Mechanisms for multiple activity modes of VTA dopamine neurons

Abstract

Midbrain ventral segmental area (VTA) dopaminergic neurons send numerous projections to cortical and sub-cortical areas, and diffusely release dopamine (DA) to their targets. DA neurons display a range of activity modes that vary in frequency and degree of burst firing. Importantly, DA neuronal bursting is associated with a significantly greater degree of DA release than an equivalent tonic activity pattern. Here, we introduce a single compartmental, conductance-based computational model for DA cell activity that captures the behavior of DA neuronal dynamics and examine the multiple factors that underlie DA firing modes: the strength of the SK conductance, the amount of drive, and GABA inhibition. Our results suggest that neurons with low SK conductance fire in a fast firing mode, are correlated with burst firing, and require higher levels of applied current before undergoing depolarization block. We go on to consider the role of GABAergic inhibition on an ensemble of dynamical classes of DA neurons and find that strong GABA inhibition suppresses burst firing. Our studies suggest differences in the distribution of the SK conductance and GABA inhibition levels may indicate subclasses of DA neurons within the VTA. We further identify, that by considering alternate potassium dynamics, the dynamics display burst patterns that terminate via depolarization block, akin to those observed in vivo in VTA DA neurons and in substantia nigra pars compacta (SNc) DA cell preparations under apamin application. In addition, we consider the generation of transient burst firing events that are NMDA-initiated or elicited by a sudden decrease of GABA inhibition, that is, disinhibition.

Keywords: GABA; NMDA; SK channel; VTA; bursting; dopamine; modeling; regular firing.

Figure 1

A plot of experimentally observed DA cell firing modes from in vivo rodent VTA adapted from Mameli-Engvall et al. (2006) contrasted with data from computational simulations. In (A), the distribution of in vivo firing modes. Along the horizontal and vertical axes are mean firing frequencies and percentage of spikes within bursts, above 20% was considered a high burst neuron. Neurons firing below 5 Hz were considered to have a low firing rate, and high firing rate was taken to be neurons firing above 5 Hz. In (B), the associated ISI histogram for the data in (A). In (C), we plot the activity modes obtained from considering a family of neurons with varying SK conductances and receiving different levels of drive, I₀ (here GABA is taken to be 0.15). We arrange the data in a similar fashion to Mameli-Engvall et al. (2006), but with the shape of the data points indicating the relative strength of the SK conductance (neurons with weak, moderate and strong SK conductance are denoted via the use of squares, disks, and asterisks, respectively). The entire high firing regime is composed of neurons with low SK conductances and a significant portion of the low firing high burst regime are of low and medium SK conductance neurons.

Figure 2

Schematic diagram of the single compartmental conductance-based model of DA neuronal activity. The model includes a generalized intrinsic current whose composition could include in vivo cholinergic drive or in vitro applied currents. The model includes ionic currents for sodium, calcium, and potassium. Both spike generating and persistent sodium currents are expressed, which are both selectively blocked by application of TTX. The potassium currents are composed of a general current, a delayed-rectifier current, an apamin-blocked, calcium-dependent SK-type current. Calcium is predominantly trafficked into the intracellular region via the L-type Ca²⁺ channel and pumped out of the cell via a pump, with the intracellular calcium undergoing fast buffering. The intracellular calcium modulates the SK potassium current and the interaction between the dominant L-type calcium current and the SK potassium current forms the mechanism for an underlying oscillation. In addition to these currents, DA cells receive excitatory synaptic drive through AMPA and NMDA receptors. In addition, DA cells receive inhibitory input from GABAergic neuronal populations.

Figure 3

The NMDA conductance depends on both the membrane potential and the level of Mg²⁺. We plot the form of the NMDA conductance for the case of low Mg²⁺ (0.5 μM) and high Mg²⁺ levels (3.2 μM), pictured as a solid and dashed line, respectively.

Figure 4

A DA neuron exhibiting a range of firing patterns with a background input of I₀ = 0.2. In (A), the neuron exhibits a tonic firing pattern (χ_APA = 1). In slice preparations, application of the drug apamin suppresses the SK-conductance and yields an increase in burst firing. The mathematical model responds in a comparable manner, by reducing the SK- conductance (χ_APA = 0.2), the DA neural activity pattern enters a burst firing regime (a representative voltage trace is shown in B). In (C,D), we consider the calcium dependency behind these firing patters by constructing bifurcation diagrams for strong or weak SK conductances, shown in (C,D), respectively. We treat the intracellular calcium level as the bifurcation parameter, and as intracellular calcium, u, varies from high to low, the hyperpolarized stable steady-state (thick solid line) is lost via a fold bifurcation (with the unstable steady-state branch shown with a dashed line). For low calcium levels, the dynamics enter a periodic orbit and the neurons exhibit fast firing. The extrema values of the oscillations are represented by circles. Trajectories of the full dynamics are superimposed. Note that I₀ = 0 and that the dynamics for a weak SK conductance (χ_APA = 0.2) admit an additional spike during a burst compared to when I₀ = 0.2, as shown in (B).

Figure 5

Bifurcation diagrams for understanding how DA firing patterns depend upon the variable I₀ for strong or weak SK conductances, (that is, χ_APA = 1.0 and χ_APA = 0.2), shown in (A,B), respectively. Here we plot membrane potential with the generalized intrinsic/applied current variable I₀ taken as the bifurcation parameter. In both cases (weak and strong SK conductance), for small I₀, the neuron exhibits quiescence. For increased I₀, the dynamics follow a periodic orbit, i.e., the neuron fires, repetitively. For larger I₀, the neuron undergoes depolarization block. The level of I₀ required to reach depolarization block depends inversely on the strength of the SK conductance. Note that for weak SK conductance for I₀ between approximately 0 and 1.0 that the periodic orbit displays a mixed-mode oscillation, indicative of endogenous burst firing, as I₀ increases, the firing displays “fast” pacemaker firing. Stable steady states are shown by thick lines and periodic solutions are labeled.

Figure 6

Instances of DA neuronal bursting terminated via depolarization block. In (A), we observe that for these parameters and for a strong SK-conductance (χ_APA = 1), this model DA neuron exhibits a relatively fast (approximately 7 Hz) tonic firing pattern. Contrast this regular firing pattern with the burst firing that occurs for a weak SK-conductance (χ_APA = 0.2), shown in (B). For weak SK conductances, the DA cell exhibit endogenous burst firing where the bursts are terminated by depolarization block via the intrinsic rhythm of the neuron. In (C,D), we plot the associated trajectories the membrane potential V and sodium inactivation h. Nullclines for both V and h are included (see labels). In (D), we note the precipitous drop in h during a burst and the termination of the burst (at point D) is an unstable depolarized state, associated with the plateaus of depolarization shown in (B). In (E,F), we show corresponding bifurcation diagrams for (A,B) taking the intracellular Ca²⁺ level is treated as the bifurcation parameters. As intracellular calcium, u, varies from high to low, the hyperpolarized stable steady-state (thick solid line) is lost via a fold bifurcation (with the unstable steady-state branch shown with a thin line). The trajectory then enters a periodic orbit whereby the neurons are said to be firing. The extrema values of the oscillations are represented by circles. For low calcium levels, there is a stable depolarized steady-state solution.

Figure 7

Bifurcation diagrams for an alternate parameter set treating I₀ as a bifurcation parameter. Here we consider both strong and weak SK conductances with χ_APA = 1.0 and χ_APA = 0.2 shown in (A,B), respectively. Note the presence of both a Poincaré-Hopf-Andronov bifurcation and a saddle-node on an invariant circle (SNIC) bifurcation. Also, a far greater I₀ is needed in order to induce depolarization block, and this value of I₀ is similar for both strong and weak SK conductances. Stable steady states are shown by thick lines and periodic solutions are labeled.

Figure 8

In these phase diagrams, we show how firing frequency, burst fraction (SWB), and the burst measure depend on both I₀ and the strength of the SK-conductance influence DA cell firing patterns. In (A), the firing frequency is plotted with I₀ and the strength of SK- conductance varying and receiving noise in the AMPA conductance at a rate of 50 Hz. In (B,C), the level of bursting is similarly plotted using the classic percentage of spikes within bursts (B) and the burst measure proposed by van Elburg and van Ooyen (2004). For small I₀ the system displays quiescence. For “moderate” I₀, DA cells display activity (neurons with a lower SK conductance fire at a moderately higher rate). For larger I₀, the DA cells cease firing (that is they undergo depolarization block) and the level of I₀ required to initiate depolarization block is inversely proportional to the SK-conductance. That is, neurons with a low SK-conductance continue to fire at levels of I₀ that would cause a neuron with a high SK conductance to cease firing.

Figure 9

The strength of the GABA inhibition has a strong influence on the firing and burst firing characteristics of a DA neuron over a range of neuronal drive levels and SK-conductance strengths. Neurons with weak, moderate, and strong SK conductance are denoted via the use of squares, disks, and asterisks, respectively. Here GABA levels listed as low, mid, and high corresponds to g_GABA = 0.01, 0.02, and 0.03, respectively. The GABA conductance included is taken to be constant and does not capture the dynamic network level changes in the mean field activity of the GABA neuronal population innervating the DA neuron.

Figure 10

An alternate phase diagram that suggests a novel activity mode of DAergic neurons. The strength of the GABA inhibition has a strong influence on the burst firing characteristics of a DA neuron over a range of neuronal drive levels and SK-conductance strengths. Neurons with weak, moderate, and strong SK conductance are denoted via the use of squares, disks, and asterisks, respectively. Again, GABA levels listed as low, mid, and high corresponds to g_GABA = 0.01, 0.02, and 0.03, respectively.

Figure 11

Bifurcation diagram for moderate GABA level with a weak SK conductance (χ_APA = 0.2) to study the neural dynamics over a range of I₀. The observed results are not in perfect accord to the phase diagram shown in Figure 10 for the frequency distribution at moderate GABA level as there is no inclusion of noise in this diagram. However, we observe that as I₀ increases from 0, the neuron enters a firing regime, but as I₀ increases further it enters a state of quiescence. With a further increase of I₀ the neuron can enter another fast firing regime. Stable steady states are shown by thick lines and periodic solutions are labeled.

Figure 12

Differential burst firing events due to an increase in the NMDA conductance for I₀ = 0.3, responses depend on both the strength of the SK conductance and the Mg²⁺ level. In (A), a neuron with a relatively strong SK conductance (χ_APA = 1.0) has NMDA applied at time t = 2 s (manifested by an immediate rise of the NMDA conductance), which elicits a burst firing event. In (C), the preparation is repeated but with a weak SK conductance (χ_APA = 0.2), results in a significantly longer burst firing event followed by pacemaker-like firing for the duration of the stimulus. In (A,C) the Mg²⁺ level was 0.5 μM, in (B,D), we repeat the experiment at an elevated level of Mg²⁺ (3.2 μM) and note the resultant endogenous burst firing during stimulation (akin to Johnson et al., 1992). In addition to tracking the membrane potential, we also display the intracellular calcium dynamics. These simulations include noise in the AMPA drive of 40 Hz.

Figure 13

Burst firing events due to NMDA increases for neurons of strong and weak SK conductance (χ_APA = 1.0 and 0.2) shown in (A,C) for low Mg²⁺ levels, respectively from depolarized (or near depolarized) states (driven by I₀ = 2.5). NMDA increases by 0.1 at time t = 2 s for a duration of 2 s. In (A), there is a transient 4 spike burst, while for a weak SK conductance (shown in C) we observe a prolonged 9 spike burst event followed by sporadic activity until the NMDA stimulus is released. In both instances, at the release of stimulation, there is a pronounced hyperpolarization of the membrane potential. In (B,D), we consider similar conditions but for high levels of Mg²⁺. We find that in each case (for both weak and strong SK conductance) that the rise in the NMDA conductance at time t = 2 s results in quasi-regular firing.

Figure 14

Transient disinhibition can induce burst firing in a manner dependent upon the strength of the SK conductance and the level of Mg²⁺ (here I₀ = 0.3). From an initial state of high GABA inhibition, g_GABA = 0.04, neurons are released from inhibition at t = 3 s (g_GABA = 0.04 → 0.01), inducing transient burst firing events at the onset of disinhibition (whose duration depends on the SK conductance and the level of Mg²⁺). In (A,C), the Mg²⁺ level is 0.5 μM, and there is some background activity both prior to and post disinhibition events. In (A), a neuron with a relatively strong SK conductance (χ_APA = 1.0) displays a brief transient burst at the onset of disinhibition then enters a pacemaker-like firing regime. Whereas in (C), a neuron with a weak SK conductance (χ_APA = 0.2) yields a longer burst firing event at the onset of disinhibition followed by endogenous burst-like firing. In (B,D), we repeat the experiment at an elevated Mg²⁺ level and consider high and low SK conductances (χ_APA = 1.0, 0.2), respectively. In (B,D), there is nearly no background activity prior to and post disinhibition events, and the resulting burst firing events at disinhibition onset are significantly longer than the case for low Mg²⁺ levels, shown in (A,C). In (A–D), following the period of disinhibition, the cell returns to its previous firing pattern with no appreciable post-stimulus hyperpolarization.