rectify at positive potentials, a property not consistent with symmetric rate theory

Transcription

1 Journal of Physiology (1988), 407, pp With 11 text-figures Printed in Great Britain PERMEATION OF BARIUM AND CADMIUM THROUGH SLOWLY INACTIVATING CALCIUM CHANNELS IN CAT SENSORY NEURONES BY W. ROWLAND TAYLOR* From the Department of Physiology, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. 2601, Australia (Received 19 January 1988) SUMMARY 1. Instantaneous current-voltage (I-V) relations were measured from tail currents with 10 mm-external calcium at 20 'C. The I-V relations had a lower potential dependence than predicted by the Goldman-Hodgkin-Katz constant-field equation. Previously proposed symmetric two-site three-barrier (2S3B) rate theory models were able to account for the I-V relations reasonably well. 2. Reversal of the current flow through the calcium channels was recorded using 10 mm-barium internally and 20 mm-barium externally. The channels appeared to rectify at positive potentials, a property not consistent with symmetric rate theory models. 3. Externally applied cadmium ions blocked the calcium channels through at least two sites. One high-affinity blocking site was located within the membrane electric field and had a dissociation constant of around 16 /tm at 0 mv. Cadmium block at this site was relieved with hyperpolarization with a voltage dependence equivalent to a divalent cation moving through about 75 % of the membrane electric field. 4. A low-affinity potential-independent blocking site also appeared to be present, having a dissociation constant of around 106 /bm. 5. Cadmium had significant effects on the tail current kinetics at potentials close to 0 mv, presumably due to slow unblocking events. The rate at which cadmium ions left the calcium channel free to conduct was estimated to be about 3300 s-5 at + 10 mv. INTRODUCTION The calcium channel is highly selective for calcium ions in the face of relatively high concentrations of sodium and potassium ions in the physiological environment. A two-site three-barrier (2S3B) rate theory model has been proposed to model calcium channel permeation in skeletal muscle (Almers & McCleskey, 1984) and in heart muscle (Hess & Tsien, 1984). The model was proposed to account for three observations. (1) When all the external calcium is removed the calcium channel becomes permeant to monovalent cations. Subsequent inclusion of micromolar concentrations of calcium in the external solution causes a 50% reduction in the - monovalent current through the calcium channel (Kostyuk & Krishtal, 1977; * Present address: Department of Neurobiology D239, Sherman Fairchild Science Building, Stanford, CA 94305, U.S.A.

2 434 W. R. TA YLOR Almers, MeCleskey & Palade, 1984; Hess & Tsien, 1984; Fukushima & Hagiwara, 1985). (2) In spite of the very tight binding of calcium ions to the channel that the previous observation implies, the single-channel conductance of 7-10 ps in mm-calcium (Cavalie, Ochi, Pelzer & Trautwein, 1983; Lux & Brown, 1984) is comparable to that of other high-selectivity channels. (3) The channel displays anomalous mole-fraction effects (of which point one is an extreme example) with various concentrations of calcium and barium ions (Almers & McCleskey, 1984; Hess & Tsien, 1984; Byerly, Chase & Stimers, 1985). The 2S3B model accounts for these observations fairly simply by assuming three basic properties of the calcium channel. First, the two energy wells (binding sites) are deep compared to the aqueous solution. The energy wells are deeper for calcium ions than formonovalent cations and barium ions. Second, the channel is not restricted to single occupancy. Finally, there is significant repulsion between two ions occupying the two sites of the channel. Repulsion between the ions in the channel produces a large increase in the measured dissociation constant for calcium ions to the channel. Thus the current-concentration relation does not saturate until the external calcium concentration is raised to millimolar concentrations (Akaike, Lee & Brown, 1978; Kostyuk, Mironov & Doroshenko, 1982; Fukushima & Hagiwara, 1985), despite the very tight binding of calcium to the channel sites. The instantaneous current-voltage relationship was examined using tail current measurements and the results were adequately described by a 2S3B model. Reversal of current flow through calcium channels is apparent in cardiac cells (Lee & Tsien, 1984) and bovine chromaffin cells (Fenwick, Marty & Neher, 1982), where monovalent cations carry outward current at positive potentials. There has only been one report of reversal of calcium current in nerve cells (Byerly et al. 1985). Symmetric models predict an essentially linear instantaneous I-V relation over the physiological voltage range. Reversal of the barium current through neuronal calcium channels was examined to test this prediction. Cadmium is a potent blocker of calcium channels in neuronal and cardiac cells (Byerly, Chase & Stimers, 1984; Lansman, Hess & Tsien, 1986). The block produced by cadmium ions is relieved as the membrane potential becomes more negative, as if cadmium were able to pass through the channels at very negative potentials. The voltage dependence of cadmium block was examined and evidence obtained for the existence of voltage-dependent and voltage-independent blocking sites. METHODS The methods used are described in detail in the accompanying paper. Instantaneous I-V relations were measured from the amplitude of tail currents after activating a constant number of channels at + 50 mv. Generally the peaks of tail currents were observed 80,us after application of a voltage step. A double-exponential function was fitted to tail current relaxations, using a modified Levenberg-Morison-Marquandt (LMM) algorithm (Osborne, 1976), which performed a non-linear least-squares fit to the currents. The amplitude of the fitted exponential extrapolated to the time of the voltage step was used as an estimate of the tail current amplitude. In these experiments 20 mm of the internal CsCl was replaced with CsF. This appeared to result in better sealing resistances without any significant effects on the kinetics or the viability of the calcium currents. All concentrations are given in millimolar. The ph of all solutions was 7-4.

3 CALCIUM CHANNEL PERMEATION 435 External solutions Standard solution: 140 NaCl; 2 KCl; 5 CaCl2; 10 N-2-hydroxyethylpiperazine-N-2-ethanesulphonic acid (HEPES); and 10 glucose. Calcium currents: 115 choline chloride: 25 tetraethylammonium bromide (TEA); 2 CsCl; 1 A9gCl2; 10 CaCl2; 10 HEPES; and 10 glucose. Internal solutions Standard solution: 120 CsCl; 20 CsF; 10 TEA; 5 ethylenegly,col-bis-(/l-aminoethylether)-.nvtetraacetic acid (EGTA); and 5 HEPES. Barium currents: 120 CsCl; 10 TEA; 10 HEPES; and 10 BaCl2. Rate theory models The methods used to calculate the current-voltage relationships for the calcium channel according to a two-site model were essentially the same as those set out by Begenisich & Cahalan (1980). The current was calculated from the net transfer of ions across the central energy barrier. Thus for two ions, A and B, the membrane current is given by =, -(NF/Na) (k3ao - k4oa + k'bo - kob) where N is the number of channels, F is Faraday's constant, Na is Avogadro's number, the ki values are the transition rates for the two ions and, for example, AO refers to the channel with the outer site occupied and the inner site empty. The rate constants were set using conventional rate theory (Glasstone, Laidler & Eyring, 1949). For example ki =YRin exp (-(Go, + zdl Vm F/RT)), k2 = vrout exp (- (G - G1-zd2 VF/RT)), where v = kt/h, z is the valency of the ion, di is the electrical distance the ion moves in reaching the transition state and Vm is the membrane potential. Go, is the Gibbs free energy at 0 mvx of the peak of the barrier between the external solution and the first binding site and G1 is the free energy of the binding site. Free energy is relative to the bulk solution. In all cases the electrical distances were symmetric with respect to the central barrier. Rin and R.u, are repulsion faetors which were set according to the occupancy of the other site and the valency of the interacting ions. The entry rate constants were multiplied by the activity of the permeant ion (ao, ai). The activity coefficienlt used was (Hess & Tsien, 1984). As usual the transmission coefficient was assumed to be one, and is not shown explicitly above. The non-homogeneous system of linear equations describinig the state diagram was obtained by setting the sum of all the occupancy states equal to unity. These were solved using Gaussian elimination with partial pivoting. RESULTS Instantaneous current-voltage (I-V) relations were obtained by measuring the peaks of tail currents at various return potentials after activating a constant number of calcium channels at +50 mv. The voltage clamp attenuated tail currents more severely at negative potentials than at positive potentials, since the current decayed more rapidly at negative potentials. In order to compensate for this artifact, the extrapolated peak tail current, that is the amplitude of the fitted exponential at the time of the repolarization, was used as an estimate of the instantaneous current level. Figure 1 shows some examples of the tail current measurements. An example of a compensated and uncompensated current-voltage relation is shown in Fig. 2A. A second source of error which may have distorted the shape of the instantaneous I V relation was series resistance. This error will be proportional to the magnitude of the membrane current. Figure 2B illustrates that the shape of the I-V relation was independent of the magnitude of the membrane current and indicates that series resistance did not introduce large errors.

4 436 W. R. TAYLOR 50 nal 1 ms -70 mv -50 mv 25 na 2 ms -30 mv -10 mv p-- lf_- I I -- F 10 mv 30 mv Fig. 1. The membrane potential was stepped to +50 mv from a holding potential of -50 mv, and returned to the test potentials shown next to each trace. Note the change in calibration between the top two and bottom four traces. The continuous lines show the recorded current relaxations and the interrupted lines show fitted double-exponential functions extrapolated back to the time of the voltage step. This is the expected current flow if the voltage clamp did not attenuate the rapidly decaying tail currents. The amplitudes of fitted exponentials were used as an estimate of the amplitude of tail currents for the instantaneous I-V relations. Parameters obtained from the fits to the -70, -50, -30, -10 and 1O mv traces were as follows: Tf = 88, 117, 158, 151 and 155 4us; r, = 0-538, 0-592, 0-774, 1-63 and 1-66 ms; A,=-278, -185, -95, -45 and -14nA; A =-25, -34, -50, -46 and -6nA. The average instantaneous I-V relation obtained from nine cells is shown in Fig. 3B. Outward current flow through calcium channels was not observed, even at potentials up to + 70 mv (Fig. 3A). Each I-V relation was normalized to the average value of the tail current at -50 mv. The dotted line through the points was produced using the Goldman-Hodgkin-Katz (GHK) constant-field equation (Goldman, 1943; Hodgkin & Katz, 1949) for a single permeant ion z2vf2 ai-a. exp (-zvmf/rt) m- PCa RT 1-exp(-zVmF/RT) (1)

5 CALCIUM CHANNEL PERMEATION 437 A mv B mv I i. * oo a-200 * * * na na * -500 u -500 Fig. 2. A, the open symbols show the instantaneous I-V relation measured directly from the observed peaks of the tail currents, and the filled symbols show the instantaneous I-V relation obtained from extrapolation measurements. Extrapolated amplitudes were independent of the time course of the current decay. B, the I-V relation was recorded before (filled circles) and after (filled squares) a proportion of the calcium current had disappeared. The open squares were obtained by scaling the smaller I-V relation so that it superimposed on the initial control I-V relation. The good agreement between the two I-V relations indicates that the shape of the I-V relation was independent of the magnitude of the membrane current and suggests that series-resistance errors were not significant. where ao and ai are the activities of calcium outside and inside the cell, Pc. is the permeability of calcium, z is the valency, Vm the membrane potential and F, R and T are the usual thermodynamic constants. The permeation parameter was varied to fit the results in Fig. 3B at 0 mv; in this case Pca = The GHK equation predicts a steeper voltage dependence for the current than was observed. The voltage dependence of current in eqn (1) is determined by the energy change the divalent ion experiences as it moves through the electric field across the membrane. The lower voltage dependence shown by the I-V relation suggests that, in crossing the membrane, the rate-limiting step involves the ion traversing some fraction of the electric field. The 2S3B models proposed by Hess & Tsien (1984) and Almers & McCleskey (1984) were able to account for the instantaneous I-V relation more accurately. The fits to the results are shown in Fig. 3 C. The parameters for the calculations were taken from their published values, and the theoretical curves were scaled by eye to fit the data points. The model of Hess & Tsien seemed to fit the data points more closely, mainly due to the higher voltage dependence of the entry rate constants. At negative potentials the Almers & McCleskey model predicts that the I-V relation should bend towards the voltage axis. This is a result of lower occupancy of the channel at negative potentials, where the rate of entry of ions into the channel becomes rate limiting. Reversal of barium currents Both the models assumed that the energy profile of the channel is symmetric for divalent cations, and both models predict an approximately linear I-V relation with comparable concentrations of divalent cations on each side of the membrane. Reversal of current through the calcium channel was examined to test this

6 438 W. R. TAYLOR A 20 na[ 2 ms B Vm (mv) C Vm (mv) E; -1 *0 a Fig. 3. A, responses to voltage steps to +50, +60 and +70 mv. Holding potential -50 mv, pulse duration 10 ms. There was very little inward or outward current during the step to +70 mv in this cell. B, the symbols show the average instantaneous I-V relation recorded from nine cells. The individual I-V relations were normalized to the average value recorded at -50 mv. At -50 mv the tail currents ranged from -630 to na with a mean of na. The standard errors are shown where they are larger than the symbols. The dotted line shows the prediction of the GHK equation (eqn (1)) constrained to pass through the 0 mv point. The continuous line shows the prediction fromn the 2S3B model (solid energy profile, Fig. II A). C, the data are replotted from B, and the lines show the fits obtained using the 2S3B models proposed by Hess & Tsien (1984. continuous line) and Almers & McCleskey (1984, dotted line). Calculations assumed a single permeant ion. prediction. Barium was chosen as the charge carrier in these experiments since such high concentrations of internal calcium ions would completely suppress the calcium current (Hagiwara & Nakajima, 1966; Kostyuk & Krishtal, 1977; Eckert & Chad, 1984). Electrodes were filled with the internal calcium current solution containing 10 mm- BaCl2 but without the divalent ion chelators CsF and EGTA. Although currents could be recorded with 10 mm-internal barium, they were smaller than normal and

7 Barium currents 20 mm-external barium 10 mm-internal barium CALCIUM CHANNEL PERMEATION 10 nal 2 ms Barium currents 10 mm-external barium 10 mm-internal barium na 2 ms Fig. 4. Barium currents recorded during 10 ms pulses to the potentials indicated next to each trace (mv). Initially the external solution contained 20 mm-barium, and there is some evidence for a slowly developing outward current particularly apparent at + 20 and + 30 mv. The small outward current was probably a residual potassium current, since the recordings were taken as soon as possible after the cell was voltage clamped, and there may have been insufficient time to completely exchange the internal potassium with caesium. This assertion is supported by the fact that the outward relaxations are absent from the second set of traces which were obtained in the same cell some minutes later after an external solution containing 10 mm-barium was applied.

8 440 W. R. TAYLOR A 6 * B 20 Im (na) //m (na) 3 10.o l I Il l l l l l l l l l l l l l I Il l l I i Vm (mv) Vm (mv) -3 0 c -6 D E 0-6 x m m~~~~~~0,e~~~~~~~~4e 0-4 E 0-4 E / 0-2 i, Vm (mv) Vm (mv) Fig. 5. A, the peak current is plotted as a function of the pulse potential for the cell shown in Fig. 4 with 10 mm-barium externally. The outward current reaches a maximum at + 40 mv and then declines with larger voltage steps. B, the peak current-voltage relation is plotted for two cells with 20 mm-barium externally. The outward current reaches a maximum level at potentials above +40 mv. C and D, normalized peak tail currents recorded at -50 mv plotted against activation potential for the same cells shown in A and B. The data demonstrate that the plateaux of the outward current evident in the peak current-voltage relations (A and B) were not caused by a reduction in the number of active channels. The continuous lines through the points show the steady-state activation curve for the calcium current (continuous line in Fig. 6B of the accompanying paper). The lines were shifted along the voltage axis to allow for changes in the surface potential. disappeared more rapidly, rarely lasting more than a few minutes. Even with these limitations it was possible to record barium currents which had kinetic properties similar to the calcium currents previously recorded. The traces in Fig. 4 show reversal of the currents recorded with 10 mm-barium internally. For the cell illustrated, the current reversed between + 20 and + 30 mv with 20 mm-external barium, and between 0 and + 10 mv with 10 mm-external barium. Peak barium current is plotted against the step potential in Fig. 5A and B. An interesting feature of these data was the plateau of the peak outward current at potentials greater than + 40 mv which occurred in both barium concentrations. This effect was not due to a decrease in the number of active calcium channels at positive potentials since the peak tail currents did not show a reduction at these potentials

9 CALCIUM CHANNEL PERMEATION (Fig. 5C and D). The lines through the points in Fig. 5C and D were taken from the control calcium current data in Fig. 6B of the accompanying paper and were shifted along the voltage axis by an appropriate amount to take into account changes in the surface charge potential. The good agreement between the shape of the curve and the data points indicates that the steady-state properties of the barium current were similar to the calcium current recorded previously. 441 A B ; jb (ms) j3 (ms) a 0 T-2 o Vm (mv) Vm (mv) Fi.6. The time constants recorded from barium current relaxations appeared to show a similar voltage dependence as those recorded for calcium currents. The fast tail current tieconstant (re) recorded from two cells is shown in A. The slow tail current time constant (s open symbols) and the activation time constant (T1, filled symbols) are shown in B. The external barium concentration was 20 mm. Currents recorded with barium ions on both sides of the membrane also appeared to be kinetically similar to the calcium currents shown in the previous paper. The magnitude and potential dependence of the time constants shown in Fig. 6 should be compared to that observed when calcium ions carry the current (Fig. 7A and B in the accompanying paper). The fast tail current time constant appeared to have a similar potential dependence and magnitude. The slow tail current time constant increased less steeply and reached a maximum at more negative potentials. Similarly, the activation time constant reached a peak at more negative potentials. When either calcium or barium was the charge carrier, the time constants reached a maximum close to the potential where half-maximal channel activation occurred. Instantaneous I-V relations were measured from tail currents recorded in barium solutions and some examples of the currents are shown in Fig. 7A. The results in Fig. 7cB were obtainerom thee cells with 20 mm-barium externally and 10 mmiinternally. Again the plateau of the current was evident at positive potentials. The null potential +d17+ was 1 mv which is about 8 mv more positive than the predicted Nernst potential for barium. The lines through the points show the predictions from the 2S3B models considered earlier and indicate that the rectification of the channel appears to be much more pronounced than expected from these models. However, it is not clear whether the asymmetry of the instantaneous I-V relation reflects an underlying asymmetry in the permeation pathway of the channel.

10 442 W. R. TA YLOR Cadmium block of the calcium channel The blocking effects of external cadmium ions were examined in an effort to gain more insight into the permeation mechanism. Cadmium is a permeant blocker, which is effective at micromolar concentrations, and as it is able to pass through the channel, the characteristics of the block should give some information about the energy profile of the channel. A 40 d ftlw 1 720,-f 0 B Vm (mv) nal 2 ms E ti _ < -2-0 Fig. 7. A, sample traces showing tail currents recorded with 10 mm-internal and 20 mmexternal barium. Note the saturation of the outward current; the current at + 40 mv was the same as that at + 50 mv. B, instantaneous I-V relation for three cells. The I-V relations were normalized to the average current value recorded at -50 mv. The lines through the points show the predictions from the Hess & Tsien (1984, continuous line) and the Almers & McCleskey (1984, interrupted line) models. The model I-V relations were calculated for a single permeant ion with 20 mm-external and 10 mm-internal barium. The measured instantaneous I-V relation deviates from the model predictions over the entire voltage range. Initially the effective dissociation constant (in 10 mm-calcium) of cadmium at + 10 mv was determined. The depression of the peak inward current at + 10 mv was measured as a fraction of the control value. The control value was taken to be the average of the initial control and the recovery current after wash-out of the cadmium. The results are shown in Fig. 8. The filled symbols are the values at +10 mv, taken from the data shown in Fig. 1O A. The fraction of channels not blocked (B = Icd/Ica) is well approximated by the equation B = 1/(1 + [Cd2+]/Kd), (2) with Kd, the dissociation constant at + 10 mv, equal to 10 /M. The fit of eqn (2) to the data is shown by the continuous line in Fig. 8. The results were described well by eqn (2), which assumes that a single Cd2+ ion is able to block the channel. The voltage sensitivity of cadmium block was examined in some detail.

11 CALCIUM CHANNEL PERMEATION 443 Instantaneous I-V relations were recorded before and after application of cadmium at four concentrations: 20, 60, 150 and 500 gm. These experiments were complicated by the disappearance of the calcium current. Cells where the current did not recover after wash-out, to within 75 % of the initial level, were rejected. No attempt was [Cd lo (M) Fig. 8. Block of the calcium channel at + 10 mv. One corresponds to complete block. The line through the points was fitted by eye using eqn (2), with Kd = 10 UM. The loss of the calcium current was allowed for by taking the average of the pulses before the application of cadmium and after washing it out. The open symbols show the results from two cells. The filled symbols for 20 and 60 /LM-cadmium were calculated from the values at + 10 mv in Fig. IOA. The 150 um point was calculated from the value predicted by the continuous line at + 10 mv in Fig. IOA. made to correct for the loss of the calcium current where it occurred. In the three cases where a second control was not obtained, the degree of block was comparable to the other results at the same concentration. Instantaneous I-V relations were obtained as described previously. Some examples of the measurements are shown in Fig. 9. The interrupted line through each trace is the double-exponential fit produced by the LMM algorithm referred to in the previous paper. The fit was extrapolated back to the time of the repolarization. The peaks of the tail currents in cadmium are indicated by the arrows. The data points in Fig. IOA are the average results from four measurements in different cells at each concentration. The error bars are standard errors. The cadmium data cannot be described by assuming voltage-sensitive binding to a single site. The fraction of channels not blocked (B = Icd/Ica)' for single-site models, is B = 1/(1 + (Kd/[Cd2+]) exp (z8vmf/rt)), (3) where Kd is the dissociation constant at 0 mv, z the valency of the blocking ion, a the fraction of the electric field the cadmium ions cross when leaving the channel, and

12 444 Cadmium (60 gm) W. R. TA YLOR 50 nal 1 ms -60 mv -40 mv IL w Iv U 7 - I 25 nal 2 ms -20 mv 0 mv Cadmium (500 gm) 1%- 50 nal 1 mg -60 mv -40 mv nal 2 ms -20 mv 10 na 2 ms 0 mv Fig. 9. For legend see facing page.

13 CALCIUM CHANNEL PERMEATION 445 Vm the membrane potential. This equation predicts that at negative potentials B -* 1 at all concentrations of cadmium. At negative potentials B approaches some value less than one in Fig. IOA, and the limiting ratio appears to become smaller as the concentration of cadmium is increased. Therefore eqn (3) was not applicable to the data. TABLE 1. Parameters in eqn (4) obtained from the fits to the data in Fig. IOA. The dissociation constants are given in micromolar. Approximate standard errors produced by the fitting routine are included [Cd2+] (/tm) Ke±S.E. Km±S.E. d+s.e Average The simplest alternative model was to assume that cadmium blocks the channel by binding to two independent sites, one within the electric field of the membrane, and the other outside the field, where the binding of cadmium is not altered by the membrane potential. The fraction of channels not blocked is then given by B = 1/(1 + [Cd2+]/Ke + (LCd2+]/Km) exp (z8vm F/RT)), (4) where Ke is the dissociation constant of the external site, and Km is the dissociation constant at 0 mv of the site within the membrane. The lines through the points in Fig. IOA were obtained by fitting eqn (4) to the data using the LMM algorithm. If this two-site model were reasonable then the parameters Ke, Km and a should have been the same at each concentration. The values obtained are shown in Table 1 and were fairly constant. The maximum value for B at each concentration is replotted in Fig. lob and the line through the points was drawn according to eqn (2). This gives an estimate of Ke of 106 /SM. The data in Fig. IOA can be modelled by assuming two independent binding sites for cadmium, one with a Kd of around 106 #M, and the other with a Kd of 16/M at 0 mv and voltage-sensitive unbinding equivalent to a divalent ion moving across approximately 75 % of the membrane electric field. Cadmium affects the kinetics of calcium channels Cadmium produced significant changes in the relaxation kinetics of calcium tail currents. The control tail current at 0 mv in Fig. 9 was fitted with a double Fig. 9. Voltage-dependent block of calcium tail currents by cadmium in two cells. The calcium current was activated by stepping to + 50 mv for 3 ms, before returning to the test potential indicated next to each trace. The inward current during the activation pulse and the larger tail currents are the control records. The interrupted lines are the doubleexponential fits to the tail currents extrapolated back to the step time. The tail currents were clearly resolved even at the highest concentration of cadmium. The arrows indicate the amplitude of the double-exponential fits to the calcium currents in the presence of cadmium. The traces show clearly the voltage dependence of the cadmium block as the test potential is made more positive.

14 446 A W. R. TAYLOR B Vm (mv) Cadmium (gm) Fig. 10. A, the ratio of the tail current in the presence of cadmium to the control tail current is plotted against potential for the four concentrations of cadmium tested. The continuous lines through the points are the best fits to eqn (4), and the values obtained are presented in Table 1. The error bars are standard errors. At each concentration the results from four cells were averaged. Better than 75 % recovery of the calcium current was obtained after wash-out of the cadmium solution. Since the test I-V relation was obtained approximately 3 min after the initial control and the second control about 3-4 min later, loss of the calcium current was considerably less than 25 % at the time the records were obtained, and so probably did not affect the results unduly. The good agreement between these results at + 10 mv and the single-pulse experiments (see Fig. 8) supports this assertion. B, the maximum fraction of channels blocked at negative potentials from A is plotted against cadmium concentration. The line through the points was drawn using eqn (2), with Kd = 106 /M. This seemed a more reasonable method of obtaining an estimate of Ke (eqn (4)) than simply averaging the values in Table 1.

15 CALCIUM CHANNEL PERMEATION exponential having time constants of 0-20 and 1-94 ms. In the presence of 60 /Mcadmium the fast component had largely disappeared and the decay time constant was 1P60 ms. However, at -60 mv there was little change in rf after cadmium application. In four cells r, at -60 and -10mV was and ,s respectively. After application of 60,uM-cadmium Tr at -60mV was essentially unchanged at Its whereas -rf at -10 mv increased 1-75-fold to ,us. The most obvious explanation for these effects is that the rate of unblock of the calcium channels was comparable to the kinetic relaxation time constants at those potentials. This is consistent with the unblocking rate having a steep voltage dependence, and the expectation that the rate of unblock will be slowest around 0 mv where the voltage gradient across the membrane is lowest. In another cell (not shown), the tail current at + 10 mv in the presence of 20 /SMcadmium was almost flat. This suggested that the rate of unblocking of the channels was equal to the rate of closure of the channels at + 10 mv, and that these two exponential relaxations cancelled. The cancellation was almost perfect and so the amplitude and time course of the two processes must have been very similar. This rather fortuitous result allowed a rough estimate of the unblocking rate to be made. The unblocking rate will be equal to the time constant of decay of the fast phase of the tail current recorded in control and the relaxation observed gave a value of 3.3 x 103 s-i for the unblocking rate. 447 DISCUSSION The paper started by examining the instantaneous I-V relation of the calcium channel. Although clear reversal of the calcium current was not observed under the conditions used for these experiments, the inward current was close to zero at +70 mv, suggesting that the reversal potential must be more positive than this value. This result is consistent with a previous study, which was able to demonstrate reversal of the calcium current above + 70 mv in 5 mm-calcium (Lee & Tsien, 1984). When Ba2+ was included on both sides of the membrane, reversal of the current flow through the calcium channels was observed, and it was shown that the steady-state and kinetic properties of the barium currents were similar to those for the calcium currents. The measured reversal potential was about 8 mv more positive than the predicted Nernst potential, and this disparity may have been due to a lower than expected concentration of internal barium caused by buffering of internal divalent ions by intracellular constituents. It is also possible that the internal perfusion of barium was not optimal, since records were taken as soon as possible after clamping the cells, due to the very rapid disappearance of the calcium channels with millimolar internal barium concentrations. The two previously published models for calcium channel permeation described the instantaneous I-V relation in calcium solutions reasonably, although the voltage dependence of the data appeared to be slightly less than predicted by the Hess & Tsien (1984) model but greater than predicted by the Almers & McCleskey (1984) model. Both these models predicted approximately linear I-V relations with comparable concentrations of permeant ions on each side of the membrane. Measurements of the reversal of the peak current and the instantaneous I-V relation

16 448 W. R. TA YLOR c A 0 uj 10 5 o -5 _ -10 _ Rin= 1 Rout= 400 Calcium d, d2= 0-21 d3= Cadmium I I di d2 d3 d4 d5 de d d2= 0*22 d3= B 1 B mv Fig. 11. A, the continuous line shows the energy profile used to fit the instantaneous I-V relation shown in Fig. 3B. The faint line shows the energy profile for cadmium ions used to produce the continuous line in B. The repulsion factors for calcium and cadmium were identical and are shown in the top right. B, the continuous line shows the proportionate block produced by 20,UM-cadmium for the hypothetical energy profiles in A. The interrupted line shows the fit of eqn (3) to the continuous line and demonstrates that the 2S3B model can be well approximated by a single voltage-dependent site. In this case the Km 11 /M and a = 0-72.

17 CALCIUM CHANNEL PERMEATION with barium as the charge carrier indicated that the rectification of the I-V relation was stronger than predicted by the 2S3B model. It was shown, through tail current measurements, that this was not due to a voltage-dependent reduction of the number of active channels. The cause of the rectification is unknown. Voltage-dependent block of the channel by an intracellular molecule is a possibility, or it may reflect a true asymmetry of the permeation pathway. To test these hypotheses exchange of the internal solution would be required, an approach which was not feasible with the present techniques, since the calcium channels survived for only a few minutes with millimolar concentrations of internal barium. Cadmium block Cadmium blocked the calcium channel with a Kd of 10/M at + 10 mv, a result that agrees well with previous observations in molluscan neurones (Byerly et al. 1985). The present results provide strong evidence for the existence of two binding sites for cadmium, one within the electric field of the membrane, and one external to this field. The data presented are not consistent with models which allow binding of cations only within the electric field, since such models will predict that the channel should be cleared of blocking ions (B -* 1) at negative potentials. However, the data do not preclude the possibility that there are two internal binding sites, but suggest that there is at least one blocking site external to the membrane electric field. Evidence for a voltage-independent external ion binding site has recently been obtained by Prod'hom, Pietrobon & Hess (1987), who found that with low external divalent ion concentrations protons were able to reduce the conductance of the calcium channel. The voltage dependence of the cadmium block may be a result of high-affinity interaction of cadmium with two internal binding sites such as have been proposed for the 2S3B models. The low Km value obtained from eqn (4) (in the presence of 10 mm-calcium), and the voltage-dependent slowing of the kinetics of the tail currents, both provide some basis for suggesting that cadmium binds with very high affinity to the calcium channel. Further, rate theory simulations using two ions in a 2S3B model indicate that the large apparent a value obtained from eqn (4) is not inconsistent with 2S3B models. Figure 11 illustrates that steep voltage-dependent block can result from energy profiles where the blocking ion traverses less than 25 % of the membrane electric field during any one step. The voltage-independent component of cadmium block can be explained if it is assumed that cadmium produces a voltage-independent reduction of the permeant ion concentration at the mouth of the pore, with a Kd of 106 fsm in 10 mm-calcium. An obvious candidate for such a binding site is that proposed to exist at the mouth of the pore and mediate proton block of the calcium channel by a similar mechanism (Prod'hom et al. 1987; see also lijima, Ciani & Hagiwara, 1986). Prod'hom and coworkers found that removal of external divalent cations unmasked a strong blocking action of protons on sodium currents through the calcium channel. This observation together with the present results suggests that the selectivity sequence for the external site might be Cd2+ > Ca2+ > H+ > Na+. If the cation binding sites at the mouth of the calcium channel effectively raise the local concentration of permeant ions then the well depths calculated for the 2S3B models considered earlier may well 15 PH Y

18 450 W. R. TAYLOR be overestimates, since they were calculated from the known calcium ion concentration in the external solution. External cadmium would be expected to reduce the single-channel current, since a reduction in the external calcium concentration is equivalent to increasing the external barrier height. Lansman et al. (1986) examined the effects of 20 /km-cadmium on the single-channel current in heart cells. The results presented here suggest that they should have observed a 20% reduction in the amplitude of the single-channel current, an effect that was not observed. This disparity might be attributed to the different charge carrier used (barium instead of calcium). It is possible that barium does not bind to the sites at the mouth of the pore as well as calcium does. Certainly, barium currents were activated from more negative potentials than calcium currents (Fig. 5), an observation that suggests that barium does not bind to and screen surface charge near neuronal calcium channels as well as calcium does. Other results are consistent with the presence of a low-affinity cation binding site at the mouth of the channel. The observation of Almers & McCleskey (1984), that cobalt and cadmium were no more effective at blocking the sodium current through the calcium channel than the calcium current, may be consistent with the model, assuming that the external sites are weakly selective for cations in skeletal muscle. Magnesium and cobalt block calcium channels with low affinity and low voltage sensitivity (Byerly et al. 1984; Lansman et al. 1986), and both these ions bind water very tightly, having long dipole relaxation times (Hille, 1984). The major blocking effects of these ions may be at the low-affinity external binding sites. Manganese and zinc have intermediate dipole relaxation times and also have low permeability through the calcium channel (Kawa, 1979; Akaike, Nishi & Oyama, 1983). These observations lead naturally to the idea that permeation through the calcium channel may involve a two-step dehydration process, similar to that proposed for the gramicidin channel (Eisenman, Sandblom & Neher, 1978). The outer sites may contain partially hydrated permeant ions which must exchange most of their water molecules with polar groups at the high-affinity binding sites within the channel before they can pass through the channel. Thus cations which bind water very tightly will permeate only very slowly. Cadmium unblocking rate The rate of unblock of the calcium channel (the exit rate of cadmium) was calculated to be 3300 s-1 at + 10 mv. To obtain this value it was assumed that the channel became unblocked when a cadmium ion left the site on the inside of the membrane, and that it was displaced by the presence of a calcium ion in the other site. Lansman et al. (1986) calculated an unblocking rate of 2000 s-1 from their blocked time distribution at -20 mv. The difference between the two estimates was not unexpected since the previous study used barium as the permeant ion, which has a lower affinity for the calcium channel, and would therefore be less efficient at displacing cadmium ions. Measurements of the exit rate of cadmium and other blocking ions will be useful for evaluating differences in ionic interactions within the calcium channel.

19 CALWIUM CHANNEL PERMEATION This work was completed in partial fulfilment of a Ph.D. degree at the Australian National University under the supervision of Professor P. W. Gage. I am indebted to Professor Gage for his guidance and generous support during the course of this work. I would also like to thank Dr J. B. Lansman for helpful comments on the manuscript and Drs R. Fyffe and S. Ghosh for supplying cat ganglia used. W. R. T. was supported by a Department of Education Post-graduate Award. REFERENCES AKAIKE, N., LEE, K. S. & BROWN, A. M. (1978). The calcium current in Helix neurones. Journal of General Physiology 71, AKAIKE, N., NISHI, K. & OYAMA, Y. (1983). Characteristics of manganese current and its comparison with current carried by other divalent cations in snail soma membranes. Journal of Membrane Biology 76, ALMERS, W. & MCCLESKEY, E. W. (1984). Non-selective conductance in calcium channels of frog muscle: calcium selectivity in a single file pore. Journal of Physiology 353, ALMERS, W., MCCLESKEY, E. W. & PALADE, P. T. (1984). A non-selective cation conductance in frog muscle blocked by micromolar external calcium ions. Journal of Physiology 353, BEGENISICH, T. B. & CAHALAN, M. D. (1980). Sodium channels permeation in squid axons. II. Nonindependence and current-voltage relations. Journal of Physiology 307, BYERLY, L., CHASE, P. B. & STIMERS, J. R. (1984). Calcium current activation kinetics in neurones of the snail Lymnaea stagnalis. Journal of Physiology 348, BYERLY, L., CHASE, P. B. & STIMERS, J. R. (1985). Permeation and interaction of divalent cations in calcium channels of snail neurones. Journal of General Physiology 85, 491. CAVALIE, A., OcHI, R., PELZER, D. & TRAUTWEIN, W. (1983). Elementary currents through Ca channels in guinea pig myocytes. Pflugers Archiv 398, ECKERT, R. & CHAD, J. E. (1984). Inactivation of calcium channels. Progress in Biophysics and Molecular Biology 44, EISENMAN, G., SANDBLOM, J. & NEHER, E. (1978). Interactions in cation permeation through the gramicidin channel: Cs, Rb, K, Na, Li, H, and effects of anion binding. Biophysical Journal 22, FENWICK, E. M., MARTY, A. & NEHER, E. (1982). Sodium and calcium channels in bovine chromaffin cells. Journal of Physiology 331, FUKUSHIMA, Y. & HAGIWARA, S. (1985). Currents carried by monovalent cations through calcium channels in mouse neoplastic B lymphocytes. Journal of Physiology 358, GLASSTONE, S., LAIDLER, K. J. & EYRING, H. (1949). The Theory of Rate Processes. New York: McGraw-Hill Book Company Inc. GOLDMAN, D. E. (1943). Potential, impedance and rectification in membranes. Journal of General Physiology 27, HAGIWARA, S. & NAKAJIMA, S. (1966). Effects of intracellular Ca ion concentration upon the excitability of the muscle fibre membrane of a barnacle. Journal of General Physiology 49, HESS, P. & TsIEN, R. W. (1984). Mechanism of ion permeation through calcium channels. Nature 309, HILLE, B. (1984). Ionic Channels of Excitable Membranes. Sunderland, MA, U.S.A.: Sinauer Associates Inc. HODGKIN, A. L. & KATZ, B. (1949). The effect of sodium ions on the electrical activity of the giant axon of the squid. Journal of Physiology 108, IIJIMA, T., CIANI, S. & HAGIWARA, S. (1986). Effects of the external ph on Ca channels: Experimental studies and theoretical considerations using a two-site, two-ion model. Proceedings of the National Academy of Sciences of the U.S.A. 83, KAWA, K. (1979). Zinc-dependent action potentials in giant neurones of the snail Euhadra quaestia. Journal of Membrane Biology 49, 325. KOSTYUK, P. G. & KRISHTAL, O. A. (1977). Effects of calcium and calcium-chelating agents on the inward and outward current in the membrane of mollusc neurones. Journal of Physiology 270,

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