Mg2" (2 67) ; Ba2" (1-93) > Co2" (1P02)

Journal of Physiology (1992), 454, pp. 267-298 267With 17 figuresPrinted in Great Britain

EXTRACELLULAR DIVALENT AND TRIVALENT CATION EFFECTS ONSODIUM CURRENT KINETICS IN SINGLE CANINE CARDIAC

PURKINJE CELLS

BY DOROTHY A. HANCK AND MICHAEL F. SHEETSFrom the Department of Medicine and the Cardiac Electrophysiology Laboratories,University of Chicago, 5841 South Maryland Avenue, Chicago, IL 60637 and theDepartment of Medicine and the Feinberg Cardiovascular Research Institute,

Northwestern University Medical School, 310 East Superior Street, Chicago, IL 60611,USA

(Received 3 September 1991)

SUMMARY

1. The effects of the extracellular divalent cations barium, calcium, cadmium,cobalt, magnesium, manganese, nickel and zinc and the trivalent cation lanthanumon macroscopic sodium current (INa) were characterized in enzymatically isolatedsingle canine cardiac Purkinje cells under voltage clamp at 9-14 'C.

2. All di(tri)valent cations produced depolarizing shifts in the conductance-voltage relationship. The order of efficacy, taken as the concentration required toproduce a 5 mV shift in the mid-point of peak INa conductance, from least to mosteffective was (mM): Ca2" (2 97) - Mg2" (2 67) ; Ba2" (1-93) > Co2" (1P02) ; Mn2+(0 88) > Ni2+ (0 54) > La3+ (0 095) t Cd2+ (0 083) t Zn2+ (0 076).

3. Addition of di(tri)valent cations also produced depolarizing shifts in voltage-dependent availability. The order of efficacy from the least to most effective was(mM): Cd2+ (7-70) ; Mg2+ (6-86) Ba2+ (450) > Ca2+ (2-47) t Co2+ (1-87) t Mn2+(1-24) - Ni2+ (1P20) > Zn2+ (0300) > La3+ (0060).

4. The Gouy-Chapman-Stern equations were used to evaluate di(tri)valent cationefficacy in binding to surface charges. Surface charge density was estimated as0-72 sites nm-2, and it was assumed that Mg2+, the divalent cation that produced thesmallest shift, screened but did not bind to surface charges. Based on voltage-dependent availability, KD from lowest to highest affinity were (mM): Ba2+ (2500) >Co2+ (1670) - Mn2+ (1430) Ca2+ = Cd2+ = Ni2+ (1200) > Zn2+ (250) > La3` (30).

5. All di(tri)valent cations also produced a concentration-dependent accelerationof INa tail current relaxation. The addition of Ca2+ and La3+ produced accelerationof tail current relaxations that could be accounted for by the surface charge effectspredicted from the shift in voltage-dependent availability. Cd2 , which producedalmost no change in voltage-dependent availability, dramatically accelerated tailcurrent relaxation. Zn2+, Ni2+, Mn2+ and Co2+ also produced greater acceleration oftail current relaxation than could be accounted for by surface charge effects.

6. Di(tri)valent cations delayed time to peak INa in a concentration-dependentmanner. The time to peak Ixa-voltage relationship was well described by anMS 9696

D. A. HANCK AND M. F. SHEETS

exponential plus a constant, and di(tri)valent cations did not affect the slope factoror constant but shifted the relationship in the depolarizing direction. Similar to theireffect on tail currents, addition of some di(tri)valent cations produced larger effectson time to peak 'Na than expected from the shift of voltage-dependent availability.

7. Kinetic effects on INa result from screening and binding to surface charges andfrom voltage-dependent block. Shifts in voltage-dependent availability are likely tobest estimate the screening and binding effects of di(tri)valent cations. The rates ofinteractions of some di(tri)valent cations with the open channel appear to be slowerthan previously thought with resultant effects on the kinetics of INa.

INTRODUCTION

Divalent cations have multiple interactions with voltage-gated sodium (Na')channels, including binding to and screening of surface charges and blockingconductance in the open channel. Kinetic effects secondary to binding of Ca2+ tosurface charge sites were first quantified in squid axons by Frankenhaeuser &Hodgkin (1957) and measured in cardiac Purkinje fibres by Weidmann (1955). Themost commonly used model for quantifying these effects has been the Gouy-Chapman-Stern equations, which assume that cations interact with uniformlysmeared charges on the lipid bilayer (e.g. Gilbert & Ehrenstein, 1969; McLaughlin,Szabo & Eisenman, 1971; Hille, Woodhull & Shapiro, 1975). More recentinvestigations, comparing kinetic shifts of currents of channels incorporated intoneutral and charged bilayers, have provided evidence that the charges that affectNa' channel kinetics are located primarily on the channel protein itself rather thanon the lipid bilayer (Green, Weiss & Andersen, 1987; Cukierman, Zinkand, French &Krueger, 1988). Despite this evidence, the Gouy-Chapman approximation hasremained a useful model for describing the interactions of cations with voltage-gatedchannels (for recent reviews see McLaughlin, 1989; Green & Anderson, 1991).

In addition to effects secondary to screening of and binding to surface charges,divalent cations have been shown also to block conductance of the open channel ina voltage-dependent manner. The most commonly used model for quantifying theseeffects has been the application of Eyring rate theory to permeation, whereby an iontransits the channel via a series of barriers and wells. Such mathematical treatmentsfor Na+ channels have involved using four barriers and three wells (e.g. Hille, 1975)or have been simplified to two barriers and a single well for the case of interactionsof cations at a single side of the channel (Woodhull, 1973).

Binding to and screening of surface charges as well as block can modify theamplitude and the time course of INa. We were interested in quantifying thecontributions of each of these phenomena to INa. The data are presented in two parts.In this paper we considered the overall form Of INa in order to characterize the effectsof extracellular di(tri)valent cations on the time course and the voltage dependenceof INa kinetics and to quantify the effects that could be explained as interactions ofdi(tri)valent cations with surface charges. In the companion paper (Sheets & Hanck,1992) we analysed block of the open channel by di(tri)valent cations.We studied a variety of di(tri)valent cations in order to help differentiate between

surface charge and blocking effects. Ca2+ and Mg2+ were studied because thesedivalent cations are present in physiological solutions. In addition, we studied

268

DI(TRI) VALENV7T EFFECTS ONV CARDIAC 'Na KINE7TICS 269

another group IIA divalent cation, Ba2", because it is commonly used to block K+channels or to substitute for Ca2" in '(a studies. The group IIB divalent cations Cd2`and Zn2" were selected because of the suggestion that these agents block cardiac INaat low concentrations in a voltage-independent manner (DiFrancesco, Ferroni,Visentin & Zaza, 1985) and the observation that there was an inverse relationship ofCd2` and Zn2" block and TTX sensitivity in heart vs. skeletal muscle andneuroblastoma cells (Frelin, Cognard. Vigne & Lazdunski, 1986). The transitiondivalent cations Co2+, Mn2' and Ni2+ were included because they have been used inINa experiments to block Ca2+ channels. The trivalent cation La3" was includedbecause it has been suggested not to affect cardiac INa (Nathan, Kanai, Clark & Giles,1988) or to block it (Bustamante, 1987) and because it also blocks Ca21 channels.At a practical level, an inadequate appreciation of the effects of divalent and

trivalent cations on INa could lead investigators to suspect fundamental differencesbetween channel types or conditions that in reality stem from differences in solutioncomposition alone. On the other hand, divergent interactions of di(tri)valent cationswith various Na' channel isoforms could point to important structural differencesbetween channel types, and these may help us understand how such differencesproduce functionally important isoform-specific characteristics.

METHODS

Cell preparationThe method of isolation of single canine Purkinje cells was as previously described (Sheets,

January & Fozzard, 1983). Briefly, hearts were removed from animals anaesthetized with sodiumpentobarbitone (,> 50 mg kg-1) or chloralose (a> 50 mg kg-1), and the free-running canine Purkinjefibres were cut into short segments (2-3 mm) and incubated in modified Eagle's minimal essentialmedium (MEM) with 5 mg ml-1 Worthington type I collagenase for l-2 h at 37 0C in a shakingwater bath. The digested fibres were washed and incubated for 15 min in 130 mM-potassiumglutamate, 5 7 mM-MgCl2, 0-12 mM-EGTA and 5 mm-HEPES (pH 6-2) at 37 'C. Fibres were thenmechanically separated into single cells by application of shear force. Cells were stored at roomtemperature in MEM (pH 7 3), which contains 1-8 mm-Ca2+, and were studied within 18 h.

Recording techniqueVoltage control was imposed via a unity gain amplifier (Burr-Brown OPA-27, Tucson, AZ, USA)

located in the headstage and connected to the outflow of a large-bore, double-barrelled glasssuction pipette (Makielski, Sheets, Hanck, January & Fozzard, 1987) via an Ag-AgCl pellet anda 3 M-KCl agar bridge. A single cell with normal striation pattern and no membrane blebs wasdrawn into the pipette aperture using hydrostatic pressure until only about one-third of the cellremained outside the pipette. The cell was allowed to seal to the aperture walls, and then the cellmembrane inside the pipette was ruptured with a manipulator-controlled wire to gain access forinternal perfusion and control of membrane voltage. Ia was measured with a virtual groundamplifier (Burr-Brown OPA-101, 5 MQ feedback resistor) connected to the outflow channel of thebath via a second 3 mM-KCl agar bridge and Ag-AgCl pellet. Currents were recorded with eithera 12-bit or 16-bit analog-to-digital converter on a Masscomp 5520 or 5450 computer (ConcurrentComputer, Tinton Falls, NJ, USA) at 100 and 300 kHz or 400 kHz. Data collected at 100 kHz wereprefiltered with an 8-pole or 16-pole Bessel filter (Frequency Devices 848 or 9002, Haverhill, MS,USA) with a corner frequency of 10 kHz. Data collected at 300 or 400 kHz were prefiltered withan 8-pole Bessel filter with a corner frequency of 50 kHz, a 16-pole Bessel filter with a cornerfrequency of 60 kHz, or were recorded unfiltered (the corner frequency of the electronics was125 kHz). A fraction of the current was fed back to compensate for the voltage drop across theseries resistance (Rj, which was 50-70 kQ across the open pipette. The primary charging timeconstant with Rs compensation was always less than 10 Ius.

All measurements were made in symmetrical Na' solutions. Extracellular solution contained(mM): 105 or 120 Cs'. 45 or 30 Na', 2 Ca2 , 154 Cl and 10 HEPES (pH 72). Intracellular solution

269

D. A. HANOCK AAND M. F. SHEETS

contained (mM): 105 or 120 Cs', 45 or 30 Na', 0 or 10 EGTA, 150 F- and 10 HEPES (pH 7 2). Insome cells 0 05 mM-MgATP or 0-2 mM-K2ATP was added to the intracellular solution, but no effectson INa were evident in these cases. Temperature was controlled using a Sensortek TS-4 feedback-controlled thermoelectric stage (Physiotemp Instruments. Inc., Clifton, NJ, USA) mounted on themicroscope, and it varied less than 0 4 'C during an experiment. Cells were studied between 9-3 and14 0C.

Experimental protocols, cell selection and data analysisVoltage protocols were imposed from a 12-bit digital-to-analog converter (MNasscomp 5450) over

a 30/1 voltage divider or from a 16-bit digital-to-analog converter (Masscomp 5520) using locallywritten control programs (D.H.). Cells were held at - 150 mV; channel availability at - 150 mV wasrequired to be greater than 98% for data to be included in the study. Cells were depolarized onceeach second or once each 15 s for 25 or 50 ms.

Currents were capacity corrected using eight or sixteen scaled current responses to voltage stepsbetween - 150 and - 190 mV. Currents were leak corrected by the amount of time-independentlinear leak estimated from the currents elicited between -110 and - 190 mV. This described thetime-independent leak well except at very positive potentials where a small outwardly rectifying,time-independent current was usually present. Leak resistance (RL), taken as the reciprocal of thelinear conductance between - 190 and -110 mV, was required to be greater than 10 MQ forindividual determinations (range 11-531 MQI). A value for each cell was calculated as the mean ofmultiple determinations over the duration of recording; the average was 68 MQI (n = 44). Currentswere normalized to surface area assuming a specific capacitance of 1 ,yF cm-2. Cell capacitance wascalculated from the integral of the current responses to summed voltage steps between - 150 and-190 mV. Average capacitance was 66+ 16 pF (mean+S.D., n = 44).PeakINa during step depolarizations was calculated as the mean of four samples (40 Its) about the

maximum current from the capacity- and leak-corrected data digitally (Gaussian) filtered at 5 kHz.INa tail currents, recorded at 300 or 400 kHz. were capacity corrected, inverted and then fitted toa sum of exponentials using DISCRETE (Provencher, 1976), which determined the number of timeconstants and gave estimates and standard errors of the estimates for the coefficients. Data wereanalysed and plotted on a Masscomp 5520 or Masscomp 5450 computer using locally writtenprograms (D.H.) or on a SUN Sparcstation I using SAS (Statistical Analysis System, Cary, NC,USA). Except for DISCRETE, fitting programs on the Masscomp used algorithms from theNumerical Algorithms Group library (NAG, Oxford. UK). Regression parameters are reported asthe estimate and standard error of the estimate (s.EE.).

Because each di(tri)valent cation could be quickly and completely washed out, multipleconcentrations, as well as multiple di(tri)valent cation species, could be studied in the same cell.Each set of experimental protocols took about 7-8 min so that up to four interventions could bestudied in long-lived cells. Sometimes re-exposure to the same di(tri)valent cation concentrationwas made to check reproducibility of experimental results, but data from only one exposure per cellper concentration were included in the grouped results presented here. Three or four concentrationsof nine di(tri)valent cations were studied. Each di(tri)valent cation concentration was studied intwo to five cells. To help ensure that included data exhibited good membrane voltage control, weexcluded data in which the slope factor of the conductance relationship (eqn (3)) in control wassteeper than -6 mV (mean value in control was - 87 mV). We have previously demonstrated thatthe conductance slope factor (Hanck & Sheets. 1992) correlates well with other measures ofmembrane voltage control.

In order to account for the time-dependent shift in kinetics that occurred during the time courseof experiments, control data were taken as the mean of determinations made before and afterexposure to a test di(tri)valent cation. In twelve of the 219 interventions washout data wereunavailable; in these cases the effect produced by the added di(tri)valent cation was calculatedfrom the control data and was adjusted for the time-dependent shift by an appropriate amountbased on the average rate of shift for all controls (Hanck & Sheets, 1992).

Theory and curve-fitting procedures for quantifying surface charge effectsThe presence of an excess number of negatively charged sites on the extracellular membrane,

whether uniformly smeared as in the Gouy-Chapman approximation, or more discretely located onthe channels themselves, creates a surface potential that produces a voltage drop across the

270

DI(TRI)VALENT EFFECTS 0ON' CARDIAC INa KIANETICS

membrane in the region of the voltage sensor different from the transmembrane potential(Grahame, 1947 McLaughlin et al. 1971; Gilbert, 1971; Hille, 1984). The negatively charged sitescan be screened by cations from the bulk solution, and this reduces the surface potential, bringingthe voltage sensed by the channels closer to the applied potential. Screening effects do not dependupon the cation species but only its charge; i.e. divalent cations are equally effective but moreefficacious than monovalent cations. We used the following form of the Grahame equation(Grahame, 1947) based on Hille et al. (1975). which describes the relationship of the magnitude ofthe surface potential to the density of the surface charge sites:

'f = 2 [(lexp { - VfGF/RT}-C +C2 exp { - 2?fOF/RT}-C2 +C3 exp { - 3?F/RT}- c3]0.65 (1)

where ao- is the density of surface charge sites available to be screened (in sites nm-2), CQ is theconcentration of monovalent cations, C2 the concentration of divalent nations, and C3 theconcentration of trivalent cations, each in M, and 3fo is the surface potential in mV. The constantsR. T and F have their usual meanings.

In addition to screening surface charges. some di(tri)valent cations also appear to bind to them.Binding neutralizes charge, thereby reducing the effective number of surface charge sites andthereby the surface potential. The binding of di(tri)valent cations to surface charge sites can betreated as a bimolecular reaction and the number of surface charges not bound, and thereforeavailable for screening, can be calculated as follows:

°f = ¢T/( 1 + i[Ci exp{-ziF~f0/RT}/KDi) (2)where o-, is the density of surface charge sites not bound by di(tri)valent cations (in sites nm-2), S0Tis the total density of surface sites, KDi is the dissociation constant in M for binding the ithdi(tri)valent cation species, Ci is the concentration of the ith species in M, zi is the valency, and?0 is the surface potential in mV. Equation (1) alone, or in combination with eqn (2), were solvediteratively using a binary search and Bus and Dekker algorithm in NAG. Appropriate values forthe dissociation constant for Ca2' and surface charge density were chosen such that the solutionsfitted the curvature of the data in the presence of various concentrations of Ca2+ and the data inthe presence of various concentrations of Mg2 , the divalent cation that produced the smallestkinetic shifts. As has been noted in the past (e.g. Hille et al. 1975), the choice of surface chargedensity and KD for Ca2+ cannot be determined uniquely from the data. In general, choices of highersurface charge density required higher estimates for dissociation constants and vice versa. However,the order of di(tri)valent cation effects would not be affected.

RESULTS

Effects of di(tri)valent cations on the conductance relationshipExamples of the effects of various di(tri)valent cations on the time course of INa

during step depolarizations to -40 mV and on the peak INa current-voltagerelationship are shown in Figs 1, 2 and 3. In each case control and washout data, i.e.in the absence of added di(tri)valent cations, are also shown. Figure 1 shows theeffects of group 11A divalent cations on 'Na. They reduced peak INa in anasymmetrical fashion, so that peak currents during steps to negative potentials weremore affected than those during steps to positive potentials. The time course of INawas prolonged; time to peak of INa occurred later and INa decayed more slowly. Thegroup IIB divalent cations, Cd2+ and Zn2 , along with the trivalent cation La3, wereeffective when added at the lowest concentrations (Fig. 2). Addition of Cd2+ and Zn2+reduced peak JNa over the entire voltage range, and at the concentrations thatproduced a large decrease in INa, there were only modest or no effects on the timecourse of the current. This voltage-independent reduction in IM was investigated inmore detail, and that analysis is presented in the companion paper (Sheets & Hanck,

271


10 mM-Ba2"

Voltage (mV)

l2 ms

1 0 mM-Ca2l1

-1

Voltage (mV)-120 -80 -40

-5 Current

4 n (pA am 2)-1U

c2

E -2

< -4

* -6

-8

-10

10 mM-Mg2+

Voltage (mV)-120 -80 -40

2 ms

30

40 80

Current(pA 1sm-2)

-10

Fig. 1. Effects of group IIA divalent cations (Ba2+, Ca2' and Mg2+) on INa. Holdingpotential was - 150 mV, and cells were depolarized to various potentials for 50 ms once

each second. Left panels show capacity- but not leak-corrected current responses duringthe first 10 ms after depolarization to -40 mV, before, during and after the addition of10 mM-divalent cations. Data were sampled at 100 kHz as described in the Methods andare shown digitally filtered at 5 kHz. In the cases where control and washout currentsdo not superimpose the washout current has a faster turn-on and faster decay as ischaracteristic of the hyperpolarizing shift in kinetics which occurs over the time periodof recording in this preparation. Right panels show the peak 'Na-voltage relationships incontrol (0), during washout (OJ), and in the presence of added divalent cations (S).Continuous lines are the fits to eqn (3) as described in the text. Parameters from the fitsare summarized below with the control parameters given as the mean of control andwashout measures.

272

0

-1

-2

A

E

4-0.

PD

u

12

Current

-4 (pA sm-2)

B

2

C4

E

-

4-

2 ms

DIl(TRIR)VVALENT EFFECTS ON CARDIAC Ixa KIN.VETICS

1992). On the other hand, in addition to reducing the magnitude of'Na over the entirevoltage range, low concentrations of the trivalent cation La3" produced verydramatic slowing of current (Fig. 2C). Several transition metals, Ni2l, Mn2+ andCo , were also examined, and these were effective at intermediate concentrations(Fig. 3).The continuous lines through peak 'Na in the right-hand panels of Figs 1, 2 and 3

are the best-fit lines of peak INa to a transform of a Boltzmann distribution:

I = (Vt-J;rev)Gmax/[1+ exp{(Vt-V)/}], (3)where I is the peak 'Na in the depolarizing step and Vt is the test potential. Theparameters estimated by the fit were Vrev, the reversal potential, Gmax, the maximumpeak conductance, 14, the half-point of the relationship, and slope factor (s) in mV.For fitting datasets with test di(tri)valent cations, reversal potential was fixed at thevalue calculated from the matching control data. We chose the simple conductancetransform rather than the Hodgkin-Huxley m3 transform because we have previouslyshown with gating charge measurements that the mid-point of charge andconductance are well matched, which indicates that for cardiac Na+ channels thevoltage dependence of activation is not evenly distributed between three closed statetransitions (Hanek, Sheets & Fozzard, 1990).Each of the di(tri)valent nations produced a depolarizing shift in the mid-point of

the conductance relationship. Data for all di(tri)valent nations are summarized inFig. 4A. In order to rank the effectiveness of the di(tri)valent nations, we appliedlinear regression analysis to quantify the measured shifts as a function of the logl0of the added di(tri)valent cation concentration. It should be recognized, however,that this treatment represents a simplification since there would be no shift ofconductance at zero added di(tri)valent nations, and so for each of these relationshipsthe data asymptotically approach zero as di(tri)valent cation concentration islowered. The regression results are summarized in Table 1. Differences between theability of di(tri)valent nations to shift the mid-point of the conductance relationshipwere not dramatic, i.e. the change in mid-point for a tenfold change in concentrationof added di(tri)valent nations (the slope of the regression) was small. Least effectivewas Ba2" (16 9 mV), but the most effective divalent nations (Ca2+ and Co2+) producedless than a twofold greater shift for a tenfold change in concentration (29 7 mV). Thetrivalent cation La3+, with the extra charge, shifted conductance 43-3 mV for atenfold change in concentration. Another method to rank efficacy was to calculatethe concentration at which each di(tri)valent cation produced an equal effect. We

Divalent Control Control Control Test Test Testcation Gmax s VJ Gmax s VI(mM) (pS Jm 2) (mV) (mV) (pSam ) (mV) (mV)

(A) 10 Ba2+ 124 -9-4 -61 123 -10-4 -43(B) 10 Ca2+ 274 -8-6 -54 239 -9-9 -34(C) 10Mg2+ 306 -7-7 -63 287 -10-2 -46(A) Barium: cell f8.03, RL 141 MQ, 53 pF, 14-0 0C. [Na+]0/[Na+Ji was 30/30.(B) Calcium: cell B3.04, RL 54 MQ, 66 pF, 11-8 0C. [Na+]J/[Na+]i was 30/30.(C) Magnesium: cell f8.04, RL 61 MQ, 60 pF, 13 8 'C. [Na]./[Nra+]i was 30/30.

273


0-1 mM-Cd2+

Voltage (mV)

-120 -80 -40L J2 ms

0-1 mM-Zn2+

L J2 ms

0-1 mM-La3"

Voltage (mV)

Current(pA ,um-2)

-10

-2)

40 80

-IIo L -1t 2 ms Current

-16 (PA #M 2)

[-20Fig. 2. Effects of group IIB divalent cations, Cd2+ and Zn2+, and the trivalent cation La3+,on INa, Format is as in Fig. 1. Parameters from the fits of eqn (3) were as follows:Di(tri)valent Control Control Control Test Test

cation Gmax 8 I Gmax s(mM) (pS um 2) (mV) (mV) (pS ,um 2) (mV)

(A) 0 1 Cd2+ 279 -7-8 -52 221 -9 1(B) 0-1 Zn2+ 166 -101 -52 94 -11-8(C) 0-1 La3+ 413 -6-2 -58 342 -8-3(A) Cadmium: cell A8.03, RL 42 MCI, 41 pF, 12-6 'C. [Na+]0/[Na+]i was 30/30.(B) Zinc: cell A8.01, RL 76 MQ, 48 pF, 12-8 'C. [Na+]0/[Na+]i was 30/30.(C) Lanthanum: cell b2.02, RL 72 MQ, 79 pF, 11P2 'C. [Na+]0/[Na+]i was 45/45.

-1

-3

-5-7-9

274

A

E03.a

c

B

E

0.CL

0

U3

C

N

E

0.

0)

1

-1

-3

-5

0

-4

-8

-12

TestIli

(mV)-46-47-45

DI(TRI)VALENT EFFECTS ON CARDIAC INa KINETICS

1 mM-Ni2+

Voltage (mV)-120 -80 -40

L J2 ms

1 mM-Mn2+

Voltage (mV)-120 -80 -40

L J2 ms

1 mM-Co2"

Voltage (mV)-120 -80 -40 40 80

u _ 2ms Currentwc (pA pm-2)

Fig. 3. Effects of transition metals, Ni2l, Mn2+ and Co2l, on I,,. Format is as in Fig. 1.Parameters from the fits of eqn (3) were as follows:

Control Controls

(mV) (mV)-86 -50-8-2 -59-7-8 -56

TestGmax

(pS /tm 2)194285266

Test Test8 I

(mV) (mV)-10-2-9.9-9-6

-39-52-50

(A) Nickel: cell 94.01, RL 65 MQ, 84 pF, 9-9 'C. [Na+]0/[Na+]1 was 45/45.(B) Manganese: cell A8.04, RL 36 MQ, 52 pF, 121 'C. [Na+]0/[Na+], was 30/30.(C) Cobalt: cell A8-05, RL 31 MO, 60 pF, 12-1 'C. [Na+],/[Na+]i was 30/30.

A

275

I--

E

0.

G)

U-

0

-2

-4

-6

-81

B

2I-N 0EZ -2Ce -~c -65 -8-10

C

-5Current(pA #m 2)

-15

21-

0.CL

a

1-1

-3

-5

-7

Divalentcation(mM)

(A) 1 Ni2+(B) 1 Mn2+(C) 1 Co2+

ControlGmax

(pS um 2)251297281

2D. A. HANXCK AND M. F. SHEETS

B_ 12

0 1 00C: 0-8a)LU

4-

0._

0-

U)

3 030 300 3000Added di(tri)valent cations (mM)

06 X T I

0*4

02

0-0 ...... . .....003 030 3.00 3000

Added di(tri)valent cations (mM)

Fig. 4. Concentration dependence of di(tri)valent cation effects on conductanceparameters. All measurements were made with a background of 2 mM-Ca2 . Plotted arethe means and S.E.M. of two to five determinations per di(tri)valent cation concentration.Note that the concentration axes are logarithmic. Ca2+(2), Mg2+ (M), Ba2+ (D2), Co2+ (c),Mn2+ (A), Ni2+ (+), La3+ (*), Cd2+ (0) and Zn2+ (*). A, shift in mid-point of theconductance relationship (from fits of eqn (3)). Continuous lines are the results of linearregression of the shifts in mid-point to the log10 of the concentration. Parameters, as theslope and concentration that produced a 5 mV shift, are given in Table 1. B, the effect ofadded di(tri)valent cations on the slope factor of the conductance relationship (fits of eqn(3)). These are plotted as the ratio of the slope factor in the presence of added di(tri)valentcations to that in control. If only screening and binding affected conductance, the ratioswould be 1 0. The concentration-dependent reduction in the slope factor and the largevariation in the reduction in the slope factor both indicate that changes in conductanceare more complex than screening and binding alone.

TABLE 1. Effects of di(tri)valent cations on the mid-point of conductance and availabilityConcentration of added di(tri)valent

cationsproducing a 5 mV shift,

(mm)

Conductance

2-982-671-931-020-880540-100-08008

Availability

2476-864-501 871-241 200-067 70030

Shift produced by tenfoldchange in concentration

(mV)

Conductance

30-5+2-3 (n = 11)20-6+2-7 (n = 8)16 9 + 1-9 (n = 7)29-7 + 2 6 (n = 11)216+2-0 (n = 7)229+30 (n = 13)42-1+5-5 (n = 8)24-7 + 3-4 (n = 9)18-9+2-5 (n = 6)

Availability

17-0+09 (n = 8)9-5 + 1-9 (n = 6)19 5 + 2-2 (n = 5)10-2 + 1-2 (n = 9)9-7 + 1-3 (n = 4)94+28 (n = 7)

16-5 + 1-8 (n = 8)2-4+ 1 1 (n = 7)5-0 + 0 8 (n = 6)

Data in Fig. 4A (conductance) and Fig. 9A (availability) were compared using linear regression.The parameters from the fits were used to calculate the concentration that would produce a 5 mVshift in conductance and in voltage-dependent availability. The shifts in mid-point for a tenfoldchange in concentration (slope of the regression) are given as the predicted values + the standarderrors of the estimates. Data are listed in the order in which they produced a 5 mV shift inconductance (from highest concentration to lowest).

A50

E 40a)c 30

a- 20c0

a 10

4-C 0cn

10 -0*0

Di(tri)valentcation

Ca2+Mg2+Ba2+Co2+Mnn2+Ni2+La3+Cd2+Zn2+

276


therefore calculated the concentration that shifted conductance mid-point by 5 mV,which gave a rank order of di(tri)valent cations from least to most efficacious of Ca2+t Mg2+ t Ba2+ <22<Co2 Mn2+ < Ni2+ < La3+

-Cd2+ <Zn2+*

We considered whether the changes in the conductance relationship could beunderstood solely as the result of extracellular di(tri)valent cations shielding or

A B

30

207 .

E

e 0 - 120 -60 0 60C',

0 Voltage (mV)

Voltage (mV)-10 _ __

-3-0 -2-5 -2-0 -1-5 -120 -60 60log10 concentration (M)

Current

Fig. 5. A, changes in surface potential predicted from the Gouy-Chapman-Sternequations in a model system with a surface charge density of 0-72 sites nm-2 (1 site140 A-2), 150 mM-monovalent cations, and various concentrations of divalent cations.Solutions are plotted relative to the case of 2 mM-divalent cation concentration in thecontrol extracellular solution. Note that the concentration axis is logarithmic. The shortdashed line is the solution for screening effects only (eqn (1)) and the medium dashed, longdashed, and continuous lines are the solutions for screening and binding (eqn (1) combinedwith eqn (2)) for divalent cations with KD values of 12, 1-2 and 0-12 M, respectively.Surface potentials at 2 mM-extracellular divalent cations were - 73-8 mV for model withonly screening, -71-6 mV when KD was set to 12 M, -63-5 mV when KD was set to 1-2 M,and -48-9 mV whenKD was set to 0 12 M. Greater binding (lower KD values) produced lesscurvature to the shift on the log1o axis. B, predictions of screening and binding on peakcurrent-voltage relationship and conductance (inset). Model system was kineticallydescribed as a two-state system obeying a Boltzmann distribution (eqn (3)). Values forslope and half-point were set to the average values found in control (ji = -50 mV andslope factor =-87 mV), and surface density was set to 0-72 sites nm-2 and KD for thedivalent cation was 1P2 M. Shown is the effect produced in this model system by additionof 10 mM-divalent cation (increased from 2 to 12 mV). Current is in arbitrary units.

binding to surface charges. Figure 5A illustrates a set of solutions of theGouy-Chapman-Stern equations. For the stimulation we chose values that matchedour experimental conditions: surface charge density of 0-72 sites nm-2 with 150 mmof monovalent cations and various concentrations of divalent cations. The dashedline shows the shifts in surface potential predicted for screening only using theGouy-Chapman approximation (eqn (1)). Also shown are the shifts predicted if, inaddition to screening, divalent cations also bind (eqn (1) combined with eqn (2)) with

277

278 D. A. HANCK AND M. F. SHEETS

a dissociation constant (KD) of 12500, 1250 or 125 mm, i.e. with very low affinity, lowaffinity or moderate affinity. With a surface charge density of 0-72 sites nm-2 the shiftin kinetics is greater at any given concentration of divalent cations when it bothbinds to as well as screens surface charge compared to only screening surface chargeand, in addition, there is less overall curvature of the relationship on the log1o axis.

A B

I -tO _ I 7 e g | -0 -co U

~0 5

o 05~~~ ~ ~ ~~~~~~~co05

0-0-120 -80-40 0 40 80

Voltage (my) (Dcc0

Voltage (mV).i I i ~~~I -120 -80-40 0 40 80

-120 -80 -40 40 80 Voltage (mV)

Current

Fig. 6. A, predictions of voltage-dependent open channel block on the peak cur-rent-voltage relationship and conductance (inset). Model system was identical to that inFig. 5. Data were scaled by the amount of voltage-dependent block according to thefollowing (also see the companion paper (Sheets & Hanck, 1992)):

PO = 1/[i + [B]/(KB(0) exp {- zFV/IR)], (7)where Po, the probability of being open, is expressed as a function of the concentration ofdivalent cation blocker, [B], the dissociation constant, which is expressed as thedissociation constant at 0 mV (KB(O)), multiplied by an exponential function of voltage.The constant F/RT at 12 0C equals 0-0408 and z = 2. KB(O) was set to 37 mm and a to 0-17.Current is expressed in arbitrary units. B, example of conductance transform of data incontrol (0) and in the presence of 10 mM-Mn2+ (@) (cell A8.04, RL 36 MQ, 52 pF, 11P90C,[Na+]0/[Na+]1 was 30/30). Note the similarity in shape between the data and the modelpredictions. The largest proportion of the shift in mid-point probably represents thecontribution of the kinetic shift like that illustrated in Fig. 5.

Thus, in the presence of screening alone or of binding and screening together, anincrease in concentration of extracellular divalent cations will shift activation tomore positive applied potentials. This is illustrated in Fig. 5B, which shows thepredicted change in the current-voltage relationship that occurs if divalent cationconcentration were increased by 10 mm (2 to 12 mm) in a model system thatkinetically obeys a Boltzmann relationship (eqn (3)) with a half-point at -50 mVand a slope of -8X7 mV, which was similar to our control data. The additionaldivalent cation produces less activation at each applied potential and produces a

DI(TRI)VALENT EFFECTS ON CARDIAC Ita KINETICS

A B

4nA

ms 150 mmM-Ba2

500ms~~~

- 0-5C

0

Vt~~~-

-200 -6-10 - -4 -200 -160 -120 -80 -40Conditioning potential (mV)

-150 mV500 Ms

C D

1s0 c 10a

and-50 mV2 D a m plda2+incoto n uigepsr o10 mM-Ca24 10mM-Mgconl 05.CC

coU

0L0L

-200 -160 -120 -80 -40 -200 -160 -120 -80 -40Conditioning potential (my) Conditioning potential (my)

Fig. 7. Effect of group IA divalent nations on voltage-dependent availability. A,superimposed currents during the first 10 ms after stepping to + 20 mV followingconditioning at potentials of -190 mV (largest INa), -115 mV, -105 mY (Tj), -100 mYand-)50 m. Data are shown capacity, but not leak, corrected. Data were sampled at100 kHz, as described in the Methods, and are shown digitally filtered at 5 kHz. Note thatwith the symmetrical Na4 gradient, INa at this test potential are outward. Protocol isdescribed in the text and is shown pictorially below the currents. Cell 02.02, RL 32 MQ,60 pF, 1 1-6 'C. [Nafl0/[Nafl1 was 30/30. B-D, voltage-dependent availability relationshipin control and during exposure to 10 mm-additional +Ba24 (B), Ca24 (C) and Mg24 (D). Bothcontrol (0>) and wash-out (El) data are shown. Wash-out data are to the left of controldata. Continuous lines are the fits to eqn (4), normalized to I.a.; for control they are themeans of the fitted parameters. Parameters from the fits were as follows:

Divalent Control Control Control Test Test Testcation Nt 'ma 8 'f max 14I(mm) (mY) (pA gm21) (mY) (mY) (pA lM-2) (mY) (mY)

(B) 10 Ba24 +40 5r5 6-2 -120 5*1 6-3 -107(C) 10 Ca24 +40 11-3 7-2 -105 10.0 7.3 -86(D) 10 Mg24 +40 13-3 5*8 -114 12-1 5-7 -107Same cells as in Fig. 1.

PHY 454

279

10


B

1 mM-Ni2+

D

1 mM-Co2"

F

0-1 mM-Zn2+

-160 -120 -80 -40Conditioning potential (mV)

-200

0.1 mM-La3+

-160 -120 -80 -40

Conditioning potential (mV)

Fig. 8. Effect of transition metals, Ni2+ (A), Mn2+ (B) and Co2+ (C), group IIB divalentcations, Cd2+ (D) and Zn2+ (E), and the trivalent cation La3+ (F) on voltage-dependentavailability. Protocol as described in text and Fig. 7 a. Both control (K>) and washout (El)data are shown. Washout data are to the left of control data. Continuous lines are themeans of the fits to the control data of eqn (4) or the fits to the data with addeddi(tri)valent cations. Data are shown normalized to the appropriate Imax. Parameters fromfits were as follows:Di(tri)valent

cation(mM)

Control Control Controlt Imax S I

(mV) (pA ,um-2) (mV) (mV)7-3 6-6 -98

Test Test TestIax s 14

(pA 4um-2) (mV) (mV)6-7 6-6 -94

280

A1*0

0-5

._

._

C._

z

1 mM-Mn2+

01L

C

1*0

C_

._

-, 0-5c

cJ

.Cz I

0

0.1 mM-Cd2+

E

1*0

05

._

._

s

(a

z2L

-200

s a a. . . . . ..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(A) 1 Nj2+ +40

DI(TRI) VALENT EFFECTS ON CARDI4C lNa KINVETICS

rightward shift in the current-voltage relationship. This is best appreciated in theinset, which shows the conductance transform. The conductance slope factor isunaffected, and at sufficiently positive potentials full activation is reached so thatGmaxis also unaffected. The most dramatic effects are the shift to the right of currentthreshold, the rightward shift of the potential at maximum peak inward current, andthe overall reduction in peak currents at negative potentials.As predicted by the model, the mid-point of peak conductance shifted in the

depolarizing direction when di(tri)valent cations were added to the extracellularsolution (Fig. 4A). However, in contrast to the predictions of this model each addeddi(tri)valent cation also produced a concentration-dependent reduction in the slopeof the conductance relationship (Fig. 4B). While complex kinetic schemes mightproduce this result, it is not an expected action of screening and binding (Fig. 5B).It is, however, consistent with voltage-dependent block of di(tri)valent cations in theopen channel, an additional expected action of these molecules. Figure 6A illustratesa simulation of the effects of voltage-dependent block by a divalent cation thatinteracts with a site 17% into the membrane field with a dissociation constant(KB(O)) of 37 mm. This model simulation did not include effects expected fromscreening of or binding to surface charges. Even in the absence of surface chargeeffects, voltage-dependent block by di(tri)valent cations would selectively reducepeak Ia at more negative potentials and produce a small rightward shift of thepotential at which maximum inward current would be recorded. In addition,progressively smaller, but noticeable reductions in current can be apparent atpositive potentials. The conductance transform shown in the inset of Fig. 6A bestillustrates that voltage-dependent block would both shift the mid-point of theconductance relationship in the depolarizing direction and make the voltagedependence of the relationship appear more shallow, making the Boltzmannequation (eqn (3)) a poor descriptor of the conductance relationship in the mostdramatic cases. All of these characteristics were observed in our experimental data;an example is shown in Fig. 6B.We conclude that the changes in the conductance relationship observed in our data

reflected both changes in kinetics secondary to binding to and screening of surfacecharges and to voltage-dependent open channel block by di(tri)valent nations.Therefore, while the change in mid-point of conductance could be used as a summarydescriptor of the overall effect of added di(tri)valent cations, it was not a good indexof the kinetic effects secondary to surface charge interactions of di(tri)valent nations.

Effects of di(tri)valent cations on voltage-dependent availabilityUnder control conditions voltage-dependent Na' channel availability shifts in a

fashion that reflects the changes in the fraction of the voltage field seen by thevoltage sensor (Hanek & Sheets, 1992). Therefore, we considered this relationship a

(B) 1 Mn2- +40 12-1 70 -108 11-6 72 -104(C) 1Co2+ +40 118 64 -103 110 65 -100(D) 01 (d2+ +40 11-3 59 -102 89 59 -101(E) 0 1 Zn2+ +20 3 4 7-6 -108 1-8 71 -107(F) 01 La3+ +40 152 60 -102 13-6 60 -94

In each case data are from the same cells as Figs 2 and 3 except for Ni2+, which is cellB3.03 RL 44 Q, 64 pF. 11 4 (1. [Na+]J/[Na+]i was 30/30.

10 2

281


good candidate for an index that would primarily reflect the contribution of surfacecharge interactions to INa Cells were held at - 150 mV and depolarized to potentialsbetween - 190 and -50 mV for 500 ms and then depolarized to a positive potential(usually +20 or +40 mV) to assess voltage-dependent availability (Fig. 7A).

A B

50 1 2

, 40 ° 1|0>~~~~~~~~~~~~E o>30 0-8

so 20 "A 0-6

.E 10 04..............

-, 0 . 002

-_10 ______________ 0.00 03 0Q30 3 00 30-00 0-03 0-30 3.00 30 00

Added di(tri)valent cations (mM) Added di(tri)valent cations (mM)Fig. 9. Concentration-dependent effects of added di(tri)valent cations on voltage-dependent availability. All measurements were made with a background of 2 mM-Ca2 .Plotted are the means and S.E.M. of two to five determinations per di(tri)valent cationconcentration. Where S.E.M. are not visible they are smaller than the symbol. Note thatthe concentration axis is logarithmic. Ca2` (-), Mg2+ (@), Ba2+ (Z), Co2+ (K), Mn2+ (A)Ni2+ (+), La'+ (*), Cd2+ (0) and Zn2+ (*). A, shift in mid-point of the availabilityrelationship. Continuous lines are the fits with linear regression of the shifts in mid-pointto the log1o of the concentration. Parameters are given in Table 1. B, the ratio of the slopefactor in the presence of added di(tri)valent cations to that in control. Screening andbinding effects predict that the ratios should be 1t0. The absence of a concentration-dependent reduction in slope was taken to indicate that the shift in the mid-point of thisrelationship was good measure of surface charge effects.

Examples of voltage-dependent availability relationships in control (control andwashout) and in the presence of one concentration of each di(tri)valent cation areshown in Figs 7B-D and 8. In each case the continuous lines are the fits to aBoltzmann distribution:

I = Ima./ I +exp I (V,,-VI)/} (4)where peak Na+ current (I) in test depolarizations elicited after conditioning atvarious voltages (VI) was expressed relative to the maximum peak current (Imax).Parameters estimated by the fit were Imax, the voltage of the half-point of therelationship (Jj), and the slope factor (s), expressed in mV. The means of theparameters from the fits to control and washout data were compared with those inthe presence of additional di(tri)valent cations.

Figure 9, which is presented in a similar format to Fig. 4, provides a graphicalsummary of the shifts induced by the addition of di(tri)valent cations. Overall theshifts in voltage-dependent availability were much less than those in conductance.

282


For comparison with the conductance data, the shifts for individual di(tri)valentcations were fitted as a function of the log1o of the added di(tri)valent cationconcentration using linear regression. The concentrations that produced an equaleffect, i.e. a 5 mV shift, and the number of millivolts that produced a tenfold shift in

A B40 40

E

'20 20

20 020 ~~~~~-201-3-0 -2-5 -2-0 -1-5 -3.0 -2-5 -2-0 -1-5log0o total di(tri)valent cations (M) logl0 di(tri)valent cations (M)

Fig. 10. Gouy-Chapman-Stern analysis of the shift in the mid-point of voltage-dependentavailability. In each case the mean and S.E.M. of the shifts are plotted. Where S.E.M.S arenot visible they are smaller than the symbol. The arrow marks the control divalent cationconcentration (2 mM-Ca2+). Note that the concentration axis is logarithmic. Lines are thesolutions to the Gouy-Chapman-Stern equations, assuming a surface charge density of0-72 sites nm-2 and a KD for Ca2+ of 12 M. This solution is shown as the dashed lines withthe Ca2+ data as filled triangles in both panels. KD values are given in Table 2 as KD(s)A: Mg2+ (@), Ba2+ (f), Zn2+ (*) and La3+ (*). Data falling above the Ca2+ data have ahigher affinity (lower KD) for binding to surface charges than Ca2+. B, other divalentcations were similar to Ca2+ and are shown as follows: Co2+ (c), Mn2+ (A), Ni2l (+) andCd2+ (0).

availability are summarized in Table 1. The concentrations that produced a 5 mVshift were similar or slightly greater than for conductance, except for Cd2 , whichproduced almost no change in the mid-point of voltage-dependent availabilityrelationship at the concentrations tested.The efficacies of these di(tri)valent cations in shifting the mid-point of voltage-

dependent availability for a tenfold change in di(tri)valent cation concentration(slopes of the regression) were quite different from their efficacies in shiftingconductance. Except for Ba2 , the shifts in voltage-dependent availability that wereproduced by a tenfold change in di(tri)valent cation concentration were significantlysmaller than the shifts in conductance. Especially dramatic were Cd2+ and Zn2+,which produced less than a 5 mV shift in the mid-point of voltage-dependentavailability while shifting conductance in the range of 20 mV. These findings wereconsistent with the hypothesis that conductance was affected by voltage-dependentblock as well as by screening and/or binding to surface charges.

In contrast to their effects on conductance none of the test di(tri)valent cationsproduced a significant change in the slope of the voltage-dependent availability (Fig.9B), which suggested that this relationship could be used to quantify the efficacy ofdi(tri)valent cations to shift the half-point of voltage-dependent availability as a

283

284 D. A. HANOCK AND M. F. SHEETS

A B1000 100

F0 Control

i~~~-

l00 L500C) ~~~ ~ ~ ~ ~ ~ ~~~ 100

-500 2m 0- 10 mM-Ca'2

-100 0 15

40 mV2 -100-150mV 100- 500,us

Fig. 11 'Na tail currents. A. protocol for assessment of tail current relaxation. Cell washeld at -150 mV and stepped to +40 mY for 800 ,as and then repolarized to -150 mY.Shown are the raw data, neither capacity nor leak corrected. Data were sampled at300 kllz as described in the Methods. Voltage protocol is drawn below. B, tail currentsrecorded in control (upper) and in the presence of 10 mM-additional Ca21 (lower) areshown superimposed. Shown are capacity- but not leak-corrected data during the first1000 Us following repolarization. The fastest relaxation occurred when the membrane washyperpolarized to -150 m, the slowest when the potential was-100 mY. Also shownare tail currents at -110, -120 -130 and -s140 mV. Note the similarity in theinstantaneous peak current just after the membrane was hyperpolarized. This reflectsvoltage-dependent block by Ca2( andis analyse in detail in the companion paper (Sheets& Hanck, 1992). Cell B3.04.

TABLE 2. Dissociation constants predicted from Gou oChapman Stern analysis of kineticparameters

KD(S) by KD(I) by KD(T) byDi(tri)valent voltage-dependent tail current time to peak

cation availability (mM) T (mM) (mM)Mg2+ No binding 1670 5000Ba'+ 2500 1670 1670Co2+ 1670 1200 330Mn2+ 1430 500 1200Ca2+ 1200 1200 1200Cd2+ 1200 1 250N>i2+ 1200 200 130Zn12+ 250 50 60La3+ 30 40 8

In each case a surface charge density of 0-72 sites nm-2 was assumed, which was chosen from theshifts in voltage-dependent availability in the presence of Ca2+ and Mg2+, assuming no binding ofMg2+ to surface charges.

combination of screening of and binding to surface charges using the Gouy-Chapman-Stern equations (eqns (1) and (2)). A graphical summary of all the datais shown in Fig. 10. All measurements were made with a background of 2 mM-Ca2 ,and the continuous lines represent the combination of the screening effects of themonovalent cations and the di(tri)valent cations, the binding from the 2 mM-Ca2,

285DI(TRI)VALENT EFFECTS ON CARDIAC 'Na KINETICS

B0 0-801

10 mM-Ba2+

E 0-60

0 04010

.E 0-20

-140 -120

Voltage (mV)

-100

0.00 L...-160

10 mm-Ca2+

-140 -120 -100

Voltage (mV)

C

I--

E

C

toC

0

0)

E

0*50

0*40.

0-30

0-20

0*10

-160

0

10 MMMg2l'

-140 -120 -100

Voltage (mV)

Fig. 12. Effect of group IIA divalent cations on tail current time constants (,r). A-C, tail

current r values from fits to tail current relaxations like those in Fig. 11IB for control and

during exposure to 10 mm-additional Ba21 (A), Ca21 (B) and Mg2+ (C). Both control (K>)

and washout (LI) data are shown. Continuous lines are the fits to the means of the control

data to eqn (6). It should be noted that offsetting the y-intercept of the exponential to

120 mV (by adding 120 to each test potential) did not affect the estimates for

parameters other than r,, but it increased the accuracy of -r, and our ability to test for

statistical differences between data sets since in this form of the equation r, is within the

range of the data rather than being estimated as a value 100 mV positive to the data. The

constant term Tc was included to account for the reduction in curvature of the data at the

most negative potentials. This was probably related to the interaction of the clamp (r <

10 pus) with deactivation at extremely negative potentials rather than to a rate-limiting,

voltage-independent closed-closed state transition (Hanck & Sheets, 1992). For the data

with added divalent cations (0) the line represents a fit to eqn (5) using the control

parameters shifted by an appropriate number of millivolts to place the control relationship

onto the data with added divalent cations. Parameters from the fits were as follows:

Divalent

cation I r S Shift

(mm) (ins) (ins) (mV 1) (mV)

(A) 10 Ba21 0-05 0-17 0-040 18-1

(B) 10 Ca2+ 0-06 0-31 0-040 15-7

(C) 10 Mg2+ 0-04 0-19 0-039 14-8

Same cells as in Fig. 1.

0*45

(I,Ecn 0*30~*0I

0

IID 0-15E

u-uu I--160

ulvv 1.


B

0-60

-

E040

en0

00 020

E=

0*00 1..

-160

0-60

1 mM-Ni2+EW 0-40(a

C

0

0020E

* . . ...................... 0*00 ...

s0 -140 -120 -100 -160Voltage (mV)

D

1 mM-Co2"

-140

050

040EI-,

030

C

8 0-200

k0-10

-120 -1000-00 _--160

Voltage (mV)

1 mM-Mn24

-140 -120 -100Voltage (mV)

0.1 mM-Cd2+

-140 -120 -100Voltage (mV)

E045

0'E0-30

0

C

0

0015In-nn I

0-1 mM-Zn2+

F

1*00

0-

Z.. 070C

0

, 0 40

Ez

0-5 mM -La3+

0-10 _L-160 -140 -120 -100 -160 -140 -120 -100

Voltage (mV) Voltage (mV)

Fig. 13. Effect of transition metals, Ni24 (A), Mn2+ (B) and C02+ (C), group IIB divalentcations, Cd2+ (D) and Zn2+ (E), and the trivalent cation La3+ (F) on the tail currentr-voltage relationship. Protocol was as described in the text and illustrated in Fig. 11 A.Both control (C') and washout (El) data are shown except for 0 5 mM-La3+, where washoutdata were unavailable. Where they can be differentiated washout data are to the left ofcontrol data. Continuous lines are the fits to the means of the control data of eqn (5). Forthe data with added di(tri)valent cations (@) the line represents the fit to eqn (5) using thecontrol parameters shifted by an appropriate number of millivolts to place the controlrelationship onto the data with added di(tri)valent cations. Parameters from fits were as

follows:

286

A

1-10

E

C

00

0

E

050

040

030

0-20

0*10.

0*000-1

vIV I-


and the best estimate of binding (KD) by the added di(tri)valent cations. The datado not dictate a unique choice for surface charge density. We therefore considered thedata obtained at various additional concentrations of Ca21 simultaneously with thedata from Mg2+, the divalent cation that produced the smallest shift in the half-pointof availability. We optimized the choice of density of sites and the KD for Ca2+ tomatch the overall curvature of the data assuming that Mg2+ only screened. It shouldbe noted that a satisfactory match with the data could have been obtained withhigher surface charge densities if binding of Mg2' had been permitted.The dissociation constants, based on the shift of voltage-dependent availability

(KD(s)), are given in Table 2. Only Zn2+ and La3+ predicted lower dissociationconstants (higher affinity binding) than did Ca2+ (Fig. 10A). Ba2+ required only amodest value for binding (Fig. 10A). Other divalent cations shifted availability verysimilarly to or only slightly less efficaciously than Ca2+ ; KD(s) values were in the rangeof 1200-1670 mm (Fig. 10B).

Tail current time constants did not always reflect surface charge effectsThe interactions of di(tri)valent cations with surface charges should manifest

effects in other kinetic parameters. We considered, therefore, INa tail currents atnegative potentials following conditioning step depolarizations to very positivepotentials that open a maximum number of channels. The instantaneous currentmeasured early after a clampback to negative potentials would reflect voltage-dependent block and the time constant of the subsequent decay of the current (tailcurrent relaxation) could be used to quantify the changes in the portion of the fieldseen by the voltage sensors.The cell membrane was depolarized from a holding potential of -150 mV to a

positive conditioning potential (between + 20 and + 60 mV) until the time of peakINa and then stepped to a negative test potential (Fig. 11A). After 25 ms the cell wasrepolarized to - 150 mV for the remainder of the 1 s cycle.

INa tail currents were capacity corrected (see Methods), were inverted, trimmed by75-100 /is, and were fitted to a sum of exponentials with DISCRETE (Fig. llB).Under control conditions at potentials between -100 and - 150 mV data were mostoften best fitted with a single exponential in keeping with the hypothesis that at verynegative potentials tail currents represent primarily the closing of open channels (O-+ C). Tail currents at test potentials more positive than -100 mV almost alwayswere fitted with two exponentials, consistent with more complicated kinetics at these

Divalentcation TC TI S Shift(mM) (ms) (Ms) (mVW1) (mV)

(A) 1 Ni2+ 0.05 020 0038 6-7(B) 1 Mn2+ 005 024 0039 7.5(C) 1 Co2+ 005 022 0039 3-1(D) 01 Cd2+ 0-04 0.18 0-038 9.0(E) 0 1 Zn2+ 0 05 0 16 0 039 4 2(F) 0-5 La3+ 0-08 019 0-048 12-2

Cells were the same as those in Fig. 8 except for La3+ which was cell b2.04, RL 83 MQ,48 pF, 11-5 'C. [Na+]0/[Na+], was 45/45.

287

D. A. HANCK AND M. F SHEETS

B

a)-0 >4 E>. _L

*' o0.-_ X

CO

40

0>m E

0

> .Q

._ o

F._en T-

0 -25 -20 -1 5log,, total di(tri)valent cations (M)

C

40

2>20 Ba_e

C C

0

-0

-20 ... .....----.....-3.0 -2 5 -2-0 -1

log09 total di(tri)valent cations (M)

D

40

a) 1-

C; >

E 20

0

> a

_ 20

I.5 -3.

W0 -25 -20 -1.5log19 total di(tri)valent cations (M)

Mg,2

1T

0 -25 -20 -1 5

loglo total di(tri)valent cations (M)

Fig. 14. Shift in tail current voltage relationship vs. concentration. In each case themean and S.E.M. of the shifts are plotted. Where S.E.M.s are not visible they are smallerthan the symbol. Lines are the solutions to the Gouy-Chapman-Stern equations,assuming a surface charge density of 0 72 sites nm-2 and a KD for Ca2 of 1-2 M. KD valuesare given in Table 2. Data falling above the Ca2' data have a higher affinity (lower KD)for binding to surface charges than Ca2+. A. Cd'+ (0) produced dramatic speeding of tailcurrent relaxation. La3+ (*) and Ca2+ (A) produced shifts in deactivation like thosepredicted for surface charge effects from the analysis of the shift in voltage-dependentavailability. Also shown are data in the presence of Mn2+ (A). B, for reference the dashedline is the solution for Ca2+. Shown are data in the presence of Zn2+ (*). Ni21 (+) and Co2+(<>). C, data in the presence of Ba2' are shown as open squares. The short dashed line isthe solution for Ca2+ (KD 1-2 M). The medium dashed line, which matches the shiftsproduced by addition of 5 and 10 mM-Ba2+, represents the solution based on a KD for Ba2+of 0-67 M, an affinity about twice that for Ca2+. The continuous line represents the solutionbased on a KD of 5 M, which is significantly lower than that for Ca2+ and more similar tothat predicted from the shifts in voltage-dependent availability. D, data in the presence

of Mg2+ are shown as filled circles. Dashed line is the solution based on KD of 1-2 M, thesame as that for Ca2+. With the addition of 20 mM-Mg2+ the KD was less than that for Ca2+,about 5 M, similar to Ba2+ and much less than for Ca2

potentials. In a small number of cases control tail currents between - 100 and- 150 mV were fitted with two exponentials better than with one, but in these cases

the second time constant contributed to less than 4% of the amplitude.

288

A

DI(TRI) VALENT EFFECTS ON- CARDIAC 'Na KLYVETICS

The time constants (T) from the control and washout tail current fits were averagedand they were used to fit an exponential equation:

T = Tc+Tl exp {S(Vt + 120)}, (5)

where the T at each test potential was described as the sum of a constant Tc that wasapproached at extremely negative potentials and a scaler (T1) representing the

TABLE 3. Correlation between di(tri)valent cation shifts in kinetic indicesTail current T Time to peak 'Na Tail current T

vs. vs. vs.

Di(tri)valent voltage-dependent vholtage-dependent time to peakcation n availability availability INaCa2+ 8 092+0-08 1 00+005 090+0 10Ba2+ 6 1-08 +0-17 0 99+0 08 1-02 +0 23Mg2+ 7 1-68 + 0-12 1-40+0-16 1-08 +0-20Mn2+ 5 1-45+0-06 1-37+0-14 1 01 +0 10Zn2+ 6 2-40+0 33 2 09+0 33 0 98+0-25Co2+ 8 1-32+007 1-74+0-08 077+005Ni2+ 8 1 80+0 10 2-17+0-13 0-82+0-05La3+ 7 087+0-15 1-46+009 0-58+0-11Cd2+ 7 8-62+3-78 1 40+0 81 4-58+0 70

The shifts in time to peak of 'Na' voltage-dependent availability and tail current r values for eachdi(tri)valent cation intervention were paired and the shifts compared with linear regression. Shownare the slopes and S.E.E. for these determinations. A slope of 1 0 indicates concordance between thetwo kinetic indices.

difference between Tc and T at - 120 mV multiplied by an exponential function ofvoltage (Vt) with slope factor S. Tail current T values from all cells were well describedby this equation. The T-voltage relationships in the presence of test di(tri)valentcations were fitted to the same equation, constraining Tc, T1 and S to the valuesdetermined from the control data, and an estimate of the shift induced by the addeddi(tri)valent cation was determined as the number of millivolts required to place thecontrol relationship onto the data in the presence of the added di(tri)valent cation.Examples of data and fits for each of the di(tri)valent nations are shown in Figs 12and 13.

Using the Gouy-Chapman--Stern equations (eqns (1) and (2)) we estimateddissociation constants from the shifts induced by added di(tri)valent cations. The dataare graphically summarized in Fig. 14, and the KD values, based on the ability ofadded di(tri)valent cations to shift the tail current values (KD(I)), are listed in Table2. The surface charge density was set to 0 72 sites nm-2 and the KD for Ca21 was setto 1200 mm, which were the same values as estimated from the shift in voltage-dependent availability (Fig. 10) and which matched the data well. In dramaticcontrast to Ca2+, Cd2", which produced only a small amount of kinetic shift involtage-dependent availability (Figs 8D and 10), produced an acceleration of tailcurrent relaxations (Fig. 13D). If this were attributed only to binding of Cd21 tosurface charges, then it would predict the KD to be 1 mm, a more than 100-fold higheraffinity than that predicted from the shift in voltage-dependent availability. Cd2+produced a greater effect than even the trivalent cation La3" (Fig. 14A) which, in

289


B

60

-

E

z

(U0a00E

4-0

10 mM-Ba2+

2-0 F

-80 -40 0Voltage (mV)

D

60 r

1 0 mM-Ca2l

-40 0Voltage (mV)

0E

a004Shr

4-01 0 mM-Mg2+

20 F

0'-8'40 80 0 -40 0

Voltage (mV)

Fig. 15. Effect of group IIA divalent cations on time to peak INa. A, currents, normalizedto peak IN., from depolarizing steps to -40 and + 40 mV in a typical cell in control andafter exposure to 20 mM-Ba2+. Data were sampled at 100 kHz as described in the Methodsand are shown digitally filtered at 5 kHz. Note that while at the more negative potentialthere was a dramatic increase in the time to peak INa and in the decay of the current, theeffect on time course was much less dramatic at the more positive potential. Cell B3.04.B-D, time to peak INC-voltage relationship in control and during exposure to 10 mm-additional Ba2+ (B), Ca2+ (C) and Mg2+ (D). Both control (0) and washout (EI) data are

shown. Where they can be differentiated washout data are to the left of control data.Continuous lines are the fits to the means of the control data to eqn (6). The intercept ofthe exponential was offset to -40 mV to place it on the steeper portion of the curve so

that tests for differences between groups of data would yield more accurate statistics. Forthe data with added divalent cations (@) the line represents the fit to eqn (6) with thecontrol parameters shifted by an appropriate number of millivolts to place the controlrelationship onto the data with added divalent cations. Parameters from the fits were as

follows:Divalentcation(mm)

(B) 10 Ba2+(C) 10 Ca2+

(D) 10 Mg2+Same cells as in Fig. 1.

TC TI S Shift

(Ms) (Ms) (mVi1) (mV)0-42 1-07 0-0380 75 2-18 0-0480 40 1-45 0 035

8'314-26-5

290

A

1

O 05

(O*0 0.N

o -05z

-1

C

12-0

40 80

-

S

(E1= 4-01

0L-80 40 80

L


keeping with the hypothesis that tail current T values should reflect surface chargeinteractions, produced similar shifts in tail current r values as it did in voltage-dependent availability (Table 2). A likely explanation for the acceleration of the off-transient r values in Cd2+ was that voltage-dependent block by Cd2+ occurred at arate comparable to channel deactivation, and this analysis is presented in thecompanion paper (Sheets & Hanck, 1992).The Gouy-Chapman-Stern analyses for other divalent cations are also shown in

Fig. 14; the data in each panel are shown on the same axes and for reference the Ca2+line is also shown. In order to facilitate comparisons, the shifts produced in tailcurrent values and the shifts in voltage-dependent availability were combinedpairwise and compared using linear regression. If the two estimators were equallygood measures of the shift in kinetics secondary to interactions of di(tri)valentcations with surface charges, as estimated by the shift in the half-point of voltage-dependent availability, then the two measures would predict similar shifts, i.e. valueswould be directly proportional and the regression slope would be 10. The results ofthis analysis, summarized in Table 3, also demonstrated that the measured shifts forCa2+ and La3+ were similar, while for Cd2+ the effect on tail current relaxation wasmuch greater than predicted by surface charge effects. Addition of Zn2+, althoughless dramatic than Cd2+, also produced greater acceleration of tail current X valuesthan expected from the shifts observed in voltage-dependent availability. Thissuggested that blocking/unblocking events might be evident over the time course ofchannel deactivation.

Tail current analyses for the group IIA divalent cations Ba2+ and Mg2+ did notproduce a simple result. In 5 and 10 mM-Ba2+ or Mg2+ (Fig. 14C and D) the changein the time constants of tail current relations were greater than expected based onthe observed shifts in voltage-dependent availability. The binding affinity for Ba2+was predicted to be slightly greater than that for Ca2+. Whereas no binding of Mg2+was assumed to explain the shifts in voltage-dependent availability, shifts in tailcurrent X values predicted binding similar to that for Ca2+. However, 20 mMMg2+and 20 mm-Ba2+ produced significantly less shift than 20 mM-Ca2 , consistent withmuch more modest binding to surface charges (KD(I) of 5 M). While the differencesbetween predicted and measured shifts are small at the lower concentrations and thepossibility of noise in the data cannot be excluded, we also observed an increasedtendency for tail currents to be better fitted with two time constants at theseconcentrations, especially in the presence of Mg2+.

Di(tri)valent cation effects on time to peak of INaIn order to see whether other kinetic indices might also be affected in a more

complex manner than predicted by the Gouy-Chapman-Stern model, we looked atthe ability of di(tri)valent cations to alter the time course of the current. Additionof most di(tri)valent cations cause the time to peak of the current elicited indepolarizing steps (Figs 1A, 2A and 3A) to be delayed. There was a con-centration-dependent shift of the potential dependence of the time to peak of INa;that is the time course of INa was more dramatically affected at negative than atpositive potentials. Figure 15A illustrates this differential effect of added divalentcations on currents recorded at -40 and + 40 mV in a typical cell in the presence of

291

D. A. HANCK AND M. F SHEETS

A

12-0

8-0

B

80

60 F

1 mM-Ni2+40 F

40 F

0

C

12 0

8-0

1 mM-Mn'+

2-0 k

0

D

80

60 F

1 mM-Co2+ 0.1 mM-Cd2+

4-0

40 F

0

E

6-0

20 F

0

F

12-0

4-00-1 mM-Zn'+ 8-0

2-0

OL

-80

0-1 mM-La"+

40

-40 -800 40 80Voltage (mV)

-40 0

Voltage (mV)40 80

Fig. 16. Effect of transition metals, Ni2+ (A), Mn2" (B) and Co"+ (C), group IIB divalentcations, Cd2" (D) and Zn2+ (E). and the trivalent cation La3" (F) on the time to peakINa-voltage relationship. Both control (0) and washout (D) data are shown. Where theycan be differentiated washout data are to the left of control data. Continuous lines are thefits to the means of the control data to eqn (6). For the data with added di(tri)valentcations (@) the line represents the solution to eqn (6) with the control parameters shiftedby an appropriate number of millivolts to place the control relationship onto the datawith added di(tri)valent cations. Parameters from fits were as follows:

292

0E

.-_

0

a,

E

(,E

-Z

a)a

0.0)E

C/,E-,

z

-)

0)

a)E

DI(TRI)ITALENVT EFFECTS ON CARDIAC INa KIXVETI(CS 293

2 and 10 mm-Ca2+. Figures 15B-D and 16 show the time to peak 'Na voltagerelationships for each of the di(tri)valent cations for the cells illustrated in Figs 1-3.In order to quantify the shift in kinetics induced by di(tri)valent nations, control andwashout time to peak 'Na-voltage datasets were averaged and an exponentialfunction was fitted to the data:

Tp = T +Texp{-S(1E+40)}, (6)

where time to peak of the current (Tp) was expressed as the sum of a constant (Tc)and a term with an exponential dependence upon voltage (Vt) expressed as a slopefactor (S) and a scaler (T,) representing the difference between Tc and the time topeak at -40 mV. The data were well fitted by this relationship, and there was nosignificant effect of any di(tri)valent cation on the slope factor (S) of the relationshipor the constant (Tc). Therefore, we analysed the data constraining Tc. T1 and S to thevalues determined from the control data, and an estimate of the shift was thendetermined as the number of millivolts required to place the control relationship ontothe data in the presence of the test di(tri)valent cations.Summary data from these fits and the estimates from the Gouy-Chapman Stern

analysis are shown in Fig. 17. As for the other kinetic indices, the value for surfacecharge density of 0 72 sites nm-2 and the KD for Ca2+ of 1200 mm matched the datawell. The data are presented in two panels for the sake of clarity, and the Ca2+ dataare shown in both panels to help in the comparison between di(tri)valent cations. Thepredicted Kd values based on the ability to shift the time to peak INa-voltagerelationship (KD(T)), are given in Table 2. The most efficacious was La3` with apredicted dissociation constant lower (higher affinity) than that predicted by anyother measure (8 mM). Mg2+ was the least efficacious, requiring the inclusion of onlya small amount of binding was to predict the shift seen in the time to peakINa-voltage relationship.

In order to compare the shifts observed in time to peak INa with those that theaddition of di(tri)valent cations produced in voltage-dependent availability, the datawere combined pairwise and were compared using linear regression. Values from theregressions are listed in Table 3. The shifts produced by Ca2' and Ba2+ were similar,i.e. slope was about 1-0. All the other di(tri)valent cations produced greater changesin time to peak INa than they did in voltage-dependent availability (1-4-2 2 times),consistent with the hypothesis that some di(tri)valent cations produce kinetic effectsmore complex than interactions with surface charges predict.

Divalentcation TC TI S Shift(mM) (Ms) (Ms) (mV 1) (mV)

(A) 1 Ni2+ 069 251 0042 125(B) 1 Mn2+ 0.59 138 0047 4.4(C) 1 Co2+ 057 158 0053 5-5(D) 0-1 Cd2+ 0-58 1 51 0-054 2 8(E) 0-1 Zn2+ 0.45 1 42 0 041 3.9(F) 01 La3+ 067 145 0059 125

In each case data are from the same cells as Figs 2 and 3.

293


A B40 40

La3+ Ca2+ o Ca2M 20 . 20 Zn..

2 Ba2+

0) Cd2+2_

-3.0 -2 5 -2-0 -1-5 -3 0 -2-5 -2-0 -1 5log10 total di(tri)valent cations (M) log10 total di(tri)valent cations (M)

Fig. 17. Shift in time to peak INa vs. concentration relationship. In each case the mean andS.E.M. are plotted. The arrow marks the control divalent cation concentration (2 mM-Ca2l). Note that the concentration axis is logarithmic. Lines are the solutions to theGouy-Chapman-Stern equations, assuming a surface charge density of 0-72 sites nm-2and a KD for Ca2+ of 1-2 M. This solution is shown as the dashed lines with the Ca2+ dataas filled triangles in both panels. KD values are given in Table 2 as KD(T) values. Datafalling above the Ca2+ data have a higher affinity (lower KD(T)) for binding to surfacecharges than Ca2+. A, Ba2+ (E), Ni2+ (+), Cd2+ (0) and La3+ (*). Note that the Cd2+ datafall just below the trajectory for Ni2+. B. Mg2+ (S), Mn2+ (A). Co2+ (K>) and Zn2+ (*).

DISCUSSION

The Gouy-Chapman-Stern model and surface charge densityThe Gouy-Chapman-Stern model assumes di(tri)valent cations interact with

uniformly smeared charges on the lipid bilayer. Although experimental data supportthe idea that the charges are primarily located on the channel protein, theGouy-Chapman-Stern model describes the data remarkably well (for a recentdiscussion see McLaughlin, 1989). Differences between observation and theoreticalpredictions are apparent near the boundaries (very low and very high cationconcentrations), and these have been discussed by a number of investigators(Haydon & Myers, 1973; Dani, 1986; Cai & Jordan, 1990).Data of the type presented here do not allow for a unique determination of surface

charge density. In general, lower estimates for surface charge density can be offsetby assuming higher association constants for Ca2+ in order to match experimentaldata to model predictions. However, the data do place limits on the values that aresuitable. For example, we used a value of 0-72 sites nm-2 (1 site 140 A-2), which is inthe range predicted from the data of Hille and colleagues (1975) in experiments infrog node of Ranvier and from the recent bilayer experiments (Chabala, Urban,Weiss, Green & Andersen, 1991) and only somewhat greater than the 1 site 200 A-2used for modelling surface charge effects in rat brain Na+ channels in bilayers(Cukierman & Krueger, 1990). However, it is about twice the density (1 site 260 A-2)predicted from earlier bilayer experiments with canine brain Na+ channels (Green etal. 1987), about three times the density (1 site > 400 A-2) predicted from bilayer

294


experiments with canine cardiac Na+ channels (Ravindran & Moczydowski, 1989),and much higher than that assumed by Brown & Noble (1978) when they measuredshifts in INa threshold in Purkinje fibres and atrial muscle. If we assumed surfacecharge density to be as low at that suggested by Ravindran and Moczyldowski, theKD values for divalent cation binding would have been dramatically lower, in themillimolar range. However, the concentration dependence of the kinetic shifts wouldhave differed from those observed. This was because lower surface charge densitiesproduce smaller surface potentials, and changes in surface potential secondary tobinding or to changes in concentration become curvilinear as surface potentialapproaches 0 mV. Rather than appearing concave downwards or straight whenplotted as shown in Fig. 5A, the data would have appeared concave upwards.Some of the differences between the estimates for surface charge density from

bilayer studies and our measurements in intact cells might result from differences inlipid composition. Cukierman and colleagues (1988) have shown that the shiftinduced by 7-5 mM-Ca2+ is increased from 17 to 25 mV when channels areincorporated into charged vs. neutral bilayers. In addition, there may be differencesbetween native channels and those modified by batrachotoxin (BTX). However, thisseems somewhat unlikely because similar charge densities have been estimated forNa+ channels in the presence and absence of BTX (e.g. Correa, Latorre & Bezanilla,1991). The model that we used assumed no binding of monovalent cations to surfacecharges and this is in keeping with the assumptions of most previous investigators.However, in recent experiments Ravindran & Moczyldowski (1989) suggested thatNa+ also binds. If we had assumed binding of Na+, then surface charge densitieswould have to have been larger for the model to match the shifts observed.

Possible causes of the complexity in kinetic effectsInteractions of di(tri)valent cations with surface charges, either secondary to

screening and/or binding, can only partially explain the kinetic effects produced bythese cations. Some of the kinetic effects appear to result from voltage-dependentblock. For example, conductance was clearly affected by both processes. TheBoltzmann model parameters, Tj and slope factor, from fits to voltage-dependentavailability curves, on the other hand, were only minimally affected by voltage-dependent block, probably because the test potential was at a constant positivepotential. Therefore, the shift in voltage-dependent availability appeared to give thebest estimate of the kinetic consequences of di(tri)valent cation screening andbinding to surface charges.Changes in tail current relaxation and in time to peak INa were more complex. Tail

current relaxations, which at very negative potentials primarily reflect thedeactivation (closing) of open channels (O -. C), were faster when di(tri)valentcations were added. However, only in the case of Ca2+ and La3+ were the changes inr values consistent with the amounts predicted by the changes in surface potentialestimated from their shifts in voltage-dependent availability. Cd2+ produced almostno shift in voltage-dependent availability at any of the concentrations we studied,but accelerated tail current relaxation. Analysis of these data within the context ofvoltage-dependent block is presented in the companion paper (Sheets & Hanck,1992). The acceleration of tail current relaxations in the case of other divalent cations

295

9). A. HARNCK AND M. F SHEETS

suggested that block was faster than channel transition times but slower than thenanosecond times previously suggested for H' (Woodhull, 1973).Most divalent nations that produced greater acceleration of tail currents than was

expected. based on their ability to shift voltage-dependent availability also delayedtime to peak 'Na to a greater extent. Time to peak of 'Na is determined by the overlapof activation and inactivation. which would appear to have different voltagedependencies, and so it was probably not surprising that shifts in time to peak 'Nathat occurred after addition of di(tri)valent cations were complex. However, pairwisecomparison of the shifts in tail current T values to the shifts in time to peak INa (Table3) showed that these measures shifted similarly for Ca2", Ba2 , Mg2 , Mn2+ and Zn2+.C(2+ and Ni2+ also produced effects on time to peak 'Na that were greater than thosefor voltage-dependent availability (by a factor of 1P7 and 2'2, respectively), but theshift in tail current time constants was significantly less than that observed for thetime to peak INa (% 0 8). La3+ significantly delayed time to peak INa more thanpredicted by either the shift in voltage-dependent availability or in tail current timeconstants. The divalent cation that produced the greatest acceleration of tail currentrelaxation. Cd2+. also shifted time to peak INa to a greater extent than predicted byits ability to shift voltage-dependent availability, but this effect was much lessdramatic than its ability to shorten tail current time constants (1 4 vs. 8 6).Togetherthese data suggest that for some di(tri)valent cations the changes in time to peak INaand tail current -r values are more complex than a simple shift in kinetics secondaryto interactions of di(tri)valent cations with surface charges.We considered whether kinetic effects secondary to voltage-dependent block could

explain these findings. If di(tri)valent cations entered the open channel andprevented the channel from gating, then mean channel open time would be prolongedas was found for local anaesthetic block of acetvlcholine channels (Neher &Steinbach, 1978). and this would predict that time to peak of the current would bedelayed, although it would also predict tail current time constants should be delayedwhich was not observed. Prevention of channel gating appears unlikely for cationslike Ca2+ and Ba2+ for which similar changes in the kinetic parameters. time to peakINa and tail current relaxations, were observed, which is also consistent withmeasurements in frog skeletal muscle (Hahin & Campbell, 1983). In addition,previous single-channel studies (Sheets, Scanley, Hanck, Makielski & Fozzard, 1987;Nilius, 1988) have demonstrated that mean channel open time was not altered whenextracellular Ca2+ was increased, which also implies that the channel may gatenormally with Ca21 in the pore. In addition, single-channel recordings in the presenceof Cd2+ show a marked decrease in channel mean open time (Baumgarten & Fozzard,1989; Backx, Alarban & Yue, 1990). which by itself should be associated with ashortening in the time to peak INa. However. we observed a prolongation in the timeto peak INa in Cd2 . Such effects would be consistent with the hypothesis thatdivalent occupancy of the channel selectively prevented channel inactivation (0 -> I)hut did not affect channel deactivation (O - C). In squid axon Armstrong & Gilly(1982) observed that extracellular Zn2+ slowed the onset of 1Na with a minimal effectOil 'Na tail currents. and they proposed that Zn2+ preferentially stabilized the voltagesensor/gating apparatus in the rested, closed state of the channel but had little effecton the voltage sensor/gating apparatus in the open state. Similar interactions of

296

DI(TRI)VALENVT EFFECTS ON CARDIAC INa KIVETICS

divalent cations with the deactivation rate of the rat brain Na' channels incorporatedin lipid bilayers have been reported for Ba2" (Cukierman & Krueger, 1990). Inaddition recent experiments by Armstrong & Cota (1990) have suggested similarcomplex effects of La3" in tail currents of GH3 cells.

In conclusion, we have demonstrated the diverse kinetic effects of extracellulardi(tri)valent cations on cardiac Na' channels. Only some of these actions appear todirectly result from interactions of di(tri)valent cations with surface charges. Ingeneral di(tri)valent cations produce more dramatic and more complex effects onconductance than on voltage-dependent availability. The effects on other kineticparameters such as the voltage dependence of tail current relaxation and the time topeak 'Na suggest that some di(tri)valent cations may block more slowly than waspreviously thought and/or that block may alter channel transition rates.

We thank 1)r Harry Fozzard for his long-standing and on-going support and encouragement. Wethank Stephanie Krueger at Northwestern University and Mona Bowman at the University ofChicago for their excellent technical assistance and Dr Jonathan Makielski for critical commentson the manuscript. This work was supported by NIH grants HL-PO1-20592 and HL-R29-44630.

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Documents

Mg2" (2 67) ; Ba2" (1-93) > Co2" (1P02)