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  Implications of G-protein-mediated Ca^sup 2+^ channel inhibition for neurotransmitter release and facilitation Bertram, Richard; Behan, Matthew. Journal of Computational Neuroscience7.3 (Nov/Dec 1999): 197- 211. Headnote  Abstract. G-protein-mediated inhibition of Ca2C current is ubiquitous in neurons, and in synaptic terminals it can lead to a reduction in transmitter release (presynaptic inhibition). This type of Ca2C current inhibition can often be relieved by prepulse depolarization, so the disinhibition of Ca2C current can combine with Ca2Cdependent mechanisms for activity-induced synaptic facilitation to amplify this form of short-term plasticity. We combine a mathematical model of a G-protein-regulated Ca2C channel with a model of transmitter secretion to study the potential effects of G-protein-mediated Ca2C channel inhibition and disinhibition on transmitter release and facilitation. We investigate several scenarios, with the goal of observing a range of behaviors that may occur in different synapses. We find that the effects of Ca2C channel disinhibition depend greatly on the location and distribution of inhibited channels. Facilitation can be greatly enhanced if all channels are subject to inhibition or if the subpopulation of channels subject to inhibition are located closer to release sites than those insensitive to inhibition, an arrangement that has been suggested by recent experiments (Stanley and Mirotznik, 1997). We also find that the effect of disinhibition on facilitation is greater for longer action potentials. Finally, in the case of homosynaptic inhibition, where Ca2C channel inhibition occurs through the binding of transmitter molecules to presynaptic autoreceptors, there will be little reduction in transmitter release during the first of two successive bursts of impulses. The reduction of release during the second burst will be significantly greater, and if the unbinding rate of autoreceptors is relatively low, then the effects of G-protein-mediated channel inhibition become more pronounced as the duration of the interburst interval is increased up to a critical point, beyond which the inhibitory effects become less pronounced. This is in contrast to presynaptic depression due to the depletion of the releasable vesicle pool, where longer interburst intervals allow for a more complete replenishment of the pool. Thus, G-protein-mediated Ca2C current inhibition leads to a reduction in transmitter release, while having a highly variable amplifying effect on synaptic facilitation. The dynamic properties of this form of presynaptic inhibition are very different from those of vesicle depletion.  Keywords: synapse, plasticity, presynaptic inhibition, secretion, mathematical model Introduction Many synapses are subject to presynaptic inhibition by a host of chemical messengers, including GABA, adenosine, glutamate, dopamine, and serotonin. These messengers typically inhibit transmitter release by activating presynaptic KC currents (Scholfield and Steel, 1988; Thompson and G ahwiler, 1992; Vaughan et al., 1997), inhibiting presynaptic Ca2C currents (Boehm and Betz, 1997; Chen and van den Pol, 1997, 1998; Dittman and Regehr, 1996, 1997; Qian et al., 1997; Takahashi et al., 1996, 1998; Toth et al., 1993; Wu and Saggau, 1994a, 1995), or affecting some process downstream of Ca2C entry (Boehm and Betz, 1997; Dittman and Regehr, 1996). Activation of a KC current indirectly reduces Ca2C entry and the subsequent release ofneurotransmitter, either by blocking action potential propagation into the presynaptic terminal or by shortening the duration of the action potential. Inhibition of Ca2C current acts directly by reducing the influx of Ca2C during an impulse. Regardless of the mode of action, the chemical regulators are often linked to presynaptic inhibition through a G protein pathway, whereby the agonist binds to presynaptic receptors, leading to activation of G proteins that bind to and modify the behavior of one or more proteins linked to transmitter release. The mechanism and properties of G-proteinmediated inhibition of Ca2C channels have been the focus of much research in recent years, due largely to the apparent ubiquity of this modulatory pathway (Hille, 1994). Data suggest that G[empty set][degrees] subunits of activated G proteins bind to the AE1 subunit of the Ca2C channel in a voltage-dependent manner, so that binding is stabilized at low voltages and destabilized at depolarized voltages (see Dolphin, 1998, for review). This voltage dependence allows for the relief of Ca2C channel inhibition by depolarizing prepulses. Such disinhibition has been observed in several preparations using long (>10 msec) prepulses (Bean, 1989; Grassi and Lux, 1989; Patil et al., 1996), and recent studies have shown that bursts of action potentials or short depolarizations are capable of relieving Ca2C current inhibition (Brody et al., 1997; Williams et al., 1997), demonstrating that disinhibition can be induced by physiological stimuli. Although the mechanism of Ca2C current inhibition is still under investigation, data suggest that the binding of one or more G proteins to a Ca2C channel puts the channel into a reluctant state, in which the probability of channel opening is greatly reduced (Bean, 1989). As a result, G-  protein-bound channels are unlikely to open during a brief depolarization such as an action potential, and only those channels in an unbound or willing state contribute to the Ca2C current. Depolarizing prepulses would then disinhibit the current by converting some of the channels from the reluctant state to a willing state by dislodging bound G proteins (Bean, 1989; Zamponi and Snutch, 1998). Because synaptic vesicle exocytosis is activated by intraterminal Ca2C (Katz and Miledi, 1968),neurotransmitter release will likely be reduced by inhibition of Ca2C channels in the synaptic terminal. In addition, chemical messengers that activate inhibitory G proteins can in principle have a profound influence on short-term synaptic plasticity. Indeed, several studies have shown that paired-pulse facilitation, where evoked release is increased when preceded by an earlier stimulus, is greater in the presence of G protein agonists (Dittman and Regehr, 1997; Dunwiddie and Haas, 1985; Isaacson et al., 1993; Shen and Johnson, 1997). Although the mechanism of facilitation has not been established, two hypotheses propose that facilitation is due primarily to either a prepulse-induced elevation of free Ca2C or to the residual binding of Ca2C to synaptic proteins (Katz and Miledi, 1968; Stanley, 1986; Kamiya and Zucker, 1994). Thus, release during the second stimulus is enhanced by residual free or bound Ca2C even if the Ca2C influx is identical during each stimulus. Presumably, the extra facilitation produced by G protein agonists is due to partial disinhibition of the Ca2C current by the first stimulus, so that the Ca2C influx is greater during the second stimulus, compounding the effects of residual free or bound Ca2C. (In some cases, some of the apparent extra facilitation may be due to a reduction in presynaptic depletion of the readily releasable vesicle pool (Dunwiddie and Haas, 1985).) In support of this mechanism, Williams et al. (1997) observed a 20% increase in whole-cell Ca2C current during the second of a pair of short depolarizations. Because transmitter release has a superlinear dependence on Ca2C current (Augustine and Charlton, 1986), it is likely that relief of inhibition will have a superlinear effect on facilitation. In the present report we combine a mathematical model of a G-protein-regulated Ca2C channel with a model of transmitter secretion to study the potential effects of G-protein-mediated channel inhibition and disinhibition on transmitter release and short-term synaptic plasticity. The aim of this study is to examine several scenarios so as to establish an intuition for the types of behavior that may occur in different synapses. We first examine a scenario in which all of the presynaptic Ca2C channels are susceptible to Gprotein-mediated  inhibition. This analysis suggests that facilitation produced during a short burst can be greatly enhanced by Ca2C channel disinhibition, particularly if the G protein agonist concentration is high and if action potentials have a relatively long duration. Thus, under certain conditions, G protein regulation of Ca2C channels can play a major role in short-term synaptic plasticity. We next examine a scenario in which only half of the Ca2C channels are susceptible to G protein regulation. This is motivated by the findings that some Ca2C channel types are more susceptible than others to regulation (see Wu and Saggau, 1997, for review) and by data from the calyx-type nerve terminal of the chick ciliary ganglion synapse showing that only Ca2C channels that are coupled to release sites through the synaptic protein syntaxin are susceptible to regulation (Stanley and Mirotznik, 1997). We find that if both regulated and unregulated channels lie at equal distances from the release sites, then the enhanced facilitation of the regulated population produces only a minor enhancement of facilitation of the total release (the sum of the release from both subpopulations of release sites). However, if regulated channels are situated closer to release sites (as may be the case if they are bound to the sites via syntaxin), then the enhanced facilitation of this closer subpopulation can have a much larger effect on the overall facilitation. Thus, the effect of G protein regulation on synaptic facilitation depends critically on the relative locations of regulated and unregulated channels. Finally, we examine a scenario in which the concentration of G protein agonist is determined by the amount of transmitter released. This is motivated by the presence of metabotropic transmitter autoreceptors in many presynaptic terminals (Langer, 1987; Starke et al., 1989; Chen and van den Pol, 1998).We find that the agonist released during the first of two bursts of impulses has little effect on release during this burst, due to depolarization-associated disinhibition of Ca2C channels. However, activated G proteins bind to channels during the interburst interval when the membrane is hyperpolarized, so presynaptic inhibition can be profound during the subsequent burst. This is in contrast to presynaptic depression mediated by the depletion of releasable quanta, in which case release would be reduced during each of two successive bursts. In addition, if the unbinding rate of autoreceptors is relatively low, then the effects of G-protein-mediated channel inhibition become more pronounced as the duration of the interburst interval is increased up to a critical point, beyond which the inhibitory effects become less pronounced. In contrast, the residual inhibitory effects of vesicle depletion
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