Journal of Physiology (1991), 443, pp. 629-650

629

With 9 ftgure8 Printed in Great Britain

SODIUM CHANNEL INACTIVATION FROM RESTING STATES IN GUINEA-PIG VENTRICULAR MYOCYTES

BY JOHN H. LAWRENCE, DAVID T. YUE*, WILLIAM C. ROSE AND EDUARDO MARBAN From the Departments of Medicine and *Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA

(Received 22 February 1991) SUMMARY

1. Unitary Na+ channel currents were recorded from isolated guinea-pig ventricular myocytes using the cell-attached patch-clamp technique with high [Na+] in the pipette to enhance the signal-to-noise ratio. 2. The probability that the channel enters the inactivated state (I) directly from resting states (C) was investigated over a wide range of membrane potentials. 3. At membrane potentials of -60 mV or more positive, Markov chain theory was used to estimate the probability of C -+ I from histograms of the number of channel openings per depolarizing period. Holding potentials at least as negative as - 136 mV were required to enspre that all channels resided in C prior to depolarization. 4. At membrane potentials negative to -60 mV, a two-pulse protocol was employed to determine the probability of C -. I from the fraction of blank sweeps during the pre-pulse with correction for missed events. 5. The probability of C -+ I was found to be steeply voltage dependent at negative potentials, falling from 0-87 + 0-03 (mean + S.D.) at -91 mV to 0-42 + 001 at -76 mV. At potentials positive to -60 mV, this probability was less steeply voltage dependent and decayed to near zero at 0 mV. 6. Under physiological conditions, C -+ I transitions may produce appreciable Na+ channel inactivation at diastolic potentials. At potentials above the action potential threshold, inactivation is much more likely to occur from the open state. INTRODUCTION

Voltage-sensitive Na+ channels mediate transient changes in membrane permeability which underlie excitability in nerve and muscle. The behaviour of these channels has been classically described by models with three classes of states: a single open state (0) that conducts current; one or more resting states (C) from which the channel may open; and an inactivated state (I) from which the channel cannot open. In the Hodgkin & Huxley (1952a, b) formulation, Na+ channel activation and inactivation proceed independently; rate constants from each resting or open state to the inactivated state are equal. Subsequently, Na+ channel inactivation from the open state has been well characterized in both whole-cell and single-channel studies, MS 9174

630

J. H LA WRENCE AND OTHERS

although the voltage dependence of this transition remains controversial (Aldrich & Stevens, 1983; Aldrich & Stevens, 1987; Follmer, Ten Eick & Yeh, 1987; Cota & Armstrong, 1989; Yue, Lawrence & Marban, 1989; Berman, Camardo, Robinson & Siegelbaum, 1990). Other studies have revealed a delay in the onset of sodium channel inactivation which suggests that activation and inactivation processes are not independent (Goldman & Schauf, 1972; Gillespie & Meves, 1980; Bean, 1981). Such a delay could imply that inactivation is strictly coupled to activation and does not occur until after the channel opens (Bezanilla & Armstrong, 1977). An alternative explanation for a delay in the onset of inactivation supposes that channels can inactivate only from one of the last of several resting states, with the delay generated by the transit time through other non-inactivating resting states (Armstrong & Gilly, 1979; Nonner, 1980; Bean, 1981). The distinction is important since one scheme obligatorily links inactivation to channel opening whereas the other allows for accommodation (i.e. inactivation without transit through the open state). Direct C -+ I transitions are difficult to prove on the basis of whole-cell experiments, particularly at membrane potentials below the action potential threshold where channel openings are brief and widely dispersed; openings at such potentials do not generate a detectable macroscopic current, but may nevertheless constitute a requisite component of the inactivation pathway for Na+ channels. A number of single-channel investigations have confirmed that Na+ channels can inactivate without first opening (Aldrich & Stevens, 1983; Vandenberg & Horn, 1984; Kunze, Lacerda, Wilson & Brown, 1985; Scanley, Hanck, Chay & Fozzard, 1990), but these studies have generally focused on a limited range of membrane potentials and have not fully characterized the voltage dependence of C -. I. The relative probability of C -+ I at voltages near the action potential threshold is of particular physiological interest in the heart. Transitions to the inactivated state at these negative potentials modulate Na+ channel availability which in turn influences membrane excitability and antiarrhythmic drug binding. We sought to determine at the single-channel level whether cardiac sodium channels can go directly from C -+ I across a broad range of membrane potentials, and to determine the kinetics, voltage dependence, and relative importance of this pathway for inactivation. Separate analytic techniques were required at potentials near threshold and at those more positive. At the more positive membrane potentials, Markov chain theory was used to determine the probability of C -+ I from histograms of the number of channel openings per depolarizing epoch (Aldrich, Corey & Stevens, 1983), whereas at the more negative potentials a two-pulse protocol was required to estimate the probability of C -+ I from the fraction of blank sweeps during the pre-pulse (Hodgkin & Huxley, 1952a). Some of the results have been reported in abstract form (Lawrence, Marban & Yue, 1989; Lawrence, Rose, Yue & Marban, 1989; Rose, Lawrence, Yue & Marban, 1990). METHODS

General methods The general methods employed for the isolation of guinea-pig ventricular myocytes have been previously described (Yue & Marban, 1988). Briefly, young guinea-pigs (250-450 g) were anaesthetized with intraperitoneal sodium pentobarbitone (80 mg kg-') and the hearts rapidly

SODIUM CHANNEL INACTIVATION

631

excised. The aorta was cannulated and perfused retrogradely with a series of solutions at 37 °C: (1) modified Tyrode solution consisting of (mM): 108 NaCl; 5 KCl; 1 MgCl2; 2 CaCl2; 5 HEPESNaOH; 5 sodium acetate; 10 glucose; pH 7-35 for 5 min; (2) a depolarizing solution containing (mM): 25 KCl; 120 potassium glutamate; 10 HEPES-KOH; 1 MgCl2; 10 glucose; pH 7-35 for 5 min; (3) an enzyme solution consisting of the depolarizing solution plus protease Type XIV (0-1 mg ml-'; Sigma, St Louis, MO, USA) and collagenase Type I (0-14 mg ml-'; Sigma) for 5-7 min; and (4) a nominally calcium-free solution consisting of the depolarizing solution plus 1 mMCa-ATP, 2 mM-EGTA and an additional 1 mM-MgCl2 with 50 units ml-' penicillin and 0 05 mg ml-' streptomycin for 5 min. The atria were removed and small pieces (approximately 1 mm3) of ventricular myocardium were minced with scissors, triturated, filtered through a nylon mesh and stored in solution (4). Sodium currents were recorded from rod-shaped myocytes with distinct striations within 20 h of enzymatic dispersion. Pipettes were fabricated from borosilicate glass (Corning, 7099S-100; Corning, NY, USA) and pipette solutions included (mM): (A), 200 NaCl; 0 5 BaCl2; 5 HEPES-NaOH; pH 7-4; (B), 300 NaCl; 0 5 BaCl2; 5 HEPES-NaOH; pH 7-4; and (C), 423 NaCl, 5 KCl; 1 MgCl2; 5 BaCl2; 5 HEPES-NaOH; pH 7-4. When pipettes containing 200 or 300 mM-NaCl were used, the bath contained solution (4). When pipettes containing 423 mM-NaCl were used, the bath solution was concentrated 1-5-fold to minimize the osmotic gradient across the patch (Yue et al. 1989). The high potassium concentration in the bath set the resting membrane potential approximately to zero, enabling estimates of absolute transpatch potentials. Experiments were performed at 20-22 'C. Cell-attached patch recordings (Hamill, Marty, Neher, Sakmann & Sigworth, 1981) were collected 5 min or more after seal formation. This delay was sufficient for stabilization of the wellrecognized shift of steady-state activation and inactivation to more negative membrane potentials (Kimitsuki, Mitsuiye & Noma, 1990). An Axopatch IA amplifier (Axon Instruments, Burlingame, CA, USA) with a CV-3-1A head stage was used. Signals were low-pass filtered (4-pole Bessel at 5-10 kHz, -3 dB) and digitized (40-100 kHz, 12-bit resolution) on a PDP 11-73 computer (Indec Systems, Sunnyvale, CA, USA). Additional digital Gaussian filtering at 4-5 kHz (effective cut-off frequency of 3-1-3-5 kHz) was required at potentials > 0 mV. Data analysis and statistical methods Single-channel records were corrected for leak currents and capacity transients by digital subtraction of templates fitted to records with no openings. Current records were then converted to an idealized form by half-height criteria (Colquhoun & Sigworth, 1983) from which ensemble averages or histograms were constructed. At potentials > 0 mV, low-amplitude events which exceeded the half-height threshold for only one sampling interval were not included as openings; this exclusion minimized the number of false events at these potentials. Ensemble averages were normalized for the number of channels in the patch, estimated from the maximum number of stacked current levels in > twenty sweeps when the membrane was depolarized from a very negative holding potential ( -140 mV). Pooled results are given as means+ standard deviations. Curve-fitting was performed with a non-linear, least-squares minimization algorithm (Marquardt-Levenberg). Compensation for missed openings and closures due to bandwidth limitations was based on the method developed by Berman et al. (1990), who presented a general solution to the problem of correcting for missed brief events in a three-state model which includes an inactivated state. Their approach is an extension of that developed by Colquhoun & Sigworth (1983) for a two-state model. The frequency of false events due to noise was estimated from the ratio of the half-height current threshold to the root mean square (r.m.s.) noise (Colquhoun & Sigworth, 1983). Compensation for differences in free surface charge due to variable [Na+] and [Ba2+] in the patch pipette Although different pipette solutions were used, results were quite consistent when compensated for the effects of varying surface charge. The correction we used is conventional, but is described explicitly here for clarity. The Gouy-Chapman or diffuse double-layer theory describes the changes in membrane surface potential induced by the electrostatic attraction of cations in the bathing solution to fixed negative charges on the membrane (McLaughlin, Szabo & Eisenman, 1971). For cell-attached patch recordings, the bathing solution is the pipette solution and therefore changes in pipette cation concentration will alter local membrane surface charge and modulate the net potential gradient across the membrane. By estimating the relative shifts induced by variable

632

J. H. LAWRENCE AND OTHERS

pipette

cation concentrations we can compare data from experiments using different pipette solutions. For a mixed electrolyte solution the Grahame eouation is a generalized form of Gouy-Chapman theory (McLaughlin et al. 1971):

Otf = J{-

))]}

C{exp( -

(1)

where oa is the apparent free surface charge density in electronic charges per square nanometre,G is a constant and has the value of (nm2 charge-') (mole litre-')05 (McLaughlin et al. 1971), C, is the concentration of the ith of N ion species in the bath solution in moles per litre with a valence ofZi, RT/F is 25-3 mV at 20 R is the gas constant, T is temperature, F is the Faraday constant, and P(0) is the membrane surface potential. The shift in membrane potential to more described by this equation reflects the screening or shielding of hyperpolarized potentials membrane anions by monovalent or divalent bath cations. A second effect of bath cations on membrane potential is due to actual binding of divalent cations membrane surface charges as follows:

2X7

°C,

to

N

(2Fw(o)

1 + Y, KiC, exp~ i-1

2

T

RT

where o- is the fixed surface charge density and K is the association constant (M-1). Fitting these myocytes, Kass equations to data from L-type calcium channels in guinea-pig and rat ventricularelectronic charge & Krafte (1987) estimated the fixed negative surface charge density as 1 bind to (2-5 nm)-2. They also found that calcium and magnesium, but not barium or strontium, these negative membrane charges with an association constant of the order of1 M-1. Assuming the above surface charge density and divalent association constants, T(0) and of for our experimental conditions were determined iteratively from. eqns (1) and (2) using the Marquardt-Levenberg algorithm on MathCAD (MathSoft Inc., CAmbridge, MA, USA). For the three pipette solutions used, the primary determinant of membrane surface potential is the pipette Na+ concentration. Relative to solution A with 200 mM-Na+ and T(0) = -48 mV, solution B with 300 mM-Na+ shifts the membrane potential + 8 mV (vP(0) = -40 mV) and solution C with 423 mM-Na+ results in a + 16 mV shift (P(0) = -32 mV). The 10-fold higher Ba2+ concentration in potential pipette solution C exerted a relatively small effect (only + 2 mV) since membrane becomes less sensitive to changes in divalent cation concentration as the monovalent cation concentration increases. For all figures, data from experiments using solutions B or C are shifted -8 or -16 mV, respectively, on the voltage axis to align with data generated from experiments using solution A. RESULTS

Sodium channel availability at steady state The availability of Na+ channels to open is regulated by the holding potential, which determines the initial distribution of channel conformations among nonconducting states. These non-conducting states include: (1) one or more resting states (C) from which the channel may open in response to membrane depolarization and (2) an inactivated state (I) from which the channel cannot open. Inactivated channels are recycled to C upon repolarization. Figure 1 illustrates the well-known influence of membrane holding potential on channel availability. Panel A shows single-channel records from a patch containing four Na+ channels during membrane depolarization from'-140 to -20 mV. Almost all sweeps are active (i.e. contain at least one opening) and exhibit multiple stacked current levels within the first few milliseconds due to simultaneous openings of multiple channels. The bottom trace is the average current from an ensemble of forty-four consecutive depolarizing steps. The peak magnitude of this current provides an estimate of the maximum channel availability, which is inversely related

SODIUM CHANNEL INACTIVATION A

B

-20 mV

-20 mV

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0.8 pA L 2 ms

0.8

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pAL 2 ms

C 1

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0 -100 -50 Membrane potential (mV) Fig. 1. Sodium channel availability as assessed by measurement of steady-state inactivation. A and B show single-channel currents (i = -1-91 pA) recorded from a patch containing four Na+ channels in response to step depolarizations from a holding potential of -140 (A) or -105 (B) mV to a test potential of -20 mV. The records were low-pass filtered at 5 kHz (-3 dB) and digitized at 100 kHz. An additional 5 kHz Gaussian filter was applied to enhance event detection resulting in a net cut-off frequency of 3-5 kHz. The ensemble-average currents shown below were generated from 44 (A) and 361 (B) sweeps, respectively. It is apparent that Na+ channel availability, as reflected by single-channel activity and peak ensemble current, is reduced when the holding potential is depolarized. C is a steady-state inactivation curve generated from a separate patch containing ten Na+ channels. The voltage protocol consisted of a holding potential of -100 mV, pre-pulse potentials ranging from -140 to -60 mV for 1200 ms and a test pulse to -30 mV. Records were filtered at 5 kHz (-3 dB) and sampled at 25 kHz. Each data point is the normalized average peak ensemble current in the test pulse from twenty-three sweeps. The curve is a best-fitting Boltzmann distribution with Vi =-107 mV and slope factor of -150

5.5 mV.

633

J. H. LA WRENCE AND OTHERS

634

to the fraction of channels that were already inactivated before the test pulse. When the holding potential is raised to - 105 mV (Fig. IB), channels are less active, as is evident from the individual sweeps and the ensemble average. The current records now include a majority (60%) of blank sweeps, i.e. those that contain no openings. A

t

1*--

-1

-40 mV

-90 mV

-120 mV B t= 0 ms

20

50

100

1 pAL 2 ms C 1

l(t)X l(t=0)

04 0

100 200 Pre-pulse duration (ms) Fig. 2. Time course of inactivation. The time course of the C I transitions at -90 mV was determined from a two-pulse protocol (A) by measuring the peak ensemble-average current after different pre-pulse durations in a two-channel patch. B shows representative ensemble-average currents at the test pulse potential (-40 mV) in the control case (t = 0) and after pre-pulses to -90 mV for 20, 50 and 100 ms, respectively; the number of sweeps was sixty-six for the control and one hundred for the protocols with pre-pulse. In C, the plot of normalized peak ensemble test pulse current vs. pre-pulse duration gives a monoexponential decay with a time constant (r) of 74 ms.

According to the conventional interpretation, a greater fraction of channels resides in I when held at - 105 mV and thus are not available to open when the membrane is depolarized. The steady-state inactivation curve defines the distribution of resting vs. inactivated states as a function of membrane potential (Hodgkin & Huxley, 1952b). A representative steady-state inactivation curve is shown in Fig. 1C. The voltage protocol consisted of a holding potential of -100 mV, with pre-pulses to different potentials for 1200 ms followed by test pulses to -30 mV. The sampling protocol consisted of repeated cycles of a series of depolarizations to each of the pre-pulse potentials, rather than repetitive consecutive steps to the same pre-pulse potential. This approach minimizes variability that might be introduced by time-dependent

635 SODIUM CHANNEL INACTIVATION changes in channel availability or patch run-down. Ensemble-average currents were generated from twenty-three sweeps at each of nine pre-pulse potentials from -140 to -60 mV. The peak current elicited during the test pulse was normalized to that elicited from a pre-pulse potential of - 140 mV. The data are fitted by a Boltzmann distribution with a 142 of - 107 mV and a slope factor of 5-5 mV. This curve correlates well with that found by Kimitsuki et al. (1990) in guinea-pig ventricular cells and by Berman et al. (1990) in canine ventricular cells using ensemble-average currents generated from single-channel records.

Time course of inactivation at membrane potentials near threshold By analogy to studies performed in axons or whole cells, the time course of Na+ channel inactivation can be examined by using a two-pulse protocol with variable pre-pulse duration as depicted in Fig. 2A. Figure 2B shows the ensemble averagecurrents in a two-channel patch during a test pulse to -40 mV with no pre-pulse (t = 0) and after pre-pulses to -90 mV for 20, 50 and 100 ms. As the pre-pulse duration increases, there is a greater chance that the channels inactivate during the pre-pulse such that the current elicited by the ensuing test pulse becomes progressively smaller. Plotting the peak ensemble current for each pre-pulse normalized by the control peak current generates the exponential curve in Fig. 2 C with a time constant of 74 ms (cf. Aldrich & Stevens, 1983). In one other experiment with this protocol, an inactivation time constant of 50 ms was obtained. Since C -+ 0 transitions are likely to be uncommon at -91 mV, especially during these relatively brief pre-pulses, and since the few channels that do open will rarely inactivate from O (Yue et al. 1989), this time constant predominantly reflects the rate of C -+ I transitions. These direct C -+ I transitions at membrane potentials near the resting potential occur rapidly enough that they are likely to influence the number of channels that are available to open during diastole in heart cells. Nevertheless, more trenchant strategies are required to assess the relative importance of C -+ I transitions over a broad range of membrane potentials. Inactivation from resting states using Markov chain theory The first approach to quantify the probability of C -+ I transitions vs. the probability of C - 0 transitions is based on Markov chain theory (Aldrich et al. 1983). Time-independent probabilities (A and B) for transitions among the three states of the standard gating model: C 1-A\\

A B

0 1-B

(M1)

I are used to construct Markov chains which define the probability, P(k), of observing k transitions into the open state before the channel enters the absorbing inactivated state. The probability of observing k openings in a sweep triggered by membrane depolarization in a single-channel patch is given by:

P(k) = 1-P0A, for k= 0 and P(k) = (PcA)(L-AB)(AB)k-1, for k > 0,

(3)

(4)

J. H. LA WRENCE AND OTHERS

636

-20 mV

A

.-w

0.5 .u

...........

1

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-40 mV

__ ______-

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-60 mV -

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2.5 pAL 2 ms

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v

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B

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v a

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v

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a

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-60

V Y

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-20 -40 Membrane potential (mV)

Fig. 3. For legend see facing page.

0v

SODIUM CHANNEL INACTIVATION 637 where Pc is the probability of the channel being in C initially. In response to step depolarizations to a test potential in a one-channel patch, a frequency histogram of the observed number of openings per sweep is generated. These data can be fitted by the above equations to solve iteratively for the unknowns Pc, A and B. However, inspection of these equations reveals that there are only two independent variables, namely the products PcA and AB. To avoid an indeterminate fit, one of the unknown variables must be constrained. We have chosen to accomplish this by maintaining a quite negative holding potential which maximally removes inactivation so that Pc becomes equal to 1. Alternatively, less negative holding potentials can be used and Pc estimated from steady-state inactivation (h.) curves prior to each series of step depolarizations (Berman et al. 1990). Once A, the probability of C -+0, is determined, then (1-A), the probability of C -+I is known. As described below, our approach differs from that originally described by Aldrich et al. (1983) and followed by others (Vandenberg & Horn, 1984; Kunze et al. 1985; Grant & Starmer, 1987; Berman et al. 1990) in that (1-A) is determined from the best fit to the entire histogram and not just from the first bin of the histogram which is the fraction of sweeps which have no openings. Figure 3A presents an example of this approach. The left-hand column shows current records from a one-channel patch triggered by membrane depolarization to -20, -40 and -60 mV. The holding potential of -140 mV is sufficiently negative to recycle the channel to resting states prior to each depolarization. Since there is only one channel in the patch, there is no ambiguity in counting the number of openings per channel per depolarization, which appears to decrease at more positive test potentials. On the right are histograms of the observed frequency of k openings per depolarization and best fits to the data (0). In this and two, other one-channel patches, the Markov chain model provided excellent fifs to the data at all potentials tested, from which the probabilities A and B were calculated. Figure 3B summarizes results from three one-channel patches. The filled symbols represent the transition probability (1-A) for inactivation from resting states. At potentials -60 mV, cardiac Na+ channels inactivate directly from resting states in fewer than 10-15% of depolarization epochs. Transition probability B, shown as open symbols, decreases monotonically with increasing membrane potential reflecting the increased likelihood of 0 -+ I vs. 0 -OC transitions with progressive depolarization (Yue et at. 1989). The transition probability (1-A), when corrected for missed openings and closures (Fig. 8), reveals an even greater tendency for the channel to open before it inactivates at the more depolarized potentials. As a further check on the validity of Markov chain theory, we derived transition rate constants with a strategy using Eyring rate theory. This theory, based on an

Fig. 3. Assessment of C -+ I transitions at potentials

> -60 mV using Markov chain theory. In A, on the left, are unitary Na+ current records from a one-channel patch triggered by membrane depolarization from -140 mV to -20, -40 and -60 mV, respectively. On the right are histograms of the observed frequency of k channel openings per depolarization. *, best fits to the data of a model based on Markov chain theory. From these fits, the transition probabilities can be estimated and the probability of C -. I can be calculated as (1-A). B summarizes data from three one-channel patches where each symbol represents a separate patch and shows (1-A) (filled symbols) and the transition probability B (open symbols) as functions of voltage before compensation for missed events.

J. H. LA WRENCE AND OTHERS

638

analysis of mean channel open time, provides a link between the rate constant describing the transition between two states and the electrochemical energy barrier between the two states. Markov chain theory and Eyring rate theory are independent analytic techniques for quantifying the transitions among states. Because the two approaches involve distinct assumptions, agreement of the results from the two methods would provide reassurance regarding their individual validity. We and others have applied Eyring rate theory to determine the voltage dependence of mean channel open time, To (Vandenberg & Horn, 1984; Aldrich & Stevens, 1987; Yue et al. 1989; Berman et al. 1990; Scanley et al. 1990):

T

=

koc(0) exp (QOCV) + koi(0) exp (QOI

(5)

where koc(O) and ko/(0) are the values of the rate constants koc and kol at V = 0 mV, and QOC and QOl are equivalent charge movements. Figure 4 shows single-channel records and cumulative open time histograms at test potentials of -86, -46 and + 4 mV from one patch. The histograms are fitted with single exponential functions. The time constants of these fits provide estimates of the mean open time at each potential. The mean open time is distinctly greater at -46 mV than at either positive or negative extreme. Indeed, since koc and koi have opposite voltage dependencies, eqn (5) predicts that the mean open time should pass through a maximum as test potential increases. Figure 5 plots the reciprocal of mean open time as a function of membrane potential from seventeen patches, which extends previous results (Yue et al. 1989). The symbols are mean values and standard deviations at potentials from -96 to + 4 mV. Above each symbol is indicated the number of patches that contributed to each mean value. The continuous curve is the best fit to the reciprocal mean open time as a biexponential function of voltage. From this fit, the following rate constants and equivalent charge movements can be derived: koc (5) = 011+ 0-02 and QOC = -1X3+005; kol (0) = 4-6+0-19 and QOl = 0-95+0 10. The individual rate constants koc and koi are shown as interrupted lines. Although the data plotted as filled symbols in Fig. 5 have not been corrected for missed openings and closures, we confirmed that the general form of the relationship was preserved in those patches where such correction could be rigorously applied. The inset to Fig. 5 shows mean reciprocal open times from the three one-channel patches, in which reliable closed-time histograms were generated thus enabling accurate compensation for missed events. In this subset of corrected data, the reciprocal open times also pass through a minimum, as predicted by eqn (5) if both koc and koi are voltage dependent. The rate constant koc presents the opportunity for a direct comparison of the two techniques for quantifying the C -+ I transition, since it can be determined from mean open times using Eyring rate theory or calculated from the transition probability B determined from Markov rate theory: B (6) To

Such a comparison is presented in Fig. 6. The continuous line is the best-fit

SODIUM CHANNEL INACTIVATION 300

-86 mV

jIr

r

-1

hg

I

ww

L

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_

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l'

[

0

2

0 .

-46 -_ mV

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Open time (ms) Fig. 4. Single-channel mean open time. On the left are single-channel current records from a three-channel patch triggered by step depolarizations to -86, -46 and 4 mV, respectively. On the right are cumulative open-time histograms at these potentials with monoexponential fits generated by a least-squares minimization routine which ignored the first few histogram bins (an interval equal to approximately twice the dead time). The apparent multiexponential character of the fit to open times at -46 mV is likely to be due to missed closed events and to the relatively low number (< 100) of total openings recorded. As the test potential was increased, unitary current decreased and mean open time, T., passed through a maximum as would be predicted by Eyring rate theory.

exponential equation for koc derived from Eyring rate theory. The symbols, one type for each of three one-channel patches, show koc calculated from the transition probability, B. The concordance between the results of the two approaches is quite close, bolstering our confidence in the estimated inactivation probabilities derived

J. H. LA WRENCE AND OTHERS

640

from Markov chain theory. Furthermore, this concordance supports the crucial assumption that all channels are indeed available (Pc = 1) at very negative holding potentials, ruling out the theoretical possibility that inactivation is not fully removed even at such potentials. 20 2

5 0 0

6

\;

~~~~~0~ ° t6010 CE

40-60 \ 4

5

44

-100

-80

-60 -40 Membrane potential (mV)

6

-20

0

Fig. 5. Relationship between the reciprocal of mean channel open time and membrane potential described by Eyring rate theory. The symbols are mean values and standard deviations from a total of seventeen patches; the numbers above each symbol denote the number of individual patches which contributed to each average. The continuous line is a best fit to the data for T.-' as a biexponential function of voltage. The inset shows the voltage dependence of mean TO-' for the three one-channel patches after correction for missed openings and missed closures.

Inactivation from resting states using a two-pulse protocol A unique advantage of the single-channel approach is the opportunity to detect brief openings during the pre-pulse. Such openings may well go undetected in macroscopic current recordings, since they may be so brief and dispersed that they contribute little to the average current. Nevertheless, the presence of such openings would make it difficult to exclude transition through the open state as an obligatory prelude to inactivation. At membrane potentials near threshold, acquisition of data for the Markov chain theory analysis approaches practical limits due to two opposing factors: slowing of inactivation and shortening of mean open time. These kinetic changes necessitate very long sampling periods to ensure that inactivation occurs, and high sampling rates to minimize missed events. To assess inactivation from resting states at these potentials, we chose a protocol which was a compromise between the competing demands of bandwidth and sampling times, and then corrected for the errors inherent to this approach. A two-pulse protocol was employed to estimate the

641 SODIUM CHANNEL INACTIVATION probability of direct C -+I transitions during a 185 ms pre-pulse to selected membrane potentials. The experimental protocol is illustrated in Fig. 7. The holding potential was maintained at - 136 mV to remove inactivation. In a control experiment in a four-channel patch (Fig. 7A), the membrane was depolarized to 5

E

10

0

-80

-40 Membrane potential (mV)

0

Fig. 6. Correlation between Eyring rate theory and Markov chain theory. The Eyring rate theory method, which determines rate constants, and the Markov chain method, which determines transition probabilities, can be directly compared, since the rate constant koc can be calculated from the transition probability B. The continuous line is the exponential curve for koc derived from Eyring theory. The symbols, one type for each of the three onechannel patches, show koc calculated from B and reveal a close match between these two independent approaches.

-30 mV without a pre-pulse. Openings were never observed at the holding potential. During the test pulse, multiple stacked openings were seen. The peak ensembleaverage current during the test pulse provided an estimate of maximal channel availability. The effects of a pre-pulse to -91 mV for 185 ms are shown in Fig. 7B. Openings during the pre-pulse, when they do occur, can often be detected at -91 mV as shown in the inset displayed on an expanded timebase. In some records a blank pre-pulse is followed by a blank test pulse, which provides strong evidence that channels were indeed capable of inactivating during the pre-pulse without ever opening. At the pre-pulse potential of -91 mV, 62 % of pre-pulses in this multichannel patch had no detectable openings. In contrast, inactivation, as gauged by the reduction in the test-pulse current, was greater than 75 %, suggesting that resting states are the primary sources for inactivation of Na+ channels at this prepulse potential. For the two-pulse experiments, if the cumulative first latency distribution has reached a plateau by the end of the pre-pulse and if there are no missed openings 21

PHY 443

J. H. LA WRENCE AND OTHERS

642

during the pre-pulse, then the probability (1-A) that the channel transits directly from C to I during the pre-pulse is given simply by the Nth root of the fraction of sweeps with no pre-pulse openings, where N is the number of channels in the patch (Aldrich et al. 1983). In a real system, neither idealization is true. The problems -30 mV

A

-30 mV B

-91

-136j

-136

AIL."

J.A m.IA

d.LAJLiJ&"jjMALjU.AAAA&LMj I&AWAblhAA-

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..A- Ak..A. AL. ILAA i A.AA& Le A.,-- -1-A--L-" rff -r-ww- -W JT rf-- -Vrqrr- ---.q-ww-rrF-m

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i-ibi.

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2 pA l2pA 20 ms

1 pA L

20 ms

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20 ms

r

1 pAL 20 ms

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Fig. 7. Evidence for direct inactivation from resting states using a two-pulse protocol. A shows single-channel and ensemble-average currents from a four-channel patch during a control voltage protocol (holding potential = - 136 mV, test potential = -30 mV). The protocol in B includes a pre-pulse to -91 mV for 185 ms. In 62 % of traces in B there are no pre-pulse openings. As estimated from the dead time and mean open time in this experiment, approximately 60% of pre-pulse openings are detectable (bottom singlechannel record, expanded display). If C -. I transitions do not occur, then the only traces in which channels could have inactivated are those with pre-pulse openings. Inactivation measured by the reduction in the peak ensemble-average current during the test pulse was over 75 %. This indicates that some channels must enter the inactivated state directly from the resting state. Records in both panels, from a four-channel patch, were filtered at 5 kHz and sampled at 25 kHz. The ensemble-average currents were derived from fortyfour sweeps in A and from seventy-six sweeps in B.

introduced by bandwidth and sampling limitations are addressed individually in the Appendix and a method is described which enables explicit compensation for both types of errors. This method for determining the probability of C -+ I (i.e. 1-A) with compensation for a truncated first latency distribution and missed events was applied to four patches which were studied at pre-pulse potentials from -91 to -76 mV (Fig. 8). At potentials negative to -91 mV, the inactivated state cannot be assumed to be absorbing based on the hc. curve (dashed curve) and therefore the true probability of C -+ I cannot be ascertained. Furthermore, at pre-pulse potentials positive to about -70 mV, where pre-pulses with no openings are infrequent in multichannel patches, this two-pulse protocol for assessing C -+ I transitions is impractical. Fortunately, the Markov chain theory approach yields (1-A) in this voltage range.

SODIUM CHANNEL INACTIVATION

643

Summary of probability of C -+ I Figure 8 summarizes the time-independent probability that the channel inactivates directly from resting states at membrane potentials ranging from -91 to 0 mV. The filled symbols are mean values and standard deviations from two to four 1.0

1-A 0.5

h.>

0.0

-150

-100 -50 Membrane potential (mV)

0

Fig. 8. Summary of the probability of C -. I across a wide range of membrane potentials after compensation for missed events. *, average probabilities of C -+ I with standard

deviations from two to four patches each; 0, represent data from individual patches. This probability is steeply voltage dependent and shows that openings are uncommon at potentials < -90 mV (i.e. C -* I dominates C - 0), while at potentials > -60 mV the channels inactivate predominantly from 0 (i.e. as C -. I transitions become less common). An equation of the form P = 1/(l +exp(V- 1l/)) with VI (the voltage at which the probability of C -* I equals 0 5) =-80 mV and , = 9-6 mV, shown as the continuous line, was determined from a fit to all data points (i.e. not just the mean data).

patches, while the open symbols represent data from only one patch at each potential. From -91 to -76 mV, the probability of a direct C -+ I transition was determined from two-pulse experiments of the type shown in Fig. 7 with compensation for a truncated first latency distribution and missed events. Near threshold, membrane potential tips the net balance to favour C - 0 over C -+ I over a quite narrow voltage range. From -60 to 0 mV, the probability of C -. I transitions was determined using Markov chain analysis as depicted in Fig. 3 with correction for missed openings and missed closures. At these potentials, the transition probability (1-A) is much less steeply voltage dependent and decays to near zero at the most positive potentials. At 0 mV, the probability of C -+ I after correcting for missed events falls slightly below zero, suggesting that a few false events due to noise had been detected. DISCUSSION

One aim of this investigation was to confirm that cardiac Na+ channels can inactivate directly from resting states over a wide range of membrane potential and subsequently to describe the voltage dependence and relative importance of this 21-2

644

J. H. LA WRENCE AND OTHERS

pathway. Our results confirm that cardiac Na+ channels can indeed inactivate without ever opening. Such C-+I transitions comprise the primary route for inactivation at membrane potentials below the action potential threshold, but play only a minor role as the membrane is depolarized to -60 mV or beyond.

Transition probabilities for C -. I from Markov chain theory Aldrich et al. (1983) applied Markov chain theory to a simple three-state model of the Na+ channel to determine transition probabilities among the states from histograms of the observed number of openings per depolarizing epoch. Transition probability (1-A) can be estimated from the fraction of blank sweeps only if Pc, the probability that all channels reside in C at the onset of depolarization, is known (cf. eqn (3) for a one-channel patch). Aldrich et al. (1983) assumed Pc was equal to 1 and determined (1-A) as the Nth root of the fraction of blank sweeps, where N is the number of channels in the patch. Berman et al. (1990) repeatedly estimated Pc from hoo curves for each holding potential. If inactivation is present, but unrecognized, then the Nth root of the fraction of blank sweeps will overestimate (1-A). Although the theory can be extended to multi-channel patches, several practical difficulties arise: (1) the estimate of (1-A) from the Nth root of the fraction of blanks is subject to a large variance, especially when the total number of sweeps is relatively small; (2) if the true (1-A) is small, then it is unlikely that any blank sweeps will be seen in a multi-channel patch; for example, if (1-A) is as high as 0 3, then in a four-channel patch on average only 0-8 % of all sweeps will be blank; (3) the estimate of the transition probability B from a N-fold convolution will also be subject to a large variance for multi-channel patches; and (4) accurate counting of the number of openings will be hampered by multiple stacked openings at depolarized potentials in patches with more than two channels. We avoided these potential problems by using exclusively one-channel patches for Markov chain analysis and by removing inactivation with a holding potential of - 136 mV. This approach provided excellent fits to the data (Fig. 3). Other investigators have questioned whether Markov chain analysis of the number of openings per depolarization can be applied in a general fashion to estimate transition probabilities for a simple three-state Na+ channel model. Vandenberg & Horn (1984) applied the Markov approach at two potentials in two separate patches from cultured GH3 cells. The analysis successfully returned realistic transition probabilities in a one-channel patch but failed at -40 mV in a two-channel patch; in the two-channel patch their estimate of A was 0-29 compared with 0-65 at the same potential in the one-channel patch, suggesting that the (unknown) resting potential was less negative in the two-channel patch. If inactivation is not completely removed prior to a test pulse (i.e. if Pc < 1) then the probability A cannot be directly estimated from the fraction of blanks. Kunze et al. (1985) studied neonatal rat myocytes and obtained meaningless values for transition probability B ( > 1 or < 0) in approximately 50% of twenty depolarizations. All patches contained three or four channels, which would be expected to raise significantly the variance of the derived parameters. Furthermore, Kunze et al. acknowledged a possible overestimation of Pc since they could not measure directly the holding potential, but also noted that compensation for this error was not sufficient to obtain physically meaningful estimates of B in some cases. Grant & Starmer (1987) obtained realizable

SODIUM CHANNEL INACTIVATION

645

probabilities in only two of eight experiments in rabbit ventricular cells, but used multi-channel patches and apparently did not compensate for Pc. Berman et al. (1990) were generally successful in applying Markov chain theory in canine ventricular cells. They used multi-channel patches but raised the holding potential to minimize the number of overlapping openings and explicitly determined Pc from ho, curves before and after each run. The Markov approach failed intermittently only at potentials < -60 mV. As they noted, at these potentials where B approaches unity, slight statistical variability in the observed number of openings per sweep due to small sampling size might cause B to be greater than 1. At -70 mV, modest overestimations of Pc would also cause B > 1. For example, if true B at -70 mV is 0-9 and true Pc is 0 5, then estimating Pc as 0-6 will generate a calculated B > 1. From our experience and that of other investigators with the Markov chain approach for estimating transition probabilities for gating in Na+ channels, it is apparent that this technique can be successfully applied at potentials -60 mV if the number of channels in the patch is minimized (preferably one or two channels) and if Pc is reliably determined.

Voltage dependence of inactivation from resting states We find that the probability of inactivation from resting states is voltage

dependent. Does this finding imply that the underlying C -+ I transition is necessarily voltage dependent? Fig. 8 depicts the voltage-dependent probability of C -+ I, fit by a Boltzmann-type equation. This fit does not represent an equilibrium distribution between two states regulated by voltage in the usual sense of a Boltzmann curve; rather, the fit would be predicted by a model whereby the rate constant for C -O0 has exponential voltage dependence, while the rate constant for C -+ I is voltage independent: kco = aexp (V/)

(M 2)

kiC

=

a.

The probability of C -+ I is then found as:

kCL CcI±CcO

1

l+exp(VA i)

(7)

where f, is the slope factor, and VI (= -,f ln[ox/i]) is the voltage at which the probability of C -+ I equals 0-5. In this model, the rate constant for C -+ I is voltage independent and relatively slow. At potentials near threshold where activation is sluggish, C -+ I transitions dominate over C -+ 0 transitions to enhance the likelihood of inactivation from resting states. Thus, the steep voltage dependence of the probability of C -+ I near threshold arises solely from the steep C -+0 voltage dependence. At more positive potentials, where activation accelerates, inactivation from C becomes less common as the voltage-enhanced C -. 0 transition rate overwhelms the C -- I transition rate. Close examination of Fig. 8 suggests that a simple Boltzmann-type curve

646

J. H. LA WRENCE AND OTHERS

(continuous line) does not perfectly fit the data at -50 mV < V < -10 mV, where the probability of C -+ I remains above the theoretical curve even after correction for missed events. Possible explanations for this discrepancy from scheme (M2) include: (1) the voltage dependence of kco is more complex than a single exponential function; (2) kc, may have mild voltage dependence; or (3) inactivation may occur from two or more resting states. A dual route for inactivation along the activation pathway, if present, would enable a crisper threshold than could be generated solely by serial voltage-dependent transitions among resting states coupled to one C -÷ I route, and thereby potentially provide finer control of excitability. Our results do not enable us to distinguish among the various possibilities that might underlie the observed deviation from the predictions of scheme (M2). Our results differ importantly from those of Scanley et al. (1990) with regard to the probability of C -+ I. These workers found a much less steep voltage dependence for C -+ I, and a much smaller probability for C -+ I at potentials > -60 mV. The discrepancies may be related to the lower temperature used in their study (13 °C), to bandwidth limitations (2 kHz), and/or to uncompensated missed events. Our own analysis is subject to possible error from false event detection which could incorrectly cause a truly 'blank' sweep to be classified as 'active'. Nevertheless, false event detection clearly cannot account for the overall conclusion that C -+ I is very improbable at -60 mV or above; false openings would have been very rare at -60 mV where the threshold-to-noise ratio was approximately 5, corresponding to less than one false event per one hundred sweeps (Colquhoun & Sigworth, 1983). Therefore, our finding that the probability of inactivation from resting states is less than 15% at -60 mV not only confirms that this probability is steeply voltage dependent, but also establishes that cardiac Na+ channels open with greater than 85% probability upon depolarization to more positive potentials.

Voltage dependence of inactivation from the open state For neuronal sodium channels (Aldrich et al. 1983; Aldrich & Stevens, 1987; Gonoi & Hille, 1987), A-type potassium channels (Zagotta, Hoshi & Aldrich, 1989; Solc & Aldrich, 1990; Zagotta & Aldrich, 1990) and T-type calcium channels (Droogmans & Nilius, 1989; Chen & Hess, 1990), the apparent voltage dependence of macroscopic inactivation is due solely to voltage-dependent transitions along the activation pathway; inactivation of open channels has little if any voltage dependence. In contrast, we find that cardiac sodium channels do exhibit voltage-dependent inactivation from the open state. Our results, summarized in Fig. 5, indicate that koi is voltage dependent in guinea-pig ventricular cells with an e-fold change per depolarization of 27 mV. Compensation for missed openings and closures (inset to Fig. 5) preserves the voltage dependence of koi. Likewise, the upturn in the reciprocal open time curve at positive potentials cannot be dismissed as being attributable to brief false events; even at the most positive potentials ( >-10 mV), less than 5 % of the detected events may have been false openings due to noise. Rarely were two or more openings appreciated in a single sweep at these potentials, suggesting that false closures were also uncommon. Furthermore, from our Markov chain theory analysis and from that of other investigators (Berman et al. 1990; Scanley et al. 1990), we expect that the majority of sweeps at potentials > -10 mV will contain single openings and that missed closures will be infrequent.

647 SODIUM CHANNEL INACTIVATION These considerations support our overall conclusion that direct inactivation from the open state is voltage dependent in cardiac Na+ channels. Similar degrees of voltage dependence have been found in canine Purkinje fibre cells (Scanley et al. 1990) and ventricular cells (Berman et al. 1990) with e-fold changes for depolarizations of 27 and 30 mV, respectively. The conclusion that 0 -+ I is voltage dependent presents a paradox, in that inactivation should become infinitely fast at very strong depolarizations (Chen & Hess, 1990). At potentials positive to -10 mV, our model predicts that: (1) the Na+ channel will open one time during each depolarization period with a mean open time which falls exponentially with voltage; and (2) the time constant of the decay phase of macroscopic Na+ current (rh) will be To-l (Yue et al. 1989). Previous whole-cell studies (Brown, Lee & Powell, 1981; Makielski, Sheets, Hanck, January & Fozzard, 1987; Follmer et al. 1987) in heart cells show that Th decreases with voltage at potentials up to + 30 mV, albeit at a rate slower than we might predict. With progressive depolarization, activation may become rate limiting and thereby reduce the voltage dependence of macroscopic inactivation. Therefore, in cardiac cells, some portion of the inactivation gate may have to enter the negatively charged inner vestibule to inactivate the Na+ channel; alternatively, the inactivation gate might be influenced by the electric field which extends out from the vestibule (Dani, 1986). Inactivation-modifying procedures such as internally applied proteases (Gonoi & Hille, 1987), site-directed antibodies (Vassilev, Scheuer & Catterall, 1988) and deletion mutations of the cytoplasmic region between the third and fourth domains (Stiihmer, Conti, Suzuki, Wang, Noda, Yahagi, Kubo & Numa, 1989) appear to slow kol by direct effects on the inactivation gate; it is not yet clear, but worth testing, whether inactivation from resting states is similarly affected by these manoeuvres. APPENDIX

Compensation for missed openings at potentials near threshold Figure 9A shows the ideal situation for determining the probability of opening during a pre-pulse: there are no missed events, and the first latency distribution has reached steady-state by the end of the pre-pulse. If in fact the cumulative first latency distribution function has not reached a plateau by the end of the pre-pulse, then the fraction of blank sweeps observed during the pre-pulse will overestimate the probability of C -+ I transitions. However, in this setting, measurement of the test pulse current provides an estimate of the residual probability of channel availability and allows computation of the true probability of C -+ I transitions as follows: When the pre-pulse terminates before the cumulative first latency distribution reaches a plateau (Fig. 9B), the true transition probability (A) for C -+ 0 transitions can be found as: (A1) A=A'+PcA, where A' is the observed fraction of pre-pulses with openings and Pc is the probability that the channel is still in C at the end of the pre-pulse and therefore still available to open. Pc can be estimated from the test pulse as the ratio of I, the peak ensembleaverage test pulse current after blank pre-pulses, to Imax the peak ensemble-average test pulse current in the control experiment (without a pre-pulse) when all channels

J. H. LA WRENCE AND OTHERS

648

are available to open. Thus, (1-A), the true transition probability for C -+ I transitions, can be determined as:

(I-A)

=

I-

Al

I

I/I:max

(A 2)

.

The same correction method can be applied to the problem of missed events arising from bandwidth limitations. System dead time for a Gaussian filter (which closely

Vt VPP

ij A

A1 A

A

cn c

0

r._

I

I

I

._0 )

0-

0) n U)

A

.)

(0 ._

0

C E 0

>0 ..-I

A

A-*

I

a

I

I

I

L

I

I

Time (ms) Fig. 9. Compensation for missed events and incomplete first latency at pre-pulse potentials near threshold. The cumulative first latency distribution function is defined as the fraction of records which have a time to first channel opening of less than time t. A, the plateau level of the first latency distribution curve for the pre-pulse provides a direct measure of the probability of C -. I from the fraction of records which have no openings. B, when the pre-pulse terminates before the first latency has reached a plateau, the true probability of C -. I can be determined from the observed fraction of blank sweeps (1-A') and the peak test pulse current. C, when the pre-pulse terminates before the first latency has reached a plateau and there are missed openings during the pre-pulse, the true probability of C -. I can again be determined from (I1-A') and the peak test pulse current. Vh, holding potential; Vpp, pre-pulse potential; , test potential.

approximates the response characteristics of the multi-pole Bessel filter used here) is given by 0 179/fc where fc is the cutoff frequency (Colquhoun & Sigworth, 1983). With a 5 kHz Bessel filter the dead time equals approximately 0036 ms. At

SODIUM CHANNEL INACTIVATION

649

-91 mV, the observed mean channel open time was 0-07 ms. Therefore the missed opening event rate at this potential was approximately [1 -exp(-0-036/0-07)] = 40 % (Blatz & Magleby, 1986). When the pre-pulse terminates before the cumulative first latency distribution reaches a plateau and there are missed openings (Fig. 9 C), A and (1-A) can again be determined from equations (Al) and (A2). In this case, Pc is the probability that the channel remains in C at the end of a blank pre-pulse or has returned to C after a brief transit into 0. Despite a relatively high fraction of missed events, Pc can be estimated from '/'max if 0 -OI transitions are uncommon at this potential. This assumption is supported by the fact that kol, the rate constant for 0 -+ I transitions, falls exponentially with decreasing membrane potential (Fig. 5); at potentials below -60 mV, ko1 is very small compared with koc, the rate constant for 0 -+ C transitions. Therefore, pre-pulse openings are rare, and when a channel does open, it is much more likely to close than to inactivate. Thus, the reduction in ensemble current after a pre-pulse to these potentials almost exclusively reflects inactivation from resting states. This work was supported by the National Institutes of Health (ROI HL-36957 and K04 HL01872 to E.M) and a Merck Fellowship (to J.H.L.). REFERENCES

ALDRICH, R. W., COREY, D. P. & STEVENS, C. F. (1983). A reinterpretation of mammalian sodium channel gating based on single channel recording. Nature 306, 436-441. ALDRICH, R. W. & STEVENS, C. F. (1983). Inactivation of open and closed sodium channels determined separately. Cold Spring Harbor Symposia on Quantitative Biology 48, 147-153. ALDRICH, R. W. & STEVENS. C. F. (1987). Voltage-dependent gating of single sodium channels from mammalian neuroblastoma cells. Journal of Neuroscience 7, 418-431. ARMSTRONG, C. M. & GILLY, W. F. (1979). Fast and slow steps in the activation of sodium channels. Journal of General Physiology 74, 691-711. BEAN, B. P. (1981). Sodium channel inactivation in the crayfish giant axon. Must channels open before inactivating? Biophysical Journal 35, 595-614. BERMAN, M. F., CAMARDO, J. S., ROBINSON, R. B. & SIEGELBAUM, S. A. (1990). Single sodium channels from canine ventricular myocytes: voltage dependence and relative rates of activation and inactivation. Journal of Physiology 415, 503-531. BEZANILLA, F. & ARMSTRONG, C. M. (1977). Inactivation of the sodium channel. I. Sodium current experiments. Journal of General Physiology 70, 549-566. BLATZ, A. L. & MAGLEBY, K. L. (1986). Correcting single channel data for missed events. Biophysical Journal 49, 967-980. BROWN, A. M., LEE, K. S. & POWELL, T. (1981). Sodium current in single rat heart muscle cells. Journal of Physiology 318, 479-500. CHEN, C. & HESS, P. (1990). Mechanism of gating of T-type calcium channels. Journal of General Physiology 96, 603-630. COLQUHOUN, D.& SIGWORTH, F. J. (1983). Fitting and statistical analysis of single-channel records. In Single-Channel Recording, ed. SAKMANN, B. & NEHER, E., pp. 191-263. Plenum Press, New York. COTA, G. & ARMSTRONG, C. M. (1989). Sodium channel gating in clonal pituitary cells: the inactivation is not voltage dependent. Journal of General Physiology 94, 213-232. DANI, J. A. (1986). Ion-channel entrances influence permeation. Biophysical Journal 49, 607-618. DROOGMANS, G. & NILIUS, B. (1989). Kinetic properties of the cardiac T-type calcium channel in the guinea-pig. Journal of Physiology 419, 627-650. FOLLMER, C. H., TEN EICK, R. E. & YEH, J. Z. (1987). Sodium current kinetics in cat atrial myocytes. Journal of Physiology 384, 169-197.

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GILLESPIE, J. I. & MEVES, H. (1980). The time course of sodium inactivation in squid giant axons. Journal of Physiology 299, 289-307. GOLDMAN, L. & SCHAUF, C. L. (1972). Inactivation of the sodium current in Myxicola giant axon. Evidence for coupling to the activation process. Journal of General Physiology 59, 659-675. GONOI, T. & HILLE, B. (1987). Gating of Na channels. Inactivation modifiers discriminate among models. Journal of General Physiology 89, 253-274. GRANT, A. 0. & STARMER, C. F. (1987). Mechanisms of closure of cardiac sodium channels in rabbit ventricular myocytes: single-channel analysis. Circulation Research 60, 897-913. HAMILL, 0. P., MARTY, A., NEHER, E., SAKMANN, B. & SIGWORTH, F. J. (1981). Improved patchclamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pfliugers Archiv 391, 85-100. HODGKIN, A. L. & HUXLEY, A. F. (1952a). The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. Journal of Physiology 116, 497-506. HODGKIN, A. L. & HUXLEY, A. F. (1952 b). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117, 500-544. KASS, R. S. & KRAFTE, D. S. (1987). Negative surface charge density near heart calcium channels: relevance to block by dihydropyridines. Journal of General Physiology 89, 629-644. KIMITSUKI, T., MITSUIYE, T. & NOMA, A. (1990). Negative shift of cardiac Na+ channel kinetics in cell-attached patch recordings. American Journal of Physiology 258, H247-254. KUNZE, D. L., LACERDA, A. E., WILSON, D. L. & BROWN, A. M. (1985). Cardiac Na currents and the inactivating, reopening, and waiting properties of single cardiac Na channels. Journal of General Physiology 86, 691-719. LAWRENCE, J. H., MARBAN, E. & YUE, D. T. (1989). Closure of single sodium channels quantified by two independent analytic approaches. Circulation 80, suppl. II, 518. LAWRENCE, J. H., ROSE, W. C., YUE, D. T. & MARBAN, E. (1989). Inactivation of single sodium channels directly from closed states. Circulation 80, suppl. II, 398. MCLAUGHLIN, S. G. A., SZABO, G. & EISENMAN, G. (1971). Divalent ions and the surface potential of charged phospholipid membranes. Journal of General Physiology 58, 667-687. MAKIELSKI, J. C., SHEETS, M. F., HANCK, D. A., JANUARY, C. T. & FOZZARD, H. A. (1987). Sodium current in voltage clamped internally perfused canine cardiac Purkinje cells. Biophysical Journal 52, 1-11. NONNER, W. (1980). Relations between the inactivation of sodium channels and the immobilization of gating charge in frog myelinated nerve. Journal of Physiology 299, 573-603. ROSE, W. C., LAWRENCE, J. H., YUE, D. T. & MARBAN, E. (1990). Inactivation of single cardiac sodium channels directly from closed states. Biophysical Journal 57, 298a. SCANLEY, B. E., HANCK, D. A., CHAY, T. & FOZZARD, H. A. (1990). Kinetic analysis of single sodium channels from canine cardiac Purkinje cells. Journal of General Physiology 95, 411-437. SOLC, K. C. & ALDRICH, R. W. (1990). Gating of single non-Shaker A-type potassium channels in larval Drosophila neurons. Journal of General Physiology 96, 135-165. STUHMER, W., CONTI, F., SUZUKI, H., WANG, X., NODA, M., YAHAGI, N., KUBO, H. & NUMA, S. (1989). Structural parts involved in activation and inactivation of the sodium channel. Nature 339, 597-603. VANDENBERG, C. A. & HORN, R. (1984). Inactivation viewed through single sodium channels. Journal of General Physiology 84, 535-564. VASSILEV, P. M., SCHEUER, T. & CATTERALL, W. A. (1989). Inhibition of inactivation of single sodium channels by a site-directed antibody. Proceedings of the National Academy of Sciences of the USA 86, 8147-8151. YUE, D. T., LAWRENCE, J. H. & MARBAN, E. (1989). Two molecular transitions influence cardiac sodium channel gating. Science 244, 349-352. YUE, D. T. & MARBAN, E. (1988). A novel cardiac potassium channel that is active and conductive at depolarized potentials. Pftugers Archiv 413, 127-133. ZAGOTTA, W. N. & ALDRICH, R. W. (1990). Voltage-dependent gating of Shaker A-type potassium channels in Drosophila muscle. Journal of General Physiology 95, 29-60. ZAGOTTA, W. N., HOSHI, T. & ALDRICH, R. W. (1989). Gating of single Shaker potassium channels in Drosophila muscle and in Xenopus oocytes injected with Shaker mRNA. Proceedings of the National Academy of Sciences of the USA 86, 7243-7247.

Sodium channel inactivation from resting states in guinea-pig ventricular myocytes.

1. Unitary Na+ channel currents were recorded from isolated guinea-pig ventricular myocytes using the cell-attached patch-clamp technique with high [N...
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