Contribution of synchronized GABAergic neurons to dopaminergic neuron firing and bursting

Presented herein ventral tegmental area microcircuit model challenges the classical view that GABA neurons exclusively reduce dopamine neuron firing and bursting. Rather, high levels of synchrony amongst GABA neurons can produce increases in firing and bursting of the dopamine neuron. Dopamine bursting can be produced in the absence of bursty excitatory input, if the neuron receives transiently synchronized GABA input. We provide an explanation of the mechanisms whereby GABA neurons could contribute to dopamine neuron burst firing.

Abstract

In the ventral tegmental area (VTA), interactions between dopamine (DA) and γ-aminobutyric acid (GABA) neurons are critical for regulating DA neuron activity and thus DA efflux. To provide a mechanistic explanation of how GABA neurons influence DA neuron firing, we developed a circuit model of the VTA. The model is based on feed-forward inhibition and recreates canonical features of the VTA neurons. Simulations revealed that γ-aminobutyric acid (GABA) receptor (GABAR) stimulation can differentially influence the firing pattern of the DA neuron, depending on the level of synchronization among GABA neurons. Asynchronous activity of GABA neurons provides a constant level of inhibition to the DA neuron and, when removed, produces a classical disinhibition burst. In contrast, when GABA neurons are synchronized by common synaptic input, their influence evokes additional spikes in the DA neuron, resulting in increased measures of firing and bursting. Distinct from previous mechanisms, the increases were not based on lowered firing rate of the GABA neurons or weaker hyperpolarization by the GABAR synaptic current. This phenomenon was induced by GABA-mediated hyperpolarization of the DA neuron that leads to decreases in intracellular calcium (Ca²⁺) concentration, thus reducing the Ca²⁺-dependent potassium (K⁺) current. In this way, the GABA-mediated hyperpolarization replaces Ca²⁺-dependent K⁺ current; however, this inhibition is pulsatile, which allows the DA neuron to fire during the rhythmic pauses in inhibition. Our results emphasize the importance of inhibition in the VTA, which has been discussed in many studies, and suggest a novel mechanism whereby computations can occur locally.

NEW & NOTEWORTHY

Presented herein ventral tegmental area microcircuit model challenges the classical view that GABA neurons exclusively reduce dopamine neuron firing and bursting. Rather, high levels of synchrony amongst GABA neurons can produce increases in firing and bursting of the dopamine neuron. Dopamine bursting can be produced in the absence of bursty excitatory input, if the neuron receives transiently synchronized GABA input. We provide an explanation of the mechanisms whereby GABA neurons could contribute to dopamine neuron burst firing.

the dopamine (da) system is an essential component of the neural circuits that mediate cognitive and executive functions. DA neurons exhibit two distinct firing modes, spontaneous background firing and high-frequency firing that occurs in short burst-like episodes. Background firing is a tonic low-frequency pattern, which is maintained even in the absence of synaptic inputs. High-frequency firing is presumably elicited by transient activation of synaptic inputs, and, in particular, N-methyl-d-aspartate (NMDA) receptor (NMDAR) activation (Chergui et al. 1993; Deister et al. 2009; Overton and Clark 1997; Johnson et al. 1992; Johnson and Wu 2004). In vivo, short-duration, high-frequency spiking (bursts) are driven by salient environmental stimuli (Bromberg-Martin et al. 2010; Paladini and Roeper 2014; Schultz 1998). The purpose of this study was to explore the local-circuit dynamics that mediate DA neuron firing.

The ventral tegmental area (VTA) and substantia nigra (SN) are the principal regions of the ventral midbrain containing DA neurons. Both regions also contain local GABA neurons that powerfully modulate DA neuron activity via direct, monosynaptic inhibitory connections (Bourdy and Barrot 2012; Johnson and North 1992a; Omelchenko and Sesack 2009; van Zessen et al. 2012). VTA DA neurons express GABA_A receptors, and tonic GABA release has been shown to inhibit DA neurons (Theile et al. 2011; Westerink et al. 1996). In vivo, stimulation of VTA GABA neurons inhibits DA neurons (Lecca et al. 2012; Tan et al. 2012), whereas inhibition of VTA GABA neurons evokes a burst via disinhibition of the DA neurons (Bocklisch et al. 2013; Johnson and North 1992b; Xia et al. 2011). Similarly, under tonic NMDA input, phasic removal of GABAR conductance in vitro leads to burst firing in the DA neuron (Lobb et al. 2010, 2011b). Thus, to enable in vivo bursts via disinhibition, both receptors should be active, with their conductances balanced, so that the DA neuron fires at low background firing frequencies (1–5 Hz). This suggests that GABAergic inhibition plays a key role in the maintenance of tonic and phasic firing of DA neurons. Thus a large body of literature suggests that a direct GABAergic input inhibits the DA neurons.

A number of studies, however, have observed “paradoxical” excitation of DA neurons by the GABA inputs (Celada et al. 1999; Grace and Bunney 1979; Tepper and Lee 2007). The increase in firing and bursting was explained by the recruitment of a disynaptic inhibitory pathway that disinhibits the DA neuron and a more depolarized GABA_A reversal potential in DA neurons. Further, recent in vivo experiments challenged the classical view that GABA signaling in the VTA exclusively reduces the DA neuron firing and bursting (Tolu et al. 2012). The authors showed that the excitation of GABA neurons by endogenous acetylcholine (ACh) elevates bursting in the VTA DA neurons. Further, Lodge and Grace (2006) showed that an input from the laterodorsal tegmental nucleus (LDT) is required for burst firing in VTA DA neurons. This data points to the possible importance of the GABA input from LDT in eliciting DA neuron bursts, because the authors discounted the possibility of the involvement of glutamate (Glu) and cholinergic components of the input. Similarly, under certain conditions, exceptions to the view that GABA reduces neuron firing have been described in other regions of the mature brain, including the hippocampus, amygdala, and the cortex (Alger and Nicoll 1979; Andersen et al. 1980; Gulledge and Stuart 2003; Woodruff et al. 2006). In addition, the effect of brief pulses of GABA on firing of the DA neuron may differ significantly from the inhibitory effect produced by tonic GABAR activation caused, for example, by the action of agonists or a persistent asynchronous barrage of interneuron firing. GABA_A mediated inhibitory postsynaptic potentials can facilitate the occurrence of postinhibitory rebound spikes due to their rapid kinetics in the cortex and hippocampus (Adhikari et al. 2012; Cobb et al. 1995; Diba et al. 2014). DA neurons are also able to fire rebound spikes by rapid recovery from hyperpolarization (Grace 1991; Tateno and Robinson 2011). Postinhibitory rebound leads to a transient frequency increase after prolonged hyperpolarization by recruiting low-threshold Ca²⁺ and hyperpolarization activated I_h currents. These studies highlighted the significance of local interactions between DA and GABA neurons and suggested that burst firing is a cooperative effect produced by interplay between excitation and inhibition.

To delineate the diverse effects of GABA neurons on DA neuron firing, we propose a computational model of the local feed-forward VTA microcircuit. We show that synchronization of VTA GABA neurons may be a critical component of the different regimes of DA neuron firing observed experimentally. Further, we demonstrate that, with increasing levels of synchrony among GABA neurons, increases in firing and bursting of the DA neuron can be achieved. We propose a novel mechanism by which synchronization of a direct GABA input, without a decrease in its average frequency or a change in the GABAR reversal potential, can facilitate DA neuron bursting.

MATERIALS AND METHODS

We propose a biologically plausible, yet sufficiently simple model of the microcircuitry within the VTA, consisting of a population of GABA neurons innervating one DA neuron (Fig. 1). Our model is a feed-forward inhibitory circuit assuming that dynamics of VTA GABA neurons is not influenced by the activity of DA neurons. Some GABA neurons express D2 receptors (Steffensen et al. 2010), but no synapses were found that can provide a direct feedback from VTA DA to VTA GABA neurons. Due to the very slow dynamics of extrasynaptic DA and slow activation of the D2 receptors, the effects that we are studying in this paper occur at a much shorter timescale. This justifies the feed-forward inhibition framework for the VTA circuit. Both DA and GABA neurons receive Glu inputs, mimicking synaptic inputs from brain structures projecting to the VTA. The model of the DA neuron is a conductance-based one-compartmental model modified from Ha and Kuznetsov (2013).

$$\{\begin{array}{c}{c}_{\text{m}}\frac{\text{d}v}{\text{d}t}=\stackrel{I_{\text{Ca}}}{\overbrace{g_{\text{Ca}}\left(v\right)\left(E_{\text{Ca}}-v\right)}}+\stackrel{I_{\text{KCa}}+I_{\text{K}}}{\overbrace{\left[g_{\text{KCa}}\left(\left[{\text{Ca}}^{\text{2}+}\right]\right)+g_{\text{K}}\left(v\right)\right]\left(E_{\text{k}}-v\right)}}\\ \underset{I_{\text{sNa}}}{+\underbrace{g_{\text{sNa}}\left(v\right)\left(E_{\text{Na}}-v\right)}}+\underset{I_{\text{leak}}}{\underbrace{g_{\text{l}}\left(E_{\text{l}}-v\right)}}+\underset{I_{\text{syn}}}{\underbrace{I_{\text{NMDA}}+I_{\mathrm{A}\mathrm{M}\mathrm{P}\mathrm{A}}+I_{\text{GABA}}}},\\ \frac{\text{d}\left[{\text{Ca}}^{\text{2}+}\right]}{\text{d}t}=\frac{\text{2}\beta }{r}\{\frac{\left[g_{\text{Ca}}\left(v\right)+0.1g_{\text{L}}\right]}{zF}\left(E_{\text{Ca}}-v\right)-{\text{P}}_{\text{Ca}}\left[{\mathrm{C}\mathrm{a}}^{\text{2}+}\right]\}\end{array}$$

Fig. 1.

Schematic of the microcircuitry within the VTA.

where v is the voltage; c_m is membrane capacitance; g_Ca is calcium conductance; E_Ca is calcium reversal potential; g_KCa is calcium-dependent potassium conductance; E_K is potassium reversal potential; g_sNa is subthreshold sodium conductance; E_Na is sodium reversal potential; g_l is leak conductance; E_l is leak reversal potential; and I_syn is synaptic current. The first five currents in the first equation represent intrinsic currents of the DA neuron: a calcium current (I_Ca), a calcium-dependent potassium current (I_K,Ca), a potassium current (I_K), a subthreshold sodium current (I_sNa), and a leak current (I_leak). α-Amino-3-hydroxy-5-methyl-4-isoxazolepropionic (AMPA) and NMDAR currents (I_AMPA and I_NMDA, respectively) model excitatory inputs and GABAR current (I_GABA) models inhibitory inputs. The first subgroup of currents mostly contributes to pacemaking mechanisms of DA neuron, while synaptic inputs produce bursts and pauses. A detailed description for the individual intrinsic currents is presented in the Mathematical Models section.

Calcium concentration varies according to the second equation in the system above. This equation represents balance between Ca²⁺ entry via the L channel and a Ca²⁺ component of the leak current, and Ca²⁺ removal via a pump. In the calcium equation, β is the calcium buffering coefficient, i.e., the ratio of free to total calcium, r is the radius of the compartment, z is the valence of calcium, and F is Faraday's constant. P_Ca represents the maximum rate of calcium removal through the pump.

We improved the DA neuron model of Ha and Kuznetsov (2013) to reproduce the compensatory action of somatic NMDA and GABA currents, as well as central features of the DA neuron, such as high-frequency firing during NMDAR activation but low-frequency firing during AMPA receptor (AMPAR) activation or a tonic depolarizing current. Model calibration is described in the appendix.

Spikes and Firing Frequencies in the Model

For simplicity, not all experimentally observed currents were included in the DA neuron model, but only currents that are necessary for modeling its main features (see the equation above). Most importantly, the DA model is built to reproduce the firing frequencies of the neuron. A DA neuron action potential is triggered when the membrane potential is depolarized to approximately −40 mV (Grace and Bunney 1984a). Previous experimental studies have shown that both high-frequency NMDA-dependent firing and slow spontaneous DA neuron firing are driven by subthreshold membrane potential oscillations (Deister et al. 2009; Wilson and Callaway, 2000). In the presence of tetrodoxin action potentials were not evoked, but calcium and membrane potential oscillations persisted (Wilson and Callaway, 2000). Based on these results, the transient spike-producing sodium current was omitted in the model, and a spike was registered whenever voltage oscillation reached the threshold of −40 mV. Voltage oscillations that were below this threshold were not counted as spikes and did not contribute to the firing frequency. Moreover, to illustrate that there is no significant differences in firing of this model and the model with spike-producing currents, we calculated firing rate of simulated DA neuron with spike-producing currents during application of depolarizing current, tonic AMPAR, NMDAR, and GABAR currents (data not shown).

Synaptic Inputs

DA neurons receive excitatory drive through AMPAR and NMDAR inhibitory drive through GABARs. Synaptic current are described by the equation below (see Table 1 for definition of constants),

$$\text{Synatic}\hspace{0.17em}\text{currents}=g_{\text{NMDA}}\left(v\right)sig\left(s_{\text{NMDA}}^{\text{act}}\right)\left(E_{\text{NMDA}}-v\right)+g_{\text{AMPA}}sig\left(s_{\text{AMPA}}^{\text{act}}{s}_{\text{AMPA}}^{\text{des}}\right)\left(E_{\text{AMPA}}-v\right)+g_{\text{GABA}}\text{GABA}\left(E_{\text{GABA}}-v\right)$$

See Table 1 and below for definitions of terms.

Table 1.

Model parameters

Parameter	Description	Value
cm	Membrane capacitance of DA and GABA neurons	1 μF/cm2
¯gK	Maximal potassium conductance on DA neuron	1 mS/cm2
¯gCa	Maximal calcium conductance on DA neuron	2.5 mS/cm2
¯gKCa	Maximal calcium-dependent potassium conductance on DA neuron	7.8 mS/cm2
¯gsNa	Maximal subthreshold sodium conductance on DA neurons	0.13 mS/cm2
gl	Leak conductance	0.18 mS/cm2
¯gNag	Maximal sodium conductance on GABA neuron	22 mS/cm2
¯gKg	Maximal potassium conductance on GABA neuron	7 mS/cm2
¯gNMDA	Maximal NMDA conductance on DA and GABA neurons	varied
gAMPA	AMPA conductance on DA and GABA neurons	varied
gGABA	GABA conductance on DA and GABA neurons	varied
EK	Potassium reversal potential on DA and GABA neurons	−90 mV
ECa	Calcium reversal potential on DA neuron	50 mV
ENa	Sodium reversal potential on DA and GABA neurons	55 mV
El	Leak reversal potential on DA neuron	−35 mV
Elg	Leak reversal potential on GABA neuron	−51 mV
ENMDA	NMDA reversal potential on DA and GABA neurons	0 mV
EAMPA	AMPA reversal potential on DA and GABA neurons	0 mV
EGABA	GABA reversal potential on DA neuron	−90 mV
τaact	AMPA receptor activation time on DA and GABA neurons	1 ms
τadeact	AMPA receptor deactivation time on DA and GABA neurons	1.6 ms
τades	AMPA receptor desensitization time on DA and GABA neurons	6.1 ms
τadesrel	AMPA receptor release from desensitization time on DA and GABA neurons	40 ms
τnact	NMDA receptor activation time on DA and GABA neurons	7 ms
τndeact	NMDA receptor deactivation time on DA and GABA neurons	170 ms
τgact	GABA receptor activation time on DA and GABA neurons	0.08 ms
τgdeact	GABA receptor deactivation time on DA and GABA neurons	10 ms
Iapp	Applied current on DA and GABA neurons	varied

Inhibitory Inputs

The major synaptic drive of the DA neurons is inhibitory. The inhibitory input in the model is produced by a population of GABA neurons. Voltage dynamics of each GABA neuron are described by Wang-Buszaki equations of a fast-spiking neuron (Wang and Buzsáki 1996), calibrated according to Richards et al. (1997). It obeys current balance and gating equations

$$c_{\text{m}}\frac{\text{d}{v}_i}{\text{d}t}={\overline{g}}_{\text{Nag}}{m}_{\infty }^3\left(v_i\right)h\left(E_{\text{Na}}-v_i\right)+{\overline{g}}_{\text{Kg}}n\left(E_{\text{K}}-v_i\right)+g_{\lg }\left(E_{\lg }-v_i\right)+g_{\text{NMDA}}sig\left(s_{\text{NMDA}}^{\text{act}}\right)\left(E_{\text{NMDA}}-v_i\right)+g_{\text{AMPA}}sig\left(s_{\text{AMPA}}^{\text{act}}{s}_{\text{AMPA}}^{\text{des}}\right)\left(E_{\text{AMPA}}-v_i\right)$$

where v_i is a voltage of ith GABA neuron in a population. The activation variable m is assumed fast and substituted by its steady-state function m_∞ = α_m/(α_m + β_m), where α_m = 0.1 (v_i + 30)/1 − exp[−(v_i + 30)/10] and β_m = 4 exp[−(v_i + 55)/18]. The inactivation variable h follows first-order kinetics, dh/dt = α_h(v)(1 − h) − β_h(v)h, where α_h = 0.07 exp [−(v_i + 53)/20] and β_h = 1/1 + exp[−(v_i + 23)/10]. The activation variable n obeys the following equation, dn/dt = α_n(v)(1 − n) − β_n(v)n, where α_n = 0.01(v_i + 29)/1 − exp[−(v_i + 29)/10] and β_n = 0.0875 exp[−(v_i + 39)/80]. This is a heterogeneous population (Margolis et al. 2012) that fires regularly (e.g., pacemaking) at high frequencies. Experimental data suggest that the range of firing rates of recorded VTA GABA neurons is very broad with the mean of 19 Hz (Steffensen et al. 1998). Therefore, model GABA neurons in the population are calibrated to fire with different intrinsic frequencies, uniformly distributed in a range of 12–22 Hz. The differences in frequencies are modeled by changing the leak conductance g_lg, according to g_lg = 0.05 + 0.05(rnd − 0.5), where g_lg = 0.05 corresponds to frequency of 17 Hz. GABA neurons are capable of firing with much higher frequencies in response to excitatory synaptic inputs, modeled by NMDAR and AMPAR currents. The activation/deactivation times of NMDA and AMPAR are the same for GABA as for DA neurons. The activity of each GABA neuron contributes to a GABA current entering DA neuron. Every time GABA neurons fire, a certain amount of neurotransmitter is released, which contributes to activation of the gating variable according to the equation

$$\frac{{\text{ds}}_{{\text{GABA}}_i}^{\text{act}}}{\text{d}t}=\frac{g_{\text{spike}}\left(v_i\right)\left(1-{\text{s}}_{{\text{GABA}}_i}^{\text{act}}\right)}{{\tau }_{\text{gact}}}-\frac{\left[1-g_{\text{spike}}\left(v_i\right)\right]{\text{s}}_{{\text{GABA}}_i}^{\text{act}}}{{\tau }_{\text{gdeact}}}$$

where

$$g_{\text{spike}}=\frac{1}{1+\exp \left(\frac{-v_i}{2}\right)}$$

The total receptor activation is a sum of contributions produced by all GABA neurons in a population, because all of them converge to one DA neuron in the model. A parameter that scales the GABA current is GABAR conductance g_GABA. We normalize the GABA gating variable by the number of neurons to keep its value in a range between zero and one. Thus, for complete synchronous GABA population, the GABAR on DA neuron will be maximally activated at time points when the neurons spike. Accordingly, the gating variable will be equal to one. In the case of asynchronous spiking, the GABAR will be partially activated and the gating variable will have a low value. Model parameters are given in Table 1.

Excitatory Inputs

The AMPA conductance is voltage independent, but the NMDA conductance (g_NMDA) has voltage sensitivity

$$g_{\text{NMDA}}\left(v\right)=\frac{{\overline{g}}_{\text{NMDA}}}{1+0.1\left[{\text{Mg}}^{2+}\right]e^{-m_{e}v}}$$

where [Mg²⁺] denotes the amount of magnesium, taken to be 1.4 mM (Li et al. 1996). The low slope of the voltage dependence (m_e = 0.062) is critical for the increase in the frequency of spikes or subthreshold oscillations during NMDA application (Ha and Kuznetsov 2013). The activation of the receptors in response to a synaptic input (s_i^act) is described by the following equation

$$\frac{\text{d}{s}_i^{\text{act}}}{\text{d}t}=\frac{j\left(1-s_i^{\text{act}}\right)}{{\tau }_{\text{act}}}-\frac{\left(1-j\right)s_i^{\text{act}}}{{\tau }_{\text{deact}}}$$

where j denotes a dimensionless synaptic input. It is normalized to change from 0 to 1 for 1-ms interval to mimic a single spike in the input. i denotes a receptor type, AMPA or NMDA. Desensitization of AMPAR is described by

$$\frac{\text{d}{s}_{\text{AMPA}}^{\text{des}}}{\text{d}t}=\frac{\left(1-j\right)\left(1-s_{\text{AMPA}}^{\text{des}}\right)}{{\tau }_{\text{adesrel}}}-\frac{j{s}_{\text{AMPA}}^{\text{des}}}{{\tau }_{\text{ades}}}$$

Comparison with Other Models

The interplay between NMDAR and GABAR currents to produce low-frequency tonic firing has been previously achieved in several multicompartmental DA neuron models (Canavier and Landry 2006; Komendantov et al. 2004; Lobb et al. 2011a). However, in Lobb et al. (2011a) the balance of somatic NMDAR and GABAR currents required large increases in the calcium pump density. This manipulation increases the maximal frequency achieved by tonic activation of the AMPAR or in response to depolarizing current injection, which contradicts experimental observations (Grace and Onn 1989; Richards et al. 1997). Furthermore, Komendantov et al. (2004) and Canavier and Landry (2006) observed regular low-frequency firing of a simulated DA neuron during the balanced activation of dendritic NMDAR and somatic GABAR. However, the mechanism of the frequency rise during application of NMDA to a dendritic compartment is different from the mechanism responsible for frequency increase when NMDA is applied to the somatic compartment (Ha and Kuznetsov 2013). Furthermore, higher values of NMDAR activation produced repetitive bursting in the model by Komendantov et al. (2004), whereas Lobb et al. (2010) demonstrate high-frequency tonic firing rather than repetitive bursting with somatic application of NMDAR current (dynamic clamp). In vivo the intrinsic mechanism for repetitive bursting in DA neurons usually does not activate, and a burst is followed by low-frequency firing without a pause. We present the model that shows NMDA-induced high-frequency firing without the repetitive bursting envelope in both in vivo and in vitro-like conditions calibrated to reproduce the most recent experiments.

Asynchronous Glu and GABA Inputs

Poisson distributed spike trains of 35 neurons with frequencies of ∼10 Hz formed an excitatory input to the model. Such an input was taken to produce a relatively constant level of NMDAR activation. To simulate the powerful effects of convergent synaptic inputs on the DA neuron, we threshold NMDAR to activate only by coincidence of two or more spikes. Inhibitory drive to the model was produced by a population of 30 GABA neurons. The number of GABA neurons projecting to a DA neuron is not known. To choose this number, we note first that the percentage of GABAergic neurons varies between 12 and 45% in different subregions of the VTA (Nair-Roberts et al. 2008). Since the GABA neurons powerfully modulate DA neuron activity via direct, monosynaptic inhibitory connections (Bourdy and Barrot 2012; Johnson and North 1992a; Omelchenko and Sesack 2009; Tepper et al. 1995; van Zessen et al. 2012), one can expect multiple GABA neurons to make connections with a single DA neuron. Second, we found that our results are valid for a wide range of the numbers of GABA neurons and start to change only if the number becomes small (10 or lower) (see Fig. A1 in the appendix). The variance of the GABA synaptic activation stays low for the number of GABA neurons greater than 10 (see Fig. A2 in the appendix). GABA neurons fire with different intrinsic frequencies in a range 12–22 Hz as described above, forming an asynchronous input.

Population of GABA Neurons Synchronized by Common Input

To produce transient synchrony between initially asynchronous GABA neurons, they were stimulated by Glu pulses, since experimental data suggest that synchrony of VTA GABA neurons could be governed by thalamocortical glutamatergic synaptic transmission (Berretta et al. 2001; Steffensen et al. 1998; Stobbs et al. 2004). Spike trains of 10 simultaneously recorded neurons from prefrontal cortex (PFC) of a urethane anesthetized rat were used as a template to simulate excitatory drive to GABA neurons. As for DA neurons, spike generation in GABA neurons was dependent on the arrival of two or more PFC spikes in a 1-ms window. For modeling of the PFC-VTA circuit, we assumed that DA and GABA neurons receive the same PFC input. We neglected synaptic delays between DA and GABA neurons, i.e., inhibitory spikes of GABA neurons evoked by PFC arrived to the DA neuron simultaneously with excitatory spikes from PFC. Considering that we are modeling the effect of local GABA neurons only, synaptic delays should be very small and do not affect modeling results.

In the model, intrinsic frequencies of GABA neurons are below 25 Hz, but much higher frequencies could be evoked synaptically or by current injection. To study the effect of high GABA neuron frequencies (up to 120 Hz) on DA neuron firing, we added a constant current to the voltage equations of GABA neurons. It has been shown that GABA neurons can transiently increase their firing to more than 100 Hz following reward or punishment (Cohen et al. 2012). Furthermore, GABA neurons can exhibit high-frequency firing when optogenetically stimulated (e.g., van Zessen et al. 2012).

Manipulating the Level of Synchrony in the GABA Population

Glu input pulses coming to each GABA neuron were jittered according to uniform distribution. This way all GABA neurons received slightly shifted Glu inputs. The range of the uniform distribution was changed to study the level of synchrony in the GABA input necessary to increase DA neuron bursting and firing. Calculations were performed 10 times for each range. To calculate whether the firing rate and bursting for each level of synchrony were significantly different from the case with an asynchronous GABA population, we used a repeated-measures ANOVA with Tukey's multiple-comparison test.

Firing Pattern Quantification

To analyze firing of the model DA neuron, we calculated an average firing rate and two measures of burstiness: the percentage of spikes within a burst (%SWB) and the coefficient of variation of interspike intervals (ISI CV). These measures were defined on the basis of 3 min of simulation time with a minimum of 200 spikes in this time interval. According to the first measure of burstiness (Grace and Bunney 1984b), bursts were identified as discrete events consisting of a sequence of spikes with burst onset defined by two consecutive spikes within an interval less than 80 ms, and burst termination defined by an ISI greater than 160 ms. The %SWB was calculated as a number of spikes within bursts divided by the total number of spikes. Unfortunately, this measure of bursting does not capture any variations in firing pattern of the neuron if it fires with frequencies higher than 12.5 Hz. If the DA neuron receives a strong tonic excitatory input driving it to relatively high frequencies, according to the first measure, the tonic firing pattern would be identified as a burst of extremely long duration. Therefore, we additionally analyzed ISI CV calculated as SD/mean of 200 ISIs to evaluate the regularity of firing.

Model of DA Release

The model of DA release is modified from Wightman and Zimmerman (1990) and is described by the following equation

$$\frac{\text{d}\left[\text{DA}\right]}{\text{d}t}={\left[\text{DA}\right]}_{\max }\delta \left(t-t_{\text{spike}}\right)-\frac{V_{\max }\left[\text{DA}\right]}{K_{\mathrm{m}}+\left[\text{DA}\right]}$$

The first term describes the release caused by spiking activity of the DA neuron. Dirac delta function δ(t − t_spike) represents the release at time of a spike. Maximum amount of DA released per spike is [DA]_max = 0.1 μM. The second term represents DA uptake described by Michaelis-Menten equation, where V_max = 0.004 μM/ms is the maximal rate of uptake by a transporter, and K_m = 0.2 μM is the affinity of the transporter for DA.

Recording of the Single-unit Activity in PFC and VTA

We performed extracellular recordings from four adult male rats (two Wistar rats and two Long Evans rats, Harlan, Indianapolis, IN). Animals were individually housed and maintained on a reverse light-dark schedule with ad libitum access to food and water. All procedures were approved by the Purdue School of Science Institutional Animal Care and Use Committee and conformed to the Guidelines for the Care and Use of Mammals in Neuroscience and Behavioral Research (2003).

Rats were anesthetized with urethane at a dose of 1.5 g/kg and placed into a stereotaxic frame for surgery. For three out of the four rats, microelectrode arrays consisting of eight tetrodes were lowered into the right medial PFC [anteroposterior (AP), +2.50; mediolateral (ML), +0.60; dorsovental (DV), −2; relative to bregma] and right VTA (AP, −6.0; ML, +2.2; DV, −8.5; 10° angle). For one rat, 64-channel Cambridge NeuroTech (Suffolk, UK) silicon probe was lowered into right VTA (AP, −6.0; ML, +1.0; DV, −8.5; 0° angle). Spikes were acquired using an Open Ephys recording system at 30 kHz. After recordings, animals were euthanized via decapitation, and their brains were extracted to assess placements. Spike sorting procedures and an example of isolation of single unit activity are presented in the appendix (see Fig. A4).

Putative GABA Neurons Identification and Cross-Correlation Analysis

Putative GABA neurons were identified by high firing rates (>10 Hz) and narrow waveforms (<0.5 ms). To access whether putative GABA neurons in VTA fire synchronously, we calculated cross-correlograms (CCGs) between pairs of neurons recorded simultaneously using bin widths of 1 ms and 0.1 ms (sampling resolution of the recording system is 0.03 ms). Prior to constructing CCGs, we removed all identical (to 0.05-ms precision) spike times that appeared on more than 10% of all of the channels. To access the statistical significance of the CCG peak, spikes of one of the neurons were time jittered 100 times randomly in a range of [−5, 5] ms to produce a jittered CCG. Based on these jittered CCGs, we calculated 95% confidence intervals for each bin (local 5% significance bands) and global significance bands (Amarasingham et al. 2012; Diba et al. 2014; Fujisawa et al. 2008). Pairs of neurons that had a significant peak in CCG at 0-ms bin (relative to the jittered CCG) were categorized as millisecond synchronous pairs.

RESULTS

We explored the role of the local VTA microcircuit and time-patterned activity of inhibitory and excitatory inputs that mimics conditions closer to in vivo experiments. Specifically, we focused on how the pattern of the inhibitory activity in the VTA influences DA neuron firing and bursting.

VTA Microcircuit: the Compensatory Action of Asynchronous NMDA and GABA Inputs

First, we investigated the influence of asynchronous Glu and GABA inputs to test whether they can be approximated by tonic currents. We quantified the changes in firing and bursting of DA neuron, depending on the combination of different NMDAR and GABAR synaptic strengths produced by asynchronous populations (Figs. 2 and 3) and compared this influence to the tonic approximation. Similar to the case of tonic inputs, there exists a region of parameters for which activity of excitatory and inhibitory populations is balanced to produce low-frequency DA neuron firing at rates similar to background firing (Fig. 3A, between the black lines). Analysis of ISI CV revealed that, for the majority of parameters, the DA neuron displays tonic firing. Example ISI distributions calculated for three different NMDAR and GABAR conductances are unimodal, indicating that firing is not bursty (Fig. 3C). However, the firing pattern of the DA neuron could be shifted from low-frequency tonic to high-frequency firing either by increasing the activity of the Glu population or by disinhibition (Fig. 2), so that it displays a mix of single spiking and bursting as observed in in vivo experiments. Disinhibition bursts could be produced, for example, by simultaneous inhibition of directly proje cting GABA neurons by inhibitory input from nucleus accumbens or other local VTA GABA neurons. Excessive firing of the Glu population induces depolarization block in the DA neuron, which could be removed by increased activity of the neurons in the GABA population (Fig. 3A).

Fig. 2.

Balanced asynchronous GABA and Glu inputs provide nearly constant levels of inhibition and excitation, respectively, and result in DA firing rates similar to background firing rates. A: Glu Poisson distributed spike trains. B: a spike raster plot of GABA neurons. C: GABAR activation on the DA neuron by inputs shown in B. D: NMDAR activation on the DA neuron by inputs shown in A. E: voltage trace of the DA neuron in response to Glu and GABA inputs displayed in A and B. Burst firing in DA neuron could be produced by disinhibition (decrease in firing of GABA neurons), while pause in firing could be produced by decrease in Glu input.

Fig. 3.

Quantification of firing rate (FR) and bursting of DA neuron receiving asynchronous synaptic Glu and GABA inputs. A: firing rate. Balanced activity of Glu and GABA populations result in low-frequency DA neuron firing (between black lines). B: coefficient of variation (CV) of ISI. For majority of g_NMDA and g_GABA parameters, CV < 0.5, indicating low variability in DA neuron firing. C: example of ISI distributions, calculated for 3 different NMDAR and GABAR conductances (these parameters are indicated by the crosses of corresponding colors superimposed on the ISI heat plot in B). ISI distributions are unimodal, demonstrating that DA neuron firing could be described as tonic.

VTA Microcircuit: Synchronous GABA Input Contributes to DA Neuron Firing

It has been shown that synchronization of VTA GABA interneurons could be induced by cortical Glu input evoked by internal capsule stimulation (Steffensen et al. 1998). As a common excitatory input to the VTA circuit, we used multielectrode recordings obtained from rats PFC under urethane anesthesia. The PFC is a brain region that sends monosynaptic excitatory connections to both GABA and DA neurons in the VTA (Christie et al. 1985; Sesack and Pickel 1992). These excitatory inputs were conceptualized as PFC to be in line with the experimental data; however, the conclusions should generalize to other Glu inputs to the VTA as well. Considering that PFC neurons fire together in up states during anesthesia, even if GABA neurons receive inputs from different PFC neurons, there is a high probability for GABA neurons to be excited with DA neurons within millisecond time scale. For these simulations, we used the same PFC input to all the GABA neurons in the population (Fig. 4A). GABA neurons were transiently synchronized by the input and then were silent for a short refractory period of time after a spike (Fig. 4, B and C). Unlike asynchronous GABA neurons, which activate the GABARs nearly tonically and provide a constant level of inhibition to the DA neuron (see Fig. 2), synchronized GABA firing produces sharp peaks in the activation of the GABAR gating variable (Fig. 4C) due to a short activation time of GABA_AR (0.08 ms) (similar to Destexhe et al. 1994), providing strong pulsatile inhibition.

Fig. 4.

Sample voltage trace of DA neuron activated by Glu input from PFC and by GABA population synchronized by common input from PFC. Transiently synchronized GABA neurons evoke additional spikes and extend DA neuron bursts. A: a spike raster plot of PFC neurons. B: a spike raster plot of GABA neurons transiently synchronized by common PFC input shown in A. C: GABAR activation on the DA neuron by inputs shown in B. D: NMDAR activation on the DA neuron by inputs shown in A. E: voltage traces of the DA neuron that receives transiently synchronized GABA input (solid line) and DA neuron that does not receive GABA input (dashed line). F1–F3: zoomed in bursting examples showing appearance of extra spikes evoked by synchronized GABA input.

We investigated the transition from completely asynchronous GABA neuron firing, which suppressed the activity of the DA neuron, to transiently synchronized GABA neurons. Our model shows that synchronized activity of GABA neurons can evoke additional spikes in the DA neuron and hence increase its firing rate and bursting. In the case of transient synchronization of GABA neurons by PFC up states, burstiness of DA neurons increases via two mechanisms: 1) suppression of background firing in between the up states, when the GABA population is desynchronized; and 2) production of extra spikes within the bursts by synchronized GABA input (Fig. 4, E and F). Combined with depolarization provided by NMDAR current, a synchronized GABA input produces extra spikes through release from phasic inhibition. Thus activity of VTA DA neurons could be regulated by an excitatory cortical input directly and indirectly through local GABA neurons.

We compared two cases of VTA neurons activation by Glu input coming from PFC: 1) PFC inputs come to the DA neuron only; 2) PFC input stimulates both the DA and VTA GABA neurons. Interestingly, the combined activation of the DA and GABA neurons by PFC input leads to increased DA neuron activity. Figure 5 illustrates the comparison of DA neuron firing rate and bursting between the two cases. When PFC stimulates both DA and GABA neurons, higher firing rate and bursting is achieved for a wider parameter space compared with DA neuron only stimulation. The observed increases in firing and bursting were caused mostly by a higher number of spikes within the bursts. This effect could be seen for intermediate values of GABAR conductance. A GABA input of intermediate strength was unable to inhibit spikes evoked by NMDA and provided brief hyperpolarization, helping DA neuron to repolarize after the spike and produce another NMDA-mediated spike (Fig. 4, F1–F3). Thus pulsatile synchronous GABAR activation is capable of facilitating the intraburst high-frequency firing.

Fig. 5.

Quantifications of firing rate (FR) and bursting of DA neuron activated by PFC firing and GABA neurons synchronized by common PFC input. A1 and A2: DA neuron firing rate. B1 and B2: ISI CV. C1 and C2: percentage of spikes within bursts (%SWB). A1–C1: PFC input comes to DA, but not to GABA neurons. A2–C2: PFC input comes to both DA and GABA neurons. Synchronization of GABA neuron by common PFC inputs leads to an increase in DA neuron firing rate and bursting for a wide range of g_NMDA and g_GABA parameters.

Synchronized GABA neurons can produce DA bursts in the absence of bursty Glu input.

Furthermore, we were interested to see if GABA neurons that are synchronized by common PFC input increase DA neuron firing and, more importantly, bursting, even if DA neuron itself does not receive bursty (glutamatergic) input. For these simulations, the DA neuron received asynchronous Glu inputs (Fig. 6A), which tonically activated NMDAR or did not receive Glu input at all. We found that the DA neuron was capable of firing additional pulsatile hyperpolarization-driven spikes during the short period of time when GABA neurons were silent after producing a spike. Interestingly, spikes occurred due to intrinsic depolarizing currents (e.g., the calcium and the subthreshold sodium), even in the absence of the Glu input to the DA neuron. However, in this case, the probability of spike initiation was low because it depended on the phase of DA neuron firing during which the inhibitory pulse arrived. A spike could be evoked only if the DA neuron was briefly released from hyperpolarization when its membrane voltage is near the spike threshold; otherwise only a subthreshold deviation in the membrane potential would be produced. The probability of spike generation by pulsatile hyperpolarization significantly increased in the presence of Glu input coming to the DA neuron. Even bursts of activity could be produced through release from pulsatile hyperpolarization, if the common input that GABA neurons receive is bursty, which is the case in our simulations (Fig. 6). Thus these simulations suggest a PFC input can indirectly produce bursts of spikes in the DA neuron, through local VTA GABA neurons, when they are not silenced, but synchronously excited.

Fig. 6.

GABA-mediated activation of DA neuron bursts. The DA neuron is able to fire bursts even in the absence of bursty excitatory input, if it receives GABA input that is synchronized by bursty input. A: Glu Poisson-distributed spike trains coming to the DA neuron. B: PFC spike trains coming to GABA neurons. C: a spike raster plot of GABA neurons transiently synchronized by common PFC input shown in B. D: GABAR activation on the DA neuron by inputs shown in C. E: NMDAR activation on the DA neuron by inputs shown in A. F: a sample DA neuron voltage trace in response to a tonic NMDA input and GABA population synchronized by a common input from PFC. The dashed line is the voltage trace in response to asynchronous NMDA and GABA inputs; the solid line is the voltage trace in response to the same NMDA input, but GABA input synchronized by the PFC.

Furthermore, we investigated how synchronized GABA neurons need to be to enhance DA neuron burstiness and firing rate. We calculated the DA neuron firing rate and %SWB dependence on the level of synchronization in the GABA population induced by a jittered Glu input (see materials and methods for the description of the procedure). Burstiness of the DA neuron receiving a GABA input with the standard deviation of spike distribution <8.7 ms (the range of Glu pulse jitter 30 ms) was significantly higher than for an asynchronous GABA input [repeated-measures ANOVA, F_(30,9) = 22.4, P < 0.0001, Tukey post hoc, Fig. 7, A1 and A2]. Thus perfect synchronization among GABA neurons is not required to achieve an increase in DA neuron bursting and firing.

Fig. 7.

Quantification of synchrony level in the GABA population necessary to enhance DA neuron bursting and firing. A1 and A2: firing rate and %SWB, respectively, are calculated as a function of the standard deviation of the GABA spike distribution induced by a jittered Glu input. For these calculations, the DA neuron receives an asynchronous Glu input, so that bursts are produced through synchronized GABA neurons. The horizontal line represents mean firings rate (%SWB) of the DA neuron that receives an asynchronous GABA input. Asterisks indicate levels of synchrony, for which the firing rate (%SWB) is significantly different from the case when the DA neuron receives input from an asynchronous GABA population.

The physiological properties of the DA neuron define its responses to the synaptic inputs and the way it fires in response to inhibitory pulses. Not all kinds of neuronal models can produce increases in firing in response to pulsatile inhibitory input. To show that the physiological properties matter, we compared the influence of inhibitory pulses on the DA neuron firing with the influence on the leaky integrate and fire (LIF) neuron firing. Figure A3 shows dependence of the firing rate of the DA neuron model and the LIF model on the GABA frequency and synaptic strength. The LIF neuron monotonically decreases firing with the increase of GABA conductance, while DA neuron has periods of increased activity. In Mechanism by which GABA input contributes to DA neuron firing and bursting below, we describe the mechanism and investigate physiological properties of the DA neuron that are important for achieving increases in frequency in response to inhibitory pulses.

Electrophysiologically recorded putative VTA GABA neurons exhibit millisecond timescale synchrony.

To validate the biological relevance of our prediction, we calculated CCGs between pairs of simultaneously recorded putative VTA GABA neurons. Overall, we recorded 78 neurons from 4 animals; 35 of these neurons were classified as putative GABA neurons. We found a large number of pairs [63 out of 236 possible pairs of putative GABA neurons (26.69%) that display millisecond timescale synchrony]. Forty (63.5%) of these synchronous pairs were recorded from different tetrodes/shanks. Synchronous spikes were observed at seemingly arbitrary times (Fig. 8C). Both of these suggest that there is likely more than one mechanism of GABA synchrony. Network of putative GABA neurons connected with millisecond synchronous connections (black lines) is shown in Fig. 8B. Representative examples of the CCGs for three pairs of putative GABA neurons from this dataset are shown in Fig. 8D. Calculation of CCGs with a higher resolution (with 0.1 ms bin) revealed that some putative GABA had temporal interactions on a finer timescale. Twenty-five percent of putative GABA neurons had a prominent peak, slightly offset from zero, surrounded by troughs, pointing to an inhibitory nature of these neurons (Fig. 8D, insets). Fine resolution (0.1-ms bin) CCGs of simultaneously recorded putative GABA neuronal pairs from all four animals sorted by maximum of the first principal component are shown in Fig. 8E. Thus many of putative VTA GABA neuron pairs exhibit synchrony at a less than 1-ms timescale, which is, according to our modeling results, more than necessary to achieve an increase in the DA neuron burstiness.

Fig. 8.

Putative VTA GABA neurons display millisecond timescale synchrony. A: electrode track from one of the recordings and approximate electrode placements for all 4 animals within VTA. B: network of putative GABA neurons connected with millisecond synchronous connections simultaneously recorded by 4 shanks with 16 electrodes each (inset, interelectrode spacing: ∼20 μm, intershank spacing: 250 μm). Millisecond synchrony between pairs recorded was observed from the same shank as well as different shanks. Only significant millisecond timescale connections are shown on the map. Distances between cells are not to scale. C: raster of putative GABA neurons shown on the connection map in A. The vertical blue dashed lines indicate instances of synchronized firing between two or more neurons. D: examples of CCGs of putative GABA cells pairs that have significant 0-ms peaks. Significant connections were accessed by calculating 95% global significant bands using 5-ms jitter. Dashed magenta lines indicate global significance bands; dashed red lines indicate local significance bands; green line represents the mean. Pairs ab and db show fine temporal interactions with a CCG peak slightly offset of 0 and accompanied by a trough (insets), featuring the inhibitory influence. Pair cb shows a central peak surrounded by inhibitory troughs. E: CCGs of all of the simultaneously recorded GABA neuronal pairs sorted by the maximum of the first principal component. CCGs were calculated with 0.1-ms bin to illustrate fine resolution interactions.

Mechanism by which GABA input contributes to DA neuron firing and bursting.

To further investigate the mechanism by which synchronized GABA neurons contribute to firing and bursting of the DA neuron, we focused on the periods of GABA synchrony. During these episodes, all GABA neurons fire simultaneously; therefore, we were able to simplify the model by considering the case of complete synchrony, in which the population is equivalent to one effective GABA neuron (with an appropriately scaled synaptic strength). To investigate how the GABA neuron firing frequency and the GABAR synaptic strength affect DA neuron firing, we stretched synchrony episodes for a longer time (on the order of several seconds) and assumed that during these periods of time the effective GABA neuron fires with approximately constant frequency.

The GABA input hyperpolarizes the cell membrane and decreases intracellular Ca²⁺ concentration by closing voltage-dependent Ca²⁺ currents (Fig. 9, B and D). The intracellular Ca²⁺ level defines the speed of depolarization in the DA neuron: for small Ca²⁺ concentrations, the hyperpolarizing calcium-dependent potassium current (I_K,Ca) is very small; therefore, the cell depolarizes and produces a spike faster. Effectively, the fast GABA-mediated hyperpolarization replaces hyperpolarization produced by Ca²⁺-dependent K⁺ current. In the case of synchronized activity of GABA neurons, the inhibition is pulsatile, and the DA neuron has an opportunity to escape and fire between the pulses (Fig. 9, A and B).

Fig. 9.

Synchronized GABA input enables a moderate increase in DA neuron firing in the absence of NMDA input. A1–A3: sample DA neuron voltage traces in the absence of NMDA for g_GABA = 1 mS/cm², g_GABA = 2.6 mS/cm², and g_GABA = 3.4 mS/cm², respectively. B1—B3: phase portraits corresponding to the voltage traces in A1–A3, respectively. In A1–A3, black line is DA neuron voltage trace in control; dashed black line represents spike detection threshold (−40 mV). In B1–B3, black solid line represents Ca²⁺ nullcline; black dashed line represents the voltage nullcline in control (g_GABA = 0 mS/cm²); dark gray dotted-dashed line represents maximal deviation of the voltage nullcline at a given value of GABAR conductance. Black closed trajectory is the model trajectory in control. C: changes in DA neuron firing rate depending on the frequency and the strength of GABA input. Crosses indicate values of GABAR conductance for which voltage traces of corresponding colors in A1–A3 were produced. D: a distribution of spike amplitudes as a function of intracellular Ca²⁺ concentration for different values of GABAR conductances. Intermediate values of GABA synaptic strengths keep Ca²⁺ concentration in the range optimal for spike production.

However, if GABA conductances are low, Ca²⁺ concentration is not significantly affected (Fig. 9, B1 and D); therefore, the DA neuron depolarizes at the similar rates as it would depolarize without GABA influence (Fig. 9A1). Strong I_K,Ca keeps counteracting cell depolarization as long as Ca²⁺ stays high in the cell. Therefore, a weak synchronized GABA input can only produce small subthreshold deviation in membrane voltage without significantly affecting the neuron's firing rate (Fig. 9, A1 and B1).

At intermediate GABA conductances, more complex regimes are possible, which correspond to more bursty firing patterns (Figs. 9, A2 and B2, and 10, A1 and B1). Moderate levels of GABA focus Ca²⁺ concentration at the level optimal for spike production (Fig. 9D), increasing the probability of the spike to be evoked. In the optimal window of Ca²⁺ concentration, a balance between hyperpolarizing GABA and Ca²⁺-dependent K⁺ currents leads to suprathreshold voltage oscillations at rates higher than in the absence of the GABA input (Fig. 9, A2 and A3). In addition to the amplitude, the timing of the inhibitory pulse is important as it defines the amplitude of voltage rebound and the probability of consequent spikes to be evoked and combine into a burst. The pulse decreases the ISI by truncating Ca²⁺ growth during a suprathreshold oscillation (Fig. 9B2). Note that a spike does not increase Ca²⁺ flux (Wilson and Callaway 2000), and Ca²⁺ oscillations are determined by the Ca²⁺-K⁺ mechanism. Thus Ca²⁺ growth can be truncated without truncating the spikes.

A strong GABA pulse resets the voltage and sets the timing for the next spike. However, the greater the conductance, the more time is required for the voltage to rebound to the threshold, and this eventually limits the amplitude to the subthreshold range, which may happen before the 1:1 entrainment (Fig. 9, A3 and B3). Even between the pulses of GABA, inhibition is not reduced enough, and the DA neuron does not reach the spike threshold. This also can be viewed as increasing overall level of inhibition, since the DA neuron works as a low-pass filter and averages the pulsatile GABA input.

In short, GABAR synaptic strength should be such that it does not allow calcium concentration to build up, but simultaneously allows the neuron enough time between the inhibitory pulses to recover and produce a spike. Therefore, intermediate values of GABAR conductance are needed for a high rate of spike production. The range of these values depends on the presence of NMDA input: if NMDAR is not activated, the optimal range of GABAR conductance in the model is 4–5 mS/cm². This range increases with the addition of NMDA input (compare Figs. 9C and 10, C1 and C2).

Fig. 10.

Synchronized GABA input significantly increases NMDA-mediated DA neuron firing and bursting. A1–A3: sample DA neuron voltage traces for g_NMDA = 15 mS/cm² and for g_GABA = 2 mS/cm², g_GABA = 5 mS/cm², and g_GABA = 18 mS/cm², respectively. B1–B3: phase portraits corresponding to the voltage traces in A1–A3, respectively. See Fig. 9 legend for description of lines. C1 and C2: dependence of DA neuron firing rate on GABA neuron frequency and GABAR synaptic strength for 2 values of NMDAR conductances: g_NMDA = 5 mS/cm² (intermediate strength), g_NMDA = 15 mS/cm² (gives maximum frequency in the absence of GABA). In C2, crosses indicate the values of GABAR conductance for which voltage traces of corresponding colors in A1–A3 were produced.

Influence of the GABA neuron firing frequency and GABAR synaptic strength on DA neuron firing.

The firing frequency of the GABA neuron along with the strength of the GABA synapse influences DA neuron firing. Areas in the parameter space of GABAR conductances exist where DA neuron firing is entrained by the GABA neuron (Fig. 10, C1 and C2). This phenomenon of entrainment of a nonlinear oscillator by the external force is well known (Pikovsky et al. 1997).

The influence of the GABA neuron frequency and the GABAR synaptic strength are inversely related: the faster GABA neurons fire, the smaller GABAR synaptic strength is needed to provide the maximum frequency increase in the DA neuron (Figs. 9C and 10, C1 and C2). The same is true for the loss of spiking, the boundary of which is a reciprocal function on the plane of these parameters. These effects are related to the duration of the time interval between pulses in GABAR activation during which the DA neuron has an opportunity to escape inhibition. If both the frequency and strength of the GABA input are relatively low, Ca²⁺ concentration has enough time to build up, which can prevent fast membrane depolarization, due to an increased I_K,Ca current (for example, Fig. 9, A1 and B1). Therefore, for a low GABA neuron frequency, higher values of GABA conductance are needed to keep Ca²⁺ concentration low enough to produce high frequency spikes.

For high frequencies of the GABA neuron, the GABAR is activated most of the time, causing a low probability for the DA neuron to escape. In this case, for the DA neuron to be able to follow the GABA input, GABAR conductance needs to be low. The window of Ca²⁺ concentration conducive for spike production becomes narrower with the increase in the frequency of GABA neuron. Therefore, the range of GABAR conductances for which frequency increase and 1:1 entrainment between GABA and DA neurons is achieved is smaller for a higher GABA neuron frequency (Figs. 9C and 10, C1 and C2). An increase in the strength of the high-frequency GABA input rapidly terminates oscillations by hyperpolarization block. For the frequencies of synchronized GABA neurons above 25 Hz, the DA neuron (in the absence of NMDA) cannot follow GABA neuron firing, perceiving it as a tonic input (Fig. 9C).

Without NMDA input, the range of GABA conductance leading to frequency elevation until the amplitude is limited to the subthreshold range is narrow. Thus there is a greater chance that the DA neuron will be inhibited by high-frequency synchronized GABA input than that rebound spikes will be produced. However, this region of the increased DA neuron frequency could be significantly expanded by adding NMDAR activation.

Synchronized GABA neurons significantly increase NMDA-mediated DA neuron firing.

In the presence of NMDAR inputs, there is a large region of 1:1 locking between GABA and DA neuron firing frequency (yellow-green region in Fig. 10, C1 and C2). The combination of tonic NMDA and pulsatile GABA inputs leads to a several-fold increase in the DA neuron frequency compared with the frequency evoked by the NMDA input alone. Based on the firing rate calculations, we can make predictions about how firing of the DA neuron receiving a GABA input with fixed parameters (frequency and strength) will change as the strength of the Glu input changes. For example, the firing pattern of the DA neuron bombarded by strong high-frequency GABA input can be switched from subthreshold oscillations to high-frequency firing by increasing the Glu drive. As a case in point, let us consider the following parameters: the GABA firing rate = 60 Hz, g_GABA = 10 mS/cm² and two cases, g_NMDA = 5 mS/cm² and g_NMDA = 15 mS/cm². In the first case, the DA neuron exhibits subthreshold oscillations; accordingly, its firing rate is zero (Fig. 10C1), while in the second case the DA neuron is entrained by the GABA input and fires with 60-Hz frequency (Fig. 10C2). This firing pattern is robust, since a significant increase in GABAR conductance (up to 17 mS/cm²) does not disrupt it. The greater NMDAR conductance, the higher frequencies could be evoked by GABAR activation, and the wider the range of GABAR conductances for which these frequencies are achieved (Fig. 10C).

NMDAR activation increases the average level of intracellular Ca²⁺, and, in particular, the level of Ca²⁺ at which the spikes can be evoked. This is because NMDAR current brings the voltage to the spike threshold even at higher activations of the Ca²⁺-dependent K⁺ current. As a result, the range of Ca²⁺ concentration allowing for the maximum frequency increase becomes significantly wider with NMDA. The higher NMDAR conductance, the greater the gap between maximum and minimum possible Ca²⁺ concentrations. The GABA input, in turn, decreases peak Ca²⁺ concentration, replacing the slow Ca²⁺-dependent K⁺ current and allowing for even faster rates of membrane depolarization than under NMDA alone (the mechanism is described in the Mechanisms by which GABA input contributes to DA neuron firing and bursting above). Therefore, in the presence of NMDA, elevated DA neuron activity is observed in wider range of GABA conductances.

Influence of GABA Neurons on Heterogeneous DA Neurons

Experimental studies showed that the midbrain DA system is composed of anatomically and electrophysiologically heterogeneous neurons, with subpopulations of DA neurons that are able to reach high frequencies by current injection or AMPAR stimulation (Blythe et al. 2009; Lammel et al. 2008; Roeper 2013). These unconventional DA neurons are more excitable and have higher spontaneous firing rates than classical DA neurons described in the previous sections. To investigate whether GABA influence on the more excitable DA neurons is different than on the classical neuron, we modified background firing frequency and the level of excitability of the DA neuron by varying leak conductance. The focus of this study is not the specific electrophysiological currents that lead to different levels of excitability, but the consequences of this heterogeneity on VTA function. As such, the leak current is nonspecific, i.e., it contains a number of different currents, and therefore suits this purpose very well.

First, we explored the dependence of the DA neuron response to depolarizing current on the value of the leak conductance. Although the leak current in the model is depolarizing (E_leak = −35 mV), an increase in leak conductance produced a decrease in the spontaneous firing frequency and the maximum frequency evoked by the applied current or AMPAR activation. This effect is observed due to the presence of a Ca²⁺ component of the leak current. A higher leak current increases the amount of intracellular Ca²⁺, promoting activation of the Ca²⁺-dependent K⁺ current, which leads to slower membrane depolarization and longer ISIs. Further increase in leak conductance would disrupt oscillations by the emergence of a stable resting state. Dependence of the firing frequencies on the amplitude of the depolarizing current and the AMPAR current for the DA neuron with low leak conductance (g_leak = 0.1 mS/cm²) is shown in Fig. 11, D1 and D2. The maximal frequency evoked by the depolarizing current is 20 Hz, which is much higher than for classical neurons. Application of tonic GABA decreases the DA neuron frequency evoked by a wide range of applied currents; however, it is able to slightly increase the frequency evoked by strong currents by decreasing the amplitude of Ca²⁺ oscillations. Second, we investigated how DA neurons with variable excitability respond to asynchronous and synchronous GABA inputs. Similar to the case of the low-frequency classical DA neuron, balanced activity of asynchronous excitatory and inhibitory inputs induced tonic low-frequency firing. However, for the same values of NMDAR conductance, higher values of GABAR conductance were needed to achieve the compensatory effect (data not shown). This is due to a higher level of excitability of this neuron, leading to a higher frequency response during NMDAR activation than in the classical DA neuron.

Fig. 11.

Firing of the nonclassical DA neuron in response to external influence (GABA, NMDA, AMPA or applied current). A1–A3: sample DA neuron voltage traces for (g_NMDA = 0 mS/cm², g_GABA = 8.4 mS/cm²), (g_NMDA = 0 mS/cm², g_GABA = 11 mS/cm²), and (g_NMDA = 15 mS/cm², g_GABA = 2 mS/cm²), respectively. B: dependence of the DA neuron firing rate on GABA neuron frequency and GABAR synaptic strength in the absence of NMDAR activation. Unconventional DA neuron is able to fire with frequency up to 25 Hz, even in the absence of NMDA input. C: a distribution of spike amplitudes as a function of intracellular Ca²⁺ concentration for different values of GABAR conductances. A wide range of GABA synaptic strengths keeps Ca²⁺ concentration in the range optimal for spike production. D1: parameter space (g_AMPA, g_GABA) of the nonclassical DA neuron. D2: parameter space (I_app, g_GABA) of the unconventional DA neuron. Maximum frequency of the nonclassical DA neuron in response to depolarizing current is 20 Hz, in response to AMPAR receptor activation is 12 Hz.

Synchronous GABA input alone is able to increase firing and induce bursting in unconventional DA neuron.

In the case of synchronized population of GABA neurons, there was a significant difference in the effect it exerted on background firing of the unconventional DA neuron. We found that the unconventional DA neuron could be entrained by a GABA input, even in the absence of NMDA (Fig. 11, A2 and B), unlike classical DA neuron (Fig. 9, A3 and C). For certain GABAR conductances, the DA neuron firing frequency reached up to 25 Hz when synaptically stimulated by a synchronized GABA input alone (Fig. 11B). The window of Ca²⁺ concentration optimal for spike production is wider for the unconventional DA neuron (Fig. 11C). A decrease in Ca²⁺ leak current reduces the Ca²⁺-dependent K⁺ current, allowing higher GABA conductance to entrain the DA neuron at a high frequency before the amplitude of oscillations is limited to the subthreshold range. Unlike the case of the classical DA neuron, bursts of activity could be produced by a GABA input in the absence of NMDA (Fig. 11A1). The area in the parameter space for which higher firing and bursting is achieved is larger for the unconventional DA neuron. However, the dependence of the DA neuron frequency on the strength/frequency of the GABA input is very similar (Figs. 9C, 10, C1 and C2, and 11B) because the mechanism of frequency elevation is the same for both types of DA neurons. Retrograde tracing experiments suggest that different VTA DA neuron subtypes project to different brain regions (Lammel et al. 2008). The ability of unconventional DA neurons to resist the tonic GABA input better than classical DA neurons and fire with higher frequencies in response to a synchronized GABA input could potentially contribute to the more sustained DA release pattern in amygdala and PFC (Garris and Wightman 1994; Mundorf et al. 2001).

GABA can synchronize DA neurons with different levels of excitability and boost DA release.

A common synchronized GABA input can transiently synchronize DA neurons with different levels of excitability and different background frequencies (Fig. 12). Simultaneous activation of DA neurons boosts the amount of transiently released DA (Fig. 12F). We considered 10 DA neurons with different leak conductances, which fire in an uncoordinated manner in the presence of asynchronous Glu and GABA inputs due to their heterogeneity. We assumed that the same GABA population projects to a number of heterogeneous DA neurons. Transient synchronization in the population of GABA neurons evokes rebound spike in all types of DA neurons, leading to their synchronization and, accordingly, simultaneous release of DA. This could be a robust mechanism of burst production and coordinated DA release in a population of heterogeneous DA neurons.

Fig. 12.

Cumulative synaptic DA concentration of the DA neurons receiving synchronous GABA input. GABA synchronization produces transient DA release in all types of DA neurons, leading to large peaks of synaptic DA concentration. A: Glu Poisson-distributed spike trains coming to the DA neuron. B: PFC spike trains coming to GABA neurons. C: GABAR activation on the DA neuron by inputs shown in B. D: NMDAR activation on the DA neuron by inputs shown in A. E: a spike raster plot of heterogeneous DA neurons synchronized by GABA input. F: cumulative DA concentration produced by activity of neurons shown in E.

DISCUSSION

To explore how temporal organization of neuron firing in the VTA affect the computations performed by this nucleus, we built a computational model of interactions between DA neurons and a population of GABA neurons, each based on biophysical models. Previously, only a mean-field circuit model of the VTA was available (Graupner and Gutkin 2009). Our model provides a new framework for the VTA circuitry as a feed-forward inhibitory network and simultaneously makes it specific for the VTA. For example, tonic background activity, responses to excitatory stimuli and balance of tonic inhibition and excitation are all specific for the VTA DA neuron. The inclusion of a biophysically plausible GABA population allows us to investigate the excitation-inhibition patterns produced by a common synaptic input to both types of neurons. The model incorporates an excitatory afferent input to the VTA, reflects changes in neural excitability caused by synaptic inputs and allows the effects of subthreshold currents, such as voltage rebound, to be assessed.

The model also reproduces the compensatory action of tonic NMDAR and GABAR activation (Fig. 2 and see Fig. A1 in the appendix). This is accomplished by an asynchronously firing population of GABA neurons that tonically inhibits the DA neuron by primarily suppressing background firing as suggested by Lobb et al. (2010, 2011b). Furthermore, under the combined influence of asynchronous Glu and GABA inputs, DA neurons can fire with average frequencies close to those observed during background firing (Fig. 3A). Thus GABAergic inhibition helps maintain low-frequency tonic firing and basal DA concentration.

In addition to its role in regulating tonic DA activity, GABA can rescue the neuron from depolarization block induced by high NMDA by hyperpolarizing the neuron (Figs. 3 and A1B). Several in vivo studies report a reversal of pharmacologically induced depolarization block by tonic hyperpolarizing GABA currents (Grace et al. 1997; Henry et al. 1992). Reversal of depolarization block by GABA can restore the DA neuron spike-generating mechanism and its ability to respond to environmental stimuli.

A number of possible mechanisms of DA burst generation have been previously proposed. Afferent inputs are necessary for burst production, including a cholinergic input (Grace et al. 2007; Grenhoff et al. 1986; Pan and Hyland 2005) and glutamatergic input activating NMDAR, which has been shown to play a role in eliciting high-frequency firing (Deister et al. 2009; Overton and Clark 1992; Tong et al. 1996; Zweifel et al. 2009). Considering that a significant proportion of inputs to DA neurons is GABAergic, ∼70% to SN DA neurons and ∼30% to VTA DA neurons (Dobi et al. 2010; Henny et al. 2012; Ribak et al. 1976), it is likely that GABA neurons are involved in controlling DA bursts as well. One well-described GABA-mediated mechanism is the disinhibition model of burst generation [Celada et al. 1999; Lobb et al. 2010, 2011a, 2011b; Tepper and Lee 2007; for a detailed review on mechanisms see Paladini and Roeper (2014)]. The mechanism is based on a decrease in inhibition received by DA neurons as a result of a reduction in the average firing rate of the GABA neurons. Our model provides a novel GABA-mediated mechanism that utilizes the temporal structure of the GABA input, as opposed to reduced activity of the GABA neurons. It is possible that these mechanisms synergize, yielding robust bursts.

Our model suggests that DA neuron activity depends not only on the average level of inhibition, but also on the level of synchronization in the population of GABA neurons innervating this DA neuron. Synchronization in the simulated GABA neurons was induced by common synaptic input, and this synchronization enhanced DA bursts (Figs. 4 and 5). Such synchronization facilitates intraburst high-frequency firing by providing brief hyperpolarization, which helps the DA neuron to repolarize after the spike and produce another NMDA-mediated spike. Specifically, GABA decreases intracellular Ca²⁺ concentration and, accordingly, the Ca²⁺-dependent K⁺ (SK) current, leading to faster rates of membrane depolarization (see Mechanism by which GABA input contributes to DA neuron firing and bursting above, Figs. 9 and 10). It has been previously suggested that DA neurons may permit burst firing by a Ca²⁺-mediated decrease in Ca²⁺-dependent K⁺ current (Kitai et al. 1999; Scroggs et al. 2001). Reduced Ca²⁺ entry to the DA cell, for example by muscarine, facilitates bursts and increases the frequency at which DA neurons can fire due to a reduction in Ca²⁺-dependent K⁺ current. A blockade of SK current increases the number of spikes in bursts (Shepard and Bunney 1991; Waroux et al. 2005). We have found a mechanism that dynamically reduces the SK current. Our model suggests that GABA-mediated hyperpolarization replaces the hyperpolarization produced by the Ca²⁺-dependent K⁺ (SK) current; however, the pulsatile pattern of this inhibitory input allows the DA neuron to fire during the pauses. Similarly, experiments show that pulsatile inhibition is important for high-frequency DA neuron firing. For instance, a high-frequency train of depolarizing current pulses interleaved by brief 5- to 10-ms hyperpolarizing current pulses, but not tonic depolarizing current, evokes a burst in the DA neuron (Deister et al. 2009).

Inhibitory circuitries within VTA and in the brain regions projecting to VTA are activated by rewarding and aversive stimuli (Cohen et al. 2012; Hong et al. 2011; Oyama et al. 2010, 2015; Pan et al. 2013) and exert powerful modulatory influence on DA neuron activity. Because of its proximity and shared excitatory inputs, the local GABA population is more likely to produce inhibitory pulses following a few millisecond delays, although other feed-forward inhibitory projections may also play this role. VTA GABA neurons, like VTA DA neurons, form heterogeneous subpopulations (Margolis et al. 2012) that likely perform diverse functions in the VTA beyond simply inhibiting DA neurons. A large subset of local VTA GABA neurons is phasically activated by reward-predicting stimuli (Pan et al. 2013), and their firing rate gradually increases toward the time when expected reward is delivered (Cohen et al. 2012). Transient simultaneous activation of GABA neurons by reward-prediction stimuli could potentially contribute to the phasic increase in firing of the DA neurons according to the results of our model.

In addition to increasing their firing rate in response to reward and reward-predicting stimuli, there are DA neurons that burst in response to salience and arousing events, regardless of their reward value (Horvitz 2000). A subpopulation of DA neurons is excited by aversive and/or stressful stimuli (Bromberg-Martin et al. 2010; Cohen et al. 2012). This increase in firing may be mediated by inputs to the VTA, such as those from the lateral habenula (LHb), which is thought to be involved in mediating behavioral responses to aversive information (Hikosaka 2010; Hong et al. 2011). LHb neurons, however, mostly project to the rostromedial tegmental nucleus (RMTg), which provides GABAergic inputs to VTA DA neuron (Jhou et al. 2009b; Kaufling et al. 2009), as well as local VTA GABA neurons (Brinschwitz et al. 2010). Aversive stimuli excite RMTg neurons (Jhou et al. 2009a) and are hypothesized to inhibit DA neurons, which makes it difficult to reconcile the observed increases in DA neuron firing to aversive stimuli. However, our data suggest that the pattern of GABAergic activity is critical for shaping DA neuron firing, which could potentially reconcile this inconsistency. Strong GABAergic input does not necessarily inhibit the DA neuron, but rather can facilitate its firing and bursting, if this input is synchronized. Hence, we hypothesize that subpopulations of local GABA neurons could be transiently synchronized by the input coming from LHb and thus contribute to DA neuron burst production via the mechanism described in Mechanisms by which GABA input contributes to DA neuron firing and bursting above (Figs. 9 and 10). Further experimental studies will be required to characterize the influence of LHB inputs to the VTA to test and refine this hypothesis. Importantly, however, our simulations indicate that positive and negative reinforcing stimuli are not simply calculated in the brain regions projecting to VTA and relayed to DA cells, but local processing within the VTA, (especially among local GABA neurons) plays a significant role in these neural computations. This is in line with a number of studies that advanced the idea of the importance of the GABA input in controlling DA neuron firing and bursting (Celada et al. 1999; Cohen et al. 2012; Eshel et al. 2015; Floresco et al. 2003; Lobb et al. 2010, 2011a, 2011b; Tepper and Lee 2007, etc.).

Optogenetic studies with stimulation of local GABA neurons on a millisecond time scale similar to the study by Eshel et al. (2015) can provide more insight into the plausibility of the model. A large proportion of the DA neurons in this study were suppressed by optogenetic activation of GABA neurons; however, a small proportion of DA neurons were activated. Authors suggested that the possible mechanism of this phenomenon is disynaptic disinhibition. Here we provide an alternative explanation: the stimulation synchronizes a proportion of GABA neurons, and the DA neurons that receive synchronized inhibition become more active. It is expected that not all of the DA neurons will be excited by synchronous GABA input, since we observe increased bursting and firing only in a certain range of parameters.

Surprisingly, we found that, even if the DA neuron does not receive a bursty excitatory input, it is able to produce bursts in response to transiently synchronized bursty GABA input through release from pulsatile inhibition (Fig. 6). Considering that some excitatory inputs to the VTA DA neurons are tonically active, e.g., STN (Wilson et al. 2004), GABA inputs may be responsible for shaping the bursts. Moreover, we show that a common synchronized GABA input can transiently synchronize heterogeneous DA neurons and thus boost the amount of transiently released DA (Fig. 12). These results could have important implications for understanding how DA neurons respond with bursts of action potentials to an unexpected reward or reward-predicting stimuli. Specifically, this suggests that these stimuli need not be encoded in increasing afferent excitatory drive directly to DA neurons. Rather, it seems the timing of the input to the GABAergic neuron and the extent to which it can synchronize this population may be a critical feature of how excitatory inputs alter DA neuron firing. In line with this view, it was recently demonstrated that local VTA GABA neurons are necessary to shape DA neuron bursting in vivo (Tolu et al. 2012). Specifically, activation of β2-containing nicotinic ACh receptors (nAChRs) on GABA neurons by endogenous ACh significantly increases firing and bursting of DA neurons. ACh pulses could act as synchronizing inputs to GABA neurons due to rapid kinetics of nAChRs. Synchronization of GABA neurons by ACh input could provide a mechanism for the elevation of DA neuron firing frequency and bursting similar to that described in Mechanisms by which GABA input contributes to DA neuron firing and bursting above.

These data add to a growing number of studies that have explored how synchronous activity of GABA interneurons alters the computational properties of neural networks. For example, inhibitory hippocampal interneurons exhibit synchrony at a millisecond timescale, leading to higher probability of rebound spikes in target excitatory neurons (Diba et al. 2014). In addition, activation of GABA neurons has been shown to increase the fidelity of information transfer in neocortical circuits via decreases in circuit noise (Sohal et al. 2009). In the VTA, it has been shown that synchronization of GABA interneurons could be induced by cortical Glu input evoked by internal capsule stimulation (Steffensen et al. 1998).

An extremely rich spectrum of functions is carried out by feed-forward inhibitory networks. These networks are characterized by monosynaptic excitation followed by precisely timed disynaptic inhibition via local interneurons (see e.g., Isaacson and Scanziani 2011; Swadlow 2002). Typical of many brain circuits, feed-forward inhibition has been identified, for example, as a predominant organizational principle of the striatum and the nucleus accumbens (see, e.g., Pennartz and Kitai 1991). The role of such a network design is believed to be balancing excitation and inhibition, controlling excitability of individual neurons and shaping the activity patterns (reviewed in Isaacson and Scanziani 2011). The excitation-inhibition sequence determines, for example, the temporal window of neuronal integration, turning the neurons from very diverse brain regions into coincidence detectors (Mittmann et al. 2005; Pouille and Scanziani 2001; Wehr and Zador 2003). Further research is needed to determine whether these functions are implemented in the VTA circuitry. In particular, the DA neuron is tonically active as opposed to excitatory neurons in other networks. It increases the frequency much more in response to NMDAR, but not AMPAR activation, as opposed to their co-activation required to increase the frequency in other neurons. Furthermore, we take into account the balance of tonic GABA and NMDA activation shown specifically for the DA neuron. These neuron properties are quite distinct from other feed-forward inhibition networks. Together with the current study, these data indicate that GABAergic interneurons provide a diverse array of neurocomputations that facilitate a rich regimen of microcircuit dynamics throughout the brain.

A central role for the VTA in guiding motivated behavior is broadly recognized (e.g., Bromberg-Martin et al. 2010; Paladini and Roeper 2014; Schultz 1998). However, a number of outstanding questions remain regarding the specific computational functions this brain region contributes to encoding motivated behaviors. The prevailing view is that DA neurons encode a signal that identifies differences in predicted vs. received rewards (Hollerman and Schultz 1998; Schultz 1998). However, a complete understanding of the neural interactions that encode this signal is still forthcoming. A number of inputs to the VTA have been suggested to influence this signal [orbitofrontal cortex, LHb, LDT, pedunculopontine nuclei (Jhou et al. 2009b; Lodge and Grace 2006; Watabe-Uchida et al. 2012)], which leaves open the question of how these inputs are integrated by VTA DA neurons to produce a biological signal capable of guiding motivated behavior. The data presented herein suggest specific underlying dynamics local to the VTA that could play a role in integrating inputs to this brain region and ultimately communicating a prediction error signal to efferent brain regions. Further refinement and testing of this model can also be used to explore how the computational properties of the VTA are altered in disease states. For example, understanding how drugs of abuse alter the computational functions of the VTA is an important and tractable future application of this model.

Mathematical Models

DA neuron intrinsic oscillator.

Tonic activity of the DA neuron is driven by voltage oscillations induced by intrinsic currents described below

$$\text{Intrinsic}\hspace{0.17em}\text{currents}=\stackrel{I_{\text{Ca}}}{\overbrace{g_{\text{Ca}}\left(v\right)\left(E_{\text{Ca}}-v\right)}}+\stackrel{I_{\text{K,Ca}}+I_{\text{K}}}{\overbrace{\left\{g_{\text{K,Ca}}\left(\left[{\text{Ca}}^{\text{2}+}\right]\right)+g_{\text{K}}\left(v\right)\right\}\left(E_{\text{k}}-v\right)}}+\stackrel{I_{\text{sNa}}}{\overbrace{g_{\text{sNa}}\left(v\right)\left(E_{\text{Na}}-v\right)}}+\stackrel{I_{\text{leak}}}{\overbrace{g_{\text{leak}}\left(E_{\text{leak}}-v\right)}}$$

The main currents of the model that produce pacemaking activity of DA neuron are an L-type voltage-dependent calcium current (I_Ca) and an SK-type calcium-dependent potassium current (I_K,Ca). Gating of the calcium current is instantaneous (Wilson and Callaway, 2000; Helton et al. 2005) and described by the function

$$g_{\text{Ca}}=\overline{g_{\text{Ca}}}\cdot \frac{{\alpha }_c^4\left(v\right)}{{\alpha }_c^4\left(v\right)+{\beta }_c^4\left(v\right)}$$

Calibration of the calcium gating function reflects an activation threshold of an L-type current, which is significantly lower in DA neurons than in other neurons, approximately −50 mV (Wilson and Callaway 2000; Durante et al. 2004). Calcium enters the cell predominantly via the L-type calcium channel. Contribution due to the NMDA channel is minor (Oster and Gutkin 2011). A large influx of Ca²⁺ leads to activation of the SK current, which contributes to repolarization as well as afterhypolarization of the DA cell. Dependence of the SK current (I_K,Ca) on calcium concentration is modeled as follows (Kohler et al. 1996)

$$g_{\text{K,Ca}}=\overline{g_{\text{K,Ca}}}\cdot \frac{{\left[{\text{Ca}}^{2+}\right]}^4}{{\left[{\text{Ca}}^{2+}\right]}^4+{\left[{\text{K}}^{+}\right]}^4}$$

The neuron is repolarized by the activation of a large family of voltage-gated potassium channels. In addition to already described potassium currents, the model contains voltage-dependent K⁺ current (I_K). Conductance of this current is given by a Boltzmann function:

$$g_{\text{K}}=\overline{g_{\text{K}}}\cdot \frac{1}{1+\exp \left[\frac{-\left(v+10\right)}{7}\right]}$$

The DA neuron expresses voltage-gated sodium channels that carry a large transient current during action potentials (the spike-producing sodium current) and a non-inactivating current present at subthreshold voltages (a subthreshold sodium current). Even though the persistent subthreshold sodium current is much smaller than the transient spike-producing current, it influences the firing pattern and the frequency of the DA neuron by contributing to depolarization below the spike threshold. We modeled the voltage dependence of the subthreshold sodium current as follows

$$g_{\text{sNa}}=\overline{g_{\text{sNa}}}\frac{1}{1+\exp \left[\frac{-\left(v+50\right)}{5}\right]}$$

The kinetics and the voltage dependence of the subthreshold sodium current were taken from Carter et al. (2012).

The leak current (I_leak) in the model has the reversal potential of −35 mV, which is higher than in the majority of neuron types. In DA neurons, several types of depolarizing, nonselective cation currents are expressed, which likely contribute to depolarization during interspike intervals.

GRANTS

This work is supported by National Institute on Alcohol Abuse and Alcoholism (NIAAA) Grant R01AA022821 (A. Kuznetsov); NIAAA Grant P60AA007611-26 (C. C. Lapish); GEIRE Grant from the Institute for Mathematical Modeling and Computational Sciences; Russian Foundation for Basic Research (project no. 14-02-00916-a) (D. Zakharov); ANR-13-NEUC-0003 GABA, ANR-10-LABX-0087 IEC, and ANR-10-IDEX-0001-02 PSL (B. Gutkin); and also partial funding from RF Golbal Competitiveness Subsidy to the NRU Higher School of Economics (B. Gutkin).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

E.O.M., B.S.G., C.C.L., and A.S.K. conception and design of research; E.O.M. and M.M. performed experiments; E.O.M. and M.M. analyzed data; E.O.M., D.Z., M.d.V., and A.S.K. interpreted results of experiments; E.O.M. prepared figures; E.O.M. drafted manuscript; E.O.M., M.M., B.S.G., C.C.L., and A.S.K. edited and revised manuscript; E.O.M., M.M., D.Z., M.d.V., B.S.G., C.C.L., and A.S.K. approved final version of manuscript.

APPENDIX

Model Calibration

We improved the DA neuron model of Ha and Kuznetsov (2013) to reproduce the compensatory action of somatic NMDA and GABA currents, as well as central features of the DA neuron, such as high-frequency firing during NMDAR activation but low-frequency firing during AMPAR activation or a tonic depolarizing current. We calibrated our model under in vitro-like conditions, with application of tonic inhibitory and excitatory inputs. Dynamic mechanisms of the influence of synaptic currents on the simplified DA neuron model that underlie the calibration of our biophysical model are described in Zakharov and Kuznetsov (2015). Dynamic clamp experiments show that balanced activation of somatic GABAR and NMDAR currents leads to DA neuron firing at frequencies comparable with background frequencies (1–5 Hz). Removal of inhibition in such conditions evokes disinhibition bursts (Lobb et al. 2010, 2011b).

Experimental studies showed that a “persistent” non-inactivating sodium current plays a significant role in pacemaking of the midbrain DA neuron by contributing to spontaneous depolarization between spikes (Puopolo et al. 2007). We critically improved our laboratory's previous model (Ha and Kuznetsov 2013) by including this current, which produced more robust background spiking. In addition, it was assumed for simplicity that Ca²⁺ predominantly enters through voltage-gated Ca²⁺ channels. Our current model takes into account Ca²⁺ entry through the leak channels in addition to voltage-gated channels. Ca²⁺ entry through NMDAR was omitted to implement the spatial segregation of NMDAR and SK channels as in the previous models (Ha and Kuznetsov 2013; Komendantov et al. 2004). We found that the subthreshold Na⁺ and Ca²⁺ leak currents are necessary to ensure that activity of the DA neuron can span the full background-firing frequency range under the influence of balanced tonic NMDAR and GABAR currents. Without these currents, the inhibitory input introduced, in addition to the NMDA inputs, was not capable of generating the firing frequencies of 1–4 Hz, but rather blocked the periodic spiking instead.

Consistent with experimental observations, the subthreshold Na⁺ current increases the excitability of the simulated DA neuron. It elevates the background firing frequency in the model and increases the maximal frequency in response to application of depolarizing current and AMPA. In turn, the Ca²⁺ component of the leak current decreases neuron's excitability and limits the frequency response to the range <10 Hz, which is observed experimentally (Richards et al. 1997). The Ca²⁺ leak current preserves the limit by reinforcing the negative feedback loop through the Ca²⁺-dependent K⁺ current and limited the maximal frequencies. Our calibration of the model allowed an inhibitory or hyperpolarizing input to reduce the frequency to an arbitrary low value. In particular, this allowed us to balance NMDA and GABA currents in a manner that optimally recreates experimentally observed levels of background firing frequency (Fig. A1B, between the black lines).

Fig. A1.

DA neuron firing patterns during application of tonic NMDAR and GABAR conductances. A1: generation of bursts and pauses in the model by phasic changes in NMDAR and GABAR inputs. A2: background firing is more sensitive to application of tonic GABAR conductance than NMDA-mediated firing. B: parameter space (g_NMDA, g_GABA) of the DA neuron model showing changes of DA neuron firing frequency depending on values of NMDAR and GABAR conductances. The crosses superimposed on the heat plot indicate the parameters used for the simulations in A1 and A2. To match the experimental conditions in (Lobb et al. 2010), we set AMPAR current to 0 and NMDAR and GABAR to I_NMDA = g_NMDA(E_NMDA − v) and I_GABA = ḡ_GABA(E_GABA − v), respectively.

Changes in the strength of the synaptic currents can switch the DA neuron firing pattern from tonic to bursty or silent state. When we deactivate the NMDAR current, moving down on the diagram, the DA neuron enters the resting state since the voltage oscillations are suppressed by the remaining GABAR current (Fig. A1A1). Conversely, if the GABAR current is deactivated (moving to the left on the diagram), the DA neuron will display high-frequency firing (Fig. A1A1). Similar to the experimental results of Lobb et al. (2010), background firing is inhibited by an application of tonic GABA; however, high-frequency firing evoked by NMDA is preserved (Fig. A1A2). A much higher GABAR conductance is needed to suppress NMDA-mediated firing (Lobb et al. 2010).

Dependence of the Variance of GABA Synaptic Activation on the Number of GABA Neurons

Asynchronous synaptic inhibition produced by 10 or more GABA neurons approximates a constant level of inhibitory conductance, because the variance of the GABA synaptic activation stays low for number of GABA neurons more than 10 (Fig. A2). A decrease in the number of GABA neurons shifts the DA neuron pattern from predominantly tonic firing to burstier firing. The reason is a higher variance of the summed GABA activity, leading to pauses and coincident spikes in the GABA population, which can lead to the production of extra spikes in the DA neuron.

Fig. A2.

Dependence of the variance and mean of GABA synaptic activation on the number of GABA neurons. A: the variance drops with the increase in the number of GABA neurons. GABA synaptic activation becomes variable only if the number of GABA neurons becomes small (10 or fewer). B: the mean GABA synaptic activation stays around 0.182 and can be scaled by the GABA conductance.

Comparison of the DA Neuron Response to the Pulsed Inhibitory Input with a Simple Integrate and Fire Model Response

The physiological properties of the DA neuron define its responses to synaptic inputs. To illustrate this, we compared the influence of inhibitory pulses on the DA neuron firing with the influence on the LIF neuron firing. The LIF model is described by the following equation

$$\tau \frac{\mathrm{d}v}{\text{d}t}=-v-80+\text{IR+}{g}_{\text{GABA}}\text{GABA}\left(E_{\text{GABA}}-v\right),\tau =500\text{ms},I=9.5,R=10,V_{\text{reset}}=-75\text{mV}$$

where I is input current, R is resistance, and V_reset is reset potential. Parameters of the LIF model were chosen to reproduce a low firing frequency, similar to the frequency of the DA neuron. Figure A3 shows the dependence of the firing rate of DA and LIF neurons on the frequency and strength of GABAR input. As oppose to the DA neuron, LIF is not capable of increasing firing in response to pulsatile GABA input.

Fig. A3.

Pulsatile GABA input increases firing rate (FR) of the DA neuron, but not of the LIF neurons. The dependence of the firing rate on the frequency and strength of the GABA input of the dopamine neuron model (A), the LIF model (B), and a comparison of the two at the GABA input frequency 25 Hz(C) is shown.

Differentiation of the Pulsatile Hyperpolarization Driven Spiking and the Disinhibition Spiking

One of the ways to differentiate disinhibition-induced firing and mechanism described in the paper is to test for hyperpolarization-induced spiking, which is based on a correlation analysis. We calculated CCGs between simulated DA and GABA neurons in two cases: 1) DA neuron receives synchronized GABA input (Fig. A4), 2) DA neuron receives an input from the GABA neuron that is occasionally inhibited by another GABA neuron (Fig. A5). In the first case, there is a millisecond timescale interaction between GABA and DA neurons, resulting in a narrow off-zero peak in the CCG (Fig. A4). In the second case the directly connected GABA neuron and the DA neuron are anti-correlated, because a pause in GABA firing disinhibits the DA neuron (Fig. A5A). CCG of disynaptically connected through another GABA neuron GABA and DA neurons is more symmetrical and has a broad peak (Fig. A5B). Firing of these neurons is correlated since an increase in firing of the disynaptically connected GABA neuron disinhibits the DA neuron by suppressing the directly projecting GABA neuron. In the model, we used simple patterns of GABA neurons' firing to calculate sample CCGs for the two cases. In practice, the DA neuron receives inputs from a number of different sources that would influence the shape of the CCG. To get a clearer picture, electrical or optical stimulations of GABA neurons with short (∼ms) vs long (∼s) and simultaneous recording of DA neurons could be useful for differentiating responses of the DA neurons to a pulsatile vs. tonic/asynchronous inhibitory input. Thus we give one example where the two cases are distinctly different, but this subject needs more investigation to capture various interactions between DA and GABA neurons in the experiments.

Fig. A4.

GABA-DA CCG in case of synchronization-induced firing.

Fig. A5.

GABA-DA CCG in case of disinhibition-induced firing. A: CCG between directly connected DA and GABA neurons. B: CCG disynaptically connected DA and GABA neurons.

Spike-Sorting Analysis

Spike sorting raw traces consisted of automatic and manual steps. For tetrodes, we used Wave_clus software (Quiroga et al. 2004) for automatic spike sorting, which sorts spikes using wavelet transform. Next, we manually checked and adjusted if necessary the results of the automatic spike sorter using Simple Clust software (https://github.com/open-ephys/simpleclust) that allows one to sort spikes using many different features, such as principal component analysis, peak/dip magnitudes, wavelets, energy, etc. To leverage the well-defined geometry of the recording sites acquires with silicone mircroelectrode arrays, we used the Phy spike sorting package (Rossant et al. 2016). An example of single fast-spiking unit activity isolation is shown in Fig. A6.

Fig. A6.

Spike sorting using phy software. A: an example of isolation of single-unit activity based on principal component features. Insets show autocorrelograms that correspond to clusters of identified units. B: waveforms of the clusters in A as they appear of each electrode. C: row voltage traces. Identified spikes are indicated by color.