Calcium Dynamics Underlying Pacemaker-Like and Burst Firing Oscillations in Midbrain Dopaminergic Neurons: A Computational Study

Abstract

A mathematical model of midbrain dopamine neurons has been developed to understand the mechanisms underlying two types of calcium-dependent firing patterns that these cells exhibit in vitro. The first is the regular, pacemaker-like firing exhibited in a slice preparation, and the second is a burst firing pattern sometimes exhibited in the presence of apamin. Because both types of oscillations are blocked by nifedipine, we have focused on the slow calcium dynamics underlying these firing modes. The underlying oscillations in membrane potential are best observed when action potentials are blocked by the application of TTX. This converts the regular single-spike firing mode to a slow oscillatory potential (SOP) and apamin-induced bursting to a slow square-wave oscillation. We hypothesize that the SOP results from the interplay between the L-type calcium current (I(Ca,L)) and the apamin-sensitive calcium-activated potassium current (I(K,Ca,SK)). We further hypothesize that the square-wave oscillation results from the alternating voltage activation and calcium inactivation of I(Ca,L). Our model consists of two components: a Hodgkin-Huxley-type membrane model and a fluid compartment model. A material balance on Ca(2+) is provided in the cytosolic fluid compartment, whereas calcium concentration is considered constant in the extracellular compartment. Model parameters were determined using both voltage-clamp and calcium-imaging data from the literature. In addition to modeling the SOP and square-wave oscillations in dopaminergic neurons, the model provides reasonable mimicry of the experimentally observed response of SOPs to TEA application and elongation of the plateau duration of the square-wave oscillations in response to calcium chelation.

A reduced model of DA neuronal dynamics that displays quiescence, tonic firing and bursting

“…We introduce a single compartmental conductance based model for the dynamics of a DA neuron that combines conductance mechanisms previously included in [11,8]. The dynamics of the membrane potential are taken to be…”

“…Under TTX application (χ T T X = 0), our model captures the qualitative subthreshold activity. As seen in Figure 2a, the system exhibits a slowly oscillating potential (SOP) [22] that is hypothesized to play a role in providing the underlying structure for regular firing (e.g., [8]). …”

“…Earlier works examine only the subthreshold, silenced behavior and then by analogy suggest what the active behavior should be (e.g., [8]). We explicitly model the fast processes associated with spike generation; these depend critically on sodium.…”

“…Given this rich behavior and due to their biological importance, much work has been done on modeling DAergic neurons. Certain existing models only consider the subthreshold behavior of the DA cells [8,9] and argue by analogy the expected behavior of the DA cells. Other models depend on the interaction between the activity at the soma and the dendrites [10,11,9] in order to produce bursting dynamics (with this approach certain parameters may be unobservable).…”

Pallidal control of substantia nigra dopaminergic neuron firing pattern and its relation to extracellular neostriatal dopamine levels

“…Considerable evidence implicates an important role for glutamatergic input and especially NMDA receptor stimulation in the burst firing pattern Clark, 1992, 1997;Chergui et al, 1993;Christoffersen and Meltzer, 1995). These conclusions are supported by several recent computational modeling studies of burst firing in dopaminergic neurons (e.g., Canavier, 1999;Amini et al, 1999;Wilson and Callaway, 2000;Medvedev et al, 2003;Komendantov et al, 2004;Kuznetsov et al, 2006). Although the ability of NMDA receptor stimulation to evoke burst firing is well established, the endogenous trigger for ''spontaneous'' burst firing in vivo has not been demonstrated and in vivo, the firing pattern of nigrostriatal neurons is potently modulated by blockade of GABA A receptors (Tepper et al, 1995;Paladini et al, 1999a).…”