinus-atrial nodal cells (SAN-AP) typically displayed a slow spontaneous depolarization followed by a rapid depolarization and short action potential duration (APD). To quantitatively charac-terize the APs, several parameters important for analyzing HERG function were measured and are summarized in Table 1. APD 10 , APD 20 , APD 50 , APD 60 , and APD 90 were determined for APD to 10%, 20%, 50%, 60% and 90% of repolarization, respectively, Figure 1. Action potential (AP) waveforms recorded from myocytes isolated from various regions of the canine heart. These AP waveforms were used for the AP-clamp studies of HERG K + channel function in HERG-expressing HEK293 cells. The quantitative characteristics of these APs are summarized in Table 1 and the voltages at the respective durations. AP amplitude (APA) and diastolic membrane potential (DMP) were measured as total amplitude of APs and voltage at diastolic interval, respectively. The rates of membrane repolarization for phase 2, phase 3 and phase 4 (RR2, RR3, and RR4, respectively) were determined by linear regressions to the steepest portion of the corresponding repolarizing phases, and the rate of secondary depolarization (SDR) was also calculated. The rate of initial repolarization (APD 10 ) was similar between various layers of ventricle and atrium, but was considerably slower in SAN. The transmural difference became prominent from the subsequent phases of repolarization. For instance, APD 20 of Mid-AP was around 2.5-fold and 5-fold longer than Endo-AP and Epi-AP, respectively, in the order of Mid-AP.Endo-AP.SAN-AP.Epi-AP = A-AP. The length of Epi-AP began to exceed that of Endo-AP from phase 2 repolarization; the order of the length of APD 50 , APD 60 , and APD 90 was Mid-AP.Epi-AP.Endo-AP.A-AP.SAN-AP. RR 1 . APA and DMP were in the same range for V-APs and A-AP, and lower for SAN-AP.

Characteristics of HERG K + channel kinetics by conventional pulse protocols
To aid understanding I HERG function and biophysics with APclamp, comparison with the conventional pulse protocol was made. Depolarizing voltage steps from 260 mV to +40 mV elicited delayed rectifier outward currents with characteristic inward rectification that was manifested at stronger depolarization. Upon repolarization back to 250 mV, slowly decaying tail currents were recorded. The inward rectification resulted in a bellshaped I-V relationship with I HERG peaking at 215 mV ( Fig. 2A).
Steady-state voltage-dependent activation. The steadystate voltage-dependent activation was determined by tail currents elicited by the voltage protocol shown in the inset of Fig. 2B. The half-maximal inactivation voltage (V 1/2 ) and the slope factor (k) determined by the Boltzmann distribution were 23062 mV and 25 mV, respectively.
Steady-state voltage-dependent inactivation. The steadystate voltage-dependent inactivation was assessed by the voltage protocol shown in the inset of Fig. 2C. I HERG was first inactivated by a 2-s depolarizing step to +40 mV and then reactivated to various extents during the hyperpolarizing pulses to various potentials of a 10-ms duration that allowed for full reactivation with minimal deactivation, and the decaying outward currents induced by the subsequent 50 ms depolarizing pulse to +20 mV represent I HERG inactivation. The half-maximal inactivation voltage (V 1/2 ) and the slope factor (k) determined by the Boltzmann distribution are 25565 mV and 218 mV, respectively.
Activation kinetics. The apparent activation time constants (t act ) of HERG channels were determined by the single exponential fit to the step I HERG during depolarizing pulse to 0 mV. The values ranged from 330 ms to 50 ms between voltage steps of 220 mV and +20 mV (Fig. 2B).
Deactivation kinetics. To evaluate the voltage-dependence of the apparent deactivation time constants (t deact ) of HERG channels, the voltage protocol as shown in Fig. 2B was applied. The decaying phase of the tail I HERG elicited at various hyperpolarizing/repolarizing steps (from 2120 mV to 250 mV), following a depolarizing prepulse to +40 mV, were fit by the single exponential to obtain t deact . It is important to note that apparent deactivation process was absent at potentials positive to 250 mV, and minor and slow deactivation was seen at potentials from 250 mV to 270 mV with time constants of 3.8 s to 1.4 s.
Inactivation kinetics. The inactivation kinetics (t inact ) was analyzed with the voltage protocol shown in the inset of Fig. 2C.
The decaying tail currents recorded upon depolarization to various potentials ranging from 280 mV to +40 mV to inactivate HERG channels, preceded by a 10-ms hyperpolarizing prepulse to 2120 mV to let channels fully recover, were fit to the monoexponential function and the values of t inact ranged from 8.5 ms to 1.3 ms between 280 mV and +40 mV.
Reactivation kinetics. The reactivation time course (t react ) was determined with the same voltage protocol as that for steadystate inactivation. The monoexponential fit was applied to the activating phase of the tail I HERG evoked at various hyperpolarizing/repolarizing steps following the inactivation steps at +40 mV. The reactivation time constants (t react ) range from 8.2 ms to 1.2 ms for voltages from 2120 mV to 240 mV.
These results indicate that (1) with respect to voltage, HERG channel inactivated from more negative potentials than it activates (255 mV vs. 230 mV) and (2) with respect to time, the time courses of inactivation and reactivation from inactivation were comparable, and were 1,2 orders of magnitude faster than the activation and 3 orders of magnitude faster than the deactivation processes within the physiological voltages spanned by an AP.

General Characteristics of I HERG Assessed by Action Potential Waveforms from Different Areas of the Heart
On the basis of our data with conventional square pulse protocols, we predicted that the activation of HERG is rapid during an AP. However, due to rapid inactivation relatively little current flows until the potential becomes less positive than 0 mV. The removal of inactivation then allows more current to flow, giving rise to the distinct pattern of I HERG changes during the AP. I HERG elicited by AP-clamp could be roughly divided into 2,3 rising phases and 2 decaying phases. The initial rising phase was rapid and corresponded to the phase 0 upstroke of AP waveform. This was followed by a slowly rising phase corresponding to the phase 2 plateau and a subsequent fast rising phase during phase 3 repolarization, with ventricular AP waveforms (V-APs). With atrial AP (A-AP) and SAN-AP waveforms, the second slowly rising phase was absent presumably because of the short phase 2 plateau duration. After reaching the peak, I HERG rapidly decayed during the final repolarization. Subsequent to the fast decay was a slowly decaying phase occurring after complete repolarization, equivalent to the tail I HERG recorded upon repolarization steps (Fig. 3). Note that there was an inward tail at the end of the trace after complete repolarization of V-APs. This was likely due to the fact that the resting membrane potential of our cells was around 274 mV and repolarizing to 280 mV with V-APs generated inward current, whereas repolarizing to 270 mV with A-AP or to 255 mV with SAN-AP produced outward tail currents.
Detailed analysis of AP-clamp revealed several novel aspects of I HERG important to our understanding of HERG function and biophysics, which would otherwise be masked by the conventional step protocols. First, although the I-V relationship of AP-clamp I HERG was bell-shaped, similar to the step I HERG , the potentials at which I HERG peaked were around 20 mV more negative with APclamp than with conventional step clamp. Specifically, I HERG peaked at 210 mV with pulse protocols, but at 230 to 240 mV with AP waveforms (Fig. 3 and Table 2). With respect to APD, I HERG peaked at the time when membrane potential reached 60-70% full repolarization, that is, APD 60 and APD 70 ( Fig. 3 and Table 2). For more straightforward view of these relationships, direct comparison between AP configuration and I HERG waveform is depicted in Fig. 4A. The vertical dash lines indicate the position where I HERG peaks in relation to APD. Note that the amplitude and duration scales are the same for all recordings in Fig. 4A and the I HERG of Endo-AP peaked to the highest level, while the I HERG of SAN-AP peaked to the lowest level, relative to the respective AP amplitudes (horizontal dash lines).
Second, to quantitatively describe the time-dependent changes of I HERG during an AP waveform, we calculated the slope (or the rates) of various rising and decaying phases by linear regression to the data points spanning the steepest portion of the given phases (Fig. 4B). The corresponding phases of APD were also analyzed for the rates of repolarization by the same methods (Fig. 4B). The resulting slopes were used to measure the rates of ascending and descending phases of I HERG . Comparison between the rates of I HERG changes and the rates of various phases of AP waveforms revealed that the rates of I HERG rising phases and decaying phase depended upon the rates of corresponding phases of membrane repolarization. That is, the greater the rate of repolarization (the steeper of the phase) of an AP was, the faster the rising (or decaying) phase of I HERG was. This point was further reinforced G was calculated by normalizing the tail currents at 250 mV by dividing the amplitude of the tail currents measured at various antecedent depolarizing potentials by that of the tail current at +40 mV. Symbols are mean of experimental data and lines represent the Boltzmann fit: where G max represents the maximal conductance at +40 mV, V 1/2 is a half-maximal activation voltage, and k is a slope factor. Middle: the apparent activation time constants (t act ) of HERG channels were determined by the single exponential fit to the step I HERG during depolarizing pulse to 0 mV. Right: the apparent deactivation time constants (t deact ) of HERG channels. The decaying phase of the tail I HERG elicited at various hyperpolarizing/repolarizing steps (from 2120 mV to 250 mV), following a depolarizing prepulse to +40 mV, were fit by the single exponential to obtain t deact . C, left: the steady-state voltage-dependent inactivation was assessed by the voltage protocol shown in the inset. The steady-state inactivation curves were constructed by plotting the channel availability or conductance G as a function of hyperpolarizing potentials. G was calculated by normalizing the tail currents elicited at +20 mV by dividing the amplitude of the tail currents measured at various antecedent hyperpolarizing potentials by that of the tail current at 2100 mV. Symbols are the mean of experimental data and lines represent the Boltzmann fit: where G max represents the maximal channel availability at 2100 mV, V 1/2 is the half-maximal inactivation voltage, and k is the slope factor. Middle: the inactivation kinetics (t inact ) of HERG channels. The decaying tail currents recorded upon depolarization to various potentials ranging from 280 mV to +40 mV to inactivate HERG channels, preceded by a 10-ms hyperpolarizing prepulse to 2120 mV to let channels fully recover, were fit to the monoexponential function to obtain the values of t inact . Right: the reactivation time course (t react ) determined with the same voltage protocol as that for steady-state inactivation. The monoexponential fit was applied to the activating phase of the tail I HERG evoked at various hyperpolarizing/repolarizing steps following the inactivation steps at +40 mV. *p,0.05 vs. Ctl; n = 12 cells. doi:10.1371/journal.pone.0072181.g002 by the fact that when the AP and the corresponding I HERG trace were superimposed, the repolarizing phases of the AP and the rising phases of the I HERG had a nearly perfect mirror-image relationship (Fig. 4A).
Third, both the voltage-dependence and time-dependence of changes of the instantaneous conductance of HERG channels (G) were analyzed according to the equation G = I/V (where I represents a given I HERG amplitude at the corresponding voltage (V) during AP-clamp). As shown in Fig. 5, the G-V relationship with V-APs and A-AP was sigmoidal and can be fit by the Boltzmann function, and the G-V relationship with SAN-AP waveform was exponential. The G-V relationship could be viewed as an instantaneous inactivation curve with conductance or channel availability decreasing as membrane depolarizes or as an instantaneous reactivation curve with conductance or channel availability increasing as membrane repolarizes; with respect to AP waveform, the latter might be more informative. The resulting instantaneous V 1/2 values for Epi-AP (251 mV) and Mid-AP (251 mV) were similar to that determined by pulse protocols and for Endo-AP (237 mV) and A-AP (238 mV) the values corresponded to more positive potentials. By comparison, the k values for Endo-AP (218 mV) and A-AP (214 mV) were close to that with pulse protocols and those for Epi-AP (228 mV) and Mid-AP (226 mV) were much shallower. When G in was expressed as a function of time (T) or duration, we obtained the instantaneous G-T relationship of HERG channels. The G-T relationship showed exponential increases with V-APs while sigmoidal increases with A-AP and SAN-AP waveforms. Finally, as already described above, I HERG peaked at around APD 60 and APD 70 with respect to APD and at between 230 mV and 240 mV with respect to membrane potential. Evidently, the rising phase of I HERG was mainly due to reactivation of HERG channels during repolarization from inactivation rendered upon initial depolarization. However, it was unclear what determines the decaying phases of I HERG during AP-clamp. One possibility is deactivation of HERG channels as commonly believed [21,23,27]. Nonetheless, close inspection of deactivation process with step protocol revealed that the deactivation time course was slow and virtually absent at potentials positive to 250 mV (Fig. 2B), implying that at the voltages where I HERG started to decline, no channel deactivation occurred. It is therefore unlikely that the decaying of I HERG during an AP is ascribed to deactivation process. To resolve the issue, we calculated the instantaneous driving forces (DF) during an AP waveform by subtracting the voltages at given time points from the reversal potential of I HERG in a given cell. DF and G were then normalized to their own maximum values. The predicted I HERG amplitude was determined by multiplying DF by G (I = G6DF). As shown in Fig. 6, the values were maximal at around 230 mV in voltage and APD 60 in duration for V-APs and 240 mV and APD 70 for A-AP and SAN-AP. Noticeably, at durations after APD 60 and APD 70 , G continually increased while DF began to reduce. The data suggest    that the rapid decaying phase of I HERG with AP-clamp was a consequence of falling of DF.

Spatial Heterogeneity of I HERG Revealed by AP-Clamp
Comparison of AP-clamp I HERG revealed some important regional differences of HERG function in terms of its voltagedependent and time-dependent properties.
First, I HERG with V-APs from three different layers all peaked at approximately 230 mV and with A-AP and SAN-AP at around 240 mV ( Fig. 3 and Table 2).
Second, I HERG elicited with V-APs peaked at duration equivalent to APD 60 , despite the transmural differences in the length of APD 60 . By comparison, I HERG recorded with A-AP or SAN-AP peaked at duration to APD 70 ( Fig. 4 and Table 2). These corresponded to 219 ms, 378 ms and 245 ms for APD 60 of Endo-AP, Mid-AP and Epi-AP, respectively, and 135 and 80 ms for APD 70 of A-AP and SAN-AP, respectively.
To better quantify the size of I HERG , we calculated the area covered by I HERG trace elicited by an AP using the integration function of Graphpad Prism software and setting the baseline at the zero current level; such analysis gives more accurate measure of K + flux carried by HERG channels during an AP. I HERG determined in this way demonstrated spatial differences and as expected, the area was in general greater in the region with longer APD. For instance, the length of APD was in the order of V-APD.A-APD.SAN-APD, and correspondingly, the size of I HERG area was also in the same order (Fig. 7A).

Transmural Heterogeneity of I HERG Revealed by AP-Clamp
Unexpectedly, when comparing I HERG elicited with AP waveforms across the left ventricular wall, the area, in the order of Endo-AP.Mid-AP.Epi-AP (Fig. 7A), did not correlate with the length of APD alone. Apparently, other factors in addition to APD also play an important role in determining the size of I HERG area. As already mentioned above, HERG reactivation or reopening depended upon the rate of membrane repolarization and DF determines the size of I HERG . This implies that the rate of repolarization (a measure of HERG conductance G) and DF during various phases of an AP should be taken into consideration for understanding the spatial heterogeneity of I HERG area. We then formulated the following equations to predict relative size of I HERG area of different regions: A~RR2|APD50 À 20|DF2zRR3|APD60 À 50 A~RR2|APD50|DF2zRR3|APD70 À 50 where A represents the area of I HERG , RR the rate of repolarization of the given phase of an AP as specified by the number, and DF the mean driving force of the given phase of an AP as specified by the number. APD 50 approximates the length of the plateau phase, DAPD 60-50 (APD 60 -APD 50 ) the duration of transition from phase 2 to phase 3 repolarization, and DAPD 90-60 (APD 90 -APD 60 ) the duration phase 3 repolarization. SDR2 indicates the rate of secondary depolarization and APD 20 approximates the duration of the secondary depolarization, which were seen with Epi-AP because of the spike-and-dome morphol- Using the values listed in Table 1, we calculated the A values for Endo-AP, Mid-AP and Epi-AP (Fig. 7A), respectively, which are in agreement with the order of I HERG area (Fig. 7B). Interestingly, when the equation was applied to A-AP and SAN-AP, the resulting A values also well reflect the relative size of I HERG area in these regions. This notion was further reinforced by the close correlation between the predicted and experimental I HERG areas (Fig. 7C).
Alterations of I HERG in Response to Blockade of I to , I Kur , or I Ca,L Ion currents activate in a certain sequence during an action potential. The one that activates in earlier phases may affect activation of the ones that activate in later phases by setting the voltage and time preconditions for the channel state. For example, the transient outward K + current (I to ) activates in the early phase of an AP and alteration of I to may change the function of the subsequently activated currents such as I Kr by altering AP morphology (voltage and duration). In a previous study, the authors showed that nicotine selectively inhibits I to at low concentrations without affecting other K + currents [28]. To investigate the potential influence of I to alteration on I Kr , we recorded APs in the presence of nicotine (500 nM) to inhibit I to in canine atrial myocytes and these APs have elevated plateau level and markedly shortened APD. The ultrarapid delayed rectifier K + current (I Kur ) is an atrium-specific and activates in the early phase of AP with partial inactivation, contributing to the plateau repolarization of atrial myocytes [25,29]. It is highly sensitive to 4-aminopyridine (4-AP) block, with micromolar concentrations of 4-AP nearly abolishing I Kur without significantly affecting other ion currents and blockade of I Kur produces some 50-60% APD lengthening. Here the APs recorded from canine right atrial cells in the presence of 100 mM 4-AP to block I Kur.d have elevated plateau level and prolonged APD. The characteristics of L-type Ca 2+ current (I CaL ) blockade by 10 mM nisodipine is the loss of plateau phase and shortening of APD, particularly the early phase repolarization (Fig. 8). The I HERG elicited by the AP waveforms recorded under these different conditions demonstrated similar but different characteristics, as shown in Fig. 9. I HERG peaked at 110 ms under control conditions and when I to was inhibited (labeled I to -). When I Kur was blocked (labeled I Kur -), the peak of I HERG shifted to 140 ms, whereas when I CaL was blocked (labeled I CaL -) I HERG peaked sooner at 75 ms. In respect with voltage, the maximum I HERG occurred at around 240 to 243 mV under control conditions or with I Kur -or I CaL -, and it was some 10 mV more negative shift when I to was inhibited. The most notable difference was the size of I HERG area. The characteristics of the atrial APs used for AP-clamp and the corresponding I HERG in the presence of varying K + channel blockers to inhibit I to , I Kur or I CaL , separately, are summarized in Table 3.

Regional Differences of I HERG in Response to Dofetilide Blockade Revealed by AP-Clamp
Since the effect of I Kr /I HERG blockers is state-dependent with most of them generally acting on the open channels and since there is regional difference of APs in terms of the repolarization rate thereby the rate of HERG reopening, we reasoned that the effects of I Kr /I HERG blockers are different in cells from different regions of the heart. To test this notion, we went on to study the effects of dofetilide on I HERG using AP-clamp with AP waveforms collected from various regions. As illustrated in Fig. 9, 10 nM dofetilide which produced approximately 5063% inhibition of I HERG area with Endo-AP reduced the current by 2761%, 2261%, 8166%, and 3062% with Mid-AP, Epi-AP, A-AP and SAN-AP, respectively ( Fig. 9A and 9B). When the data were normalized to Epi-AP, it was clear that the degree of blockade of I HERG with A-AP was around 4-times greater than with Epi-AP and about 2,3-times greater than in APs of other regions (Fig. 9C). Also important is that there were transmural differences of I HERG in response to dofetilide block. For example, the blockade of I HERG with Endo-AP was 2.5-fold greater than with Epi-AP and 2-fold greater than with Mid-AP (Fig. 9C). Noticeably, these differential effects of dofetilide caused a remarkable change in the pattern of transmural difference of I HERG ; the normal I HERG gradient was changed to Mid-AP.Epi-AP$Endo-AP by dofetilide.

Novel Properties of HERG Channel Reported by AP-Clamp
The present study with AP-clamp revealed several important features of HERG K + channel function, which are otherwise masked with the conventional voltage pulse protocols. Some of these features have been described by previous work from other laboratories using AP-clamp techniques and therefore they will not be repeated in Discussion. Below are the selected aspects which we believe to represent the novel findings on HERG function revealed by the present study.
(1) With AP-clamp, I HERG in ventricular cells peaks at around 230 mV (V Peak ) and in atrial and SAN cells at 240 mV, with respect to voltage, as revealed by the instantaneous I-V relationships (Fig. 3). By comparison, I HERG peaked at 210 mV with conventional pulse protocol. This implies that pulse protocols introduced ,20-30 mV voltage error to measurement of the voltage-dependence of HERG channel. The fully activated I-V relationship, obtained by various reactivating (repolarizing) steps following an inactivating (depolarizing) pulse with conventional pulse protocols or by ramp protocols, demonstrated the maximum I HERG at 230 mV [21,23], approximating the AP-clamp value. Unfortunately, the protocol could not distinguish the regional difference of V Peak or the voltage-dependence of HERG channel, especially the difference between V-APs and A-AP. (2) AP-clamp revealed that with respect to APD, I HERG in ventricular cells peaked near APD 60 and in atrial and SAN cells it peaked near APD 70 (APD Peak ). The data imply that APD Peak is predicable regardless of the length of APD. For example, the length of Mid-AP (APD 90 ) was around 400 ms and that of Endo-AP and Epi-AP was approximately 250 ms, but I HERG in these regions all peaks at APD 60 that corresponded to the length of phase 2 plateau. This was consistent with the view that I Kr serves to terminate the phase 2 plateau of APs. Conventional pulse protocols do not provide The initial rising phase (phase 1) of I HERG was elicited by the depolarization phase of an AP and the major rising phases of I HERG (phase 2 and phase 3) corresponded to the repolarization phases of an AP. The rate of rising phase was determined by the rate of membrane repolarization. No such conclusion can be drawn with conventional pulse protocols. (4) There was transmural heterogeneity of I HERG function as indicated by the differences in I HERG area, a measure of total K + passing through HERG channels during an AP. The size of I HERG area was found to be in the order of Endo-AP.Mid-AP.Epi-AP. Conventional pulse protocols would mask this important property of HERG channel. (5) There was regional difference of I HERG in response to dofetilide blockade. Our results demonstrated that the effects of dofetilide on I HERG elicited with APs from different regions of the heart were quantitatively different. The % blockade of I HERG with A-AP was some 4-fold greater than Epi-AP and 2-3 fold greater than APs of other regions. The differences also existed among different layers of left ventricular wall with significantly greater inhibition seen with Endo-AP than with Mid-AP and Epi-AP. Importantly, this transmural difference of I HERG blockade by dofetilide broke the normal pattern of transmural gradient of I HERG from Endo-AP.Mid-AP.Epi-AP under control conditions to Mid-AP.Epi-AP$Endo-AP in the presence of dofetilide. And the maximum transmural difference was also diminished from 6 (Endo-AP minus Epi-AP) to 2.5 (Mid-AP minus Endo-AP). Obviously, these differences cannot be revealed by using conventional pulse protocols. (6) During an AP, the complex nature of the interactions between different currents means that small changes in one current could alter the behavior of others. Indeed, our data show that I HERG function was influenced by alterations of preceding currents. Our data show that I HERG function varied in response to selective inhibition of any given current activated prior to I Kr . For instance, blockade of I Kur markedly enhanced I HERG and in contrast, blockade of I CaL caused pronounced reduction of I HERG (Fig. 8).

Biophysical Mechanisms for HERG Channel Reported by AP-Clamp
Evidently, HERG function is determined by HERG properties and AP characteristics; the latter indicates the differences in the rate of repolarization that governs the gating of HERG channels.
(1) The dynamic changes of I HERG (or the rising phase) during an AP were determined by rapid reactivation or removal of inactivation of HERG channels, a process depending upon the dynamic changes in rate of repolarization. (2) Voltage-dependent rapid reactivation of I HERG determined the regenerative (all-or-none) repolarization. Under normal conditions, the cardiac repolarization process, once initiated, will carry on itself until it reaches full repolarization. The present study provides an explanation for the regenerative repolarization process: Membrane repolarization initiated by I to activation and I Ca,L inactivation tends to reactivates I HERG , and I HERG reactivation in turn further repolarizes membrane which results in more I HERG reactivation and further more repolarization. (3) The decaying phase of I HERG with AP-clamp has been thought to be the balance between reactivation and deactivation of HERG channels [23,30]. Our data, however, provide an alternative mechanism for that. According to our data in Figure 2 as well as previous studies, no apparent deactivation process was seen at potentials positive to 250 mV and slow deactivation was noted at 260 mV to 280 mV with time constants of over 1 s. Considering that the decaying phase of I HERG during a ventricular AP started from 240 mV and spanned ,50 ms in duration, it is unlikely that deactivation process was involved. Similarly, changes in HERG conductance did not account for the decline either because during the whole decaying phase of I HERG , HERG conductance oppositely kept increasing (Fig. 6). In sharp contrast, the fall of driving force paralleled the declining of I HERG . Thus, driving force or the electrochemical gradient may be the major factor determining I HERG decay after the peak. This notion let us speculate that the rapid fall in driving force terminated repolarization and prevented excessive cardiac hyperpolarization that could otherwise happen with regenerative HERG reactivation during repolarization. (4) We used the area covered by I HERG trace to quantify the size of I HERG because it is a more accurate measure of K + efflux through HERG channels during the whole period of an AP. By comparison, I HERG amplitude determined by the peak value only represents the size of I HERG at that particular time point. Due to differences of AP morphology or of the rate of membrane repolarization, I HERG amplitude at any time point was different; changes in membrane potential during an AP were dynamic and so was the I HERG amplitude. To integrate the dynamics, measuring the area is a better method for defining HERG function. Indeed, with the use of area, we were able to identify the regional and transmural heterogeneity of HERG function and variation of drug blockade of I HERG . We found that the volume of K + carried by HERG channels during an AP, that is the area under I HERG trace, was determined by at least three factors: rate of repolarization, duration of repolarization and driving force. Using these three parameters we were able to predict the relative size of areas of APs from various regions with the pattern consistent with the experimental data: Endo-AP.Mid-AP.Epi-AP$A-AP. SAN-AP. With I HERG amplitude as a parameter, such regional differences cannot be revealed.

Potential Implications of the Results
One of the important implications of our findings is that the repolarization-dependent reactivation of HERG channels contributing to the regenerative repolarization process of cardiac cells may help to suppress arrhythmias initiated by early afterdepolarizations and premature beats [11,23]. I HERG reactivates to the maximum extent at around APD 60 -APD 70 with respect to APD (APD Peak ) and at 230 mV to 240 mV with respect to transmembrane potential (V Peak ), which on one hand can avoid interfering with normal Ca 2+ entry into the cells to initiate excitation-contraction coupling because I CaL normally peaks at around 210 mV, and on the other hand can prevent excessive or secondary I CaL activation by generating large volume of outward K + flow. This mechanism can serve to counteract any secondary depolarizations falling during this phase, particularly those generated by I CaL .
Another important implication of our findings is that there exist regional heterogeneity and transmural gradient of I HERG , when assessed with I HERG area. Given that myocytes from different layers of ventricle or from different regions of the heart bear the same I Kr current densities [26], the differences of I HERG area may reflect the true regional heterogeneity and transmural gradient. These regional differences of I HERG may partially account for the regional variations of cardiac repolarization and may have some important pathophysiological implications: being antiarrhythmic under physiological conditions but also being proarrhythmic or arrhythmogenic when in presence of HERG blockers which create transmural dispersion of repolarization. One example of the latter has been documented by Di Diego et al [31] who showed that cisapride (a potent blocker of HERG channel) induced transmural dispersion of repolarization and torsade de pointes in the canine left ventricular wedge preparation during epicardial stimulation. Also significant is that the extents of drug blockade of I HERG , specifically, the effects of dofetilide on I HERG are different with APs from different regions. Dofetilide at a concentration of 10 nM demonstrates the greatest inhibition of I HERG (as assessed by area) with A-AP, relative to APs from other regions. Intriguingly, dofetilide is currently in clinical use for suppressing atrial arrhythmias. Moreover, in the heart, the contribution of HERG to cardiac repolarization in any given cell type will also depend on the level of channel expression in that cell. A study reported by Gintant [32] suggests that in canine heart I Kr density in atrium is approximately 50% higher than in ventricle. In terms of the transmural differences of dofetilide blockade of I HERG , our results show that dofetilide diminishes the maximum transmural differences of I HERG area to 2.5 (Mid-AP minus Endo-AP) from 6 (Endo-AP minus Epi-AP) for control. Unfortunately, we are unable to draw any conclusions from the present study as to whether the reduction of the transmural difference of I HERG will increase or decrease transmural dispersion of repolarization.
Finally, our data revealed for the first time the interactions between I Kr /HERG and I to , I Kur or I CaL that activates before I Kr / HERG does. The important message from these results can be understood as a gate-safeguard mechanism of HERG function for cardiac repolarization. It is known that I Kur activates rapidly upon membrane depolarization with a linear or slightly outward rectifying I-V relationship and stays activated with only partial inactivation during the whole course of an AP [25,29], indicating that it contributes to various phases of repolarization, particularly the phase 2 plateau. The present study demonstrates that when I Kur is suppressed, I Kr /HERG tends to increase. This can serve as a compensatory mechanism or a ''repolarization reserve'' to minimize the excessive slowing of repolarization due to I Kur blockade. In sharp contrast, when I CaL is depressed, I Kr /HERG tends to decrease. This on one hand can allow a longer time for more Ca 2+ entry for contractile function and on the other hand can limit the excessive acceleration of repolarization consequent to I CaL reduction. Interestingly, I to , which contributes mainly to the initial repolarization, when blocked does not significantly alter I Kr /HERG that has relatively small contribution to phase 1 repolarization. It is tempting to speculate that in atrial fibrillation when Ca 2+ channel function is depressed [33], I Kr will decrease accordingly so as to promote Ca 2+ entry and minimize APD shortening.

Limitations of the Study
The assessment of I HERG in the present study was based upon a few selected AP waveforms, which are representative of APs in different regions of the heart. However, it should be noted that the results may not be extrapolated to cells from other regions or subregions as AP waveforms are different in every different cells. Moreover, in native cells with co-existing multiple ion currents that can influence the function of HERG channels, the properties of I Kr may not be the same as I HERG recorded in a HERGoverexpressing cell line.

Author Contributions
Conceived and designed the experiments: ZPS. Performed the experiments: PZ PG. Analyzed the data: PZ PG XLB. Contributed reagents/ materials/analysis tools: XLB. Wrote the paper: ZPS.