Kinetics of the subunit-specific nAChR model in response to Nic and/or Ach

Since the nAChRs are the exclusive points of action for Nic that affect DA activity in the VTA, a model of the nAChR that incorporates the response properties of the considered receptor subtypes is key for our approach. In addition, since the circuit model describes the mean activities of the DA and GABA neuronal populations, we describe the average macroscopic receptor-mediated currents as opposed to the fine details of single receptor kinetics and pharmacology. Accordingly, the receptor activation is elicited by the mean input rate of endogenous ACh release which is expressed as a concentration. We use a classical 4-state model of the nAChR adapted from Katz and Thesleff [22], [23] (see Text S2.) briefly described in [24]) accounting for subtype-specific activation and desensitization as recorded in response to Nic and ACh [25]–[30].

Fast nAChR activation in response to acetylcholine and/or nicotine (transition from deactivated/sensitized to activated/sensitized in the model; see Fig. 1B) gives rise to an initial peak current, and the slower desensitization reduces the current during sustained presence of the agonist (Fig. 2A and B for α4β2 and α7, respectively). After wash-out of agonists, the receptor recovers to the deactivated/sensitized state within seconds-to-minutes [7], [13] (see insets in Fig. 2A and B).

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Figure 2. Nicotinic acetylcholine receptor model responses to nicotine and acetylcholine.

Response properties of α4β2 (panels A,C,E) and α7 nAChRs (panels B,D,E). (A&B) Dynamics of α4β2- (A) and α7-containing nAChRs (B) in response to Nic. The dynamics of the activation, a, (purple lines) and sensitization, s, (orange lines) are shown during and after the exposure to a constant Nic concentration of 100 µM for 200 ms starting at ms. The normalized receptor activation, , is shown in blue and is proportional to the actual current. The inset shows the dynamics of the same variables on a longer time scale. (C&D) Dose-response curves of α4β2- (C) and α7-containing nAChRs (D) in response to Nic and ACh. The peak current mediated by the receptor during a 200 ms exposure to the respective agonist concentration is shown. The responses to Nic (ACh) are depicted in blue (red). The arrows indicate physiologically relevant nicotine concentrations [11], [31]. The half-maximum effective concentrations for ACh-evoked responses are indicated by the dotted black lines. (E) Reduction of the half-maximum response evoked by ACh in the presence of 0.5 µM Nic. The half-maximum effective concentration of the peak current in the absence of Nic is µM for α4β2, and µM for α7 nAChRs (green bars, see C and D). The red bars show the peak current in response to the same ACh concentration in the presence of a constant concentration of µM. See Table 1 for parameters.

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In order to account for the response differences between the two considered nAChR subtypes, two distinct sets of parameters were identified (see Models with respect to details of the parameter adjustment). Most importantly, the potency of nicotine and acetylcholine for the α4β2 nAChR is much higher than for the α7 nAChR (see dose-response curves in Fig. 2C and D). Hence the α4β2 but not the α7 nAChRs shows a partial response at the relatively low, physiologically relevant Nic concentration of 0.5 µM [11], [31] (indicated in Fig. 2C and D).

Both receptor subtypes show distinct temporal desensitization dynamics. Desensitization is relatively slow for α4β2 nAChRs: α4β2 nAChR-mediated currents decrease slowly over the course of agonist exposure (Fig. 2A) and the receptor recovers slowly (∼10 min) from the desensitized state after removal of the agonist (inset in Fig. 2A). On the contrary, at high agonist concentrations fast desensitization of α7-containing receptors completely suppresses the evoked current on the time scale of ∼100 ms (Fig. 2B) and the receptor recovers from desensitization within ∼2 min (inset in Fig. 2B).

The α4β2- and α7-nAChR model responses to ACh show another crucial difference when a physiologically relevant concentration of Nic is present (0.5 µM, Fig. 2E). Pretreatment with Nic reduces the half-maximum response by ∼73% for α4β2 nAChRs, whereas this response decreases only by ∼13% for α7 nAChRs (Fig. 2E). This is due to the lower potency of Nic for desensitizing α7 nAChRs as compared to α4β2 nAChRs, i.e., (see Models and Table 1). As a result, a smaller fraction of α7 nAChRs is driven into the desensitized state. Please note that the desensitized fraction of α4β2 nAChRs is ∼70%; their response is not completely abolished at 0.5 µM Nic. While Nic reduces the maximum amplitudes for both receptors, it does not affect the effective half-maximum ACh concentrations [24]. In the absence of ACh, Nic evokes a small activation of the receptors [24] that has also been seen experimentally for α4β2 nAChRs [12].

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Table 1. Parameters of nAChR activation and desensitization kinetics.

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In summary, the simple nAChR model is constrained to capture the key properties of the subtype specific responses to Nic and ACh. Most significant for this study is that Nic at physiologically relevant concentrations significantly activates and desensitizes α4β2 but not α7 receptors.

Data used to constrain the model parameters are obtained in the absence of acetylcholinesterase [25]–[30]. Under such conditions, persistent presence of Nic and of ACh both activates and desensitizes the nAChRs in the model. However, rapid ACh hydrolysis and a higher efficiency of Nic to desensitize the receptor seem to prevent ACh from desensitizing nAChRs in vivo [9], [10], [32]. In the following, we model conditions where acetylcholine is rapidly hydrolyzed and drives only the transition from deactivated to activated state (see Fig. 1B and C), hence desensitization is driven by nicotine only. We also investigate, later in the manuscript, how our results are affected in case of low acetylcholinesterase activity, that is, when also ACh drives receptor desensitization (see “ACh-driven desensitization through low acetylcholinesterase activity”).

The VTA responses to nicotine in vitro and in vivo

We next ask whether we can identify the specific circuit-level pathways of nicotine action in the VTA all the while reconciling the in vitro and in vivo data. First we show that the VTA model endowed with the description of the nAChR dynamics captures in vitro nicotine evoked modulation of excitatory and inhibitory inputs to DA neurons [18], [19]. We then demonstrate that a simple change in the constant afferent input strengths allows the model to also account for in vivo DA responses in both wild type and nAChR knockout mice [17].

Nicotine-dependent modulation of excitatory and inhibitory input to DA cells in vitro

Recordings from DA neurons in VTA slices show that bath application of 1 µM nicotine initially increases the frequency of IPSCs followed by a drop below baseline after Nic perfusion [19]. Furthermore, 1 µM nicotine evokes a robust enhancement of the spontaneous EPSC frequency in DA neurons [18]. To account for these data we start out by setting the afferent input strength to relatively low levels which characterizes the in vitro situation (illustrated by the scissors in Fig. 3A and B).

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Figure 3. Model VTA responses to nicotine in vitro.

Left hand panels (A,C,E and left side of panel G) show the results on GABAergic input changes to VTA DA cells, while the panels on the right-hand side (B,D,F and right side of G) depict results on glutamatergic input increases to VTA DA cells in response to 1 µM nicotine for 2 min starting at t = 1 min. (A&B) Illustration of the simulated experimental situation during in vitro experiments. Grey shaded parts and black crosses show pharmacologically blocked transmission pathways, and the scissors illustrate the truncation of the input pathways in vitro. (C&D) Time course of GABAergic, , (C) and glutamatergic input, , (D) changes to VTA DA neurons during and after Nic exposure (black bar on top of the panels, Nic time-course shown in insets). The increase (green) and the decrease (magenta in C) of the input currents with respect to baseline are illustrated in both panels. (E&F) Maximal change of GABAergic (E) and glutamatergic input currents (F) as a function of the Nic concentration applied. The lines show the results of the model for control conditions (in green in both panels and magenta for decrease in panel E), with α4β2 nAChRs blocked (cyan in panel E, and green in panel F), and with α7 nAChRs blocked (green and magenta in panel E, orange in panel F). The squares show experimental results adapted from [19] (E) and [18] (F) for different experimental situations : control conditions - green squares; with α7 nAChR specific antagonist - orange squares; and with antagonist for non- α7 nAChRs - cyan squares. (G) Comparison of relative input changes between model and experiment for the case of 1 µM nicotine for 2 min. Model results are shown with shaded bars and experimental results with filled bars. Both, GABAergic- (left) and glutamatergic input changes (right) are shown for the three discussed cases : control conditions - green and magenta, α4β2 nAChR blocked - cyan, and α7 nAChR blocked - orange and magenta (experimental data adapted from [18], [19]; µM and in all panels, see Table 1 and Models section for other parameters).

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In line with experiments, the nicotine-evoked initial increase of inhibition and subsequent drop below baseline are exclusively mediated by α4β2 nAChRs (Fig. 3C). The α4β2 nAChRs located on VTA GABAergic cells are activated by application of 1 µM Nic for 2 min. This increases the GABAergic population activity and in turn leads to an increase in the GABA input () to the DA cells (see green lines in Fig. 3C and E). The first peak of this response arises from fast receptor activation counterbalanced by slower desensitization. The subsequent steady and smaller increase follows the time course of Nic concentration build-up (Fig. 3C). After washout of the drug, a significant fraction of nAChRs remains desensitized and recovers at a slow time-scale (Fig. 3C). This desensitized fraction of nAChRs reduces the GABA cell response to the constant cholinergic input so that falls below baseline after nicotine is removed (illustrated in magenta in Fig. 3C and E). The recovery time course is governed by the maximal desensitization time constant, , of α4β2 nAChRs. Based on experimental data, that time constant was set to approximately 10 min (see Table 1; [17], [19]). To account for the block of Glu transmission during these experiments we set (see Models).

As expected, blocking α4β2 nAChRs in our model abolishes the Nic-evoked modulation in IPSC frequency (cyan line in Fig. 3E, [19]). In contrast, the α7 nAChRs have little or no impact on the response (green line and orange square in Fig. 3E, [19]). Our model accounts for the in vitro data in both the control, the α4β2- and the α7-nAChR blocked conditions. Note that in order to do so, the average cholinergic drive to the GABAergic cells needs to be set at µM, giving a 300% increase of GABAergic input at 1 µM Nic. The drop below baseline in our simulations matches experimental data without further fitting of the model (Fig. 3E).

The present model furthermore accounts for the increase of glutamatergic () input to the DA cells in response to a 2 min application of 1 µM Nic under GABA block (Fig. 3D). This concentration-dependent increase stems from activation of the presynaptic α7 nAChRs by nicotine (Fig. 3F). The model accounts for a number of experimental data: in control condition (green line and squares), in the presence of an α7 nAChR specific antagonist (orange line and square), and in the presence of an antagonist for non- α7 nAChRs (green line and cyan square).

To account quantitatively for the nicotine-induced increase in Glu input to DA cells () we set the mean firing rate of the Glu afferents () such that the relative increase attains 325% of baseline level. This intermediate value satisfies the experimental data obtained both in the control case (400% increase) and with the α4β2 nAChRs blocked (275% increase, see [19] and Fig. 3F). In the model, blocking the α4β2 nAChRs does not have an effect on the Glu input change since the nicotine-dependent increase stems from activation of α7 nAChRs only (Fig. 3B, D and F). We use the ACh rate as fixed above ( µM) which results in a weak activation of α7 nAChRs on average in the absence of nicotine.

In summary, we show that the model reproduces the relative change in IPSC and EPSC frequency to VTA DA neurons during in vitro nicotine perfusions. The model also accounts for the supra-linear (increasing slope) increase in EPSC frequency in the nicotine range from 0.1 to 1 µM Nic (green line and squares in Fig. 3F) and predicts a sub-linear increase (decreasing slope) for the IPSC frequency in the same range of nicotine (Fig. 3E). This difference stems from the dissimilar potencies of Nic for the α7 and the α4β2 receptors: the high Nic potency α4β2 starts to saturate in this range.

Nicotine-evoked increase of DA cell activity in vivo: Direct stimulation vs. disinhibition mechanisms

To translate the VTA circuit model to in vivo conditions, we kept all parameters fixed and modified only the afferent input strength. This “increased input” model accounts for the following in vivo data : (i) An intravenous injection of nicotine in wild-type mice increases the firing rate of DA cells. (ii) This increase is completely abolished in α4β2 knockout mice and is only weakly diminished in α7 knockout mice [17].

We identify two different plausible model regimes that could address the in vivo experiments. The scenario in which α4β2 nAChR-mediated action is predominantly exerted through activation on the DA cells is referred to as “direct stimulation” (Fig. 4A). The scenario where α4β2 nAChRs mainly influence the GABAergic activity through desensitization we term “disinhibition” (Fig. 4B). The model can be shifted between these scenarios by a change in the relative expression levels of α4β2 nAChRs on the DA and the GABA neurons using the parameter r. To illustrate the qualitative behavior of the model in each scenario, we use for direct stimulation and we set for disinhibition. We do not use the extreme case () for direct stimulation since the existence of α4β2 nAChRs on GABA cells has been shown experimentally [19], [33]. In general, the conditions for direct stimulation are met as long as and for disinhibition for (see below).

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Figure 4. Model VTA responses to nicotine in vivo.

Panels on the left-hand side (A,C,E) show results of the direct stimulation scenario (, µM, ) and panels on the right-hand side (B,D,F) depict results for disinhibition (, µM, ). (A&B) Illustration of the simulated experimental situation in vivo. Note the difference in α4β2 nAChR distribution between the direct stimulation (A, ) and the disinhibition case (B, ). (C&E) Normalized DA (C) and GABA neuron activity (E) in response to the application of 1 µM nicotine in case of direct stimulation. The full lines show the time course of the normalized (C) and (E) for three different durations of nicotine exposure, (as indicated by the bar on top of C). The full and the dashed blue lines depict the responses for low ( µM) and high endogenous cholinergic input rates ( µM), respectively ( min). (D&F) Normalized DA (D) and GABAergic neuron activity (F) in response to 1 µM nicotine for 2 min in case of disinhibition. The full lines show the time course of the normalized (D) and (F) for three different maximal desensitization time constants of α4β2 nAChRs, (as indicated in the upper panel). The full and the dashed blue lines depict the responses for high ( µM) and low cholinergic input rates ( µM), respectively ( min). (G) Comparison of model results (purple and orange bars) and experimental data (green bars) on relative DA neuron activity changes in response to 1 µM nicotine. The maximal relative increase of DA activity in wild type ( min for direct stimulation; and min with min for disinhibition) and mutant mice is shown (experimental data adapted from [17]). (H) Comparison of the total duration of elevated DA neuron activity with respect to the duration of Nic application, . The duration of elevated activity is taken to be the time between the two points where attains half-of-maximum activity (as illustrated by arrows in C and D and depicted by square and circle, respectively). This duration is plotted for direct stimulation (purple) and disinhibition (orange).

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Direct Stimulation (single cell level mechanism; ) : Our simulations reveal two important requirements necessary for direct stimulation to produce a boost of the DA activity on time scales observed in the data [17]. First, the cholinergic input rate to the VTA has to be low, activating the α4β2 nAChR only weakly ( µM; and ). Nic can further activate these nAChRs. Second, we see that the duration of elevated DA activity cannot outlast the presence of Nic (here 1 µM, Fig. 4C), implying that in this scenario the time-course of DA activity is directly determined by the time course of Nic in the VTA.

When the endogenous ACh input rate is increased ( µM), Nic produces only a very brief initial peak followed by a sustained depression of the DA activity (dashed blue line in Fig. 4C). In general we find that as long as more α4β2 nAChRs are expressed on DA than on GABA neurons (), the cholinergic input rate has to be below 0.38 µM in order to observe a net increase of DA activity in response to Nic application (note that we define a DA increase as a positive integral of the difference between the nicotine-modulated- and the baseline DA activity, ).

Disinhibition (circuit level mechanism; ) : Our simulations reveal two conditions necessary for the GABA-dependent mechanism of nicotine-evoked DA activity increases. First, we observe that in order for a 2 min exposure to 1 µM Nic to boost DA activity sufficiently to account for the data, the endogenous cholinergic input to the VTA must be high ( µM, Fig. 4D). Such cholinergic drive assures that nicotine mainly drives α4β2 receptor desensitization after a brief initial period of activation (Fig. 4D,F). Second, the nicotine-induced desensitization suppresses the GABAergic cell response to ACh, reducing it below baseline during and after the exposure to Nic (Fig. 4F, full lines). The return to baseline that follows the Nic removal is governed by the maximal desensitization time constant of α4β2 nAChRs (; Fig. 4D,F for three different values of ). The duration of the DA boost therefore outlasts the presence of Nic as it depends on the recovery of α4β2 nAChRs from desensitization and thereby the removal of inhibition.

When the ACh drive is decreased in the disinhibition case, the DA activity shows a drop below baseline (Fig. 4D, dashed blue line, µM), mirroring an increase of GABA cell activity (dashed blue line in Fig. 4F). In general, we find that the endogenous cholinergic input has to be larger than µM in order to see an increase of DA activity in response to Nic.

Our model points out that the two pathways can be disambiguated by the relative dynamical profiles of the DA and GABA neuron responses to nicotine. For the direct stimulation, the activity of the GABAergic neurons (Fig. 4E) matches the DA neuron activity but with a smaller amplitude (due to the smaller fraction of α4β2 nAChRs on GABAergic cells, ). The disinhibition circuit, on the other hand, shows that the profile of DA activity is a mirror-image of the GABAergic activity (compare Fig. 4D and F). For the level of Nic used in our simulations the DA neurons are slaved to the GABA neurons since only the high potency α4β2 receptors on GABA neurons are recruited.

In summary, we demonstrate that direct stimulation, through receptor activation, and disinhibition, through receptor desensitization, require distinct conditions in order to account for nicotine-induced DA activity changes in wild type, α4β2-, and α7-knockout mice (see summary in Fig. 4G). Endogenous cholinergic input rate has to be low for direct stimulation and high for disinhibition. Our simulations further uncover a tell-tale difference in the time course of the DA activity: for direct stimulation the duration of nicotine presence directly determines the duration of the DA response, whereas for disinhibition the recovery from desensitization of the α4β2 nAChRs defines the temporal scale of the DA activity. For a given duration of nicotine application these results predict longer-lasting increases in DA activity with disinhibition as compared to direct stimulation (in our model the difference is on the order of 12 min, Fig. 4H).

Predictions and experimental protocols to pin down the major pathway of nicotine action

In view of our results, the experimental data available so far are not sufficient to determine conclusively to what extent direct stimulation or disinhibition of DA cells is at the origin of DA responses to Nic. In addition to the differences we uncover above, we propose a series of feasible experiments to conclusively determine whether direct stimulation or dishinibition of DA cells is at the origin of DA responses to Nic. First, we examine the DA cell response for a range of endogenous cholinergic input rates and nicotine concentrations. We then vary the balance of α4β2 nAChRs between DA and GABA cells and investigate the DA response to Nic in the in vitro (low endogenous ACh input) and the in vivo (high endogenous ACh input) regimes.

In the first set of experiments we suggest to measure how the DA response to physiologically relevant nicotine injections (e.g., 1 µM Nic) depends on the endogenous ACh input rate. The endogenous ACh rate could be manipulated by stimulation or inhibition of activity in the laterodorsal tegmental nucleus or the pedunculopontine tegemental nucleus (Fig. 1A). We predict that for direct stimulation, the DA response should decrease with rising ACh input rate (Fig. 5A,C). In contrast, disinhibition implies that the total boost in DA activity should increase with the ACh input (Fig. 5B,C). These differences are explained as follows: the ACh drive sets the basal level of activated α4β2 nAChRs and available to be desensitized. At high ACh levels, for direct stimulation, the Nic-induced desensitization of α4β2 nAChRs reduces the excitatory drive to the DA, depressing the DA activity. In contrast, under disinhibition, α4β2 nAChR desensitization decreases the excitatory drive to the GABA cells (Fig. 5B,C), removing the inhibition to the DA population and hence liberating the DA activity. Consequently, the boost of DA activity would become more pronounced under high ACh input rates. The result that the endogenous ACh input rate determines the nAChR-mediated action of Nic holds for a large range of receptor characterizations when actylcholinesterase activity is high (see below and Text S1).

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Figure 5. Predicted dynamics of the DA neuron population in the VTA in response to varying cholinergic input rates and Nic concentrations in case of direct stimulation (A,D) and disinhibition (B,E).

Nic was applied for 10 min in the direct stimulation scenario, and for 2 min in the disinhibition scenario, whereas the endogenous ACh input rate is modeled to be constant (see text). (A&B) Temporal dynamics of DA neuron activity in response to 1 µM nicotine and varying endogenous cholinergic input rates (ACh range: 0.1-blue lines, 0.5, 1.0, 1.5, 1.77-red lines, 2.0 µM). (C) Maximal increase of DA activity in response to 1.0 µM Nic as a function of the cholinergic input rate (, ). (D&E) Temporal dynamics of DA activity in response to 0.5 µM (blue lines) and 3 µM nicotine (red lines) in case of direct stimulation (D, , µM, , ), or disinhibition (E, , µM, , ). (F) The maximal DA response as a function of applied Nic concentration is depicted for direct stimulation (orange line) and disinhibition (purple line). Data point (green) adapted from [17].

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A second set of experiments should examine the dependence of DA activity on the injected Nic dose at a pre-set endogenous ACh input rate. Our model indicates that the two pathways imply distinct time scales for the maximal DA activity. Direct stimulation results in a DA peak directly at the onset of Nic injection (Fig. 5D), whereas the disinhibition case gives a delayed peak after the Nic clearance (Fig. 5E). Moreover, for direct stimulation, the peak amplitude of the maximal DA response increases with rising Nic dose, but levels off rapidly (at ∼0.5 µM nicotine) for the disinhibition case (Fig. 5F). Again, the difference is explained by the dynamics of the α4β2 receptor in response to nicotine. The maximal increase for direct stimulation is due to fast activation of α4β2 nAChRs, whereas in the disinhibition case, the increase arises due to the delayed desensitization of these receptors. For direct stimulation, higher nicotine levels result in stronger receptor activation and an increase in peak amplitude. In contrast, the fraction of receptors driven into the desensitized state saturates at lower Nic for disinhibition with the peak amplitude saturating. This is because the maximal fraction ( µM) and the minimal rate of desensitization, , ( µM) are already attained at ∼0.5 µM nicotine (see Table 1). Note that in these simulations Nic is applied for 2 min in the case of disinhibition and for 10 min in the case of direct stimulation in order to achieve comparable durations of DA activity increases (compare Fig. 4H).

Shifting the balance of the α4β2 nAChR action between the DA and the GABA cells allows to further clarify how the interplay between α4β2 nAChR expression and cholinergic input levels conjointly determine DA activity. In order to do so, we study the acute DA response to 1 µM nicotine for in vitro (Fig. 6A) and in vivo conditions (Fig. 6B) while varying the value of r continuously. For the in vitro regime (low afferent input), the net DA activity is increased as long as (e.g., direct stimulation case: , red curve in Fig. 6A). On the other hand, in vivo (high afferent input) a net DA increase (after a small negative transient) requires (e.g., disinhibition case: , blue curve in Fig. 6B). The extent to which α4β2 nAChR mediated effects inhibit DA cells for low (GABA mediated inhibition for , Fig. 6A) and high (desensitization of α4β2-mediated inhibition for , Fig. 6B) endogenous ACh input scenarios depends on the strength of the glutamatergic input to DA cells. In the model, we set the ratio of Glu to GABAergic input weight, , as well as Glu to direct α4β2 nAChR input weight, , to unity. Had we chosen , and , for example, the DA cell activity would exhibit no decrease in activity neither in the in vitro nor in the in vivo scenarios (results not shown). The case , and would mean that DA cell activity is dominated by nicotine driven Glu input increases, giving more significance to the α7 nAChRs in generating nicotine-dependent DA responses.

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Figure 6. Temporal dynamics of DA neuron activity in response to 1 µM nicotine for 2 min for different values of r and afferent input strengths.

(A) The DA response in the presence of constant low cholinergic and glutamatergic afferent input to the VTA, i.e., in vitro like conditions ( µM,). (B) The DA response in the presence of constant high cholinergic and glutamatergic afferent input to the VTA, i.e., in vivo like conditions ( µM, ). In both panels, the distribution of α4β2 nAChRs is changed by varying the control parameter r in steps of 0.2 from 0 to 1 (as indicated). The examples with values of r as used for the direct stimulation (, red) and disinhibition (, blue) cases in this study are highlighted.

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Our analysis reveals key experimental manipulations that would pinpoint the mechanistic basis for nicotine effects in the VTA: manipulating the cholinergic drive to the VTA during nicotine application, and/or changing the nicotine concentration administered. Decreasing the cholinergic drive to the VTA further boosts DA activity increases for direct stimulation but diminishes them for disinhibition (Fig. 5C). The maximal DA response saturates at low nicotine concentrations (∼0.5 µM) for disinhibition, but continues to rise with higher nicotine concentrations for direct stimulation (Fig. 5F).

ACh-driven desensitization through low acetylcholinesterase activity

In all results reported so far, receptor desensitization is driven by nicotine only. We now investigate what happens if nicotine and acetylcholine together drive receptor desensitization of the dominant α4β2 subtype. This might occur whenever acetylcholinesterase activity is reduced. In the model, we vary the amount of ACh contributing to α4β2 nAChR desensitization by the parameter η and study the impact on GABA and DA neuron responses for direct stimulation and disinhibition. η varies between 0 - only Nic drives desensitization - and 1 - Nic and the ACh induce desensitization to equal amounts (see Models).

Direct stimulation is only marginally affected by ACh-driven desensitization since the α4β2-mediated receptor current predominantly arises from activation through Nic (Fig. 7A,C). The weak endogenous ACh rate induces initial desensitization which reduces the steady-state current but also diminishes the amount of further desensitization through Nic resulting in a negligible net effect (Fig. S1).

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Figure 7. Temporal dynamics of GABA and DA neuron activity in response to 1 µM nicotine in case α4β2 receptor desensitization is driven by Nic and ACh.

(A,C) GABA (A) and DA (C) neuron activity in the direct stimulation case (same as in Fig. 4C,E full blue lines; , µM, , ) for different efficacies of ACh to drive α4β2 receptor desensitization (η given in panel A). (B,D) GABA (B) and DA (D) neuron activity in the disinhibition case (, µM, , ) for different efficacies of ACh to drive α4β2 receptor desensitization (η given in panel B, see Models).

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In contrast, for the disinhibition scenario, the α4β2 nAChR-mediated current changes from inhibitory to excitatory with increasing the amount of ACh-driven desensitization (Fig. 7B). The high endogenous ACh rate induces strong desensitization and further desensitization by Nic is not enough to overcome receptor activation (Fig. S1E). In turn, GABA neuron activity is increased in response to Nic inhibiting DA neuron activity (purple lines in Fig. 7 B,D).

In summary, acetylcholinesterase activity determines Nic action for disinhibition but has little effect on direct stimulation. In case Nic action is mediated through GABAergic neurons (disinhibtion), varying ACh hydrolysis rates could provide a dynamical means to control Nic action.

Mean-field description of dopaminergic and GABAergic VTA neurons

The temporal dynamics of the average activities of dopaminergic and GABAergic neuron populations is characterized by(1)(2) and are the mean firing rates of the DA and GABAergic neuron populations, respectively. and are membrane time constants of the neurons specifying how quickly the neurons integrate input changes ( ms). and characterize excitatory inputs to both neuron populations mediated by glutamate receptors and α4β2-containing nAChRs, respectively. is the local inhibitory input to DA neurons emanating from VTA GABAergic neurons. is an intrinsic current of DA cells giving rise to intrinsic activity in the absence of external inputs [62]. We further assumed that accounts for other input sources which are not affected by nicotine and therefore provide a constant background input (e.g., α6-containing nAChR mediated cholinergic input to DA cells [63]; inhibitory input originating in other brain regions, etc.). is the steady-state current-to-rate transfer function. For simplicity, we assumed that Φ(I) is threshold-linear: if and otherwise. The control parameter r sets the balance of α4β2 nAChR action through GABAergic or DA cells in the VTA. For : α4β2 containing nAChRs act through GABAergic neurons only, whereas for : α4β2 receptors influence DA neurons only. Both neuron populations are influenced by α4β2 nAChRs for intermediate values of r. In practice, this balance is determined by the expression level of α4β2 nAChRs, the overall impact of local GABAergic inputs on DA activity, and by the location of α4β2 nAChRs on the somatodendritic tree of DA and GABAergic cells.

The input currents in Eqs. (1) and (2) are given by(3)(4)(5)where the 's (with x = G, Glu, α4β2) specify the total strength of the respective input since the activation variables (, , ) are normalized to vary between 0 and 1. For our qualitative investigations, we used (with x = G, Glu, α4β2). Inhibitory input to DA cells, , depends on the GABAergic neuron population activity, . Glutamatergic input is provided either by upstream glutamatergic activity, , or by activation of α7 nAChRs on presynaptic glutamatergic terminals, (see below). Nicotine-evoked glutamatergic transmission is independent of action potential activation in presynaptic neurons [18]. Hence, either of both inputs can fully activate glutamatergic transmission(6)The activation of α4β2 nAChRs, (see next section), determines the level of direct excitatory input, , evoked by nicotine or acetylcholine [63].

Modeling the activation and desensitization of nAChRs driven by Nic and ACh

We implemented nAChR activation and desensitization as transitions of two independent state variables: an activation gate and a desensitization gate. This yields four different states of the nAChR: deactivated/sensitized (also resting or responsive state), activated/sensitized, activated/desensitized and deactivated/desensitized state (Fig. 1B). Of those states, three are closed and the activated/sensitized state is the only open state of the receptor in which it mediates an excitatory current. Note that compared to other models of allosteric transitions of the nAChR, we chose to leave aside the rapidly and slowly desensitized states [64], deeper-level desensitized state or inactivated states [65]. Such states are collapsed in the desensitized state here. Our model was modified from the cyclic desensitization model of Katz and Thesleff [22] where “effective” and “refractory” in their model refer to sensitized and desensitized here, respectively (see Text S2.). Assuming independent transitions of the activation and the desensitization variables entails another simplification compared to cyclic allosteric transition schemes. In our model, the reaction rates are the same on opposite sides of the reaction cycle (Fig. 1B), e.g., the rate from deactivated/sensitized to activated/sensitized is the same as the transition rate from deactivated/desensitized to activated/desensitized.

The model accounts for the opening of the channel (transition from deactivated/sensitive to activated/sensitive, Fig. 1B,C) in response to both Nic and ACh; while desensitization is driven by nicotine and ACh if (transition into the activated/desensitized state, Fig. 1B,C). The inverse transitions, i.e., from activated to deactivated and from desensitized to sensitized, occur after the removal of Nic and ACh.

The mean total activation level of nAChRs (, ) is modeled as the product of the fraction of receptors in the activated state, a, and the fraction of receptors in the sensitized state, s. The total normalized nAChR activation is therefore with x = α4β2 or α7. The time course of the activation and the sensitization variables is given by(7)where refers to the Nic/ACh concentration-dependent time constant at which the asymptotically achievable steady-state is attained. The maximal achievable activation or sensitization, for a given Nic/ACh concentration, or respectively, are given by Hill equations of the form(8)(9) and are the half-maximal concentrations of nAChR activation and sensitization, respectively. The factor α>1 accounts for the higher potency of Nic to evoke a response as compared to ACh: , [26]–[28], [30] (see Fig. 2C,D and Table 1). and are the Hill coefficients of activation and sensitization. η varies between 0 and 1 and controls the fraction of the ACh concentration driving receptor desensitization.

The transition from the deactivated to the activated state is fast (∼µs, ms) [64] compared to the time scales investigated here that are of the order of seconds to minutes. We therefore simplified the activation time constant, , to be independent of the acetylcholine/nicotine concentration, i.e., . The time course of Nic-driven desensitization is characterized by a concentration-dependent time constant(10) refers to the recovery time constant from desensitization in the absence of ligands (). is the fastest time constant at which the receptor is driven into the desensitized state at high ligand concentrations. is the concentration at which the desensitization time constant attains half of its minimum (). η varies between 0 and 1 and controls the fraction of the ACh concentration influencing the desensitization time constant. The parameters describing activation and desensitization of the two nAChR subtypes were taken from a number of studies on heterologously expressed human nAChRs and are listed in Table 1 [25]–[30]. Note that we used min for α4β2 nAChRs in order to match the time course of DA activity recorded in vivo, while Fenster et al. [25] recorded a value of min in vitro during experiments at room temperature. We adjusted the minimal time constant by which the receptors are driven into the desensitized state, , such that the model currents qualitatively captured the experimentally measured time course of nAChR currents evoked by Nic and ACh [25]–[30]. This fit yielded a faster minimal desensitization time constant for the α7 nAChR, i.e., (Table 1).

In our simulations, we assumed that both the nicotine bath application and the intravenous injection imply a slow build-up of the nicotine concentration at the site of the receptor. That is, the applied nicotine concentration is not immediately available but increases/decays exponentially with a time constant of 1 min. The fast activation of nAChRs, a (transition from deactivated/sensitive to activated/sensitive, Fig. 1B), was therefore taken to be in steady-state with the Nic concentration at all times (except in Fig. 2).

Clearly, the above presented simple model of nAChR activation and desensitization did not resolve all the details of nAChR kinetics. For example, it was assumed that ACh- and Nic-evoked responses reach the same maximal amplitude and that, despite different potencies, Nic and ACh dose-response curves can be characterized by the same Hill coefficient. These assumptions are approximately met for α7-containing nAChRs [66]. ACh evokes however twice the response of Nic with human α4β2 nAChRs in a study by Chavez-Noriega et al. [66], but the same response according to other studies [28], [67]. We simplified the dose-response curve using a single Hill equation, rather than using a sum of two Hill equations as suggested by Buisson and Bertrand [28]. Nevertheless the simple model presented here captured the qualitative time course of nAChR currents evoked in response to Nic and ACh exposures (see Results, [24]). It furthermore quantitatively accounts for the time course of DA and GABA neuron activity responses in vivo for single and repetitive Nic applications [37].