The Journal of Neurophysiology Vol. 77 No. 4 April 1997, pp. 2040-2048
Copyright ©1997 by the American Physiological Society

Speed of Ca²⁺ Channel Modulation by Neurotransmitters in Rat Sympathetic Neurons

Jiuying Zhou, Mark S. Shapiro, and Bertil Hille

Department of Physiology and Biophysics, University of Washington, Seattle, Washington 98195-7290

	ABSTRACT

Abstract Introduction Methods Results Discussion References

Zhou, Jiuying, Mark S. Shapiro, and Bertil Hille. Speed of Ca²⁺ channel modulation by neurotransmitters in rat sympathetic neurons. J. Neurophysiol. 77: 2040-2048, 1997. We have measured the onset and recovery speed of inhibition of N-type Ca²⁺ channels in adult rat superior cervical ganglion neurons by somatostatin (SS), norepinephrine (NE), and oxotremorine-M (oxo-M, a muscarinic agonist), using the whole cell configuration of the patch-clamp method with 5 mM external Ca²⁺. With a local perfusion pipette system that changed the solution surrounding the cell within 50 ms, we applied agonists at various times before a brief depolarization from 80 mV that elicited I_Ca. At concentrations that produced maximal inhibition, the onset time constants for membrane-delimited inhibition by SS (0.5 µM), NE (10 µM), and oxo-M (20 µM) were 2.1, 0.7, and 1.0 s, respectively. The time constants for NE inhibition depended only weakly on the concentration, ranging from 1.2 to 0.4 s in the concentration range from 0.5 to 100 µM. Inhibition by oxo-M (20 µM) through a different G-protein pathway that uses a diffusible cytoplasmic messenger had a time constant near 9 s. The recovery rate constant from membrane-delimited inhibition was between 0.09 and 0.18 s¹, significantly higher than the intrinsic GTPase rate of purified G protein G_o, suggesting that Ca²⁺ channels or other proteins in the plasma membrane act as GTPase activating proteins. We also measured the rate of channel reinhibition after relief by strong depolarizing prepulses, which should reflect the kinetics of final steps in the inhibition process. In the presence of different concentrations of NE, reinhibition was four to seven times faster than the onset of inhibition, indicating that the slowest step of inhibition must precede the binding of G protein to the channel. We propose a kinetic model for the membrane-delimited NE inhibition of Ca²⁺ channels. It postulates two populations of receptors with different affinities for NE, a single population of G proteins, and a single population of Ca²⁺ channels. This model closely simulated the time courses of onset and recovery of inhibition and reinhibition, as well as the dose-response curve for inhibition of Ca²⁺ channels by NE.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

Influx of extracellular Ca²⁺ through voltage-gated Ca²⁺ channels is required for neurotransmitter release and also contributes to spike-frequency encoding. Therefore, depression of Ca²⁺ channels by modulatory transmitters can play important roles in regulation of neural signaling. In rat superior cervical ganglion (SCG) neurons, many neurotransmitters inhibit N-type Ca²⁺ channels through at least five different intracellular pathways (for review, see Hille 1994). Somatostatin (SS), norepinephrine (NE), and muscarinic agonists inhibit Ca²⁺ channels through a widely studied signaling pathway that uses pertussis toxin (PTX)-sensitive G proteins and is membrane-delimited and voltage dependent (the standard pathway). NE also acts through another membrane-delimited pathway that differs from this standard pathway only in that the G protein involved is PTX insensitive (Beech et al. 1992). Muscarinic agonists, on the other hand, also activate a pathway requiring a diffusible second messenger. It uses a PTX-insensitive G protein, is voltage independent, and is sensitive to calcium chelators in the recording pipette (the slow muscarinic pathway) (Beech et al. 1991; Bernheim et al. 1991).

To understand how modulation shapes dynamic responses of the nervous system, it is essential to know its kinetic properties. Although previous work (Bernheim et al. 1991) has shown that inhibition through the membrane-delimited pathways is much faster than that through the second-messenger-requiring pathway, the speed of neurotransmitter inhibition of Ca²⁺ channels has not been extensively studied. Here, we measured the onset and recovery kinetics of SS, NE, and muscarinic inhibition of N-type Ca²⁺ channels and its dependence on agonist concentration. We also measured the kinetics of the last steps in membrane-delimited channel inhibition by studying the rate of channel reinhibition after a strong depolarizing pulse. We propose a kinetic model describing membrane-delimited inhibition.

	METHODS

Abstract Introduction Methods Results Discussion References

Materials

Reagents were obtained as follows: papain (Worthington Biochemical), dispase (Boehringer Mannheim), somatostatin (Peninsula), oxotremorine-M (RBI), bis-(o-aminophenoxy)-N,N,N,N-tetraacetic acid (BAPTA; Molecular Probes), leupeptin (GIBCO), and ATP and GTP (Pharmacia LKB Biotechnology). All other chemicals were from Sigma.

Preparation of rat sympathetic neurons

Neurons were dissociated acutely from the SCG of 4- to 6-wk-old Sprague-Dawley rats, using methods of Bernheim et al. (1991), slightly modified by Shapiro and Hille (1993). Briefly, rats were anesthetized with methoxyflurane and decapitated. Ganglia were dissociated in modified Hank's solution containing (in mM) 137 NaCl, 0.34 Na₂HPO₄·7H₂O, 5.4 KCl, 0.44 KH₂PO₄, 5 glucose,and 5 N-2-hydroxyethylpiperazine-N-2-ethanesulfonic acid (HEPES), pH 7.4 with NaOH.

Solutions

The external Ringer solution contained (in mM) 160 NaCl, 2.5 KCl, 5 CaCl₂, 1 MgCl₂, 10 HEPES, and 8 glucose plus 500 nM tetrodotoxin, pH adjusted to 7.4 with NaOH. The standard pipette solution contained (in mM) 175 CsCl, 5 MgCl₂, 5 HEPES, 0,1 BAPTA, 3 Na₂ATP, 0.1 NaGTP, and 0.08 leupeptin, pH 7.4 with CsOH. When measuring current inhibition by oxotremorine-M through the membrane-delimited pathway, 20 mM BAPTA was used in the pipette solution. When measuring the actions of NE, we included 1 µM propranolol in all solutions to block -adrenergic receptors.

Fast perfusion setup

We positioned a theta tube next to the neuron being studied to apply neurotransmitters rapidly. One barrel of the theta tube (barrel 1) was filled with the desired transmitter dissolved in Ringer solution. The other barrel (barrel 2) was filled with a low-Ba²⁺ Ringer solution where the normal 5 mM CaCl₂ was replaced with 0.2 mM BaCl₂. The flow from each barrel was controlled by solenoid valves (Lee, Westbrook, CT) triggered on and off by the computer. When we measured the speed of transmitter inhibition, the neuron was placed directly in front of barrel 1, ~100 µm from the opening to achieve maximal solution exchange speed. The exchange speed was calibrated for most of the neurons by moving the neuron to an equivalent position in front of barrel 2 and measuring how quickly the Ca²⁺ current was reduced; the current amplitude reached steady state in 40-70 ms, with an average of 50 ms. The recording chamber was perfused continuously with normal Ringer solution. This othogonal flow of Ringer solution served to wash off any transmitters diffusing from the end of the theta tube when its valve was off.

Electrophysiological recording and data analysis

The whole cell configuration of the patch-clamp method was used to measure Ca²⁺ currents (Hamill et al. 1981). Electrodes were pulled from glass hematocrit tubes (VWR Scientific, Seattle, WA) and had resistances of 1-3 M. The whole cell access resistance ranged from 3 to 8 M. Current was measured using a List EPC-7 patch-clamp amplifier with pipette and membrane capacitance cancellation. The BASIC-FASTLAB software and hardware package (INDEC Systems, Capitola, CA) was used to acquire and analyze data. Membrane potentials were corrected for a 2 mV junction potential. Current was filtered at 2 kHz and sampled at 5 kHz. Values are given as means ± SE.

The experimental protocols for studying the onset of inhibition were as follows. Baseline Ca²⁺ current was first measured 10-20 times with brief depolarizations to +10 mV, and then the rate of membrane-delimited inhibition was measured with the protocol in Fig. 1. The pulse interval was typically 2 s. Flow of transmitter-containing solution was begun at a certain time interval (t) before a test pulse (b) and turned off after inhibition reached the steady state level for that particular concentration (c). For t  2 s, the pulse interval was set to that value and NE flow was turned on at the beginning of pulse a. The protocol was repeated with different t values, and the amount of inhibition that developed during t relative to the steady state inhibition was plotted against t to obtain the onset time course. When measuring the speed of the slow muscarinic inhibition, we could use a simpler protocol because high time resolution was not needed. We simply set the pulse interval to 1 s, turned on the flow of oxo-M solution coincident with a test pulse, and measured continuously with maintained flow until the inhibition reached steady state. The time courses for the onset, reinhibition, and recovery were fitted with single exponential time functions to obtain their time constants. For the onset of inhibition, the time-axis intercept of the fitted function was taken as measure of the delay before the start of inhibition.

View larger version (17K): [in this window] [in a new window]   FIG. 1. Protocol for measuring onset speed of membrane-delimited inhibition. Membrane potential (Vm) was held at 80 mV and stepped to +10 mV every 2-4 s (top). After current amplitude stabilized (Ia), flow of transmitter-containing solution was turned on at t before pulse b and maintained until inhibition reached steady state (Ic).

Model

To describe the actions of NE, we devised the following kinetic model, which simulated the membrane-delimited inhibition of Ca²⁺ channels by agonist (A) acting via two populations of G-protein-coupled receptors (R₁ and R₂) where G, G*, and C stand for inactive G protein, activated G protein, and Ca²⁺ channels. The rate of G-protein activation was taken as proportional to receptor occupancy [AR], which is the sum of [AR₁] and [AR₂]. Channels are inhibited by the binding of activated G protein G*, which, in this case, we consider to be the -dimers of the G protein and not the -subunits (Herlitze et al. 1996; Ikeda 1996). The percent current inhibition as a function of time is calculated by r·[G*C], where r is the percent inhibition of macroscopic current when all channels are fully modulated. Simulation was carried out with the Euler integration method in time steps of 0.25 ms. For calculating the time course of recovery from inhibition, we set the NE concentration back to 0 after the inhibition had reached steady state, and the simulation was continued with the same parameters. To simulate reinhibition after a strong depolarization, we abruptly returned 80% of the G*C population to the G* + C state after the inhibition had reached steady state, and the simulation was allowed to continue.

The parameters of the model were found empirically. The pools of receptors, channels, and G proteins were in relative units: R₁ = 0.22, R₂ = 1, G = 25, C = 1. This corresponds to a small population of high-affinity receptors and a larger population of low-affinity receptors, with an excess of G proteins over receptors and channels. The rate constants were chosen to make the middle step, that of catalyzing production of G*, rate limiting. The final values used were k₁₁ = 3 × 10⁷ M¹ s¹, k₂₁ = 5 s¹, k₁₂ = 2 × 10⁶ M¹ s¹, k₂₂ = 150 s¹, k₃ = 0.16 s¹, k₄ = 1.1 s¹, k₅ = 4.9 s¹, k₆ = 1 s¹, r = 74%. The resulting dissociation constants for the two receptor populations are 0.17 (k₂₁/k₁₁) and 75 (k₂₂/k₁₂) µM, respectively. For comparison with dose-response data, the simulated steady-state percent inhibition () at different NE concentrations was plotted against the concentration and fitted with the following two-site equation where ₁ and ₂ are the maximal contributions of the first and second populations of binding sites and (K_1/2)₁ and (K_1/2)₂ are their half-inhibiting concentrations.

	RESULTS

Abstract Introduction Methods Results Discussion References

NE inhibits N-type Ca²⁺ channels in SCG neurons through membrane-delimited pathways. We first measured the speed of inhibition by NE at 80 mV. Figure 2A shows typical results in one cell. Currents (right) were measured with 10-ms depolarizations to +10 mV from a holding potential of 80 mV, and their peak amplitudes plotted on the left. At 300 ms before pulse b, the flow of 10 µM NE was turned on, and after another two voltage pulses, turned off. Approximately 40% of the maximal inhibition developed during this initial 300 ms. By repeating this protocol on the same cell while varying t, we obtained the time course of the onset of NE inhibition, shown in Fig. 2D. We similarly measured the speed of inhibition by somatostatin (SS), which inhibits N-type Ca²⁺ channels solely through the standard pathway. Figure 2B shows an example in another cell of inhibition after a 1.5-s time interval for 0.5 µM SS, during which ~50% of the maximal inhibition occurred.

View larger version (20K): [in this window] [in a new window]   FIG. 2. Onset of Ca2+ channel inhibition. A-C: peak Ca2+ current amplitudes (left; without leak subtraction) measured by test pulses at +0 mV from a holding potential of 80 mV. Bars mark period of transmitter application. Right: whole cell current traces (without leak subtraction) from pulses identified (left). Capacity current transients are distorted both by filtering at 2 kHz and by clipping in the digital sampling. A: inhibition of Ca2+ currents developed during a 300-ms exposure to 10 µM norepinephrine (NE). Peak Ca2+ current amplitudes measured every 4 s. NE flow was turned on 300 ms before pulse b and maintained for 2 more pulses. Dashed lines, an exponential curve fitted to recovery period. B: inhibition by a 2-s exposure to 0.5 µM somatostatin (SS). Peak current amplitudes (left) measured every 2 s by 8-ms pulses. Flow of SS was turned on at beginning of pulse a. C: inhibition by 20 µM oxotremorine-M (oxo-M) after treating the cell with 50 µM N-ethylmaleimide (NEM) for 2 min to isolate slow muscarinic pathway. Peak current amplitudes measured every second. Flow of oxo-M was turned on at beginning of pulse a. D: time course of inhibition for 3 cells shown in A-C. Lines are single exponential curves fitted for each cell with time constants of 0.73, 1.85, and 10 s for NE, SS, and oxo-M, respectively.

The muscarinic agonist oxotremorine M (oxo-M) inhibits N-type Ca²⁺ channels via two G protein pathways, the standard one and a slow pathway that requires a diffusible cytoplasmic second messenger. We could study muscarinic inhibition through the standard pathway in isolation by including 20 mM BAPTA in the pipette solution; this disrupts the slow pathway (Beech et al. 1991). The average exponential time constant of inhibition with 20 µM oxo-M was then 1.0 ± 0.09 s (n = 8). Conversely, we isolated the slow muscarinic pathway by treating the cell with 50 µM N-ethylmaleimide (NEM) for 2 min to inactivate PTX-sensitive G proteins and inhibition through the standard pathway (Shapiro et al. 1994). An example of the time course of inhibition through the slow muscarinic pathway is shown in Fig. 2C. We consistently observed a biphasic change in the current amplitude: an initial fast drop when oxo-M was applied was followed by a slow decline (fitted with an exponential function, solid line).

Figure 2D summarizes the time courses of inhibition by NE, SS, and oxo-M for the cells shown in Fig. 2, A-C. Fitting single-exponential functions to such time courses for each cell yielded the time constants and the delays in the onset of inhibition, summarized in Table 1.

What kinetic steps limit the rate of onset of inhibition? We first probed the initial binding of NE to its receptors. At sufficiently low concentrations, the agonist binding step would be rate limiting and as the concentration is increased, the rate of binding should increase proportionally. If the binding step were rate limiting throughout the concentration range, then the speed of current inhibition also would increase proportionally. Figure 3 shows the onset of inhibition at 0.5, 10, and 100 µM NE concentrations. The time constant at 10 µM (Table 1) is not statistically different from that at 0.5 µM, whereas that at 100 µM is statistically smaller than the other two at the P < 0.025 level. Thus with a 200-fold increase in concentration, the speed of inhibition increased by only a modest threefold (Table 1). This suggests that agonist-binding steps are not rate limiting above 0.5 µM NE and that slower steps after the binding determine the overall time course of channel inhibition.

View larger version (17K): [in this window] [in a new window]   FIG. 3. Concentration dependence of onset kinetics of NE inhibition. Three different groups of cells were exposed to 0.5, 10, and 100 µM NE, respectively. Relative inhibition at each time point was averaged across all cells in the group and plotted as mean ± SE. Lines, exponential fits (1  a·et/) with time constants  set at 1.17, 0.68, and 0.39 s. Intercepts of these functions on time axis are 0.14, 0.04, and 0 s, respectively.

Next we turned to the final step in the inhibition process. The inhibition by NE is voltage dependent and can be relieved partially by a strong depolarization (Elmslie et al. 1990). According to models of direct G-protein-channel interaction (Bean 1989; Boland and Bean 1993; Elmslie et al. 1990; Golard and Siegelbaum 1993), binding of activated G-protein -subunits (Herlitze et al. 1996; Ikeda 1996) causes the channels to go into a "reluctant mode" in which they need stronger depolarizations to open. Depolarization favors the dissociation of G proteins from the channels and thus a return to the normal, or "willing mode." However, when the membrane potential is returned to the holding potential after a strong depolarization, the inhibition redevelops as channels rebind G-protein subunits. Thus in this model, reinhibition after a strong depolarization should have the same kinetics as those of the G-protein-channel binding step during the onset of inhibition. We measured the reinhibition kinetics at 80 mV using the protocol shown in Fig. 4A. The difference of current during the two test pulses, I₂  I₁, was plotted against t, the interval between the strong depolarization and the second test pulse. The difference current was used for three reasons. 1) It represents channels that had G proteins bound during pulse 1 but unbound during the strong depolarization, and it will decline to 0 as they rebind G proteins during time t and become inhibited again. 2) Its time course, unlike that of the ratio I₂:I₁, is not influenced by the amplitudes of I₁ and I₂ or the extent of relief. 3) Its time course should be similar to that of the channel G-protein binding step during the onset of inhibition. Examples of reinhibition at three NE concentrations are shown in Fig. 4B. The time constants of reinhibition decreased from 160 ± 30 ms (n = 7) at 0.5 µM to 94 ± 11 ms (n = 5) at 1 mM, reflecting modestly higher active G-protein concentrations with increasing agonist concentration; however, the change is small considering the 2,000-fold range of transmitter concentration used. These values are about one-seventh to one-fourth of those for the overall onset process, suggesting that steps before the G protein-channel bindingand after agonist-receptor bindingcontribute more significantly to the overall time course of channel inhibition.

View larger version (18K): [in this window] [in a new window]   FIG. 4. Reinhibition kinetics with NE. A, inset: pulse protocol. Membrane holding potential was 80 mV. Two identical 10-ms test pulses (1 and 2) to +10 mV were given to measure peak Ca2+ currents (I1 and I2), with the 2nd pulse given after a variable time interval (t) following a 24-ms pulse to +125 mV. This pulse pattern was repeated 3 times at 4-s intervals for each t value, and results were averaged. Recording chamber was perfused continuously with NE solution. Current amplitudes of I1 and I2 from example cell exposed to 10 µM NE are shown. B: concentration dependence of reinhibition. Three different cells were exposed to 0.5, 10, and 100 µM NE, respectively, and time course of (I2  I1) was plotted. Three groups of data points then each were fitted with a single-exponential function, a + b·et/. Plotted points are 100 × [1 + (I2  I1)/|b|], and the time constants of exponential fits are 0.15, 0.13, and 0.083 s.

The recovery time course of I_Ca after removal of transmitters also can be described by an exponential time function, as shown by the dashed lines in Fig. 2, A and B. The time constants were 6.1 ± 0.2 s (n = 27) for 10 µM NE, 5.55 ± 0.03 s (n = 7) for 100 µM NE, and 10.6 ± 0.8 s (n = 16) for 0.5 µM SS. The recovery from slow muscarinic inhibition was often incomplete, with a time constant of 32 ± 6 s(n = 3).

To facilitate interpreting the experimental data for membrane-delimited inhibition by NE, we constructed a kinetic model to simulate the observations (see METHODS). A model with only one receptor population did not work because we could not account for a modest increase in rate and extent of inhibition both in the 0.5-10 µM range of NE and in the 10-100- to 100-1,000-µM range. If receptor saturation was placed in the lower range, we could get no further increase of rate and extent of inhibition in the upper range, and if the saturation was placed in the upper range, we got too much concentration dependence in the lower range. Therefore, we incorporated a second receptor population in the model. The simulated time courses for the onset, reinhibition, and recovery from inhibition are shown in Fig. 5A. By fitting single exponential functions to each of these time courses, we obtained the time constants for these simulated processes (Table 2). The simulated steady state inhibition at each NE concentration is plotted in Fig. 5B. Fitting the predicted dose-response relation with a two-receptor equation gave half-inhibiting concentrations (K_1/2) of 0.049 and 29 µM and maximal inhibitions of 61 and 10% for the two receptor populations. The two K_1/2 values are smaller than the dissociation constants for the two receptor populations, 0.17 and 75 µM, calculated from the ratio of forward and reverse rate constants, showing that the model can be called a "spare receptor" model and that inhibition approaches its maximum before all the receptors are occupied. Table 2 compares values obtained from the simulation with the experimental data and shows that there is good agreement. Thus a simple three-step model, with the slowest step being the middle one that generates a pool of activated G proteins, captures the main features of the modulation.

View larger version (15K): [in this window] [in a new window]   FIG. 5. Simulation of membrane-delimited NE inhibition. A: concentration dependence. Horizontal bar indicates duration of NE application. Four curves, from bottom to top, are for NE concentrations of 0.5, 10, 100, and 1,000 µM. Reinhibition time course (downward spike during NE application) is shown only for 10 µM NE for clarity. B: simulated dose-response relationship for NE inhibition (). Solid line, a fit using 2-site binding isotherm with half-inhibiting concentrations of 0.049 and 29 µM and maximal inhibitions of 61 and 10% for 2 receptor populations. Open square, measured percent inhibition by NE.

	DISCUSSION

Abstract Introduction Methods Results Discussion References

We have studied the kinetics of Ca²⁺ current inhibition in adult rat SCG neurons by three transmitters that use three distinct intracellular pathways. The membrane-delimited inhibition by NE and oxo-M develops with time constants of less than or near 1 s, whereas inhibition by somatostatin at 0.5 µM develops with a time constant of 2.1 s. With increasing concentration, the speed of NE inhibition increases, indicating that higher transmitter concentration results in more rapid receptor and G-protein activation. To develop a qualitative interpretation of these kinetic measurements, we reasoned that the inhibition process has three major steps: binding of agonist (A) to receptors (R), G-protein activation (G^*), and association of activated G-proteins to the Ca²⁺ channels (C) We find that the speed of NE inhibition does not increase in proportion to the NE concentration, and the reinhibition time constants, which reflect the kinetics of the last step based on the direct G protein-channel association model, are much shorter than the overall onset time constants. Thus neither the binding of NE to its receptors nor the association of G protein with Ca²⁺ channels appear to be the rate-limiting steps in the concentration range 0.5-100 µM where maximal or near maximal inhibition occurs. This suggests that the middle step, that of G-protein activation, contributes the most to the overall time course of inhibition. Based on two-dimensional diffusion considerations (Hille 1992), a 0.4-s time constant requires that the receptors, G proteins and the Ca²⁺ channels be located within <1 µm of each other in the cell membrane. Assuming that at presynaptic terminals the speed of modulation is the same or greater (Pfrieger et al. 1994), this means that receptors and G proteins need to be within <1 µm to participate in downregulating the Ca²⁺ currents that trigger transmitter release.

NE inhibits Ca²⁺ current through two membrane-delimited pathways: the standard one uses PTX-sensitive G proteins and the other uses PTX-insensitive G proteins. The steady state inhibition by 10 µM NE is ~55% when both pathways are present and ~30% through the PTX-insensitive pathway alone. Although the two pathways could have different kinetics, we did not observe two phases in the overall kinetics. This could mean that the two pathways have very similar kinetics, or that the inhibition through one pathway dominates such that the measurements are biased to the speed of that pathway. Isolating the PTX-insensitive pathway and measuring its kinetics might distinguish these two possibilities. One might imagine that the two receptor populations we postulated in our model could correspond to PTX-sensitive and -insensitive pathways, but the fractional contribution of the low-affinity receptors at 10 µM NE is too small to account for either of these pathways.

Although NE and SS inhibit Ca²⁺ current through similar pathways, at 0.5 µM the time constant of inhibition by SS is about twice as long as that for NE (see Table 1). This difference may arise from different forward binding rates of SS and NE to their respective receptors, because SS (molecular weight 1,640) is a much larger molecule than NE (molecular weight 169), from a lower abundance of SS receptors or from a slower catalysis rate for SS receptors to activate G proteins. Because of rapid desensitization with high concentrations of SS, it was not possible to explore the onset rate above 0.5 µM. It will be interesting to compare directly the binding rate constants for NE and SS in rat sympathetic neurons when they become available. The forward rate constant for NE binding to its receptors (k₁₁ and k₁₂) are not well determined by our data, but the values we used are several orders of magnitude smaller than what would be possible for a diffusion-limited reaction with a fully accessible receptor (>10⁹ M¹ s¹).

The recovery of Ca²⁺ currents after removal of NE and SS is near complete and has time constants ranging from 5.6 to 10.6 s, corresponding to rate constants of 0.09 to 0.18 s¹. These values fall between the in vitro GTPase rate of solubilized brain G_o proteins (~0.03 s¹) (Higashijima et al. 1987) and that of the deactivation of atrial myocyte I_K(ACh) current after removal of muscarinic agonist (~2.3 s¹) (Breitwieser and Szabo 1988), consistent with the idea that Ca²⁺ channels or other proteins, e.g., proteins of the regulator of G-protein signaling (RGS) family (Hunt et al. 1996; Watson et al. 1996), function as GTPase activating proteins and increase the hydrolysis rate of GTP bound to the -subunits of G proteins. The GTPase rate constant actually used in our model was 1.1 s¹.

Inhibition through the slow muscarinic pathway develops with a time constant near 10 s. This is similar to -adrenergic stimulation of L-type Ca²⁺ channels in cardiac cells measured with photo-released adenosine 3,5-cyclic monophosphate at 23°C (Nargeot et al. 1983), except the response there develops with a delay of ~6 s whereas our slow muscarinic inhibition has no delay. The slow muscarinic inhibition is clearly biphasic: an immediate drop of current amplitude precedes the slow exponential decline (Fig. 1C) (see also Fig. 6B in Beech et al. 1992). The rapid drop is brought into focus by the fast application methods. As NEM treatment (50 µM for 2 min) and overnight PTX treatment (500 ng/ml) reduced the SS inhibition to <10% (Shapiro et al. 1994) (data not shown), we believe that the standard pathway that muscarinic agonists use is blocked almost completely. Therefore the biphasic inhibition may be characteristic of the slow muscarinic pathway. The slow phase is presumably due to slow production and action of the cytoplasmic second messenger, whereas the fast phase may indicate that this PTX-insensitive G protein (G_q/11) also mediates a fast, membrane-delimited inhibition itself. Indeed it seems likely that every G-protein coupled pathway would generate -subunits that would have a fast membrane-delimited action. Another possibility that we consider less likely is that there still may be some PTX-sensitive G proteins not inactivated by PTX or NEM treatments and still able to mediate the membrane-delimited inhibition of the current.

In our whole cell recording configuration, recovery from slow muscarinic inhibition is often incomplete and has a time constant of ~32 s or a rate constant of ~0.03 s¹. This rate does fall within the range of the in vitro GTPase rates of G proteins but may well reflect the life time of the second messenger and any channel modification it induces.

Our measurements of the membrane-delimited inhibition are consistent with studies of other direct G-protein-mediated effects on ion channels at similar temperatures. In atrial myocytes, acetylcholine, acting on muscarinic receptors, rapidly opens a potassium channel [I_K(ACh)]. The receptors couple to PTX-sensitive G proteins whose -subunits then directly bind to the channels, causing them to open. The time course of activation of these channels consists of a delay of 63-275 ms and an exponential rise with time constants ranging between 100 and 1,000 ms (Szabo et al. 1993). In frog sympathetic neurons, the time for half-maximal inhibition of Ca²⁺ currents by NE and luteinizing hormone releasing hormone (LHRH) is ~2 s (Jones 1991). In guinea pig enteric neurons, NE released from presynaptic fibers or applied directly induced hyperpolarizations that peaked in 150 ms by opening a G-protein-gated K channel (Surprenant and North 1988). In hippocampal neurons, locally perfused 50 µM baclofen, acting through presynaptic -aminobutyric acid-B receptors, inhibits spike-evoked Ca²⁺ currents and synaptic transmission in 350 ms (Pfrieger et al. 1994). It thus seems that typical time constants for membrane-delimited G-protein modulation of channels are on the order of 0.2-1 s. They presumably depend on the spatial organization of the components of this signaling mechanism as well as the intrinsic reaction rate constants.

Facilitation and reinhibition have been studied extensively because they are characteristic of the voltage-dependent inhibition of N-type Ca²⁺ channels and provide tests for possible mechanisms of direct G-protein binding to the channels. Reinhibition kinetics were measured at room temperature in NG108-15 neuroblastoma-glioma cells with a -opiate agonist (Kasai 1992), in bullfrog sympathetic neurons with NE and LHRH (Boland and Bean 1993; Elmslie and Jones 1994), in embryonic chick sympathetic neurons with SS and NE (Golard and Siegelbaum 1993), and in rat sympathetic neurons with NE and vasoactive intestinal peptide (Ehrlich and Elmslie 1995). The reinhibition time constants we measured are slightly longer than those from previous studies (94-191 ms vs. 50-140 ms), even when comparing measurements in cells prepared from the same ganglion, rat SCG (Ehrlich and Elmslie 1995). The difference may arise from some difference in our cell dissociation, culture, or electrophysiological methods. There is good published evidence that reinhibition speeds up as agonist concentrations are raised, even when the inhibition of Ca²⁺ channels already has saturated (Ehrlich and Elmslie 1995; Elmslie and Jones 1994; Golard and Siegelbaum 1993). We also found that reinhibition is faster at 1 mM NE than at 10 or 0.5 µM NE. Such observations are consistent with the direct interaction of channels with G proteins in a system with spare receptors and G proteins.

Our kinetic simulations suggest several properties of the membrane-delimited inhibition by NE. First, there are at least two populations of receptors with different affinities for NE. This could arise from multiple subtypes of ₂ adrenergic receptors in SCG neurons or from a change of affinity of a single receptor subtype by its interaction with G proteins (Freissmuth et al. 1989). Also possible, considering the extremely low apparent affinity (75 µM) of the second population, is that this population describes nonspecific activation of other nonadrenergic G-protein-coupled receptors or competition with propranolol at -adrenergic receptors at these very elevated NE concentrations. The low-affinity receptor is about three times more abundant than the high-affinity receptor, in accord with a "spare-receptor" hypothesis. Second, there appears to be a single homogeneous population of G proteins. As discussed earlier, this suggests that the PTX-sensitive and -insensitive G proteins are kinetically indistinguishable in terms of their activation and interaction with the channels. They may have the same -subunits, or one of the G proteins might dominate the overall rate. Third, the rate constant for activating G proteins (k₃·[AR]) is at most 0.2 s¹ (0.16 × 1.22) when all receptors are occupied by agonists. Thus G-protein activation is much slower than the on-rate for receptor binding (k₁₁ and k₁₂) or the G-protein-channel binding rate (k₅). Fourth, the deactivation rate for the G proteins (k₄) is 1.1 s¹, which is much faster than the intrinsic GTPase rate of purified G proteins. As mentioned earlier, this suggests that there are GTPase activating proteins in the cell. Our model is highly simplified and represents the interaction of channel with G proteins as a simple bimolecular reaction without taking into account any of the effects of channel gating. This description may be suitable for cells held at 80 mV where the channels are closed and would not explicitly describe the consequences of depolarization, for which more rigorous models of G protein binding to channels have been given (Boland and Bean 1993; Golard and Siegelbaum 1993).

The simulated dose-response relationship for inhibition of Ca²⁺ current by NE matches well with our measurements at three NE concentrations. The two half-inhibiting concentrations from fits to the model are 0.049 and 29 µM. As might be expected, a previously reported half-inhibiting concentration of 0.2 µM obtained in a single-site analysis (Schofield 1990) falls between these values.

The initial concentration of glutamate at fast excitatory synapses may reach 1 mM with the release of a single transmitter vesicle (Clements et al. 1992). In this paper, we showed that at concentrations of NE or muscarinic agonists >1 µM, the N-type Ca²⁺ channels in neuronal somas can be inhibited through G-protein-coupled receptors in a fraction of a second. Recovery from this inhibition takes 6 s. Thus such inhibitory mechanisms participate in the regulation of synaptic transmission in a time domain between very fast mechanisms such as postsynaptic receptor desensitization and slow, second-messenger-mediated events such as protein phosphorylation.

	ACKNOWLEDGEMENTS

  We are indebted to Drs. Jeffry Issacson, Duk-Su Koh, Michael Loose, and Ken Mackie for critically reading the manuscript.

  This work is supported by National Institute of Neurological Disorders and Stroke Grant NS-08174 and the W. M. Keck Foundation.

	FOOTNOTES

  Address for reprint requests: B. Hille, Dept. of Physiology and Biophysics, G424 Health Science Bldg., University of Washington, Box 357290, Seattle, WA 98195-7290.

  Received 30 September 1996; accepted in final form 19 December 1996.

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