Brain Research 746 Ž1997. 285–293
Research report
Voltage-dependent Ca2q influx into identified leech neurones Paul W. Dierkes, Peter Hochstrate, Wolf-R. Schlue
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Institut fur UniÕersitatstr. 1, 40225 Dusseldorf, Germany ¨ Neurobiologie, Heinrich-Heine-UniÕersitat ¨ Dusseldorf, ¨ ¨ ¨ Accepted 8 October 1996
Abstract We determined the relationships between the intracellular free Ca2q concentration ŽwCa2q x i . and the membrane potential Ž Em . of six different neurones in the leech central nervous system: Retzius, 50 ŽLeydig., AP, AE, P, and N neurones. The wCa2q x i was monitored by using iontophoretically injected fura-2. The membrane depolarization evoked by raising the extracellular Kq concentration ŽwKqxo . up to 89 mM caused a persistent increase in wCa2q x i , which was abolished in Ca2q-free solution indicating that it was due to Ca2q influx. The threshold membrane potential that must be reached in the different types of neurones to induce a wCa2q x i increase ranged between y40 and y25 mV. The different threshold potentials as well as differences in the relationships between wCa2q x i and Em were partly due to the cell-specific generation of action potentials. In Naq-free solution, the action potentials were suppressed and the wCa2q x irEm relationships were similar. The Kq-induced wCa2q x i increase was inhibited by the polyvalent cations Co 2q, Ni 2q, Mn2q, Cd 2q, and La3q, as well as by the cyclic alcohol menthol. Neither the polyvalent cations nor menthol had a significant effect on the Kq-induced membrane depolarization. Our results suggest that different leech neurones possess voltage-dependent Ca2q channels with similar properties. Keywords: Medicinal leech; Intracellular Ca2q; Extracellular Kq; Ca2q channel; Polyvalent cation; Menthol
1. Introduction The influx of Ca2q into the cytosol of excitable cells provides a link between electrical excitation and intracellular signaling. In vertebrate neurones, Ca2q may enter the cytosol through different types of voltage-dependent Ca2q channels w4,28,41x, ionotropic neurotransmitter receptors w24x, the Naq-Ca2q exchanger operating in the reverse mode w5,12x, as well as by Ca2q release from intracellular organelles w15,40,42x. In neurones of the leech nervous system, the only pathway for Ca2q entry into the cytosol known so far are voltage-dependent Ca2q channels. Voltage-dependent Ca2q channels have been characterized in the ‘multifunctional’ Retzius neurones, the mechanosensory T, P, and N neurones, HN interneurones as well as in the unclassified AP neurones w1,6,13,22,23,32,34,35 x. Except for the HN interneurones, the Ca2q channels require relatively strong membrane depolarizations for activation and exhibit no or only weak inactivation. In addition to the demonstration of Ca2q currents by electrophysiological techniques, an increase in the intracellular free Ca2q concentration ŽwCa2q x i . due to membrane depolarization has been detected by )
Corresponding author. Fax: q49 Ž221. 81-13415.
means of optical methods in cultured Retzius, AE and sensory neurones w30x, as well as in Retzius neurones in situ w18x. In a number of leech neurones, a wCa2q x i increase is also evoked by the application of glutamatergic agonists w9,16x. The observation that both agonist-induced membrane depolarization and wCa2q x i increase were abolished in Naq-free solution strongly suggests that the wCa2q x i increase was due to Ca2q influx through voltage-dependent Ca2q channels. To investigate the Ca2q influx evoked by glutamatergic or other excitatory agonists such as acetylcholine w38x in more detail, we determined the relationship between wCa2q x i and the membrane potential Ž Em . in six different leech neurones: Retzius neurones, unclassified 50 ŽLeydig. and AP neurones, AE motoneurones, as well as P and N neurones. The results show that the different leech neurones possess voltage-dependent Ca2q channels with similar properties.
2. Materials and methods 2.1. Preparation and fluorescence recording The experimental procedures and the set-up have been described in detail previously w9,16–18x. The experiments
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Fig. 1. Effect of raising wKqx o on wCa2q xi and Em in P and AE neurones. a: raising wKqx o to 89 mM Žextracellular Naq completely replaced by Kq . induced an increase in wCa2q x i , which was reversibly abolished in Ca2q-free solution Ž5 mM EGTA.. The Kq-induced wCa2q x i increase was not affected by CNQX Ž6-cyano-7-dinitroquinoxaline; w19x. and D-tubocurarine Žeach 0.1 mM.. b: the Kq-induced membrane depolarization was unchanged in Ca2q-free solution as well as in the presence of CNQX and D-tubocurarine.
were performed on Retzius, 50 ŽLeydig., AP, AE, N, and P neurones in intact segmental ganglia of adult leeches, Hirudo medicinalis Žsee w25x.. All segmental ganglia were used for the experiments, except ganglia 5 and 6 which were discarded. The ganglia were fixed at their connectives in a special holder by means of fine steel clips. The neurones were identified by the size and the location of their cell bodies as well as by the amplitude, frequency, and the time course of their spontaneous action potentials,
as described by Dierkes et al. w9x. The cells were iontophoretically loaded with fura-2 ŽMolecular Probes; Eugene, OR, USA. by using single-barreled microelectrodes, tip-filled with a 100 mM aqueous solution of the pentapotassium salt of the dye. The injection of the dye had no significant effect on the resting potential of the cells or on frequency and amplitude of the spontaneous action potentials. After dye injection the preparation was transferred into
Fig. 2. Effect of raising wKqx o to 10, 20, 40, and 89 mM on the wCa2q x i of 50 neurones Ža. and of P neurones Žb.. Three experimental protocols were applied. Kq pulse: elevation of wKqx o for 1 min each, interrupted by 5 to 10 min periods in physiological solution; Kq step: step-like rise of wKqx o every 5 min; Kq steprNaq-free: as Kq step protocol, but extracellular Naq replaced by NMDGq. Arrows mark wCa2q x i overshoots in the 50 neurone upon application of the Kq step protocol.
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a flow chamber mounted on the object table of an inverted microscope ŽDiaphot-TMD; Nikon., which was part of a commercial microspectrofluorimeter ŽDeltascan 4000; Photomed, Wedel, Germany.. The chamber was steadily perfused with a flow rate of 4 ml miny1 , which exchanged the chamber volume about 15 times per min. The fluorescence was alternately excited via the microscope objective ŽCF Fluor DL-40x; Nikon. with wavelengths of 340 and 380 nm. The fluorescent light collected by the objective was filtered through a 510r540 nm barrier filter and measured by a photon-counting photomultiplier tube Ždata acquisition rate of 1 sy1 .. The fura-2 fluorescence Ž F340 , F380 . was obtained by correcting the raw data for the autofluorescence of the preparation, which was either measured in a neighboring non-injected position in the same ganglion or in an untreated ganglion. The fluorescence of the injected fura-2 was 10 to 50 times larger than the autofluorescence of the preparations.
fluorescence ratio of the Ca2q-free and Ca2q-saturated form of fura-2 upon 380 nm excitation; K d is the apparent dissociation constant of the Ca2qP fura-2 complex. The parameters R min , R max and FfrFs were determined using solutions of fura-2 in 100 mM KCl, buffered to pH 7.4 with 50 mM HEPES Ž N-w2-hydroxyethylxpiperazineN X-w2-ethanesulfonic acidx; Roth, Karlsruhe, Germany. to which either 10 mM CaCl 2 or 10 mM EGTA ŽwEthylenebisŽoxyethylenenitrilo.xtetraacetic acid; Sigma, Deisenhofen, Germany. were added. For K d a value of 135 nM was used which was measured under similar conditions by Grynkiewicz et al. w14x and which closely corresponds to K d values obtained by in situ calibrations in exposed leech neuropile glial cells w26,27x. Mean values of wCa2q x i were determined by averaging the ratios RŽ340r380. measured in the individual experiments.
2.2. Calculation of [Ca 2 q ]i
Membrane potential recordings were carried out by using single-barreled microelectrodes filled with 3 M KCl in a conventional experimental set-up, as described previously w2x. The time resolution of the recording system was limited to 50 Hz by the chart recorder Ž2200 S, Gould Inc.; Cleveland, OH, USA.. The experimental chamber was perfused with the same flow rate as in the fluorescence measurements.
The wCa2q x i was calculated from the ratio R s F340rF380 , according to the equation given by Grynkiewicz et al. w14x: wCa2q x i s K d P ŽŽ R y R min .rŽ R max y R .. P Ž FfrFs ., whereby R min designates the minimum R which is measured in the absence of Ca2q, and R max the maximum R at saturating Ca2q concentrations. FfrFs is the
2.3. Electrophysiological recordings
Fig. 3. Relationships between wCa2q x i and wKqx o Ža. and between wCa2q x i and Em Žb. in six different leech neurones. Data obtained by applying the three experimental protocols illustrated in Fig. 2. wCa2q x irEm relationships obtained by plotting the mean wCa2q x i measured at the various wKqx o against the corresponding mean Em determined in separate experiments under the same experimental conditions. Upon application of Kq steps, wCa2q x i was determined at the end of the respective step. Each data point is based on n s 5 to 9 wCa2q x i measurements or, respectively, 4 to 6 Em recordings. For reasons of clearity, standard deviations ŽS.D.. of wCa2q xi and Em data given only for one data point Žmiddle diagram in b.. The S.D. of the other data points were similar or Žmostly. smaller.
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2.4. Solutions The physiological solution had the following composition Žin mM.: 85 NaCl, 4 KCl, 2 CaCl 2 , 1 MgCl 2 , 10 HEPES, adjusted to pH 7.40 with NaOH. In the 89 mM Kq solution NaCl was replaced by KCl and the pH adjusted with KOH. Solutions with an intermediate Kq concentration were obtained by mixing appropriate volumes of the physiological and the 89 mM Kq solution. In Ca2q-free solutions, Ca2q was omitted and 5 mM EGTA were added; in Naq-free solutions, Naq was replaced by N-methyl-D-glucamine ŽSigma. and the pH was adjusted with KOH. Solutions containing La3q, Cd 2q, Co 2q, Ni 2q, or Mn2q were prepared by adding appropriate amounts of 1 M stock solutions of the corresponding chloride salts to the respective saline without osmotic compensation. Žy .Menthol Ž5-methyl-2-w1-methyl-ethylxcyclohexanol; Sigma. was added in solid form shortly before use; to obtain a menthol concentration of 2 mM the solutions had to be heated slightly.
2b.: wCa2q x i was unaffected at 10 or 20 mM Kq but increased only at 40 and 89 mM Kq. In particular, the Kq-induced wCa2q x i increase in P neurones was virtually independent of extracellular Naq, and the same result was obtained in Retzius, AP, and AE neurones. The relationships between wCa2q x i and wKqx o and between wCa2q x i and Em of all neurones investigated are shown in Fig. 3. In general, wKqx o had to be raised to more than 10 mM to evoke a wCa2q x i increase, and further increases in wKqx o evoked corresponding further increases in wCa2q x i . Besides the 50 neurones ŽFig. 2a., the AE neurones deviated from this general behaviour: Kq steps from 40 to 89 mM were without effect on wCa2q x i or even caused a drop in wCa2q x i , although the cells depolarized by about 8 mV Žsee Fig. 3b.. In N neurones, and to a lesser extent in Retzius, AP, and AE neurones, the relationships between wCa2q x i and Em were steeper when applying the pulse protocol as compared to those obtained by applying the step protocols ŽFig. 3b.. Furthermore, the threshold
3. Results The effect of raising wKqx o to 89 mM on wCa2q x i and on the membrane potential Ž Em . of leech P neurones or, respectively, AE neurones is shown in Fig. 1. Raising wKqx o induced an increase in wCa2q x i , which was reversibly abolished in Ca2q-free solution, but was unaffected by the quinoxalinedione CNQX, a blocker of AMPArkainate receptors w9,10x or by D-tubocurarine, a blocker of nicotinic acetylcholine receptors w31,38x. The Kq-induced membrane depolarization was unchanged in Ca2q-free solution or in the presence of CNQX and Dtubocurarine ŽFig. 1b.. Similar results as in P and AE neurones were obtained in Retzius, 50, AP, and N neurones. The effect of raising wKqx o to 10, 20, 40, and 89 mM on the wCa2q x i of 50 and P neurones is shown in Fig. 2. In 50 neurones, 1 min pulses of 10 mM Kq had no significant effect on wCa2q x i ŽFig. 2a.. A slight increase in wCa2q x i was evoked by 20 mM Kq pulses, and with 40 and 89 mM Kq pulses, the wCa2q x i increase was markedly enhanced. Upon applying 5 min Kq steps, the wCa2q x i already increased at 10 mM Kq, and further wKqx o augmentations caused corresponding further wCa2q x i increases. In Naq-free solution, however, Kq steps to 10 mM were without effect, and in most cells wCa2q x i was increased only at 40 and 89 mM Kq. In Naq-containing solutions, wCa2q x i often passed through a transient maximum before reaching a steady state Žarrows in Fig. 2a.; these wCa2q x i overshoots were absent in Naq-free solutions. Similar Naq-dependent wCa2q x i overshoots also occurred in N neurones. In contrast to 50 neurones, the Kq-induced wCa2q x i increase in P neurones did not depend on the experimental protocol ŽFig.
Fig. 4. Enhanced generation of action potentials upon raising wKq x o . a: in Retzius, 50, AP, AE, and N neurones, raising wKq x o to 89 mM transiently enhanced the frequency of spontaneous action potentials. In the P neurone, only a solitary action potential occurred. b: in 50 neurones, the frequency of spontaneous action potentials was enhanced persistently upon raising wKq x o moderately to 10 mM.
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Fig. 5. Inhibition of the Kq-induced wCa2q x i increase by Co 2q in an AP neurone and by La3q in a Retzius neurone. a: in contrast to the effect Co 2q Žand the other divalent cations tested; see Fig. 6., the inhibitory action of La3q was not reversed by superfusion with physiological solution Žup to 30 min., but complete reversal was achieved by applying EDTA Ž6 mM.. b: in the presence of Co 2q or La3q Žor other polyvalent cations., the Kq-induced membrane depolarization was substantially preserved. At the beginning of the experiments, both neurones generated spontaneous action potentials which were abolished following the first Kq application. Note that EDTA in the Retzius neurone caused a marked membrane depolarization that was not paralleled by a wCa2q xi increase.
potential at which a wCa2q x i increase became detectable was shifted to more positive values in Naq-free solutions. In Naq-containing solutions, the threshold potentials varied between y40 and y25 mV, and in Naq-free solutions between y30 and y15 mV.
The differences in the wCa2q x irEm relationships may be partly due to the different action potential activity of the neurones following the increase in wKqx o . In Retzius, 50, AP, AE, and N neurones, raising wKqx o enhanced the frequency of action potentials, which were particularly
Fig. 6. Inhibition of the Kq-induced wCa2q x i increase by polyvalent cations ŽwKqx o s 89 mM.. a: effect of 1 mM Co 2q, Ni 2q, Mn2q, Cd 2q, and La3q. Bars give the wCa2q x i increase in the presence of the blocking ions normalized to the mean increase measured before and afterwards in their absence Žsee Fig. 5.. Data are the mean Ž"S.D.. of n s 4 to 7 experiments. b: dose-dependency of the blocking effect of Co 2q, Ni 2q, and Mn2q. Continuous lines were calculated by using a Hill coefficient of 2.
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large in N and 50 neurones Žup to 90 mV; Fig. 4a.. The action potentials ceased within 5 to 100 s, depending on cell type and wKqx o . Solely in 50 neurones, the action potential frequency was enhanced persistently at 10 mM Kq, and often also at 20 mM Kq ŽFig. 4b.. In contrast to the other neurones, P neurones generated no or only single action potentials, not only in physiological solution but also at raised wKqx o ŽFig. 4a.. In all cells no action potentials were observed in Naq-free solution. The Kq-induced wCa2q x i increase in Retzius, 50, AP, AE, P and N neurones was blocked by the polyvalent cations Co 2q, Ni 2q, Mn2q, Cd 2q, and La3q ŽFigs. 5 and 6.. With the exception of La3q, the blocking effect was reversed within a few min by superfusing the preparation with physiological solution, as shown in Fig. 5a for the effect of Co 2q in an AP neurone. The La3q effect persisted for at least 30 min after wash-out, but complete reversal was achieved by applying chelating agents such as EDTA ŽFig. 5a.. The addition of Co 2q, Ni 2q, and La3q to the bathing medium caused no change of the fura-2 fluorescence Ž F340 , F380 ; see Section 2... The changes in F340 and F380 evoked by rasising wKqx o in the presence of non-saturating concentrations of these cations were fully reversible. In the presence of Cd 2q Ž0.3 or 1 mM., however, raising wKqx o evoked an irreversible drop in F380 by 10 to 30%, leading to a persistent increase in RŽ340r380. by 0.3 to 0.6 units. A wCa2q x i increase in the presence of Cd 2q was reflected by a transient component in the F380 signal as well as by a
reversible increase in F340 Ždata not shown.. A slight irreversible reduction in both F340 and F380 was also occasionally observed upon raising wKqx o in the presence of 0.5 to 2 mM Mn2q. Some polyvalent cations caused a slight shift of the resting Em to more positive values, but the Kq-induced membrane depolarization was not affected significantly ŽFig. 5b.. The efficacy of the polyvalent cations to block the Kq-induced wCa2q x i increase in the different neurones was similar: La3q) Cd 2q) Ni 2q; Co 2q) Mn2q ŽFig. 6a.. The dose-dependencies of the blocking action determined for Co 2q, Ni 2q, and Mn2q were relatively steep. Both Co 2q and Ni 2q were uneffective at concentrations below 10y4 M, but the block was virtually complete at a concentration of 3 mM. To evoke comparable effects with Mn2q, about three times higher concentrations were necessary ŽFig. 6b.. In Retzius, AP, and AE neurones, the Kq-induced wCa2q x i increase was also blocked by 2 mM menthol ŽFig. 7a.. In 50, N, and P neurones, menthol itself evoked a marked wCa2q x i increase, which was reversibly reduced upon raising wKqx o . During the 1 min Kq application, wCa2q x i clearly fell below the levels reached before and after menthol exposure, and the steady-state wCa2q x i reached upon prolonged application of augmented wKqx o in the presence of menthol was even lower Žbroken line in Fig. 7a.. The menthol-induced wCa2q x i increase was strongly reduced but not abolished in Ca2q-free solution, suggesting that it was mainly due to Ca2q influx from the
Fig. 7. Effect of menthol on wCa2q x i and Em in AP and P neurones. a: in AP neurones, 2 mM menthol suppressed reversibly the Kq-induced wCa2q x i increase without affecting wCa2q x i by itself. Similar results were obtained in Retzius and AE neurones. In P neurones, however, menthol evoked a marked wCa2q x i increase that was reversibly suppressed upon raising wKqx o . Broken line gives putative course of the trace upon prolonged Kq exposure, as observed in different experiments. Similar results as in P neurones were obtained in 50 and N neurones. b: menthol had no effect on the resting Em or on the Kq-induced membrane depolarization.
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external medium Ždata not shown.. The residual mentholinduced wCa2q x i increase in Ca2q-free solution might be due to Ca2q release from intracellular stores Žsee w8,39x.. Neither the resting Em nor the Kq-induced membrane depolarization were affected by menthol ŽFig. 7b..
4. Discussion The wCa2q x i increase in leech Retzius, 50, AP, AE, P, and N neurones induced by raising wKqx o was due to Ca2q influx from the external medium, because the wCa2q x i increase was reversibly abolished in Ca2q-free solution ŽFig. 1.. The Ca2q influx was caused by the depolarization of the neurones but not by excitatory inputs from other cells, because the wCa2q x i increase was not affected by inhibiting glutamatergic or nicotinergic neurotransmission. The relationships between wCa2q x i and Em revealed distinct threshold potentials for the Kq-induced wCa2q x i increase ŽFigs. 2 and 3., indicating that the Ca2q influx was mediated by voltage-dependent Ca2q channels. This conclusion is strengthened by the blocking action of Co 2q, Ni 2q, Mn2q, Cd 2q, and La3q ŽFigs. 5 and 6., which have been shown to inhibit voltage-dependent Ca2q channels in various preparations w7x. The Ca2q channels remain activated during sustained membrane depolarization, because wCa2q x i remained increased upon long-lasting augmentation of wKqx o ŽFig. 2.. Furthermore, the relationships between wCa2q x i and Em measured upon application of the Kq pulse protocol were essentially the same as those measured under the Kq step protocol ŽFigs. 2 and 3.. The smaller slope of the wCa2q x irEm relationships obtained with the Kq step protocol in N neurones, and to some extent also in Retzius, AP, and AE neurones may reflect a partial inactivation of the voltage-dependent Ca2q channels. The inactivation of the Ca2q channels might also explain the wCa2q x i overshoot in 50 and N neurones ŽFig. 2a., as well as the uneffectiveness of Kq steps from 40 to 89 mM in AE neurones ŽFig. 3.. However, the differences between Kq pulse and Kq step data may also be due to the transient generation of action potentials. The difference was most striking in N neurones, which generated a burst of action potentials of large amplitude, and it was less pronounced in Retzius, AP and AE neurones, in which the action potentials were of smaller amplitude ŽFig. 4a.. The contribution of action potentials to the Kq-induced wCa2q x i increase was particularly evident in 50 neurones, in which the action potential frequency was increased persistently at moderately elevated wKqx o ŽFig. 4b.. The action potentials were suppressed in Naq-free solution, and the wCa2q x irEm relationship was similar to those in the other types of neurones ŽFig. 3b.. In P neurones, action potentials were virtually absent, not only in physiological solution but also in solutions with augmented wKqx o ŽFig. 4a., and correspondingly, the discrepancy between Kq pulse and Kq step data was negligi-
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ble Žsee Fig. 2b.. The transient generation of action potentials might also explain the observation that the Kq-induced wCa2q x i increase in Retzius neurones did not develop monotonically but contained two or more components w18x. Furthermore, the shift of the wCa2q x irEm relationships in Naq-free solution to a more positive Em may be due to the suppression of the action potential activity. In Retzius, AP, AE, N, and P neurones, wKqx o had to be raised to more than 10 mM to induce a measurable wCa2q x i increase ŽFig. 3a.. It has been shown that in the leech nervous system the wKqx o increase evoked by electrical stimulation of the nerve roots is limited to an upper level of about 8 mM w3,29x, and therefore, it seems unlikely that under physiological conditions an increase in the extracellular Kq concentration could cause Ca2q channel activation. However, a rise in wKqx o may facilitate the activation of the voltage-dependent Ca2q channels following the release of excitatory neurotransmitters such as glutamate or acetylcholine w9,10,21,38x. In 50 neurones, in contrast to the other neurones investigated, moderate but long-lasting wKqx o changes were sufficient to evoke prominent wCa2q x i increases ŽFigs. 2 and 3.. The efficacy of the tested polyvalent cations to block the Kq-induced wCa2q x i increase was similar in the different neurones ŽFig. 6.. The Ca2q channels seem to be slightly permeable for Cd 2q and Mn2q, as suggested by irreversible changes in the fura-2 fluorescence upon raising wKqx o . On the other hand, the channels appear to be impermeable for Co 2q, Ni 2q, and La3q, because no irreversible changes in the fura-2 fluorescence were observed. In Retzius, AP, and AE neurones, the Kq-induced wCa2q x i increase was also inhibited by menthol ŽFig. 7a., which confirms and extends previous observations in Retzius neurones and in leech neuropile glial cells w18x. A modulation of Ca2q currents by menthol has been found previously in Helix neurones, dorsal root ganglion cells, and in neuroblastoma cells w33,36,37x. In 50, N, and P neurones, menthol evoked a marked wCa2q x i increase which appears to be mainly due to Ca2q influx. The menthol-induced Ca2q influx probably occurs through a voltage-independent conductance because Em was not affected by menthol ŽFig. 7b.. Membrane depolarization in the presence of menthol may have two counteracting effects: Ž1. the reduction of the driving force for the menthol-induced Ca2q influx Žsee w11,20x.; Ž2. the induction of an additional Ca2q influx by activation of the voltage-dependent Ca2q channels, provided that these channels were not blocked by menthol. The first effect should cause a decrease in wCa2q x i , while the second one should cause a wCa2q x i increase. Raising wKqx o in the presence of menthol caused a decrease in wCa2q xi which shows that the reduction of the menthol-induced Ca2q influx overcompensates a possibly induced additional Ca2q influx through the voltage-dependent Ca2q channels. That at raised wKqx o the wCa2q x i was markedly lower in the presence of menthol than in its absence strongly suggests
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that the voltage-dependent Ca2q channels in 50, N, and P neurones were also blocked by menthol, as were those in Retzius, AP, and AE neurones. Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft ŽSPP Functions of Glial Cells; Schl 169r122.. We thank Claudia Roderigo for excellent technical assistance. The data are part of a planned doctoral thesis of P.W. Dierkes.
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