Potassium permeability of embryonic heart cells in tissue culture C. RUSSELL Department
HORRES,
of Physiology,
JAMES F. AITON, AND Duke University Medical
HORRES, RUSSELL (&JAMES F. AITON, AND MELVYN LIEBERMAN. Potassium permeability of embryonic avian heart ceils in tissue dture. Am. J. Physiol. 236(3): C163-C170, 1979 or Am. J. Physiol.: Cell Physiol. 5(2): C163-C170, 1979.-The relationship between the external potassium concentration ([K],) and membrane permeability has been reexamined using a tissue-cultured preparation of embryonic chick heart cells in which diffusional limitations are minimal. The unidirectional K efflux and electrochemical gradients were determined as a function of [K],, and the results showed that potassium permeability was constant within the range of l-20 mM [K],,. Membrane potentials were obtained in K-free solutions and correlated with 42K efflux and intracellular ion content measurements under the same conditions. In contrast to preparations of the intact embryonic chick heart, 42K efflux does not decrease in K-free media. Simulations of tracer measurements at reduced [K],, from naturally occurring cardiac muscle indicate that the experimentally observed decrease in 42K efflux could result from diffusional limitations. This observation, when coupled with the experimental results, suggests that the effect of low [KIO on membrane permeability in homeothermic preparations of cardiac muscle should be reevaluated.
cardiac muscle; pacemaker efflux; diffusional limitations
THE
MEMBRANE
OF
activity;
CARDIAC
membrane
MUSCLE
CELLS
potentials;
at
rest
K
is
highly permeable to potassium ions. Therefore, it is not surprising that cardiac cells depolarize in response to elevated concentrations of external potassium. However, the embryonic chick heart (4), as well as several preparations of adult cardiac muscle (I, 3, 22, 24-26, 30), also depolarize when the external potassium 6 concentration [K10 is reduced below 1 mM. Based on 4LK flux measurements, the depolarization in the embryonic chick heart has been ascribed to a decrease in membrane permeability to potassium (4). The validity of such an explanation is questionable because the interpretation of ionic flux measurements from preparations of embryonic and adult cardiac muscle are greatly complicated by the fact that tracer kinetics are not describable by single exponential rate processes (for discussion, see Horres and Lieberman (15)). Using a newly developed preparation of cardiac muscle in tissue culture (16), we have reexamined the relationship between external potassium concentration and membrane permeability by determining the unidirectional K efflux and electrochemical gradients as a function of external K. 0363-6143/79/0000-0000$01.25
Copyright
0 1979 the American
Physiological
avian
MELVYN LIEBERMAN Center, Durham, North
Carolina,
27710
METHODS
Tissue culture. Primary cultures of spontaneously contracting heart cells were derived from 11-day-old embryonic chick hearts that were subjected to multiple periods of enzymatic (trypsin) disaggregation (16). Nylon monofilament (20 pm OD) was used as the substrate to orient the cells and promote the formation of cylindrical preparations approximately 5 mm in length with a mean diameter (inclusive of nylon core) of 60 pm. The proportion of muscle cells in culture was increased by using a differential attachment technique (16). However, as with the observations reported from the laboratories of Kasten (17) and Sperelakis and McLean (27), the residual nonmuscle (fibroblastlike) cells proliferate within 5 days and comprise a substantial proportion of the total cell population. In one series of experiments in which intracellular ion content was determined, 3-day-old primary cultures of confluent, muscle-enriched heart cells were studied to minimize the contribution of the nonmuscle cells. Preparations of nonmuscle cells were obtained by subculturing primary heart cells (16). All preparations were grown in medium 199 (GIBCO) with 10% fetal calf serum, 2% chick embryo extract, and a 1% solutiori of penicillinstreptomycin (16). The preparations were incubated at 37°C in an environment of 4% CO2 and 96% air for 3-7 days. Potassium efflux. Preparations were incubated from 45 to 90 min, except as indicated, in modified Earle’s balanced salt solution (pH 7.4) containing 5.4 mM “K (New England Nuclear, Boston, MA or Nuclear Energy Services, N. Carolina State Univ., Raleigh, NC) under controlled humidity at 37.5”C with 5% COa/air as a buffer. The solution contained 7.0 g/l of neutralized bovine serum albumin, 5.6 mM glucose, and the following salts (mM): NaCl, 118; NaH2P04 gHZO, 0.94; MgS04 7H20, 0.81; NaHCOz, 26.2; and CaCla, 2.7. The preparations were perfused with filter-sterilized solutions of the same composition; KC1 was added as needed to obtain the desired concentration of [K],,. After incubation, the preparations were quickly transferred to a flux chamber (15), which was then sealed to permit constant volume perfusion. During the efflux period, to minimize the possible changes in the efflux results due to spontaneous tissue activity in the various [K],, the contractile rate was controlled at 150 min-’ by field stimulation with silver plate electrodes. Samples of the l
Society
c 163
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C164
HURRES,
perfusate were collected at l-mm intervals and were analyzed by counting in a well-type NaI scintillation system (model 1100, Nucleus). The data were corrected for background and decay and were subsequently subjected to compartmental analysis by fitting the data points with a curve defined by the sum of two exponential functions Y = ICI exp(-#It)
+ I&
AITON,
AND
LIEBERMAN
t 5% CO2 /Atr
eXp(-K&)
where IC represents the initial conditions in compartments 1 and 2 and K represents the respective rate constants, one of which was assigned the value determined from preparations containing only nonmuscle cells (slow compartment). By curve fitting with an analog computer, the efflux rate constant for the fast compartment, together with the respective compartment sizes, were derived. (A more detailed description of the efflux methodology and compartmental analysis has been reported elsewhere (15) .) 1un content. Muscle-enriched heart cells were seeded at 7 x 10" cells per 35-mm dish and grown for 3 days to confluency, at which time widespread areas of synchronously contracting cells were noted. Following removal of the culture medium, the cells were rinsed and incubated in 3 ml of 5.4 mM K or K-free solutions. The incubation solutions were discarded and the cells rapidly rinsed four times with cold (4°C) isotonic choline chloride. Intracellular Na and K were extracted during an overnight incubation in a solution containing 5 mM cesium chloride and 0.125 ml/l Acationox. Samples were measured using an atomic absorption flame spectrophotometer (model 460, Perkin-Elmer). Electrical recording. Transmembrane potentials were recorded from preparations placed in a chamber designed specifically to simulate the perfusion conditions of the 42K efflux experiments (Fig. 1). With such a system, it was possible to rapidly change the composition of the perfusate in the chamber within 4 s, while maintaining the temperature constant to within HL~“@. A television microscopy system (model 4300 Cohu television; M-5 Wild microscope) was used to view the preparation at an effective magnification of X400. Bevel-edged glass microelectrodes (tip diam, 50 pm) were used to stimulate the preparations at frequencies of 120-150 cycles*min-‘. Transmembrane potentials were recorded from the cells through glass microelectrodes filled with 3 M KC1 (30-50 ML!). A Ag-AgCl wire connected the microelectrode to a high-input-impedance preamplifier (20). The stimulus return electrode was a silver wire placed peripherally in the bath; rectangular voltage calibrating pulses (model CA5, Bioelectric Instruments) were applied between the silver inlet manifold and ground. The signals were channeled to a dual beam oscilloscope (model 565, Tektronix) equipped with a differential plug-in unit (model 3A3, Tektronix). Records were obtained photographically with an oscillographic camera (model C4, Grass) and a chart recorder (model 220, Brush). Data were tabulated from recordings in which the resting and action potentials were free of contractile artifacts, and the base line returned to its initial value after removal of the microelectrode.
J
1. Schematic representation of perfusion apparatus for electrical measurements. Lucite perfusion chamber contained a glass bottom and was mounted on an aluminum platform maintained at 37.5”C by dissipating regulated DC power in resistors (HI%10, Dale Electronics), Thermostatically controlled solutions (37.5”C), flowing at a rate of 16 ml. min-’ through insulated stainless steel tubing on the platform, were admitted to the chamber (l.O-ml vol) through a grounded silver manifold. A pneumatically controlled arrangement of valves (D) was used to select between the perfusate solutions in the fluid reservoirs (A or B) (see insert). Pneumatic actuators (model AVCA, Lee CO.) were wired to a DPDT master switch (23) that commanded pneumatic valves to direct fluid flow from Harvard pump (C) to perfusion chamber or to a recycling loop into fluid reservoirs. RE, return electrode (Ag/AgCl wire) to stimulus isolation unit; TP, temperature probe (Yellow Springs Instruments); ME, microelectrode; LS, fiber-optic illuminator (DolanJenner); TV/M, television microscopy system. Stimulus electrode and voltage calibrator not shown in drawing. FIG.
RESULTS
Effects of externalpotassium on 42K efflux. The results in Fig. 2 show that 42K exchange in these preparations cannot be described by a single exponential process because of the presence of muscle and nonmuscle cells (15). It is evident that the contribution of the slowly exchanging nonmuscle cells can be minimized, but not entirely eliminated, by reducing the 42K loading time of the preparation. Therefore, to deduce the efflux rate constant of the muscle cells, it is necessary to assess the contribution of the slowly exchanging compartment from similar experiments with a homogeneous population of nonmuscle cells. The effect of increasing [K10 over the range of LO-20 mM on 42K efflux kinetics was studied in both muscle-enriched and nonmuscle cell preparations. Representative results obtained from muscle-enriched preparations (Fig. 3) show that increasing the concentration of K, is accompanied by a small increase in the rate of 42K efflux. The results obtained with the nonmuscle cells were used in the evaluation of the data from the contractile preparations (Table 1). At a [K&, of 5,4 mM, the efflux rate constant for the muscle cells was 0.067 min-I, in contrast to a value of 0.015 min-’ for the nonmuscle
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K PERMEABILITY
OF
GROWTH-ORIENTED
HEART
Cl65
CELLS
0
l 0 l O l 0 a0 l
0 0 l
0 l
0 a
0 0
l
0 l
0 l
0 0
l
0 l
0 a
0 l
0 l
0 0
a
0 l
0 l
0 0
l
0 a
0 l
0 a a l a a l
l o
5
*a
l m
l *
l o
l m
-8
2
0
5
IO
I5
20
25
20.0mM g* **a
K
I 20
I 25
30
FIG. 2. Effect of loading time on 42K efflux kinetics of growth-oriented heart cells in 5.4 mM external potassium. Two preparations from same culture were loaded with 42K for either 5 min (closed circles) or 45 min (open circles).
cells. Whereas little change was noted when [K-J0 was decreased to 2.0 mM, a 40% decrease in the efflux rate constant was observed in 1.0 mM [K],. The rate constant increased by 45% when [KJ, was increased to 20 mM. Values for potassium efflux were calculated for the different concentrations of K, between LO and 20 mM and were determined to be within the range 9.4-22.8 pmol. cmB2.8. Efflux experiments in nominally K-free media (~0.1 mM) produced interesting results (Fig. 4). It was found that the rate of tracer efflux was not decreased in K-free media, as might have been expected from previous studies (3, 4, 21). In the continued absence of [K],, the rate of 42K loss from the preparation increased and, after approximately 10 min of perfusion, contractile activity ceased and the preparation was unresponsive to the field stimulation. When 5.4 mM K was restored to the perfusate, contractility returned and the rate of 42K efflux decreased slightly. A similar pattern of change in efflux kinetics was observed, albeit slower, from preparations of the nonmuscle cells (14). In all of these experiments loss of potassium from the preparation greatly complicates the multicompartmental analysis of the data, so that only qualitative evaluations of 42K efflux kinetics can be made. However, by performing experiments with 42K loading times of 5 min, more information about the K-exchange kinetics of the muscle cells could be obtained (Fig. 2). The results shown in Fig. 5 indicate an increasing trend in the rate of 42K efflux with time in K-free solution. As nonlabeled K is unavailable in the extracellular space,
I 5
I 0
Time (mid
1 to
I 15 MINUTES
3. Effect of external potassium on 42K efflux kinetics of electrically stimulated preparations of heart cells in 1.0, 2.0, 5.4, and 20 mM external potassium. First few points (O-2 min) represent both carryover of the loading solution and 42K exchange in extracellular space. Counts per minute (cpm) on ordinate represent total activity in preparation. FIG,
TABLE 1. Compartmental analysis of 42K efflux data as a function of [Kjo _-.--- _-.- ~-[K]o, mM
1.0 2.0 5.4 20.0
n
4 5 22 4
Rate Constant*
0,040 0,068 0.067 0.097
t * t t
(K),
0.004 0.007 0.009 0.016
min
’
Potassium Efflyx+ ( JK), pmol-cm Les-’
9.4 16.9 15.7 22.8
* t * k
0.9 1.6 1.5 2.7
[K],, external potassium concentration; n, number of determinations. The measured internal potassium concentration [K]i increased by less than 15% over the range of 1.0-20 mM [K],. Efflux values were calculated at a [K]i of 133 mM, measured in 5.4 mM [K& (16). * Mean value & SE. The rate constants of the nonmuscle cells used in the compartmental analysis for the respective values of [Klo were 0.010, 0.013, 0.015, 0.026 min-’ (see Ref. 14), t Efflux values derived from the relationship Jk = K V/A[K]i are presented as the derived results & relative error calculated from the standard error. V/A, the volume to surface area of the preparation, was 1.06 X lop4 cm.
the loss of tracer in these experiments is indicative of a decrease in the internal potassium concentration [K]i. Direct measurements of intracellular K and Na content (Fig. 6) support the results of the tracer experiments and show the rapid decrease [K]i to be concomitant with an increase in internal sodium concentration ([Na];). Effects of [Kjo on potassium permeability. To arrive at relative values of potassium permeability for the different concentrations of K,, it was necessary to determine
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HORRES,
l .a
0
AITON,
AND
LIEBERMAN
I
I
I
I
1
I
10
20
30
40
50
60
Time(min)
IIO
I 1 20 30 M i nutes
I 40
FIG. 4. Effect of K-free perfusate on 42K efflux of electrically stimulated heart cells. Vertical arrows indicate loss of synchronous contractile activity in K-free solution and subsequent recovery when preparation was returned to 54 mM K.
Time
(mid
5. Potassium efflux kinetics of heart cells in K-free solution. Preparations were loaded in 42K for 5 min, Vertical bars represent envelope of standard deviation of results obtained from 9 individual experiments. FIG.
FIG. 6, Effect of K-free solution on intracellular ion content of 3day-old confluent primary cultures of heart cells. Sodium (open circles) and potassium (closed circZes) content were determined by atomic absorption spectrophotometry. Each point represents mean value -+ SD of 3-11 determinations.
the electrochemical gradient responsible for the unidirectional 42K effluxes reported in the previous section. Because the preparations normally contract spontaneously, they were stimulated at a rate equivalent to that used in the flux experiments. Table 2 summarizes the maximal diastolic potential of the membrane potentials (I&P) recorded at different concentrations of K, and relates these measurements to the calculated values for the potassium equilibrium potential (EK). The index used to describe the electrical gradient for potassium efflux was the maximal diastolic potential, the most negative value of membrane potential during the stimulation cycle. Note that &nP deviates from Ek at all levels of [K&, the most marked differences occurring at [K10 < 5.4 mM. These potentials were combined with the flux results presented in the previous section by using the Goldman equation, as modified by Hodgkin and Katz (13), to calculate values for membrane permeability (PM&. It is evident from Table 2 that no consistent relationship exists between [KIO and PMDP. However, the range of values centers about 5.2 x 10m7 cm& and is similar to the calculated value of 6.2 x 10B7cm, s-l reported by Katz (18) from data of frog skeletal muscle obtained by Hodgkin and Horowitz (12)1 Figure 7 illustrates an alternative approach taken to calculate the potassium permeability in contracting preparations. The index of the electrical gradient for K flux is designated as the time average of the transmembrane potential, E TAP.This potential represents a time-distributed profile of an action potential for a complete cardiac cycle and therefore takes into account any changes in action potential configuration that occur when the prep-
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K PERMEABILITY TABLE
OF
2. Membrane
GROWTH-ORIENTED
potassium heart cells
of growth-oriented
HEART
permeability
EMLW*,
mV
1.0 2.0 5.4 20.0
-131 -112 -86 -51
-93 -78 -66 -46
-+ t t t
1 1 1 1
20 5 10 8
6.4 7.2 5.2 4.6
-62 -45 -41 -29
Cl67
CELLS
2.8 3s 2.8 3.1
n, Number of measurements. “E~bp, maximal diastolic potential (mean value t SE). t EF~*P, time-averaged potential (see Fig. 4) obtained from representative potentials, having a maximal diastolic potential equal to that of the mean value of EMill’. * PMDP, P’I’AP, represent the potassium permeability calculated from the GoldmanHodgkin-Katz equation (13), using the respective values of E~br and
FIG. 7. Schematic representation of transmembrane action potentials recorded from growth-oriented heart cells. Cross-hatched region represents a time distribution profile of action potential, TAP, the magnitude of which is indicated by middle horizontal solid line. Upper horizontal line is zero reference potential.
aration is exposed to different K concentrations. It is evident from Table 2 that for a given [K],, ETAP is significantly less negative than the corresponding value of EMnP and thereby indicates a greater electrical gradient for the same value of potassium efflux. Consequently, when the values of ETAP are used to calculate the potassium permeability, an apparent decrease in membrane permeability, PTAP, is obtained when compared with values of P MDP at the corresponding [KIO. The calculated values of P TAP, which vary between 2.8 and 3.1 X 1Od7 cmos-‘, show less variation with [K”JO than the calculated values of PMDP. Determination of the membrane permeability in the absence of potassium was complicated by alterations in the intrinsic activity of the preparations as well as in changes in the absolute value of the membrane potential. Figure 8 contains a continuous recording of membrane potentials obtained from a preparation perfused with Kfree solution. The membrane potential hyperpolarized to a value of 83 t 6 mV (mean & SD, n = 9) within 10 s and was accompanied by a substantial increase in the rate of spontaneous activity and the force of contraction (as viewed on the television monitor). As the preparations depolarized, the enhanced spontaneous rate subsided and within 5 min the membrane potential stabilized at a value of 42 t- 7 mV and contractions ceased. Contrary to the observed transient hyperpolarization, a stable hyperpolarization was reported for periods of up to 15 min in preparations of adult frog (2, II) and guinea pig (9) cardiac muscle. These results, however, differ from those
obtained from the ungulate Purkinje fiber in which a similar experimental maneuver arrests the process of repolarization and maintains a state of depolarization (often accompanied by oscillations) at the plateau level (3, 6, 8). It should be noted that the time course of the observed changes in the transmembrane potential from cultured heart cells is characteristic of that recorded from pacemaker cells of the sinoatrial node (24). DISCUSSION
In a previous publication (15)) consideration was given to the limitations of radioisotopic tracer determinations of transmembrane flux in naturally occurring preparations of cardiac muscle. We recognized that problems associated with tracer reflux and cellular heterogeneity could severely compromise the determination of transmembrane flux and values of permeability derived from these measurements. In this study we therefore sought to reevaluate the relationship between potassium concentration and membrane permeability by using a preparation of differentiated heart cells in tissue culture characterized by a defined cell population, short diffusional distances, and simple extracellular space (16). The Goldman equation as modified by Hodgkin and Katz (13) has generally been accepted as a working hypothesis for calculating the electrochemical driving force for ionic fluxes and obtaining a measure of the membrane permeability to a particular ion. Because tissue-cultured preparations of cardiac muscle are spontaneously active, definition of the electrochemical gradient for potassium efflux is complicated by the fact that the membrane potential is not held at a constant value throughout the duration of the efflux experiment. This problem is not uniquely associated with cardiac cells in tissue culture and can complicate the experimental results obtained from naturally occurring preparations of cardiac muscle. For example, oscillatory membrane potentials and pacemaker activity were induced in ungulate Purkinje fibers when the external potassium concentration was reduced to a level of 52.7 mM (3, 6, 8, 29). Although pacemaker activity could perhaps have been modified by the use of pharmacologic agents or ionic substitutions, such interventions could have undetermined effects on the membrane properties of the cells. Therefore, we addressed the problem of spontaneous activity in two ways: a) stimulating the preparations at a fixed rate for the concentrations of K, over which steady state could be maintained (LO-20 mM) and b) determining the relative potassium permeability (PK) by calculating the electrochemical driving force from either the membrane potential closest to the potassium equilibrium potential, i.e., the maximal diastolic potential (4), or (as shown in Fig. 7) the time-averaged transmembrane potential. In either case, the results of this study show that relative membrane permeability of growth-oriented heart cells is independent of the external potassium concentration in the range of LO-20 mM. Furthermore, the relation between EMDP and K, for values of LO-20 mM K, (see Table 2) is indicative of a membrane with a constant P&l% (28). Interpretation of membrane permeability in the ab-
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Cl68
HORRES,
W
lmin
sence of K, is constrained by the lack of steady-state conditions. The presence of a large gradient for-net K efflux, coupled with the inhibition of active transport (6, 8, 1% leads to a gradual increase in Nai and a decrease in Ki (Figs. 4-6). Until approximately 30% of Ki was exchanged for Nai, membrane depolarization could be attributed to a loss of Ki rather than to a decrease in potassium permeability. It would be premature to speculate about the mechanism responsible for the ensuing loss of spontaneous activity and state of maintained depolarization without additional measurements to evaluate changes in the permeability to other ions such as Na i‘he above findings are consistent with those of Haas et al. (ll), who reported that potassium permeability of frog atria1 cells appeared to be a material constant of the membrane. Because these findings are contrary to those that reported a nearly constant value for PK for the range of 25-25 mM potassium but a decrease in potassium permeability at values of [KJ, < 2.0 mM (3, 4, lo), it is necessary to draw attention to several assumptions on which the earlier reported studies were based. In determining the transmembrane flux of naturally occurring cardiac muscle, the preparations generally have been regarded as homogeneous both with respect to cell type and intracellular concentration, thereby making the tracer data amenable to interpretation without the use of multicompartment analysis. It has also been assumed that the extracellular morphology does not significantly limit tracer efflux and that changes in the concentration of the nonlabeled species in extracellular space, such as [K-J,, should not influence the accuracy of the tracer technique. However, using a mathematical simulation of tracer efflux measurements obtained from cardiac cells, we have shown the accuracy of the tracer method for potassium to be extremely sensitive to tissue geometry (15). Indeed, determinations of transmembrane flux in preparations of the size used in previous studies, such as 0.5-1.00 mm in diameter (3, 4, 10, 26), were shown to be significantly underestimated by extracellular diffusional limitations. By assuming a constant membrane flux, this analysis could be extended to account for the possible effects of external potassium on tracer efflux in diffusional limited preparations. At a transmembrane flux of 10 pmol*cmW2 s-l, Fig. 9 shows that errors in the tracer flux can be considerable, becorr,ing markedly pronounced as [K10 is reduced. In such cases, as nonlabeled K in the extracellular medium is decreased, the specific activity of the extracellular fluid would increase and thereby promote tracer reflux into the cells. Consequently, if one takes the 42K tracer data at face value, it would appear l
AITON,
AND
LIEBERMAN
FIG. 8. A continuous recording of transmembrane action potentials recorded from spontaneously active heart cells in presence and absence of potassium. Upper trace is perfusate temperature. Lower trace is a graphic representation of transmembrane potential protile.
EXTERNAL
POTASSIUM
hM)
9. Percent error in tracer-measured potassium flux as a function of external potassium in presence of radial diffusion limitations. Error in tracer measured vs. true potassium efflux was calculated from solutions of radial diffusion equations (15), in which true flux was assumed to be constant at 10 pmol~cm~“~s~‘; cell volume to surface area, 1.0 X lop4 cm; cell-packing fraction, 0.75, and internal potassium, 150 mM/l. Radial diffusion time was assumed to be 75 s. FIG.
that potassium efflux is reduced. Recent evidence obtained from cow Purkinje fibers (5) tends to support the simulated results shown in Fig. 9. As [K]” was reduced from 54 to 5.4 mM, the multicompartmental nature of the efflux kinetics decreased markedly, as would be expected if extracellular diffusional limitations become more significant at reduced values of [K],. In fact, if the preparation were sufficiently large in diameter, tracer efflux kinetics would become totally dominated by exchange in extracellular space. Therefore, calculations of PK based on data from preparations with diffusional limitations would be inaccurate solely on the basis of the tracer efflux measurements.
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K PERMEABILITY
OF
GROWTH-ORIENTED
HEART
Cl69
CELLS
In the present study, we failed to observe a decrease in 42K tracer efflux beyond that expected from the change in the electrochemical gradient; and, in fact, scrutinization of the d ata in K-free solution revealed a trend toward an increase in 42K tracer efflux (Fig. 5). Although we are it is currently unable to account for this observation, clearly inconsistent with th .e decrease in potassium permeability we hypothesized from similar findings with preparations of embryonic chick hearts (4), the tissue of origin for the current study. Because tissue culture techniques do not appear to alter the physiological properties of -growth-oriented cardiac muscle cells (16, 23), tissue geometry would be a plausible explanation that can account for the observed differences in potassium permeability between naturally occurring cardiac muscle and preparations of cultured heart cells. Previous efforts have combined measurements of potassium flux with those of relative membrane resistance to corroborate the hypothesis of a reduced PK in low [KIO (3). Notwithstanding the problems associated with the diffusional limitations described above, the electrical measurements with two microelectrodes are also su bject to question because no single relationship exists that would relate measurements of input resistance from a Purkinje fiber to membrane resistance and cytoplasmic resistivity by the chosen methods of analysis (23). Furthermore, removal of external K from the perfusate is known to inhibit active transport (6, 8, 19) and consequently promote the uncoupling of electrical activity between myocardial cells (7, 31). The experimental procedure would then compromise th .e unique interpretation of the data relating the increase in measured input re-
sistance to an increase in membrane resistance, because the experimental maneuver has been shown to be accompanied by a substantial increase in longitudinal (coupling) resistance, resulting from the reduction (uncoupling) of intercellular connections. We recognize that under certain conditions, it may be appropriate to exert some caution when extrapolating the results obtained from tissue-cultured heart cells to that of naturally occurring preparations. However, until the inherent morphological complexities of certain preparations of naturally occurring cardiac muscle are fully recognized as a potential limitation for experiments of the kind described in this report, caution should be exercised before introducing complex modifications into a particular membrane model, such as that of Hodgkin and Katz (13). Although such a model may represent an oversimplification of the actual membrane properties, it does provide a reasonable framework with which to describe the relationship between potassium flux measurements and the electrochemical driving force in tissuecultured preparations of cardiac muscle. We thank Dr. Brian Curtis for his critical review of the manuscript. This research was supported in part by grants from the National Institutes of Health (HL-12157), the North Carolina Heart Association, the Walker P. Inman Fund, an Established Investigatorship of the American Heart Association to M. Lieberman, and postdoctoral research support from the Wellcome Foundation and the North Carolina Heart Association to J. F. Aiton. A preliminary report of this study was presented at the 21st Annual Meeting of the Biophysical Society (Biophys. J. 17: 153a, 1977). Received
8 May
1978; accepted
in final
form
7 November
1978.
REFERENCES C. Establishment of ionic permeabilities of the myocardial membrane during embryonic development of the rat. In: Developmental and PhysioLogicaL CorreZates of Cardiac MusCZe, edited by M. Lieberman and T. Sano. New York: Raven, 1976, p. 169-184. BRADY, A. J., AND J. W. WOODBURY. The sodium-potassium hypothesis as the basis of electrical activity in frog ventricle. J. PhysioZ. London 154: 385-407, 1960. CARMELIET, E. E. ChZoride and Potassium Permeability in Cardiac Purkinje Fibers. Brussels: Editions Arsicia, S, A., 1961, p. 8% 124. CARMELIET, E. E., C. R. HORRES, M. LIEBERMAN, AND J. S. VEREECKE. Developmental aspects of potassium flux and permeability of the embryonic chick heart. J. PhysioZ. London 254: 673692, 1976. CARMELIET, E. E., AND F. VERDONCK. Reduction of potassium permeability by chloride substitution in cardiac cells. J. PhysioZ. London 265: 193-206, 1977. DEITMER, J. W., AND D. ELLIS. Changes in the intracellular sodium activity of sheep heart Purkinje fibres produced by calcium and other divalent cations. J. PhysioZ. London 277: 437-453, 1978. DEMELLO, W. C. Influence of the sodium pump on intercellular communication in heart fibers: effect of intracellular injection of sodium ion on electrical coupling. J. Physiol. London 263: 171-197, 1976. ELLIS, D. The effects of external cations and ouabain on the intracellular sodium activity of sheep heart Purkinje fibres. J. PhysioZ. London 273: 211-240, 1977. GLITSCH, H. G. Activation of the electrogenic sodium pump in guinea-pig atria by external potassium ions. J. PhysioZ. London. 276: 515-524, 1978. GOERKE, J., AND E. PAGE. Cat heart muscle in vitro. VI. Potassium exchange in DaDillarv muscles. J. Gen. Physiol. 48: 933-948, 1965.
1. BERNARD,
2.
3.
4.
5.
6.
7.
8.
9.
10.
Il.
12. 13.
14.
15.
16.
17,
18. 19.
20.
21.
HAAS, H. G., H. G. GLITSCH, AND R. KERN. Kalium-Fluxe und Membranpotential am Froschvorhof in Abhangigkeit von der Kalium-Aussenkonzentration. Pfluegers Arch. 291: 69-84, 1977. HODGKIN, A. L., AND P. HOROWICZ. Movements of Na and K in single muscle fibres. J. Physiol. London 145: 405-432, 1959. HODGKIN, A. L., AND B. KATZ. The effects of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. London 108: 37-77, 1949. HORRES, C. R. Potassium Tracer Kinetics of Growth Oriented Heart Cells in Tissue Culture. (Ph.D. dissertation). Duke University, Durham, NC, 1975. HORRES, C. R., AND M. LIEBERMAN. Compartmental analysis of potassium efflux from growth oriented heart cells. J. Membr. Biol. 34: 331-350, 1977. HORRES, C. R., M. LIEBERMAN, AND J. E. PURDY. Growth orientation of heart cells on nylon monofilament. Determination of the volume-to-surface area ratio and intracellular potassium concentration. J. Membr. BioZ. 34: 313-329, 1977. KASTEN, F. H. Mammalian myocardial cells. In: Tissue CuZture Methods and AppZications, edited by P. F. Kruse, Jr., and M. K. Patterson, Jr. New York: Academic, 1973, p. 72-81. KATZ, B, Nerve, MuscZe and Synapse. New York: McGraw, 1966, p. 61. KEENAN, M. J., AND R. NIEDERGERKE. Intracellular sodium concentration and resting sodium fluxes of the frog heart ventricle. J. Physiol. London 188: 235-260, 1967. KOOTSEY, J. M., AND E. A. JOHNSON. Buffer amplifier with femtofarad input capacity using operational amplifiers. IEEE Trcins. Biomed. Eng. 20: 389-391, 1978. LANGER, G. A., AND A. J. BRADY. Potassium in dog ventricular muscle: kinetic studies of distribution and effects of varying frequency of contraction and potassium concentration perfusate. Circ. Res. 18: 164-177, 1966.
Downloaded from www.physiology.org/journal/ajpcell by ${individualUser.givenNames} ${individualUser.surname} (131.170.021.110) on January 2, 2019.
Cl70 22. LEE, C. O., AND H. A. FOZZARD. Influence of low external K concentrations on membrane potential of sheep Purkinje fibers (Abstract). Federatiort Proc. 36: 436, 1977. 23. LIEBERMAN, M., AND T. SAWANOBORI, J. M. KOOTSEY, E. A. JOHNSON. A synthetic strand of cardiac muscle. Its passive electrical properties. J. Gen. Physio1. 65: 527-550, 1975. 24. NOMA, A., AND H. IRISAWA. Electrogenic sodium pump in rabbit sinoatrial nodal cell. Pfluegers Arch, 351: 177-182, 1974. 25. PAGE, E. Cat heart muscle in vitro. II. The steady state resting potential in quiescent papillary muscle. J. Gen. PhysioZ. 46: 189199, 1962. 26. POLIMENI, P. E,, AND M. VASSALLE. Potassium fluxes in Purkinje and ventricular muscle fibers during rest and activity. Am. J. Physiol. 218: 1381-1388, 1970.
HURRES, 27.
28.
29. 30. 31.
AITON,
AND
LIEBERMAN
N., AND M. J. MCLEAN. Electrical properties of cultured heart cells. In: Cardiac Adaptation, edited by T. Kobayashi, Y. Ito, and G. Rona. Baltimore: University Park Press, 1978, p. 64% 666. SPERELAKIS, N., AND K. SHIGENOBU. Changes in membrane properties of chick embryonic hearts during development. J. Gen. Physiol. 60: 430-453, 1972. VASSALLE, M. Cardiac pacemaker potentials at different extra- and intracellular K concentrations. Am. J. Physiol. 208: 770-775, 1965. WEIDMANN, S. Electrophysiologie der Herzmuskelfaser. Bern: Hans Huber, 1965, p. 39-40. WEINGART, R. The actions of ouabain on intercellular coupling and conduction velocity in mammalian ventricular muscle. J. PhysioE. London. 264: 341-365, 1977. SPERELAKIS,
Downloaded from www.physiology.org/journal/ajpcell by ${individualUser.givenNames} ${individualUser.surname} (131.170.021.110) on January 2, 2019.
HORRES,
of Physiology,
JAMES F. AITON, AND Duke University Medical
HORRES, RUSSELL (&JAMES F. AITON, AND MELVYN LIEBERMAN. Potassium permeability of embryonic avian heart ceils in tissue dture. Am. J. Physiol. 236(3): C163-C170, 1979 or Am. J. Physiol.: Cell Physiol. 5(2): C163-C170, 1979.-The relationship between the external potassium concentration ([K],) and membrane permeability has been reexamined using a tissue-cultured preparation of embryonic chick heart cells in which diffusional limitations are minimal. The unidirectional K efflux and electrochemical gradients were determined as a function of [K],, and the results showed that potassium permeability was constant within the range of l-20 mM [K],,. Membrane potentials were obtained in K-free solutions and correlated with 42K efflux and intracellular ion content measurements under the same conditions. In contrast to preparations of the intact embryonic chick heart, 42K efflux does not decrease in K-free media. Simulations of tracer measurements at reduced [K],, from naturally occurring cardiac muscle indicate that the experimentally observed decrease in 42K efflux could result from diffusional limitations. This observation, when coupled with the experimental results, suggests that the effect of low [KIO on membrane permeability in homeothermic preparations of cardiac muscle should be reevaluated.
cardiac muscle; pacemaker efflux; diffusional limitations
THE
MEMBRANE
OF
activity;
CARDIAC
membrane
MUSCLE
CELLS
potentials;
at
rest
K
is
highly permeable to potassium ions. Therefore, it is not surprising that cardiac cells depolarize in response to elevated concentrations of external potassium. However, the embryonic chick heart (4), as well as several preparations of adult cardiac muscle (I, 3, 22, 24-26, 30), also depolarize when the external potassium 6 concentration [K10 is reduced below 1 mM. Based on 4LK flux measurements, the depolarization in the embryonic chick heart has been ascribed to a decrease in membrane permeability to potassium (4). The validity of such an explanation is questionable because the interpretation of ionic flux measurements from preparations of embryonic and adult cardiac muscle are greatly complicated by the fact that tracer kinetics are not describable by single exponential rate processes (for discussion, see Horres and Lieberman (15)). Using a newly developed preparation of cardiac muscle in tissue culture (16), we have reexamined the relationship between external potassium concentration and membrane permeability by determining the unidirectional K efflux and electrochemical gradients as a function of external K. 0363-6143/79/0000-0000$01.25
Copyright
0 1979 the American
Physiological
avian
MELVYN LIEBERMAN Center, Durham, North
Carolina,
27710
METHODS
Tissue culture. Primary cultures of spontaneously contracting heart cells were derived from 11-day-old embryonic chick hearts that were subjected to multiple periods of enzymatic (trypsin) disaggregation (16). Nylon monofilament (20 pm OD) was used as the substrate to orient the cells and promote the formation of cylindrical preparations approximately 5 mm in length with a mean diameter (inclusive of nylon core) of 60 pm. The proportion of muscle cells in culture was increased by using a differential attachment technique (16). However, as with the observations reported from the laboratories of Kasten (17) and Sperelakis and McLean (27), the residual nonmuscle (fibroblastlike) cells proliferate within 5 days and comprise a substantial proportion of the total cell population. In one series of experiments in which intracellular ion content was determined, 3-day-old primary cultures of confluent, muscle-enriched heart cells were studied to minimize the contribution of the nonmuscle cells. Preparations of nonmuscle cells were obtained by subculturing primary heart cells (16). All preparations were grown in medium 199 (GIBCO) with 10% fetal calf serum, 2% chick embryo extract, and a 1% solutiori of penicillinstreptomycin (16). The preparations were incubated at 37°C in an environment of 4% CO2 and 96% air for 3-7 days. Potassium efflux. Preparations were incubated from 45 to 90 min, except as indicated, in modified Earle’s balanced salt solution (pH 7.4) containing 5.4 mM “K (New England Nuclear, Boston, MA or Nuclear Energy Services, N. Carolina State Univ., Raleigh, NC) under controlled humidity at 37.5”C with 5% COa/air as a buffer. The solution contained 7.0 g/l of neutralized bovine serum albumin, 5.6 mM glucose, and the following salts (mM): NaCl, 118; NaH2P04 gHZO, 0.94; MgS04 7H20, 0.81; NaHCOz, 26.2; and CaCla, 2.7. The preparations were perfused with filter-sterilized solutions of the same composition; KC1 was added as needed to obtain the desired concentration of [K],,. After incubation, the preparations were quickly transferred to a flux chamber (15), which was then sealed to permit constant volume perfusion. During the efflux period, to minimize the possible changes in the efflux results due to spontaneous tissue activity in the various [K],, the contractile rate was controlled at 150 min-’ by field stimulation with silver plate electrodes. Samples of the l
Society
c 163
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C164
HURRES,
perfusate were collected at l-mm intervals and were analyzed by counting in a well-type NaI scintillation system (model 1100, Nucleus). The data were corrected for background and decay and were subsequently subjected to compartmental analysis by fitting the data points with a curve defined by the sum of two exponential functions Y = ICI exp(-#It)
+ I&
AITON,
AND
LIEBERMAN
t 5% CO2 /Atr
eXp(-K&)
where IC represents the initial conditions in compartments 1 and 2 and K represents the respective rate constants, one of which was assigned the value determined from preparations containing only nonmuscle cells (slow compartment). By curve fitting with an analog computer, the efflux rate constant for the fast compartment, together with the respective compartment sizes, were derived. (A more detailed description of the efflux methodology and compartmental analysis has been reported elsewhere (15) .) 1un content. Muscle-enriched heart cells were seeded at 7 x 10" cells per 35-mm dish and grown for 3 days to confluency, at which time widespread areas of synchronously contracting cells were noted. Following removal of the culture medium, the cells were rinsed and incubated in 3 ml of 5.4 mM K or K-free solutions. The incubation solutions were discarded and the cells rapidly rinsed four times with cold (4°C) isotonic choline chloride. Intracellular Na and K were extracted during an overnight incubation in a solution containing 5 mM cesium chloride and 0.125 ml/l Acationox. Samples were measured using an atomic absorption flame spectrophotometer (model 460, Perkin-Elmer). Electrical recording. Transmembrane potentials were recorded from preparations placed in a chamber designed specifically to simulate the perfusion conditions of the 42K efflux experiments (Fig. 1). With such a system, it was possible to rapidly change the composition of the perfusate in the chamber within 4 s, while maintaining the temperature constant to within HL~“@. A television microscopy system (model 4300 Cohu television; M-5 Wild microscope) was used to view the preparation at an effective magnification of X400. Bevel-edged glass microelectrodes (tip diam, 50 pm) were used to stimulate the preparations at frequencies of 120-150 cycles*min-‘. Transmembrane potentials were recorded from the cells through glass microelectrodes filled with 3 M KC1 (30-50 ML!). A Ag-AgCl wire connected the microelectrode to a high-input-impedance preamplifier (20). The stimulus return electrode was a silver wire placed peripherally in the bath; rectangular voltage calibrating pulses (model CA5, Bioelectric Instruments) were applied between the silver inlet manifold and ground. The signals were channeled to a dual beam oscilloscope (model 565, Tektronix) equipped with a differential plug-in unit (model 3A3, Tektronix). Records were obtained photographically with an oscillographic camera (model C4, Grass) and a chart recorder (model 220, Brush). Data were tabulated from recordings in which the resting and action potentials were free of contractile artifacts, and the base line returned to its initial value after removal of the microelectrode.
J
1. Schematic representation of perfusion apparatus for electrical measurements. Lucite perfusion chamber contained a glass bottom and was mounted on an aluminum platform maintained at 37.5”C by dissipating regulated DC power in resistors (HI%10, Dale Electronics), Thermostatically controlled solutions (37.5”C), flowing at a rate of 16 ml. min-’ through insulated stainless steel tubing on the platform, were admitted to the chamber (l.O-ml vol) through a grounded silver manifold. A pneumatically controlled arrangement of valves (D) was used to select between the perfusate solutions in the fluid reservoirs (A or B) (see insert). Pneumatic actuators (model AVCA, Lee CO.) were wired to a DPDT master switch (23) that commanded pneumatic valves to direct fluid flow from Harvard pump (C) to perfusion chamber or to a recycling loop into fluid reservoirs. RE, return electrode (Ag/AgCl wire) to stimulus isolation unit; TP, temperature probe (Yellow Springs Instruments); ME, microelectrode; LS, fiber-optic illuminator (DolanJenner); TV/M, television microscopy system. Stimulus electrode and voltage calibrator not shown in drawing. FIG.
RESULTS
Effects of externalpotassium on 42K efflux. The results in Fig. 2 show that 42K exchange in these preparations cannot be described by a single exponential process because of the presence of muscle and nonmuscle cells (15). It is evident that the contribution of the slowly exchanging nonmuscle cells can be minimized, but not entirely eliminated, by reducing the 42K loading time of the preparation. Therefore, to deduce the efflux rate constant of the muscle cells, it is necessary to assess the contribution of the slowly exchanging compartment from similar experiments with a homogeneous population of nonmuscle cells. The effect of increasing [K10 over the range of LO-20 mM on 42K efflux kinetics was studied in both muscle-enriched and nonmuscle cell preparations. Representative results obtained from muscle-enriched preparations (Fig. 3) show that increasing the concentration of K, is accompanied by a small increase in the rate of 42K efflux. The results obtained with the nonmuscle cells were used in the evaluation of the data from the contractile preparations (Table 1). At a [K&, of 5,4 mM, the efflux rate constant for the muscle cells was 0.067 min-I, in contrast to a value of 0.015 min-’ for the nonmuscle
Downloaded from www.physiology.org/journal/ajpcell by ${individualUser.givenNames} ${individualUser.surname} (131.170.021.110) on January 2, 2019.
K PERMEABILITY
OF
GROWTH-ORIENTED
HEART
Cl65
CELLS
0
l 0 l O l 0 a0 l
0 0 l
0 l
0 a
0 0
l
0 l
0 l
0 0
l
0 l
0 a
0 l
0 l
0 0
a
0 l
0 l
0 0
l
0 a
0 l
0 a a l a a l
l o
5
*a
l m
l *
l o
l m
-8
2
0
5
IO
I5
20
25
20.0mM g* **a
K
I 20
I 25
30
FIG. 2. Effect of loading time on 42K efflux kinetics of growth-oriented heart cells in 5.4 mM external potassium. Two preparations from same culture were loaded with 42K for either 5 min (closed circles) or 45 min (open circles).
cells. Whereas little change was noted when [K-J0 was decreased to 2.0 mM, a 40% decrease in the efflux rate constant was observed in 1.0 mM [K],. The rate constant increased by 45% when [KJ, was increased to 20 mM. Values for potassium efflux were calculated for the different concentrations of K, between LO and 20 mM and were determined to be within the range 9.4-22.8 pmol. cmB2.8. Efflux experiments in nominally K-free media (~0.1 mM) produced interesting results (Fig. 4). It was found that the rate of tracer efflux was not decreased in K-free media, as might have been expected from previous studies (3, 4, 21). In the continued absence of [K],, the rate of 42K loss from the preparation increased and, after approximately 10 min of perfusion, contractile activity ceased and the preparation was unresponsive to the field stimulation. When 5.4 mM K was restored to the perfusate, contractility returned and the rate of 42K efflux decreased slightly. A similar pattern of change in efflux kinetics was observed, albeit slower, from preparations of the nonmuscle cells (14). In all of these experiments loss of potassium from the preparation greatly complicates the multicompartmental analysis of the data, so that only qualitative evaluations of 42K efflux kinetics can be made. However, by performing experiments with 42K loading times of 5 min, more information about the K-exchange kinetics of the muscle cells could be obtained (Fig. 2). The results shown in Fig. 5 indicate an increasing trend in the rate of 42K efflux with time in K-free solution. As nonlabeled K is unavailable in the extracellular space,
I 5
I 0
Time (mid
1 to
I 15 MINUTES
3. Effect of external potassium on 42K efflux kinetics of electrically stimulated preparations of heart cells in 1.0, 2.0, 5.4, and 20 mM external potassium. First few points (O-2 min) represent both carryover of the loading solution and 42K exchange in extracellular space. Counts per minute (cpm) on ordinate represent total activity in preparation. FIG,
TABLE 1. Compartmental analysis of 42K efflux data as a function of [Kjo _-.--- _-.- ~-[K]o, mM
1.0 2.0 5.4 20.0
n
4 5 22 4
Rate Constant*
0,040 0,068 0.067 0.097
t * t t
(K),
0.004 0.007 0.009 0.016
min
’
Potassium Efflyx+ ( JK), pmol-cm Les-’
9.4 16.9 15.7 22.8
* t * k
0.9 1.6 1.5 2.7
[K],, external potassium concentration; n, number of determinations. The measured internal potassium concentration [K]i increased by less than 15% over the range of 1.0-20 mM [K],. Efflux values were calculated at a [K]i of 133 mM, measured in 5.4 mM [K& (16). * Mean value & SE. The rate constants of the nonmuscle cells used in the compartmental analysis for the respective values of [Klo were 0.010, 0.013, 0.015, 0.026 min-’ (see Ref. 14), t Efflux values derived from the relationship Jk = K V/A[K]i are presented as the derived results & relative error calculated from the standard error. V/A, the volume to surface area of the preparation, was 1.06 X lop4 cm.
the loss of tracer in these experiments is indicative of a decrease in the internal potassium concentration [K]i. Direct measurements of intracellular K and Na content (Fig. 6) support the results of the tracer experiments and show the rapid decrease [K]i to be concomitant with an increase in internal sodium concentration ([Na];). Effects of [Kjo on potassium permeability. To arrive at relative values of potassium permeability for the different concentrations of K,, it was necessary to determine
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HORRES,
l .a
0
AITON,
AND
LIEBERMAN
I
I
I
I
1
I
10
20
30
40
50
60
Time(min)
IIO
I 1 20 30 M i nutes
I 40
FIG. 4. Effect of K-free perfusate on 42K efflux of electrically stimulated heart cells. Vertical arrows indicate loss of synchronous contractile activity in K-free solution and subsequent recovery when preparation was returned to 54 mM K.
Time
(mid
5. Potassium efflux kinetics of heart cells in K-free solution. Preparations were loaded in 42K for 5 min, Vertical bars represent envelope of standard deviation of results obtained from 9 individual experiments. FIG.
FIG. 6, Effect of K-free solution on intracellular ion content of 3day-old confluent primary cultures of heart cells. Sodium (open circles) and potassium (closed circZes) content were determined by atomic absorption spectrophotometry. Each point represents mean value -+ SD of 3-11 determinations.
the electrochemical gradient responsible for the unidirectional 42K effluxes reported in the previous section. Because the preparations normally contract spontaneously, they were stimulated at a rate equivalent to that used in the flux experiments. Table 2 summarizes the maximal diastolic potential of the membrane potentials (I&P) recorded at different concentrations of K, and relates these measurements to the calculated values for the potassium equilibrium potential (EK). The index used to describe the electrical gradient for potassium efflux was the maximal diastolic potential, the most negative value of membrane potential during the stimulation cycle. Note that &nP deviates from Ek at all levels of [K&, the most marked differences occurring at [K10 < 5.4 mM. These potentials were combined with the flux results presented in the previous section by using the Goldman equation, as modified by Hodgkin and Katz (13), to calculate values for membrane permeability (PM&. It is evident from Table 2 that no consistent relationship exists between [KIO and PMDP. However, the range of values centers about 5.2 x 10m7 cm& and is similar to the calculated value of 6.2 x 10B7cm, s-l reported by Katz (18) from data of frog skeletal muscle obtained by Hodgkin and Horowitz (12)1 Figure 7 illustrates an alternative approach taken to calculate the potassium permeability in contracting preparations. The index of the electrical gradient for K flux is designated as the time average of the transmembrane potential, E TAP.This potential represents a time-distributed profile of an action potential for a complete cardiac cycle and therefore takes into account any changes in action potential configuration that occur when the prep-
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K PERMEABILITY TABLE
OF
2. Membrane
GROWTH-ORIENTED
potassium heart cells
of growth-oriented
HEART
permeability
EMLW*,
mV
1.0 2.0 5.4 20.0
-131 -112 -86 -51
-93 -78 -66 -46
-+ t t t
1 1 1 1
20 5 10 8
6.4 7.2 5.2 4.6
-62 -45 -41 -29
Cl67
CELLS
2.8 3s 2.8 3.1
n, Number of measurements. “E~bp, maximal diastolic potential (mean value t SE). t EF~*P, time-averaged potential (see Fig. 4) obtained from representative potentials, having a maximal diastolic potential equal to that of the mean value of EMill’. * PMDP, P’I’AP, represent the potassium permeability calculated from the GoldmanHodgkin-Katz equation (13), using the respective values of E~br and
FIG. 7. Schematic representation of transmembrane action potentials recorded from growth-oriented heart cells. Cross-hatched region represents a time distribution profile of action potential, TAP, the magnitude of which is indicated by middle horizontal solid line. Upper horizontal line is zero reference potential.
aration is exposed to different K concentrations. It is evident from Table 2 that for a given [K],, ETAP is significantly less negative than the corresponding value of EMnP and thereby indicates a greater electrical gradient for the same value of potassium efflux. Consequently, when the values of ETAP are used to calculate the potassium permeability, an apparent decrease in membrane permeability, PTAP, is obtained when compared with values of P MDP at the corresponding [KIO. The calculated values of P TAP, which vary between 2.8 and 3.1 X 1Od7 cmos-‘, show less variation with [K”JO than the calculated values of PMDP. Determination of the membrane permeability in the absence of potassium was complicated by alterations in the intrinsic activity of the preparations as well as in changes in the absolute value of the membrane potential. Figure 8 contains a continuous recording of membrane potentials obtained from a preparation perfused with Kfree solution. The membrane potential hyperpolarized to a value of 83 t 6 mV (mean & SD, n = 9) within 10 s and was accompanied by a substantial increase in the rate of spontaneous activity and the force of contraction (as viewed on the television monitor). As the preparations depolarized, the enhanced spontaneous rate subsided and within 5 min the membrane potential stabilized at a value of 42 t- 7 mV and contractions ceased. Contrary to the observed transient hyperpolarization, a stable hyperpolarization was reported for periods of up to 15 min in preparations of adult frog (2, II) and guinea pig (9) cardiac muscle. These results, however, differ from those
obtained from the ungulate Purkinje fiber in which a similar experimental maneuver arrests the process of repolarization and maintains a state of depolarization (often accompanied by oscillations) at the plateau level (3, 6, 8). It should be noted that the time course of the observed changes in the transmembrane potential from cultured heart cells is characteristic of that recorded from pacemaker cells of the sinoatrial node (24). DISCUSSION
In a previous publication (15)) consideration was given to the limitations of radioisotopic tracer determinations of transmembrane flux in naturally occurring preparations of cardiac muscle. We recognized that problems associated with tracer reflux and cellular heterogeneity could severely compromise the determination of transmembrane flux and values of permeability derived from these measurements. In this study we therefore sought to reevaluate the relationship between potassium concentration and membrane permeability by using a preparation of differentiated heart cells in tissue culture characterized by a defined cell population, short diffusional distances, and simple extracellular space (16). The Goldman equation as modified by Hodgkin and Katz (13) has generally been accepted as a working hypothesis for calculating the electrochemical driving force for ionic fluxes and obtaining a measure of the membrane permeability to a particular ion. Because tissue-cultured preparations of cardiac muscle are spontaneously active, definition of the electrochemical gradient for potassium efflux is complicated by the fact that the membrane potential is not held at a constant value throughout the duration of the efflux experiment. This problem is not uniquely associated with cardiac cells in tissue culture and can complicate the experimental results obtained from naturally occurring preparations of cardiac muscle. For example, oscillatory membrane potentials and pacemaker activity were induced in ungulate Purkinje fibers when the external potassium concentration was reduced to a level of 52.7 mM (3, 6, 8, 29). Although pacemaker activity could perhaps have been modified by the use of pharmacologic agents or ionic substitutions, such interventions could have undetermined effects on the membrane properties of the cells. Therefore, we addressed the problem of spontaneous activity in two ways: a) stimulating the preparations at a fixed rate for the concentrations of K, over which steady state could be maintained (LO-20 mM) and b) determining the relative potassium permeability (PK) by calculating the electrochemical driving force from either the membrane potential closest to the potassium equilibrium potential, i.e., the maximal diastolic potential (4), or (as shown in Fig. 7) the time-averaged transmembrane potential. In either case, the results of this study show that relative membrane permeability of growth-oriented heart cells is independent of the external potassium concentration in the range of LO-20 mM. Furthermore, the relation between EMDP and K, for values of LO-20 mM K, (see Table 2) is indicative of a membrane with a constant P&l% (28). Interpretation of membrane permeability in the ab-
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Cl68
HORRES,
W
lmin
sence of K, is constrained by the lack of steady-state conditions. The presence of a large gradient for-net K efflux, coupled with the inhibition of active transport (6, 8, 1% leads to a gradual increase in Nai and a decrease in Ki (Figs. 4-6). Until approximately 30% of Ki was exchanged for Nai, membrane depolarization could be attributed to a loss of Ki rather than to a decrease in potassium permeability. It would be premature to speculate about the mechanism responsible for the ensuing loss of spontaneous activity and state of maintained depolarization without additional measurements to evaluate changes in the permeability to other ions such as Na i‘he above findings are consistent with those of Haas et al. (ll), who reported that potassium permeability of frog atria1 cells appeared to be a material constant of the membrane. Because these findings are contrary to those that reported a nearly constant value for PK for the range of 25-25 mM potassium but a decrease in potassium permeability at values of [KJ, < 2.0 mM (3, 4, lo), it is necessary to draw attention to several assumptions on which the earlier reported studies were based. In determining the transmembrane flux of naturally occurring cardiac muscle, the preparations generally have been regarded as homogeneous both with respect to cell type and intracellular concentration, thereby making the tracer data amenable to interpretation without the use of multicompartment analysis. It has also been assumed that the extracellular morphology does not significantly limit tracer efflux and that changes in the concentration of the nonlabeled species in extracellular space, such as [K-J,, should not influence the accuracy of the tracer technique. However, using a mathematical simulation of tracer efflux measurements obtained from cardiac cells, we have shown the accuracy of the tracer method for potassium to be extremely sensitive to tissue geometry (15). Indeed, determinations of transmembrane flux in preparations of the size used in previous studies, such as 0.5-1.00 mm in diameter (3, 4, 10, 26), were shown to be significantly underestimated by extracellular diffusional limitations. By assuming a constant membrane flux, this analysis could be extended to account for the possible effects of external potassium on tracer efflux in diffusional limited preparations. At a transmembrane flux of 10 pmol*cmW2 s-l, Fig. 9 shows that errors in the tracer flux can be considerable, becorr,ing markedly pronounced as [K10 is reduced. In such cases, as nonlabeled K in the extracellular medium is decreased, the specific activity of the extracellular fluid would increase and thereby promote tracer reflux into the cells. Consequently, if one takes the 42K tracer data at face value, it would appear l
AITON,
AND
LIEBERMAN
FIG. 8. A continuous recording of transmembrane action potentials recorded from spontaneously active heart cells in presence and absence of potassium. Upper trace is perfusate temperature. Lower trace is a graphic representation of transmembrane potential protile.
EXTERNAL
POTASSIUM
hM)
9. Percent error in tracer-measured potassium flux as a function of external potassium in presence of radial diffusion limitations. Error in tracer measured vs. true potassium efflux was calculated from solutions of radial diffusion equations (15), in which true flux was assumed to be constant at 10 pmol~cm~“~s~‘; cell volume to surface area, 1.0 X lop4 cm; cell-packing fraction, 0.75, and internal potassium, 150 mM/l. Radial diffusion time was assumed to be 75 s. FIG.
that potassium efflux is reduced. Recent evidence obtained from cow Purkinje fibers (5) tends to support the simulated results shown in Fig. 9. As [K]” was reduced from 54 to 5.4 mM, the multicompartmental nature of the efflux kinetics decreased markedly, as would be expected if extracellular diffusional limitations become more significant at reduced values of [K],. In fact, if the preparation were sufficiently large in diameter, tracer efflux kinetics would become totally dominated by exchange in extracellular space. Therefore, calculations of PK based on data from preparations with diffusional limitations would be inaccurate solely on the basis of the tracer efflux measurements.
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K PERMEABILITY
OF
GROWTH-ORIENTED
HEART
Cl69
CELLS
In the present study, we failed to observe a decrease in 42K tracer efflux beyond that expected from the change in the electrochemical gradient; and, in fact, scrutinization of the d ata in K-free solution revealed a trend toward an increase in 42K tracer efflux (Fig. 5). Although we are it is currently unable to account for this observation, clearly inconsistent with th .e decrease in potassium permeability we hypothesized from similar findings with preparations of embryonic chick hearts (4), the tissue of origin for the current study. Because tissue culture techniques do not appear to alter the physiological properties of -growth-oriented cardiac muscle cells (16, 23), tissue geometry would be a plausible explanation that can account for the observed differences in potassium permeability between naturally occurring cardiac muscle and preparations of cultured heart cells. Previous efforts have combined measurements of potassium flux with those of relative membrane resistance to corroborate the hypothesis of a reduced PK in low [KIO (3). Notwithstanding the problems associated with the diffusional limitations described above, the electrical measurements with two microelectrodes are also su bject to question because no single relationship exists that would relate measurements of input resistance from a Purkinje fiber to membrane resistance and cytoplasmic resistivity by the chosen methods of analysis (23). Furthermore, removal of external K from the perfusate is known to inhibit active transport (6, 8, 19) and consequently promote the uncoupling of electrical activity between myocardial cells (7, 31). The experimental procedure would then compromise th .e unique interpretation of the data relating the increase in measured input re-
sistance to an increase in membrane resistance, because the experimental maneuver has been shown to be accompanied by a substantial increase in longitudinal (coupling) resistance, resulting from the reduction (uncoupling) of intercellular connections. We recognize that under certain conditions, it may be appropriate to exert some caution when extrapolating the results obtained from tissue-cultured heart cells to that of naturally occurring preparations. However, until the inherent morphological complexities of certain preparations of naturally occurring cardiac muscle are fully recognized as a potential limitation for experiments of the kind described in this report, caution should be exercised before introducing complex modifications into a particular membrane model, such as that of Hodgkin and Katz (13). Although such a model may represent an oversimplification of the actual membrane properties, it does provide a reasonable framework with which to describe the relationship between potassium flux measurements and the electrochemical driving force in tissuecultured preparations of cardiac muscle. We thank Dr. Brian Curtis for his critical review of the manuscript. This research was supported in part by grants from the National Institutes of Health (HL-12157), the North Carolina Heart Association, the Walker P. Inman Fund, an Established Investigatorship of the American Heart Association to M. Lieberman, and postdoctoral research support from the Wellcome Foundation and the North Carolina Heart Association to J. F. Aiton. A preliminary report of this study was presented at the 21st Annual Meeting of the Biophysical Society (Biophys. J. 17: 153a, 1977). Received
8 May
1978; accepted
in final
form
7 November
1978.
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