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Interactions of divalent cations with single calcium channels from rat brain synaptosomes.

Voltage-dependent calcium channels from a rat brain membrane preparation ("synaptosomes") were incorporated into planar lipid bilayers. The effects of calcium, barium, strontium, manganese, and cadmium ions on the amplitudes and kinetics of single channel currents were examined. The order of single channel conductances was gBa greater than gSr greater than gMn, which was the inverse of the order of the mean channel open times: TMn greater than TCa = TSr greater than TBa. In contrast, the identity of the charge carrier had little or no effect on the mean closed times of the channel. Manganese, in the absence of other permeant ions, can pass through single channels (gMn = 4 pS). However, when added to a solution that contained another type of permeant divalent cation, manganese reduced the single channel current in a voltage-dependent manner. Cadmium, a potent blocker of macroscopic "ensemble" calcium currents in many preparations, reduced the current through an open channel in a manner consistent with Cd ions both not being measurably permeant and interacting with a single site. The permeant ions competed with cadmium for this site with the following order: Mn greater than Sr = Ca greater than Ba. These results are consistent with the existence of no less than one divalent cation binding site in the channel that regulates ion permeation.


INTRODUCTION
Calcium ions that enter many excitable cells through voltage-dependent channels affect many important physiological processes, including neurotransmitter release and muscle contraction (cf. Hagiwara and Byerly, 1981 ;Tsien, 1983). One important step in ion permeation through the calcium channel may be the association of Ca" with a binding site in the channel (cf. Hagiwara and Byerly, 1981). The existence of a binding site that regulates ion permeation has been supported by the observation that blocking ions such as cadmium reduce calcium currents in a manner consistent with them competing with the permeant ions (e .g., Ca 2+ , Ba t+ , Sr") for a single site . However, recent studies that have examined the effects of mixtures of permeant ions on calcium channel currents suggest that two binding sites may regulate ion permeation and selectivity (Kostyuk et al., 1983 ;Hess and Tsien, 1984;Almers and McCleskey, 1984). Furthermore, the interpretation of the effects of permeant ions on calcium channel behavior has been complicated by evidence indicating that the gating of the calcium channel is affected by the ions passing through it (Siami and Kung, 1982;Deitmer, 1983;Cavalie et al ., 1983;. To characterize the dependence ofsingle calcium channel kinetics and currents on permeant and blocking divalent cations, single calcium channels from rat brain synaptosomes were incorporated into planar lipid bilayers . These channels have been shown to be voltage dependent and to select for calcium, barium, and strontium over monovalent ions  and magnesium (Nelson, 1985x).
In this study, it is shown that manganese ions can permeate single calcium channels from brain synaptosomes. In the presence of a more permeant divalent cation, manganese ions can reduce current through single channels. The nature of the permeant ion affected not only the magnitude of the single channel current, but it also affected the mean open time of the channel . When added to one side of a single channel, blocking ions such as cadmium reduced the single channel current in a dose-dependent manner . The results are consistent with the permeant and blocking ions interacting with the same binding site in the permeation pathway .

Planar Lipid Bilayers and Solutions
Planar lipid bilayers composed of phosphatidylethanolamine (33 mg/ml, bovine brain, Avanti Polar Lipids, Inc., Birmingham, AL) and phosphatidylserine (13-26 mg/ml, bovine brain, Avanti Polar Lipids, Inc.) in decane were painted across a 100-250-jm hole in a polystyrene or Lexan partition separating two identical solutions containing 250 mM of a divalent cation (CaCl2, BaCl2, SrC12, or MnC12), 7.5 mM HEPES, pH 7 .0. The use of symmetric solutions minimized surface potential differences. High divalent cation concentrations were used for two reasons . (a) The single channel current is maximal at divalent cation concentrations of >150 mM  . This eliminates variation in the measured current that could result from small changes in the activity of the permeant ions at the channel's mouth . (b) With these concentrations ofdivalent cations, the bilayer membrane is saturated with divalent cations (McLaughlin et al., 1981) . Cadmium ions were normally added from CdCl2 concentrated stocks. Although the ion levels are expressed in concentrations, the activities of all ions are expected to be much lower than the concentrations (cf. Robinson and Stokes, 1959) . The activity coefficients of the chloride salts of the four charge carriers (i.e., Ba, Ca, Sr, Mn) should be about the same. Therefore, the different effects of the four divalent ion types used here were not due to variations in ion activities. Cadmium forms complexes with chloride and has an activity coefficient lower than that of the permeant divalent cations (Robinson and Stokes, 1959) .
Preparation ofMembrane Vesicles THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 87 -1986 The median eminence was chosen as a source of Ca" channels because it is rich in nerve terminals and virtually devoid of neuronal cell bodies (cf. Moore and Johnston, 1982) .

203
Nerve terminals are thought to have a high density of calcium channels. The membranes were prepared from 10-15 rat brain median eminences by a centrifugation procedure similar to that for preparing rat whole brain synaptosomes (Krueger et al., 1979;Nelson et al., 1983), with the omission of the sucrose gradient step. The synaptosome preparation has been shown to contain pinched-off resealed nerve terminals (Blaustein et al., 1977) . These "resealed" nerve terminals are physiologically functional; they maintain resting potentials (Blaustein and Goldring, 1975), release neurotransmitters upon depolarization (cf. Nelson and Blaustein, 1982), and have functional sodium channels (Krueger and Blaustein, 1980) and calcium channels (Nachshen and Blaustein, 1980). The median eminences were obtained from freshly killed rats and were homogenized in 0.32 M sucrose (HEPES-buffered, pH 7.0, with 0.2% bovine serum albumin) at 900 rpm (12 strokes) in a glass-Teflon homogenizer. The homogenate was then centrifuged at 1,000 g for 10 min and the supernatant was retained . The pellet was washed in 0.32 M sucrose, homogenized, and centrifuged again at 1,000 g for 10 min. The pooled supernatants were centrifuged for 10 min at 1,000 g and the resulting pellet was discarded. The supernatant was then centrifuged at 12,000 g for 20 min and the supernatant was discarded. This final pellet was suspended in 0.4 M sucrose and frozen at -77°C in small aliquots (still in 0.4 M sucrose). This "synaptosome" preparation (^-300 ug total protein) was stored in^-20 aliquots of 15 fag protein each in 100 Al of 0.4 M sucrose (^-0.15 mg protein/ml) at -77°C. Identical results were obtained with both fresh and frozen material. The thawed "synaptosomes" in 0.4 M sucrose were sonicated (probe type, model 1510, Braun Instruments, Burlingame, CA) for 20 s before use. This membrane vesicle suspension was added to one side (defined as the cis side) of a preformed planar bilayer at a final concentration of 0.1-0.5 Ecg protein/ml solution.
Incorporation of Channels Using the procedure described above, channels spontaneously incorporated into preformed planar lipid bilayers. When many channels were incorporated into a bilayer, the protein concentration was reduced accordingly in order to reduce the probability of ion channel incorporation . As shown by , the channels described in this report exhibit characteristic constant unitary conductances and voltage-dependent kinetics . These properties were used to identify incorporated calcium channels. In the absence of high divalent cations, a variety of K+ channels (Nelson and Reinhardt, 1984) and a batrachotoxin-activated, saxitoxin-sensitive sodium channel (cf. Krueger et al., 1983) have been incorporated from this preparation into planar lipid bilayers. However, thus far, in divalent cation solutions, the calcium channel presented here was the primary channel type observed. Occasionally, a high-conductance (^"400 pS) anion-selective channel (cf. Blatz and Magleby, 1983) was seen in divalent cation ion salt solutions . The incorporation ofcalcium channels does not appear to depend on the nature of the divalent cation (Ca",Bat+,Sr2+,or Mn 21) in the cis side, and does not depend on the presence of an osmotic gradient (cf. Cohen et al., 1982). In addition, negatively charged phospholipids in the bilayer do not appear to play a critical role in channel incorporation. Similar observations have been made for the incorporation of saxitoxin-sensitive Na' channels from rat brain into planar lipid bilayers (Worley, 1984) . However, for the incorporation of both Ca 21 channels and Na' channels from brain, the presence of higher ionic strength solutions (e.g., having >100 mM CaCl2 or 150 mM NaCl in the cis side) seemed to improve the probability of incorporating a functional channel . Furthermore, after incorporation of ion channels, perfusion of the cis side with a vesicle-free solution did not prevent further incorporation, which suggests that perfusion cannot remove vesicles that are in close approximation to the bilayer membrane (see Fig. 5) (cf. Cohen et al., 1982) . Therefore, the cis or trans side of the bilayer was perfused only when the ionic composition needed to be changed . These channels preferentially (>90%) incorporated into the bilayer with the orientation shown in the figures, i.e., cis-positive potentials caused the channels to open . Single channels that incorporated with the opposite orientation could be easily identified by their characteristic voltage dependence (cf.  .

Electrical Recording
The side of the bilayer to which brain membrane vesicles were added was defined as the cis side and the opposite side of the bilayer was defined as the trans side. The voltages indicated in all experiments are cis minus trans, with the trans side held at virtual ground . The current across the bilayer was measured and command voltages were applied to the solutions via a pair of Ag/AgCI electrodes (Krueger et al., 1983 ;French et al., 1984;. The cutoff frequency (-3 dB) of the current-to-voltage converter (10" St feedback resistor) was 600 Hz. Ionic current records were recorded continuously on an FM tape recorder (Store 4, Racal, Sarasota, FL) . Experiments were conducted at room temperature (20-24°C) . The conductance of the phospholipid bilayer before the addition of biological material was <10 pS . As inferred from their voltage dependence, these calcium channels have incorporated into the bilayer oriented with the extracellular ends of the channels facing the trans side and their cytoplasmic ends facing the cis side. The voltages reported here would then correspond to the usual cellular convention (inside minus outside) . Therefore, the upward current deflections shown in the figures correspond to outward currents (positive charges moving from the cis side to the trans side, i.e., from inside to outside) (cf. Lee and Tsien, 1984).

Analysis
For the open time analysis, experiments with a low number of channels (one to three) were used. The open times were determined (by hand) from single-level fluctuations that terminated in a closure; simultaneous openings were rare and were not counted . If a conductance level corresponds to a single, time-homogeneous Markovian kinetic state (e.g., Colquhoun and Hawkes, 1981) where the mean lifetime of the open state is equal to 1/kc and t is the time after the channel opened . The PDF for the closed time intervals should be equal to: where the mean lifetime of the closed state of an individual channel is equal to I /ko, t is the time after a channel closed, and N is the number of functional channels in the membrane . It should be emphasized that a two-state model is clearly a simplification . As can be seen in Figs . 1 A, 3A, and 8, the open state is punctuated by unresolved, brief fluctuations (<10 ms) toward the closed state. These brief closures cannot be fully resolved because of the large bilayer membrane current noise (^-I pA rms noise at 500 Hz) and the small single channel currents (<I pA). These fast fluctuations suggest that the synaptosomal calcium channel possesses a second closed state (i.e., two closed states and an open state) (cf. Reuter et al ., 1982 ;Brown et al., 1982 ;Fenwick et al ., 1982 ;Hagiwara and Ohmori, 1983 ;Cavalie et al., 1983) .

Ion Dependence ofthe Single Channel Conductances and Open Times
Voltage-dependent channels were identified as "calcium" channels because they select for divalent cations over monovalent cations, anions, and magnesium (see below), and permit either Bat+, Sr2+, and Cat+ to permeate Nelson, 1985c) . Fig. 1 A shows that in addition to barium and strontium ions, manganese can also move through open single calcium channels from synaptosomes incorporated into planar lipid bilayers (see also Fig. 5A). Fig. 1 B shows that with equimolar concentrations of Ba, Sr, and Mn, the following order of single channel conductances was observed : Ba (7 .5 pS) > Sr (6 pS) > Mn (4 pS). The single channel conductance with calcium as the charge carrier was the same as that with strontium (see . Over the voltage range examined, the current carried by these ions through single channels was approximately proportional to the applied voltage (i .e., the single channel conductances were voltage independent) .
The species of ion carrying charge through a single channel affected not only the single channel conductance, but it also affected the channel's open times. For example, at +100 mV, channels with Ba l' as the charge carrier had a shorter mean open time than when Ca 2+ or Sr 21 was the charge carrier . This study further extends this observation of  by showing that Mn2+, which has the lowest permeation rate of the ions studied ( Fig. 1 B), has the longest mean open time ( Fig. 1 C) . At +120 mV, the mean open times with Bat+, Sr2+, and Mn2+ were 266, 501, and 1,067 ms, respectively ( Fig. 1 C) . Thus, the sequence of single channel conductances and closing rate constants [= 1 /(mean open times)] for the permeant ions is the same : Ba t+ > Sr2+ = Ca 2+ > Mn2+. Fig. 1 C shows that open time distributions for the different current carriers can be fit by single exponentials .
One possible explanation for the effect of the permeant ion on the single channel open time is that these ions affect the voltage dependence of the channel. Fig. 2 shows that the closing rate constant (1/mean open time) decreases e-fold for a 30-mV depolarization, regardless of the nature of the permeant ion. Although the permeant ion did not appear to affect the voltage dependence of the closing rate constants (i.e., the slopes of 1/To vs. voltage plots), it did cause a shift in this plot . This shift could be interpreted as an effect on the internal free energy of closing, i.e., the free energy of channel closing at 0 mV (cf. Miller and Rosenberg, 1979). Interactions ofMixtures ofPermeant Ions: Mn 2+ Blocks Fig. 1 shows that in the absence of other permeant ions, manganese can pass through these single channels. Fig . 3 shows that when added to a solution that contains another species of permeant ion (e.g., Sr), Mn 21 can block. The addition of 25 mM Mn 21 to the cis side reduced the single channel current at +100 mV by 27% (Fig. 3, A and B). The reduction in single channel current by Mn 21 was more pronounced at +50 mV (46%) (Fig. 3 C). Therefore, the "block" by Mn 2+ Effect of voltage on the log transform of the closing rate constants . The closing rate constants were determined from the open time distributions (e.g., Fig. 1 C; also see Eqs . 1 and 2). In the case of a single energy barrier, the voltage dependence of the rate constants will be given by: where ko is the opening rate constant, kc is the closing rate constant, koo .5 and kco.5 are the rate constants at Vo.5 and are equal, and m is the fraction of the membrane potential that influences the transition from the closed state to the open state at the peak of the energy barrier. Because the voltage dependences of lnk c and lnko (not shown; however, see Fig. 3C of  were about equal, this suggests that m is^-0 .5 and that q (the apparent "gating" charge) is -1 .7. In other words, the closing and opening rate constants changed e-fold for^-30 mV depolarization . ", Bat+; ", Sr" ; A, Mn2+.
appears to be voltage dependent, with less positive voltages favoring block. In addition, the amplitudes of the single channel currents in this Mn2+/Sr2+ mixture at +100 mV were similar to that in Mn2+ alone (cf. Fig . 1). Furthermore, Mn 21 not only reduced the single channel conductance with Sr2+ as the charge carrier, but it also increased the mean open time (Fig. 4A) . This result suggests that the effects of the permeant ions on the amplitudes of the single channel currents and mean open times may be related (see Discussion) .

Ion Dependence ofChannel Closed Times
The addition of Mn2+ to an Sr2+-containing solution caused a decrease in the single channel conductance and the closing rate constant (Figs . 3 and 4A). In contrast, Fig. 4B shows that Mn 2' did not significantly affect the mean closed time, which suggests that the opening rate constant is not substantially influenced by the ionic composition of the bathing solution . Furthermore, if the effect of Mn 21 on the open times was mediated by a simple surface charge effect, then one would expect that the channel's closed times would decrease because they are also voltage sensitive (cf. . (a) One approach is to determine the number of channels in the membrane . This approach requires that the number of channels in the membrane not change during the course of the measurements and that sufficiently long records be taken when the channel has a reasonably high probability of being open (i .e ., P > 0.3). This approach was used to determine that there were two functional channels in the membrane of the Mn" experiment shown in Fig. 1 (Mn 21 was the charge carrier and the real mean closed time was 23 .3 s at +100 mV). In this experiment, the number of channels did not change over a 1-h period (i .e ., the apparent mean closed times at +100, +120, and +150 mV did not change) and it was possible to depolarize the membrane to +200 mV (P > 0.6) to verify the number of functional channels . However, this approach is often difficult to implement because the number of channels in the bilayer often increases with time (i .e., Fig . 5). (b) An alternative approach is to determine how the apparent mean closed time decreases as channels incorporate or become functional . Fig .  5 illustrates such an experiment, where it was possible to monitor the incorporation of calcium channels by determining how the apparent mean closed times decreased with time. In this experiment, the number of channels in the bilayer appeared to increase from 1 to 15 over 70 min (i.e., the apparent mean closed time decreased 15-fold) . Fig . 5, A and B, shows that when Sr2+ was exchanged for Mn2+, the apparent mean closed time decreased from 8.1 to 4.6 s. Therefore, after the solution change, there were five functional channels in the bilayer, i.e ., the real mean closed time with Mn 21 (23 .3 s from the experiment in Fig. 1) divided by the apparent mean closed time (4 .6 s) . In the experiment shown in Fig. 5, at the beginning of the experiment, the apparent mean closed time (21 .6 s) with Sr 21 as the charge carrier was similar to the real closed time with Mn 2+. These results suggest that there was one functional channel in the bilayer at the beginning of the experiment in Fig. 5, and then two more channels incorporated into the bilayer. Sr 21 was then replaced by Mn 2' and the number of channels increased from 3 to 5 and eventually to 15 . The real opening rate of the channel at this percent block at three different voltages . Percent block is the percent reduction of the single channel currents, with 50% block being one-half the single current in the absence of Cd 2 ' and 100% block being zero-current flow through the channel. The curve was derived from Eq . 3. ", +150 mV ; " , +120 mV ; A, +100 mV .
voltage was therefore -0 .04 s-' and was not dependent on the nature of the charge carrier.
Reduction of Single Channel Currents by Cd 2 + Cadmium ions are potent blockers of calcium currents in a variety of preparations (see Hagiwara and Byerly, 1981). Fig. 6 shows that when cadmium is added to the cis side of a bilayer containing a calcium channel, the single channel current amplitude is reduced. Fig. 6B shows that the relationship between the cadmium concentration and the percent reduction of the single channel current can be fit with a rectangular hyperbola (Eq. 3), with Ko .5 being the concentration (9 .3 MM) of cadmium that reduces the single channel current by 50% and the maximal block (Block ,a) (100%) being the percent of the current reduced by infinite concentrations of Cd 2 + (see below and Discussion).
Furthermore, the efficacy of block was not substantially affected by voltages between +100 and +150 mV (Fig . 6B).
In synaptosomes (Nachshen, 1984) as in other preparations (cf. Hagiwara et al ., 1974), competition between the permeant ions and the blocking ions determines the rate of ion movement through the channel. To test this proposal on the single channel level, the effects on Cd2+ on single channel currents carried by Bat+ , Ca 2+, Sr2+ and Mn 2+ were tested (Fig . 7) . In all cases, Cd 2+ reduced the single channel current in a dose-dependent manner . However, as illustrated in the double-reciprocal plots of Cd 2+ vs . block (Fig . 7 B), the concentration of Cd2+ needed for 50% block (Ko.5) depended on the nature of the permeant ion, with Ko .5(Mn) > Ko .5(CA) = Ko .5(sr) > Ko .5(w). Furthermore, in high concentrations of Cd 2+ , the single channel current was <1% of the current in the absence of Cd 2+ ,which indicates that in the presence of Ca t+ , Sr 2+ , Ba t+ , or Mn 2+ , Cd ions cannot permeate rapidly enough to support a measurable single channel current . These results suggest that a binding site accessible from the cis side regulates the block by inorganic ions .
Sidedness of Block by Cd 2 + Fig. 8 shows that Cd2 + on the cis side was more effective in blocking ionic current from the cis side to the trans side. Cd2+ (24 mM), when added to the trans side, resulted in a 26% reduction in single channel current. The same concentration of Cd2+ , when added to the cis side, resulted in a greater reduction (71 %) in single channel current. The reason for the differences in the efficacy of block is not yet clear. A lower apparent affinity for block by Cd2+ on the trans side could be explained by the following possibilities: (a) the block by Cd2+ is voltage dependent; (b) voltage-dependent binding of a permeant ion in the channel reduces the affinity of Cd2+; (c) the channel has two different Cd2+ binding sites, one accessible from the cis side and the other accessible from the trans side. 2s 0.5 pA[ + ~ Cis Cd2 -FIGURE 8. Sidedness of Cd2+ block. At +100 mV, with Sr2' as the charge carrier, the single channel current was 0.62 pA (n > 50). After the addition of CdC1 2 (24 mM) to the cis side, the mean single channel current was 0.19 pA (n > 50). To restore the original single channel current, the cis side was then perfused with 0-Cd2+ solution . CdCl2 (final concentration, 24 mM) was then added to the trans side and the single channel current was reduced to 0.46 pA (n > 50).

Effects of La, Mg, Na, and K Ions on the Single Channel Currents
The efficacy of block depended not only on the nature of permeant ion species but also on the nature of the blocking ion. La" was found to be the most potent inorganic blocker, with a Ko .s of^-150 uM (with Sr 21) . Fig.  3 shows that Mn" is a less potent blocker than both Las' and Cd2+. Mg ions did not affect divalent cation movement through these Ca channels. When cis CaCl2 solution was replaced with a solution containing 3 mM CaC12 and 247 mM MgC12, the resulting single channel current-voltage relationship extrapolated to a potential (+35 mV) that was close to the Ca equilibrium potential (Eca, +55 mV). By contrast, the Mg equilibrium potential (EMg) was nominally negative infinity and the Cl equilibrium potential (Ec,) was 0 mV . This result indicates that these channels select for Ca 21 over Mgt' and Cl-. Furthermore, Mg ions did not affect the single channel conductance (5.1 pS) or the mean open times (250 ms, at +100 mV). Since the channels are selecting for Ca`over Mgt+, these results suggest that with 3 mM Ca 21 on the cis side, the channels were saturated with respect to the charge carrier. Saturation of the Ca 2+ channel at such concentrations is in accord with the information obtained from intact synaptosomes (Nachshen and Blaustein, 1982). These results suggest that Mgt+, even in high concentrations, does not block the channel.
Furthermore, high concentrations (200 mM) of Na and K ions did not reduce the single channel currents . For example, the single channel conductance with Ca2+ as the charge carrier was 5 .3 ± 0 .4 pS and, in the presence of the same concentration of Ca 2+ (150 mM) plus 200 mM K, the single channel conductance was 5.4 ± 0.4 pS . The order of potency of the inorganic ions, tested thus far, in reducing current flow through this Ca 21 channel was: La" > Cd2+ > Mn 2+ >> Mg 2+ Na+, K+.

DISCUSSION
Comparison with Other Ca`Channels THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 87 -1986 The properties of synaptosomal Ca 2+ channels from rat brain have been extensively characterized by investigating the properties of divalent cation isotopic influx that has been stimulated by depolarizing with high external K+ (Nachshen and Blaustein, 1979Drapeau and Nachshen, 1984;Nachshen, 1984) . The synaptosomal Ca 21 channels as characterized by isotopic flux techniques share the following properties with the synaptosomal Ca 21 channels incorporated into planar lipid bilayers. (a) Bat+, Ca 21, Sr2+, and Mn 21 pass through both types of the channels with the same order of maximum flux rates. (b) Mn2+ can both permeate and block. (c) Inorganic blocking ions, when added to one side of the membrane, compete with the permeant ions for a single site. (d) The order of apparent affinities of the permeant ions for the site is the same: Mn > Ca > Sr > Ba. (e) The order of apparent affinities of the blocking ions for this site is also the same : La > Cd > Mn >> K, Na. (f) In both systems, the channels are inhibited by micromolar concentrations of the organic blockers D-600 and verapamil (Nelson, 1985c) and the channels do not completely inactivate.
Although the properties of single calcium channels in the bilayer and those of "intact" synaptosomes are similar, it would be desirable to compare the properties of single channels in the intact tissue and in the bilayer. Because of the small size of the synaptosomes (<1 um diam) (Blaustein et al., 1977), it has not been possible to measure single channel currents by means of the patch-clamp technique. However, single calcium channels in some other tissues have been studied with the patch-clamp technique (Reuter et al., 1982;Brown et al., 1982Brown et al., , 1984Fenwick et al., 1982 ;Hagiwara and Ohmori, 1983 ;Cavalie et al ., 1983). In addition, Ca 21 channels from Paramecium cilia have been incorporated into planar lipid bilayers (Ehrlich et al., 1984). The conductances of single Ca 2+ channels with Ba t+ as the charge carrier (usually -100 mM) have ranged from^-2 (Ehrlich et al., 1984) to 25 pS (Reuter et al., 1982). The conductances of single Cac hannels from rat clonal pituitary cells (Hagiwara and Ohmori, 1983) and from rat brain synaptosomes  were similar (7-9 pS with Bat' as the charge carrier). Ba ions permeate single Ca 21 channels more rapidly than Ca ions (Lux and Nagy, 1981 ;Cavalie et al., 1983;. Although the ability of Sr ions to permeate calcium channels can be considered one of the criteria for the identification of a calcium channel (Hagiwara and Byerly, 1981 ;Nelson, 1985a), this property has not been extensively investigated at the single channel level in other tissues. With the exception of cardiac muscle, the effects of inorganic calcium channel blockers have not been investigated at the single channel level in other preparations . In cardiac muscle, cadmium ions caused discrete interruptions in current flow through single channels, which is consistent with the block mechanism presented below .
Single calcium channel activity has been difficult to measure in excised patches (cf. Fenwick et al., 1982 ;Cavalie et al ., 1983; but see Carbone and Lux, 1984;Nilius et al., 1985 ;Reuter, 1985). One possible explanation for the viability of calcium channels in the bilayer is that certain calcium channel types require the presence of intracellular constituents such as phosphorylating enzyme systems for an appreciable opening probability (Reuter, 1983 ;Cachelin et al ., 1983;Bean et al ., 1984). In the absence of such regulation, the curve of the probability of the channel being open is shifted toward more positive potentials. Therefore, at physiological membrane potentials, such a nonphosphorylated calcium channel would appear "nonfunctional ." However, with the bilayer method, a very wide voltage range can be explored (-200 to +200 mV) and the new activation curve for the channel can be found. In fact, the activation curve for the calcium channel reported here is shifted toward more positive potentials (Nelson, 1985a) . Therefore, this channel would appear nonfunctional at 0 mV. Another explanation for the viability of single calcium channels in the bilayer is that some types of calcium channels may be more stable than others . For example, in squid axons (DiPolo et al., 1983) and in barnacle muscle cells (Keynes et al., 1973), calcium channels can survive extensive perfusion of the internal compartment, whereas calcium channels in other preparations seem to be somewhat labile (cf. Lee and Tsien, 1984). Thus, in a cell membrane that contains multiple types of calcium channels (Nachshen and Blaustein, 1980;Nowycky et al., 1985), it is possible that one type of channel may be more stable than another (cf. Armstrong and Matteson, 1984 ;Nilius et al ., 1985).

Ion Movement Through Single Ca Channels from Brain Synaptosomes
To move through a calcium channel, a divalent cation must bind and dissociate with a site(s) in the permeation pathway (cf. Hagiwara and Byerly, 1981). Blocking ions such as lanthanum, cobalt, cadmium, and nickel appear to exert their effects by binding to this site with high affinity . Although it has been generally assumed that the blocking site is the same as the permeation site, studies on the block by cadmium of calcium currents and sodium currents through calcium channels in frog skeletal muscle have suggested that this may not be the case (Almers and McCleskey, 1984).
In this paper, evidence for the mechanism of inhibition of ion movement through calcium channels by the inorganic blocking ions is presented. The block by cadmium can be explained by a mechanism whereby one cadmium ion binds to a single site in the open state. When a cadmium ion is bound to this site, other more permeant ions cannot pass through the channel and cadmium itself leaves the site too slowly to support a measurable current. If an equilibrium exists between the free Cd2+ and cadmium bound to this site, then the open channel should fluctuate between conducting and nonconducting states . However, if the lifetimes of the blocked and unblocked states are too brief (<3 ms) to be resolved by the recording system, then, in the presence of cadmium, the apparent open channel current corresponds to a time-averaged value determined by rapid blocking and unblocking events . Increasing concentrations of Cd2+ should then reduce this time-averaged conductance in a single-site binding scheme (see Eq. 3) (cf. Woodhull, 1973), as was observed .
The concentration of cadmium needed to reduce the single channel current by 50% (Ko.5) depended on the nature of the permeant ion, which suggests that permeant ions and the blocking ions interact at the same site. For a single-site scheme, the Ko.S for the cadmium will be inversely related to the dissociation constant of the permeant ion [K,(M)] for the site [Eq. 4, assuming that the concentration of permeant ion, M, is much greater than K.(M)] (cf. Hagiwara et al ., 1974 ;Nachshen and Blaustein, 1982;Byerly et al., 1985). This assumption is supported by the observation that lowering the concentration of permeant ion from 250 to 100 mM did not affect the single channel conductance . Km(B) is the dissociation constant of the blocking ion, and kof and ko are the off rate and on rate constants for an ion that binds to this site . The Ko.5 depended on the nature of the charge carrier, with Ko.5(Mn) > Ko.5(Ca, Sr) > Ko.5(Ba) (Fig.  7). Because the concentration of the permeant ions was the same in each experiment, the effect of the permeant ion on Ko .5 Should reflect differences in the dissociation constants of the permeant ions for the site, with the order of dissociation constants of the permeant ions being opposite to that of the halfblock constant of cadmium [i .e., K,(Ba) > K.(Ca) = Km(Sr) > Km(Mn)]. This order of dissociation constants of the permeant divalent cations is the same as the order of the single channel conductances of the four current carriers (Fig.  1). The parallel sequence between the dissociation constants and the single channel currents is consistent with the rate of ion movement through a channel (i.e., the single channel current) approximating the off rate constant of the permeant ion from the site . Thus, if the on rate constants for the four permeant ions are similar, then the sequence of dissociation constants should be the same as the sequence of single channel currents or off rate constants (Eq. 5).
To obtain an estimate of the K, of a permeant ion, the on rate constant is assumed to be diffusion-limited or^-109 M-' s-' (cf. Almers and McCleskey, 1984). Without information to the contrary, this assumption is reasonable because: (a) the on rate constant for calcium ions to block sodium currents through single calcium channels was close to diffusion-limited ; (b) the block by cadmium was not voltage dependent over a 50-mV range, which suggests that the site may be close to the aqueous phase on the cis side (Fig. 6); (c) the on rate constants of calcium onto other calcium binding proteins also appear to be diffusion-limited (e.g., troponin C; Potter and Johnson, 1982). If the primary pathway for an ion to leave the site is into the trans side, then the single channel current should closely approximate the off rate constant for an ion from the binding site (at +120 mV, kaff for barium ions should be -2 .7 X 106 s-') . Therefore, the dissociation constant for barium would then be^-2.7 mM (Eq. 5). This value for the Km is similar to the values that were reported for synaptosomal calcium channels as measured by barium isotopic flux (Nachshen and Blaustein, 1982) or for other calcium channels (Hagiwara and Byerly, 1981 ; but see Hess and Tsien, 1984;Almers and McCleskey, 1984).
Furthermore, from the ratio of Ko.5 with different current carriers, a ratio of dissociation constants for the permeant ions can be obtained [Eq. 6,M and K,(B) are constant].
Using K,(Ba) = 2.7 mM and Eq. 6, the dissociation constants of strontium, calcium, manganese, cadmium, and lanthanum have been estimated to be 1 .2 mM, 1 .2 mM, 0.5 mM, 44 uM, and 0.7 juM, respectively . The differences in the dissociation constants of the four permeant ions are greater than predicted from the differences in single channel currents, which suggests that the unitary currents are not a completely accurate measure of the off rate constants or that permeant ions have different on rate constants. Furthermore, if the channel has two divalent cation binding sites that exhibit ion-ion repulsion, then the true dissociation constants will be less than those calculated above (Hess and Tsien, 1984 ;Almers and McCleskey, 1984). Using the calculated K, for cadmium (44 juM) and assuming that the on rate constant is also diffusion-limited, the off rate constant of cadmium from the site can be calculated to be -4.4 X 104S-1 (Eq. 5). If cadmium ions could move from the binding site to the trans side, this kof would correspond to a current of 0.015 pA. A cadmium current of this magnitude is below the limit of detection of the recording system (^-0.1 pA). This kof is in accord with the observation that cadmium ions cannot support a measurable single channel current (Fig. 7). From the koff of cadmium, an estimate for the mean blocked time (Tblock) can be determined : Tbl«k = I /*off The calculated mean block time (23 js) is clearly far below the experimental resolution (3 ms).
The effects of cadmium ions on single channel currents support the existence of one binding site in the channel. However, the effects of manganese ions on single channel currents carried by a more permeant ion (e.g., Sr2+) suggest a more complicated picture. With the ratio K,(Sr)/K.(Mn) being^-2.4/1 and the single channel conductances for Sr and Mn being 6 and 4 pS, respectively, the single-site scheme presented above predicts that in the presence of 250 mM Sr2+ , concentrations of manganese >1 M would be needed to reduce the single channel conductance to a level close to that of Mn alone. Surprisingly, at +100 mV, 25 mM Mn2+ reduced the single channel conductance to the level supported by Mn2+ alone (4 pS). This concentration of Mn 2+ would have been predicted to reduce the single channel conductance from -6 to 5 .6 pS or by 0.04 pA at +100 mV. Furthermore, the block was more pronounced at +50 mV and the single channel conductance level appeared to be less than that in Mn alone. These results cannot be easily explained by a simple one-site model of the channel. However, currents through a channel that contains two binding sites could be affected by Mn ions in such a manner (cf. Hess and Tsien, 1984;Almers and McCleskey, 1984).

Ion Dependence of the Single Channel Open Times
The identity of the charge carrier has been shown to affect the kinetics of single calcium currents in ventricular myocytes (Cavalie et al., 1983) and macroscopic calcium channel currents (Siami and Kung, 1982;Deitmer, 1983). As determined from noise analysis, a similar relationship has been found between the single channel conductances and the closing rate constants when different alkali cations carry current through the acetylcholine receptor channel (Ascher et al., 1978 ;Marchais and Marty, 1979 ;Gage and Van Heiden, 1979). In addition, a similar conclusion has been obtained from comparisons of Rb+ and K+ movement through squid axon K+ channels (Swenson and Armstrong, 1981) and single K+ channels from skeletal muscle (Spruce et al., 1984).
One possible explanation for the ion dependence of the open times is that the binding of a permeant ion to a site in the channel affects another conformational transition, i .e., channel closing. This is supported by the observation that the order of the single channel currents and closing rate constants is the same, i.e., Ba > Ca = Sr > Mn. In fact, there appeared to be a parallel change in the dissociation constants and the closing rate constants on changing the permeant ion. For example, the ratio K ,(Ba)/Km(Ca, Sr) and the ratio of closing rate constants, k,,(Ba)/kc(Ca, Sr), were 2.2 and 1 .9, respectively . Furthermore, the ratios K,(Ba)/Km(Mn) and k,(Ba)/kc (Mn) were 5.4 and 4.0, respectively . These observations suggest that there is a relationship between the free energy of binding of a permeant ion to a site in the channel and the energy barrier that the channel has to overcome in order to close.
Another possible explanation for the effects of the permeant ion on open times and single channel currents is that the calcium channel fluctuates rapidly between two different conducting states, each having a different lifetime. These conducting states could represent a blocked and unblocked configuration of the channel (Neher and Steinbach, 1978) or two different conducting conformations of the channel (Lauger, 1984). As shown in Fig. 1, the open state of the calcium channel is punctuated by very brief current deflections toward the closed state, which supports the existence of another state of the channel. The measured single channel current and mean open time would be an average of the time spent at the two conductance levels. The permeant ion could affect the single channel current level and the mean open time by affecting the distribution between the two conducting conformations. Furthermore, the effects of the permeant ions on the open times of calcium channels raise the interesting possibility that the open times are also concentration dependent (I~uger, 1984). It may be possible to distinguish between these possibilities by incorporating calcium channels into much smaller bilayers, thus enabling higher-resolution recordings .
In conclusion, the work presented in this report supports the existence of at least one binding site in the channel that regulates ion permeation and affects the channel's kinetics. The inorganic calcium channel blockers appear to exert their effects by competing with the permeant ions for this site .