Although small-conductance Ca(2+)-activated K(+) (SK) channels and various types of voltage-gated Ca(2+) (Cav) channels have been described in midbrain dopaminergic neurons, the nature of their interactions is unclear. More particularly, the role of various Cav channel types in either promoting irregularity of firing (by generating an inward current during SK channel blockade) or promoting regularity of firing (by providing the source of Ca(2+) for the activation of SK channels) has not been systematically explored. We addressed this question using intracellular and extracellular recordings from substantia nigra, pars compacta (SNc), dopaminergic neurons in rat midbrain slices. Neurons were pharmacologically isolated from their differences. When examining the ability of various Cav channel blockers to inhibit the SK-mediated afterhyperpolarization (AHP), we found that only the N-type Cav channel blocker ω-conotoxin-GVIA was able to reduce the apamin-sensitive AHP, but only partially (~40%). Specific blockers of L, P/Q, T or R channels had no effect on this AHP. Combining ω-conotoxin-GVIA and other specific blockers did not yield greater block and even the broad Cav blocker Cd(2+) induced a submaximal (~75%) effect. Extracellular recordings examining firing regularity yielded congruent results: none of the specific blockers was able to increase firing irregularity to the extent that the specific SK blocker apamin did. The irregularity of firing observed with apamin could only be reversed by blocking L-type Ca(2+) channels. Thus various sources of Ca(2+) appear to be required for SK channel activation in SNc neurons (some of them still unidentified), ensuring robustness of pacemaking regularity.

Midbrain dopaminergic neurons are endowed with endogenous slow pacemaking properties. In recent years, many different groups have studied the basis for this phenomenon, often with conflicting conclusions. In particular, the role of a slowly-inactivating L-type calcium channel in the depolarizing phase between spikes is controversial, and the analysis of slow oscillatory potential (SOP) recordings during the blockade of sodium channels has led to conflicting conclusions. Based on a minimal model of a dopaminergic neuron, our analysis suggests that the same experimental protocol may lead to drastically different observations in almost identical neurons. For example, complete L-type calcium channel blockade eliminates spontaneous firing or has almost no effect in two neurons differing by less than 1% in their maximal sodium conductance. The same prediction can be reproduced in a state of the art detailed model of a dopaminergic neuron. Some of these predictions are confirmed experimentally using single-cell recordings in brain slices. Our minimal model exhibits SOPs when sodium channels are blocked, these SOPs being uncorrelated with the spiking activity, as has been shown experimentally. We also show that block of a specific conductance (in this case, the SK conductance) can have a different effect on these two oscillatory behaviors (pacemaking and SOPs), despite the fact that they have the same initiating mechanism. These results highlight the fact that computational approaches, besides their well known confirmatory and predictive interests in neurophysiology, may also be useful to resolve apparent discrepancies between experimental results.

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons.

Switches in brain states, synaptic plasticity and neuromodulation are fundamental processes in our brain that take place concomitantly across several spatial and timescales. All these processes target neuron intrinsic properties and connectivity to achieve specific physiological goals, raising the question of how they can operate without interfering with each other. Here, we highlight the central importance of a timescale separation in the activation of sodium and T-type calcium channels to sustain robust switches in brain states in thalamic neurons that are compatible with synaptic plasticity and neuromodulation. We quantify the role of this timescale separation by comparing the robustness of rhythms of six published conductance-based models at the cellular, circuit and network levels. We show that robust rhythm generation requires a T-type calcium channel activation whose kinetics are situated between sodium channel activation and T-type calcium channel inactivation in all models despite their quantitative differences.

Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained a core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of FitzHugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which calcium channels control the two distinct firing modes of thalamocortical neurons.

Assessing the role of biophysical parameter variations in neuronal activity is critical to the understanding of modulation, robustness, and homeostasis of neuronal signalling. The paper proposes that this question can be addressed through the analysis of dynamic input conductances. Those voltage-dependent curves aggregate the concomitant activity of all ion channels in distinct timescales. They are shown to shape the current-voltage dynamical relationships that determine neuronal spiking. We propose an experimental protocol to measure dynamic input conductances in neurons. In addition, we provide a computational method to extract dynamic input conductances from arbitrary conductance-based models and to analyze their sensitivity to arbitrary parameters. We illustrate the relevance of the proposed approach for modulation, compensation, and robustness studies in a published neuron model based on data of the stomatogastric ganglion of the crab Cancer borealis.

Midbrain dopaminergic neurons in the substantia nigra, pars compacta and ventral tegmental area are critically important in many physiological functions. These neurons exhibit firing patterns that include tonic slow pacemaking, irregular firing and bursting, and the amount of dopamine that is present in the synaptic cleft is much increased during bursting. The mechanisms responsible for the switch between these spiking patterns remain unclear. Using both in-vivo recordings combined with microiontophoretic or intraperitoneal drug applications and in-vitro experiments, we have found that M-type channels, which are present in midbrain dopaminergic cells, modulate the firing during bursting without affecting the background low-frequency pacemaker firing. Thus, a selective blocker of these channels, 10,10-bis(4-pyridinylmethyl)-9(10H)-anthracenone dihydrochloride, specifically potentiated burst firing. Computer modeling of the dopamine neuron confirmed the possibility of a differential influence of M-type channels on excitability during various firing patterns. Therefore, these channels may provide a novel target for the treatment of dopamine-related diseases, including Parkinson's disease and drug addiction. Moreover, our results demonstrate that the influence of M-type channels on the excitability of these slow pacemaker neurons is conditional upon their firing pattern.