Interaction of NMDA receptor and pacemaking mechanisms in the midbrain dopaminergic neuron

Abstract

Dopamine neurotransmission has been found to play a role in addictive behavior and is altered in psychiatric disorders. Dopaminergic (DA) neurons display two functionally distinct modes of electrophysiological activity: low- and high-frequency firing. A puzzling feature of the DA neuron is the following combination of its responses: N-methyl-D-aspartate receptor (NMDAR) activation evokes high-frequency firing, whereas other tonic excitatory stimuli (α-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate receptor (AMPAR) activation or applied depolarization) block firing instead. We suggest a new computational model that reproduces this combination of responses and explains recent experimental data. Namely, somatic NMDAR stimulation evokes high-frequency firing and is more effective than distal dendritic stimulation. We further reduce the model to a single compartment and analyze the mechanism of the distinct high-frequency response to NMDAR activation vs. other stimuli. Standard nullcline analysis shows that the mechanism is based on a decrease in the amplitude of calcium oscillations. The analysis confirms that the nonlinear voltage dependence provided by the magnesium block of the NMDAR determine its capacity to elevate the firing frequency. We further predict that the moderate slope of the voltage dependence plays the central role in the frequency elevation. Additionally, we suggest a repolarizing current that sustains calcium-independent firing or firing in the absence of calcium-dependent repolarizing currents. We predict that the ether-a-go-go current (ERG), which has been observed in the DA neuron, is the best fit for this critical role. We show that a calcium-dependent and a calcium-independent oscillatory mechanisms form a structure of interlocked negative feedback loops in the DA neuron. The structure connects research of DA neuron firing with circadian biology and determines common minimal models for investigation of robustness of oscillations, which is critical for normal function of both systems.

Figure 1. Model calibration.

(A) The activation curve and the time constant of the ERG current. (B) The comparison of the activation curves for the NMDAR conductance in the present (solid bold) and the previous (solid thin) models, and the calcium current (dashed). All conductances are normalized to the maximum value of 1.

Figure 2. Somatic NMDA receptor activation effectively elevates the frequency.

(A) NMDA is activated only in the soma for 1 sec ( = 26 mS/cm²). The frequency rises to 25 Hz in response. (B) Simulated whole bath application of NMDA agonist evokes yet higher frequency than the focal somatic ( = 26 mS/cm²). (C) Excessive NMDA activation blocks the oscillations ( = 39 mS/cm²). (D) The dependence of the frequency on the maximal conductance of the NMDA current. The thin curves are for the model without the fast sodium current. A minimum amplitude of 5 mV is set for all calculations of the frequency in order to exclude the small amplitude oscillations.

Figure 3. Achieving high frequency requires simultaneous NMDA receptor stimulation of distal dendrites.

(A) The dendrites receiving NMDA stimulation are marked in read ( = 14 mS/cm²). (B) Firing a somatic spike (black) requires simultaneous firing of the three dendrites. The membrane potential for the dendrites 1 and 2 are shown in red and blue respectively. A spike in dendrite 1 alone evokes only a small spikelet in the soma.

Figure 4. Tonic applied depolarization and AMPA receptor activation are unable to significantly elevate the frequency.

(A) An applied current is injected into the soma for 1000 ms at an intensity slightly lower than that causing blockade of oscillations (700 pA). (B) Tonic AMPA receptor stimulation causes complex oscillations and, consequently, only reduces the frequency. (C) and (D) The dependence of the frequency on the applied current and AMPA maximal conductance, respectively. The oscillations are blocked at the end of each curve.

Figure 5. Oscillations persist under SK current blockade.

(A) The blockade moderately increases the frequency of oscillations. (B) A very weak applied depolarization (320 pA) is enough to block the oscillations. (C) NMDA receptor activation elevates the frequency as effectively as in the presence of the SK current. (D) A moderate NMDAR activation rescues the neuron from the blockade of oscillations caused by applied depolarization. (E,F) The dependence of the frequency on the NMDAR conductance and the applied current. The plots are similar to Fig. 2D and Fig. 4C respectively, but both horizontal scales are expanded and depolarization block occurs at lower values than with the SK current.

Figure 6. The ERG (solid line) and SK (dashed line) currents at the onset of the SK current blockade.

The activation of the ERG current is much stronger when the SK current is blocked.

Figure 7. Typical responses of the one-compartmental model to NMDA, AMPA receptor stimulation and somatic depolarization are very close to those of the reconstructed morphology.

As in Fig. 4, the values for the applied current and AMPAR stimulation are chosen slightly lower than those causing blockade of oscillations. (D) The frequency as a function of NMDAR conductance in the one-compartment model (compare with Fig. 2D). The solid curve is for spiking model. It is truncated at a sharp transition to subthreshold oscillations. The dashed curve is for the model with no spikes. The frequency continues to grow until oscillations are suppressed around  = 26 mS/cm². (E) The frequency as a function of the applied current in the single-compartment nonspiking model. Oscillations are suppressed approximately at I = 580 pA.

Figure 8. Oscillations of the voltage and Ca²⁺ concentration.

(A) At the onset of high-frequency oscillations, the amplitude of Ca²⁺ concentration is dramatically reduced (dashed: Ca²⁺ concentration; solid: the voltage). (B) Oscillations are presented by a closed loop in the Ca²⁺-V plane. The oscillations circumscribe folding of the voltage nullcline (dotted). (C) The oscillations are blocked if the intersection of the voltage and Ca²⁺ nullclines interrupts the loop.

Figure 9. Changes in the voltage nullcline caused by the increasing applied current and maximal NMDAR conductance.

(A) During applied depolarization, an equilibrium state interrupts the oscillatory cycle. During NMDAR activation, the voltage nullcline becomes more flat, and this causes a frequency increase. (B) If the NMDAR has a steeper voltage dependence, the voltage nullcline remains strongly folded, and the frequency remains low.

Figure 10. The dependence of the oscillation frequency on the magnesium concentration at a fixed NMDAR current density ().

Figure 11. The structure of the model.

Two negative feedback loops are interlocked by the voltage variable. Hammerheads show inhibition and arrows show activation.

Figure 12. Three-dimensional structure of the model allows for complex modes and bistability.

(A) Two simultaneously stable oscillatory solutions with very different amplitudes are shown in blue and red respectively. The voltage and n-nullclines extend onto null-surfaces. The Ca²⁺-nullcline is not shown for clarity. (B) and (C) Projections of the two solutions show their separation along Ca²⁺ concentration and the gating variable of the ERG current, n. Sections of the voltage null-surface are shown for a few values of the third variable: (B) [Ca²⁺]  = 30, 60, 70; (C) n = 0.1, 0.4, 0.5. The Ca²⁺ and n-nullclines (black) are the same for any value of the third variable.