Single Channel Analysis of the Inward Rectifier K Current in the Rabbit Ventricular Cells

Japanese Journal of Physiology, 33,1039-1056, 1983

Masaki KAMEYAMA, Tatsuto KIYOsUE,* and Mlchimasa SOEJIMA**

The National Institute for Physiological Sciences, Okazaki, Aichi, 444 Japan *Department of Physiology , Medical College of Oita, Oita, Oita, 879-56 Japan **Department of Internal Medicine , Jikei University School of Medicine, Minato-ku, Tokyo, 105 Japan

Abstract The inward rectifier K channel in rabbit ventricular cells was studied by the patch-clamp method. Single channel currents were recorded in giga-sealed cell-attached patches with 150 mM K+ in the pipette. The slope conductance in the membrane potential range from -140 to -40 mV was 46.6±6.7 pS (mean±S.D., n=16), and was reduced by decreasing [K+] in the pipette (20 or 50 mM). The channel was blocked by an application of Cs+ or Ba2+ (0.04-1 mM) in the pipette. Outwardly directed current, recorded with 50 mM K+ in the pipette, revealed the inward rectification of the single channel current. The probability of the channel being open was 0.33±0.05 (n=10) at the resting potential (RP=-81.7±1.7 mV, n=16) with 150 mM K+ in the pipette, and it decreased with hyperpolarization. The mean open time of the channel was 178±25 msec (n=6) at RP. The closed time of the channel seemed to have two exponential components, with time constants of 11.0±2.0 msec and 1.92±0.52 sec (n=6) at RP. The slower time constant was increased with hyperpolarization. The averaged patch current recorded upon hyperpolarizing pulses demonstrated a time-dependent current decay as expected from the single channel kinetics. The results indicated that the inward rectifier K+ current has time- and voltage-dependent kinetics.

Key Words: patch clamp, inward rectifier channel, single ventricular cell.

The membrane currents of cardiac cells exhibit inward-going (anomalous) rectification when the membrane is hyperpolarized (WEIDMANN,1955; NUTTER and NOBLE,1960). This feature has been accounted for by postulating channels

Received for publication July 9, 1983

1039 1040 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA which allow K+ current to flow more readily in the inward than in the outward direction in Purkinje fibers (CARMELIET,1961; HALL et al., 1963; DECK and TRAUTWEIN,1964; NOBLE, 1965; HAASand KERN, 1966) and in ventricular cells (CLEEMANand MORAD, 1976, 1979; MCDONALDand TRAUTWEIN,1978). The inward-rectifying K+ current in cardiac cells has several common features to those reported in skeletal muscle fibers (ref. e.g., ADRIANet al., 1970) and in egg cells (ref, e.g., HAGIWARAet al., 1976) : 1) the instantaneous current-voltage relation shows inward rectification (MCALLISTERand NOBLE, 1966; NOBLEand TSIEN, 1968); 2) the conductance change is a function of both the membrane potential and the external K+ concentration rather than the potential alone (NOBLE,1965; MCALLISTERand NOBLE,1966); 3) the channel is blocked by cations such as Cs+ and Ba2+ (ISENBERG,1976; CLEEMANand MORAD,1976). Recent advances in patch-clamp techniques (HAMILLet al., 1981) allowed the isolation of single channel currents through the inward rectifier channels in cardiac cells (TRUBEet al., 1981) as well as in tunicate egg cells (FUKUSHIMA,1981, 1982) and cultured rat myotubes (OHMORIet al., 1981). In this paper, the inward rectifier K+ channel in single ventricular cells of the rabbit was further studied by the patch-clamp method. It is shown that the unitary conductance of the channel shows a rectification and the inward rectifier current has time- and voltage-dependent kinetics.

METHODS Preparation. Rabbit ventricular cells were isolated using a procedure similar to that described elsewhere (TANIGUCHIet al., 1981; ISENBERGand KLOCKNER, 1982). The heart was dissected and perfused with nominally Ca2+-free Tyrode solution containing collagenase (0.4 mg/ml; Sigma type I) through the coronary artery for 60 min at 36-37°C. After washing out collagenase, the heart was im- mersed in the "storage solution" for at least 1 hr at 4°C before electrophysiological experiments. The storage solution contained (in mM) : glutamic acid 70, KCl 25, taurine 10, oxalic acid 10, KH2PO4 10, HEPES 10, glucose 11, and EGTA 0.5; pH was adjusted to 7.4 by adding KOH. Patch clamp. Ventricular cells, dispersed in a recording chamber on the stage of an inverted phase-contrast microscope, were perfused with normal Tyrode solution. The electrical set-up for the patch clamp was similar to that described elsewhere (SIGWORTHand NEHER, 1980; HAMILLet al., 1981). Single channel currents were recorded from cell-attached membrane patches using fire-polished glass micro-electrodes filled with 150 mM KCI (2-10 Me). Sealing resistance was increased to 5-100 GS2 by applying negative pressure ('-S.'-50 cm H20) to the inside of the electrode. The potential inside the electrode was changed to alter the membrane potential of the patch. The single channel currents and the potential inside the electrode were displayed on a storage-type oscilloscope and were stored

Japanese Journal of Physiology INWARD RECTIFIER CHANNEL IN HEART CELLS 1041 on magnetic tape. The patch currents were low-pass filtered at 0.2-1 kHz with a fall of 48 dB/octave and were processed by computer. Solutions. The normal Tyrode solution contained (in mM) : NaCI 136.9, NaHC03 6.0, KCl 5.4, CaCl2 1.8, MgCl2 0.53, NaH2P04 0.33, glucose 5.5, and HEPES 5.0; pH was 7.3-7.4. The high K+ solution contained: KCl 140, KH2P04 0.5, MgCl2 0.5, glucose 5.5, EGTA 1.0, and HEPES 5.0; pH was 7.4. In this solution, EGTA minimized the accumulation of intracellular Ca during changes of the bathing solution. The pipette solution consisted of (in mM): KCl 150 and HEPES 5.0 with pH 7.3-7.4. In low K+ solutions, NaCI was isosmotically substituted for KCI. Cs+ and Ba2~ (0.01-1 mM) were simply added to the solution. In some experiments 1.8 mM CaC12 was added to the pipette solution to improve the sealing resistance between the pipette and the membrane patch. Experiments were carried out at 31-36°C.

RESULTS I. Identification of the inward rectifying K+ channel The dissociated ventricular cells used in the experiments were rod-shaped and quiescent in the normal Tyrode solution. The resting membrane potential (RP) was - 81.7+ 1.7 mV (mean±S.D., n=16), when recorded with the patch-clamp pipettes after a puncture of the membrane patches. The action potentials elicited by stimuli were 110-130 mV in amplitude and 200-500 msec in duration. Thus, the dissociated cells retained their normal membrane electrical properties even after enzymatic treatment. Current were recorded from the cell-attached membrane patches with a pipette solution containing 150 mM KCl in the normal Tyrode solution (Fig. 1). Figure 1 A shows an example of the most frequently recorded current type at membrane potentials from 60 mV negative to the resting potential (RP-60 mV) to RP+ 120 mV. In the potential range between RP-60 and RP+40 mV, all-or-none pulse- like inward currents were recorded in most patches (82 out of 96 patches). The currents were considered to be flowing through a single ionic channel since the amplitude of the pulse-like events was quite uniform at a given membrane potential, and varied reversibly with changing the membrane potential. In 60 out of 96 patches, the currents showed two or more amplitude steps which were usually in- tegral multiples of the unitary currents (i). Thus, the recorded patch currents were those through discrete channels of a single type. The number of channels in a patch was estimated from the maximum number of current steps. The average number of channels was 2.1 ± 1.7 (n=91) with a pipette resistance of 3-10 MS2. Some patch currents, however, had smaller amplitudes than i, which will be discussed in Section IV. The probability of the channel being open became higher at more positive potentials (up to RP+40 mV), and was interrupted by short closings. The current-voltage (I V) curve of the channel was linear in the potential

Vol. 33, No. 6, 1983 1042 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA

Fig. 1. Single-channel currents of the inward rectifier channel. A : series of patch currents recorded at various membrane potentials indicated at the left of each trace as a voltage deviation from the resting potential (RPM -82 mV). Pipette resistance was 10 MSS. Currents were low-pass filtered at 800 Hz. B : current-voltage relation of the patch current illustrated in A. The slope conductance was 50 pS. Broken lines indicate the noise level of +0,4 pA.

range between RP-60 and RP+40 mV (Fig. 1 B). The slope conductance (r) of the channel was 50 pS. At potentials more positive than RP+60 mY, the amplitude of the single channel current was reduced, while the noise level increased mainly due to the decrease in the sealing resistance. The current reversal was dif- ficult to detect even at RPM 120 mY in most experiments, suggesting a small i and/or a low opening probability in this potential range. The patch current seemed to be carried by K+ since the current was not observed with K+-free Nat-rich solution in the pipette. Chloride ion was unlikely to carry the current because a current of similar amplitude was consistently recorded when KCl in the pipette was substituted by K-aspartate (not shown in figure). To examine the K+-dependency of the current further, the single channel current was measured with 20, 50, and 150 mM KCl in the pipette (Fig. 2). The amplitude of the current at the corresponding potential was significantly reduced by decreasing K+ . The values of r with 150, 50, and 20 mM K+ were 46.6± 6.7 (n=16), 36.1± 5.4 (n=7), and 20.1 ± 5.1 (n=7) pS, respectively. The slope conductance was roughly proportional to the square root of [K+] in the pipette solution (Fig. 2, inset). These results indicated that the current was predominantly carried by K~ . Zero-current potential, defined by a linear extrapolation of I -V

Japanese Journal of Physiology INWARD RECTIFIER CHANNEL IN HEART CELLS 1043

Fig. 2. Dependency of the channel conductance on external K+ concentrations. Am- plitudes of the patch current with 150, 50, and 20 mNi K+ in the pipette are plotted against the potential deviation from RP. Each plot indicates mean + S.E.M. and the number of experiments. Linearly extrapolated zero-current potentials are also shown on the potential axis as mean+S.E.M. Inset shows the slope conductance plotted against the square root of K+ concentration.

Fig. 3. Blocking effects of Cs+ and Ba2+ on the patch current at three different potentials. A, control; B, with 0.04 mM Cs+ in the pipette; C, with 0.04 mM Ba2+. Currents were low-pass filtered at 0.8 (A and C) and 1 kHz (B).

Vol. 33, No. 6, 1983 1044 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA curve, was shifted to the negative direction on reducing K+ from RP+61±3 (mean±S.D. in 150 mM K+, n=16) to RP±46±7 (in 50 mM K+, n=7), and RP±22±9 (in 20 mM K+, n=7) mY. These values, however, were 10-25 mY negative to the estimated K1- equilibrium potential (EK) for each external [K+], assuming an intracellular [K+] of 130-140 mi. Effects of external Cs+ or Ba2+ on the probability of the channel being open (p0) was illustrated in Fig. 3. Cs+ (0.04 mM) produced marked interruptions of channel opening, having a very short period in the closed state (Fig. 3 B). The values of po were 0.37 (0.34, 0.37, and 0.39, n=3) with 0.04 mM Cs, and 0.25 (0.1$, 0.27, and 0.29, n=3) with 0.2 mM Cs+ at RP with 150 mM K+ in the pipette. The latter value was small compared to that obtained without Cs, 0.33 (0.25- 0.41 in 10 patches). Ba2+ shortened the open time without increasing the number of brief interruptions (Fig. 3 C). With 0.04 mM Ba2+, po was 0.04±0.03 (n=4) at the resting potential.

II. Inward rectification of the single channel I -V relation In order to examine the single channel current at potentials positive to EK, we employed a high K+ bathing solution and a pipette solution containing 50 mM K-1-. In this condition, the resting potential of the cell was approximately zero and EK in the patch was estimated -26 mY. Thus, one would expect to record an outwardly directed K+ current without excess noise. Such an example

Fig. 4. Current reversal of the inward rectifier channel. A : series of patch currents at membrane potentials from -60 to 40 mY, with 50 mM K+ in the pipette. The cell was bathed in high K+ solution. Broken lines indicate the zero-current level. Currents were low-pass filtered at 200 Hz. B : I -V relation of the current in A, indicated as mean ± S.E.M. of seven measurements. Slope conductances were 37 pS for the inward and 14 pS for the outward current.

Japanese Journal of Physiology INWARD RECTIFIER CHANNEL IN HEART CELLS 1045 is illustrated in Fig. 4. At -60 and -40 mV, the single channel current was inwardly directed, whereas outward current was observed at 0-40 mV. Since the maximum number of current steps agreed in both direction, we considered that both the inward and outward currents were flowing through the same channel. The reversal potential of the current was estimated -23 mV, which was comparable to Eg. The opening probability of the channel at -60 and -40 mV was nearly unity, and it decreased at potentials positive to the reversal potential. It is thus possible that the channel has a gating process which is deactivated at potentials exceeding the reversal potential. The single channel I V curve revealed that the slope conductance was much smaller in the outward than in the inward current. Above results indicate that the channel has: 1) a relatively high distribution density in the membrane (cf. NoMAet al.,1984); 2) an inward rectification; 3) a K+ dependency; and 4) a sensitivity to Cs+ as well as Bat, all of which are consistent

Fig. 5. Voltage dependency of the probability of channel opening. A : amplitude histogram of the single-channel current at the resting potential with 150 mM K+ in the pipette. Unitary current and opening probability were calculated to be 2.72 pA and 0.32, respectively. Low-pass filter of 800 Hz was used. Step size of the current amplitude was 0.065 pA. B : probability of the channel being open plotted against the membrane potential. Zero-potential indicates the resting membrane potential. C: mean patch current obtained by integrating the current trace.

Vol. 33, No. 6, 1983 1046 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA with the properties of the inward rectifying K+ current. We concluded, therefore, that the isolated currents were those through the inward rectifier K+ channel.

III. Voltage-dependent inactivation of the inward rectifier channel The discrete nature of open-close transition of the channel was examined in the same condition as in Fig. 1. The histogram of current amplitude shown in Fig. 5 A consisted of two Gaussian curves separated by 2.72 pA with standard deviation of 0.26 pA, indicating that closing and opening of the channel could be distinguished from the fluctuation of the background noise level. Thus, two areas of the Gaussian curves represent the probabilities of channel being closed and open at a given membrane potential. When two or more channels were simul- taneously recorded in a patch, the amplitude histogram showed three or more discrete areas, fractions of which were well fit to a binominal distribution. This finding suggested that each channel opens and closes independently. A voltage- dependency of po was examined in three patches, in which the maximum numbers of current steps were unity (Fig. 5 B). It was consistently observed that po increased with depolarization of the membrane patch. In 10 patches po was 0.33+ 0.05 at RP. The mean current of the single channel was obtained by averaging the current amplitude throughout the trace for more than 16 sec (Fig. 5 C). The mean current was identical in principle to the product of i xpo. Then mean current was the maximum (approximately 0.9 pA) at 0-20 mY positive to RP and was reduced by either hyperpolarization or depolarization.

Fig. 6. Histograms of the open time (A) and the closed time (B). Exponential lines were obtained by the least square method. Time bins are 50 msec for A and 2 msec for B. In the measurements, closed times shorten than 2 msec were neglected to avoid compli- cations due to the low-pass filter (0.8-1.2 kHz) and substate openings. The number of events (n) and the time constants (r0 and zf) are indicated in each graph.

Japanese Journal of Physiology INWARD RECTIFIER CHANNEL IN HEART CELLS 1047

The histograms of open and closed time, recorded at RP with 150 mM in the pipette, are illustrated in Fig. 6. The distribution of open time was well fit to a single exponential curve, suggesting a first order process of the channel closing (Fig. 6 A). The averaged time constant of the open time (zo) and the mean open time were 181+27 and 178+25 msec (n=6), respectively, at RP. The distribution of closed time, however, did not fit to a single exponential curve, but had at least two components, fast and slow (Fig. 6 B). By neglecting the closed time longer than 50 msec, the fast component of the histogram could be fit to a single exponential curve with a time constant (r f) of 12.3 msec. The averaged values of zf and the mean closed time were 11.0+2.0 and 364+194 msec (n=6), respectively, at RP. The existence of the fast component of the closed time was evident in the single-channel current traces in Figs. 1 A and 3 A, in which opening of the channels was usually interrupted by a series of brief period of closings. The channels thus appeared to open in bursts. To examine the properties of burst- like opening of the channel, the bursting time was defined as a period of successive opening and closing during which no closed time was longer than 3 times t, i.e. the critical time T~. The inter-burst interval thus would be the duration of closed states longer than T~. Figure 7 A shows a reconstruction of bursts of openings. Histograms for the bursting time and the inter-burst interval could be well fit to single exponential curves except in the initial part of the histogram of inter-burst

Fig. 7. Histograms of the bursting time (B) and the inter-burst interval (C). Original current trace (A, upper) and reconstructed bursting time (A, lower) are shown. Time bins for B and C are 100 and 400 msec, respectively.

Vol. 33, No. 6, 1983 1048 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA

Fig. 8. Voltage dependency of the time constants of open-close kinetics. A: time constants for the open time (open symbols) and the fast component of the closed time (filled symbols). B : time constants for the bursting time (open symbols) and the inter- burst intervals (filled symbols). Different symbols represent different patches. 0 mV indicates the resting potential in both A and B. interval (Fig. 7 B and C). Time constants for burst time (TB) and inter-burst interval (zs) were 564±68 msec and 1.92±0.52 sec (n=6), respectively, at RP. The four time constants zo, z f, zB, and zs at various membrane potentials were obtained in a similar way, and they were plotted as a function of the potential in Fig. 8. It is evident that zo and zB decreased, whereas zs increased with hyperpolarization in the potential range from RP-40 to RP+40 mV. However zf did not show a significant change in this potential range. Number of openings during a burst was 3.9± 1.2 (n=6) at RP. The kinetic properties of the inward rectifier channel suggested that the current flowing through this channel had a time- and voltage-dependent inactivation process. Since each channel seems to function independently, the sum of many current records in the patch clamp should correspond to the current measured in a whole-cell voltage clamp. On this basis, hyperpolarizing pulses from RP+20 to RP-10 mV for 500 msec were applied to the membrane patch and the currents of 57 traces were averaged (Fig. 9 A). Figure 9 B illustrates 5 representative original traces in which the capacitative surge was subtracted. It is clear that the averaged current jumped inwardly to a new level at the onset of the hyperpolarizing pulse due to a sudden increase in the driving force, and that it subsequently decreased during the clamp pulse, indicating an inactivation process of the channel. At the end of the step pulse, the current jumped outwardly to a less negative level

Tnnnnncv lnurnnl of Phvcinlncv INWARD RECTIFIER CHANNEL IN HEART CELLS 1049

Fig. 9. Time-dependent decay of the averaged patch current of the inward rectifier channel. A : time course of the averaged current of 57 trials in a patch membrane. The membrane-patch was hyperpolarized from RP +20 to RP- 10 mV for 500 msec as indicated by a horizontal bar. This bar also indicates the zero current level. Continuous line is a theoretical curve derived from the kinetic model (see APPENDIX)with a1=92, t1=4.1, a2=0.81, and j2=11.6 sec' at RP+20 mV and a1=70, i3=6.6, a2=0.62, and 12=18.8 at RP-10 mV. B : five examples of original current traces. This patch contained five channels. Pipette resistance was 7 M2. Low-pass filter of 500 Hz was used. and gradually increased to reach its initial level. The averaged current of the inward rectifier channel was thus time-dependent. IV. Other features of the inward rectifier channel The single-channel current of the inward rectifier channel revealed a smaller "sublevel" of 65-85 % of the unit amplitude (Fig . 10). The sublevel was identified as a step-like decrease in the current, which usually lasted for less than 20 msec. Since no outward deflection of current was observed during closure of the channels, superimposition of some other outward currents on the inward rectifier channel was unlikely. The sublevel, however, occurred less frequently compared to the full-open state. Therefore, we did not analyze it systematically. In the course of the experiment, channels with small unit amplitudes were

Vol. 33, No. 6, 1983 1050 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA

Fig. 10. Sublevel opening of the inward rectifier channel. A : single-channel current at various membrane potentials. 0 mV indicates the resting potential. Continuous lines indicate the zero-current level. B: 1 V relations of the full-open state (open circles) and the sub-state (filled circles). sonietimes recorded. These channels were easily distinguishable from the inward rectifier channel when the both currents appeared in a patch. One type of these channels had r of 22-36 pS with 150 mM K+ and a mean open time similar to the inward rectifier channel. Thus, it is possible that this type of channels might be the inward rectifier channel located in the membrane where the potential was out of control, such as the "rim channel" (NEHERet a!., 1978). Another type of small patch current had much smaller po than the inward rectifier channel and an al- most constant r of 12-17 pS. Thus this type of channel was considered to be different from the inward rectifier channel.

DISCUSSION

This study identified the inward rectifier K+ channel and revealed two major features of the channel in mammalian ventricular cells. Firstly, the single channel current-voltage relation of the inward rectifier is not linear around its reversal potential. Secondly, the inward rectifier channel has voltage-dependent transition kinetics between the open and closed states. Identification of the inward rectifier channel. The inward rectifier channel has quite similar properties to the IK1defined by NOBLE(1962) in Purkinje fibers. Igl has also been described in ventricular cells (BEELERand REUTER,1970; Mc-

Japanese Journal of Physiology INWARD RECTIFIER CHANNEL IN HEART CELLS 1051

DONALDand TRAUTWEIN,1978) and in atrial cells (ROUGIERet al., 1968; NOBLE, 1976), where it was often referred to as the background K+ current. Igi shows inward rectification (NUTTERand NOBLE,1960; NOBLE, 1962, 1965; MCALLISTER and NOBLE,1966) and its conductance is dependent on both the electro-chemical gradient for K+ and the external K+ concentration (HALL et al., 1963; DAUT, 1982). Furthermore, the current is blocked by an application of either Cs+ or Ba2+ (ISENBERG,1976; CLEEMANand MORAD, 1979). These properties are also demonstrated for the inward-rectifying channel in the present study. Firstly, the conductance of the channel is dependent on the external [K+J; r is roughly proportional to the square root of the external [K+] (Fig. 2; see also HAGIWARA and TAKAHASHI,1974; DAUT, 1982). Secondly, the channel has the inwardly rectifying 1-V relationship as shown in Fig. 4. The negative shift of the linearly extrapolated zero-current potentials relative to the estimated K+ equilibrium potentials (Fig. 2) might also support the rectification in the single channel I V curve. Finally, the opening probability of the channel is reduced by external Cs+ or Ba2+ (0.04-1 mM). These results are consistent with those reported preliminarily in guinea pig ventricular cells (TRUBEet al., 1981). Thus, it can be concluded that the current through the inward rectifier channels is identical to IK1. The average number of channels observed in a single patch is 2.1. When the membrane patch is assumed to form a hemispheric shape with diameter ranging 0.5-1.5µm, the channel density would be 0.3-3/µm2. With the further assumption of r in 5.4 mM external [K+] to be 10 pS, from the extrapolated [K+]-conductance curve in Fig. 2, the maximum conductance of the inward rectifier would be 3-30 mS/cm2. This value is comparable to that obtained in the whole-cell clamp study (approximately 5 mS/cm2; Kameyama, unpublished data) in the normal Tyrode solution. Rectifying properties of the channel. The total current through a mass of homogeneous ionic channels (I) can be expressed as :

I=Npoi, where N, p°, and i are the total number of channels, the opening probability, and the unitary current amplitude, respectively. The inward rectification of the channel may be attributed to the voltage-dependent change of both po and i. As discussed above, i has an inwardly rectifying I -V relation. This property may account for the non-linearity of the instantaneous 1-V relation of IK1, since po and N do not change appreciably at the step change in the membrane potential. In the steady state, both po as well as i may contribute to the rectification because po seems to decrease with depolarization when the channel current is outwardly directed (Fig. 4 A). Thus, the negative slope in the I -V curve of Igi (DECK and TRAUTWEIN, 1964; MCALLISTERand NOBLE, 1966) is possibly due to the voltage dependent reduction of p0. Voltage-dependent inactivation of the channel. The inward rectifier K+ current in cardiac cells has been regarded as a time-independent background current

Vol. 33, No. 6, 1983 1052 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA

Fig. 11. Kinetic parameters of the inward rectifier channel. A and B : transition rate constants for the kinetic model of the inward rectifier channel. C : probabilities of the channel being in open (p0), closedi (poi), and closed2 (pa) states. D : time constants for the macroscopic current of the inward rectifier channel. Ordinate: Zi on the left side and r2 on the right side. Zero-potential indicates the resting membrane potential of about - 82 mV.

(NOBLE,1975), and the time-dependent decay upon hyperpolarizing pulses was considered as due to the depletion of extracellular K+ (NOBLE,1975; BAUMGARTEN and ISENBERG,1977; MCDONALDand TRAUTWEIN,1978). The results in this study, however, indicate that the open-close kinetics of the channel is voltage- dependent. Therefore, the macroscopic current of the inward rectifier channel should also exhibit a time-dependent change when the membrane potential is changed. A time-dependent current decay is demonstrated in the averaged time

Japanese Journal of Physiology INWARD RECTIFIER CHANNEL IN HEART CELLS 1053 course of the patch current (Fig. 9 A). The transition kinetics between open and closed states of the inward rectifier channel cannot be explained by a scheme of simple first-order kinetics since the closed time histogram shows two exponential components. One of the diagrams to account for the experimental data shown in Fig. 8 might be to assume 2 closed states (CONTIand NEHER, 1980) as :

al a2 open closedl 2 closed2, s~ ~z where a's and j3's refer to apparent rate constants of the respective transitions. Theoretical analysis of this model predicts one exponential component for the open time and two exponential components for the close time histogram, which is consistent with the results of the present study. With p°, zo, z f, and zs, one can calculate the rate constants of the model (see APPENDIX). Figure 11 shows the rate constants, the probability of each state and the time constants (zl and z2) of the relaxation of macroscopic current. The rate constants are a1=77+12, ~1= 5.6+0.8, a2 =0.68 +0.25, and j32=16.0+ 6.6 sec-' at the resting potential in 6 patches. The values of a1 and a2 seem to decrease with hyperpolarization about e-fold per 113 and 112 mY, respectively. On the other hand, j1 and J32 increase with hyperpolarization about e-fold per. 63 and 61 mY, respectively. The probabilities of the channel being in the open (p0) and closedl state (poi) decreased, whereas that in the closed2 state (pC2)increased, upon hyperpolarization (Fig. 11 C). The time constants of the macroscopic current seem to decrease with hyperpolarization (Fig. 11 D). The fraction of the fast component, however, is small since pal is small (N 0.04) compared to p0 and pC2in the tested potential range. The theoretical time course of the macroscopic current can be derived from the rate constants in the model. An example is shown in Fig. 9 A, where the theoretical curve seems to be in good agreement with the time course of the averaged patch current. It should be remembered, however, that the model is applicable only at the potentials negative to EK since the possible gating process of activation is not considered in the model, and that the results in the present study do not exclude other kinetic models. Further studies are needed to clarify the kinetic behavior of the inward rectifier channel.

We would like to thank Professor H. Irisawa and Dr. A. Noma for their valuable suggestions and discussions. We are also grateful to Drs. J. Kimura, H. Omori, and Y. Fukushima for their critical reviews of the manuscript. T. K. thanks Prof. M. Arita, and M. S. thanks Prof. T. Miyahara for their providing the opportunities to study in N.I.P.S. The technical assistance to M. Ohara and 0. Nagata is appreciated. This work was supported in part by a Grant-in- Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.

APPENDIX

The model described here deals with the open-close kinetics observed in single channel recordings. The channel has one open state and two closed states as :

Vol. 33, No. 6, 1983 1054 M. KAMEYAMA, T. KIYOSUE, and M. SOEJIMA

al a~ open ± closed (1) ~ closed (2) , (1) where a's and /3's are apparent rate constants which are functions of the membrane potential at a given extracellular [K+]. The steady state probability of each state, po, pal, and pC2,would be: Po=1/(1 +Ki(1 +K2)) , (2) p21=K,/(1 +K,(1 +K2)) , (3) pC2=K,K2/(1+K,(1+K2)) , (4) where K1=91/al and K2=/32/a2. The probability density functions for the open time, fo(t), and the closed time, f,(t), are : f0(t)=j3, eXp (-jSlt) (S) and fC( t) = al(~1_'~ a2) eXp (-al) t + al(a2 "2) eXp (-/l2t), (") where Al and A2(A1>A2) are the roots of characteristic equation: A2-(a,+a2+il2)A+ala2=0. (7) The channel thus has one exponential component for the open time and two for the closed time. In the open and closed time histograms, zo, z,-, and zs correspond to /31-1,Al -1, and A2-1,respectively. Therefore, the rate constants would be: a,=(rS-i+zf-1)_(l -pa)zo/(pozfzs) , (8) j3,=v0 ' , (9) a2=1/(zfzSal), (10) ~2=(1-Po)zo/(pozfzs)-a2 . (11) The time constants of the macroscopic current would be the roots of the following equation : (ala2+ j3la2+ j31/32)z2-(a,+/31+a2+32)z+ 1=0. (12)

REFERENCES

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