The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord.

Spontaneous episodic activity occurs throughout the developing nervous system because immature circuits are hyperexcitable. It is not fully understood how the temporal pattern of this activity is regulated. Here, we study the role of activity-dependent depression of network excitability in the generation and regulation of spontaneous activity in the embryonic chick spinal cord. We demonstrate that the duration of an episode of activity depends on the network excitability at the beginning of the episode. We found a positive correlation between episode duration and the preceding inter-episode interval, but not with the following interval, suggesting that episode onset is stochastic whereas episode termination occurs deterministically, when network excitability falls to a fixed level. This is true over a wide range of developmental stages and under blockade of glutamatergic or GABAergic/glycinergic synapses. We also demonstrate that during glutamatergic blockade the remaining part of the network becomes more excitable, compensating for the loss of glutamatergic synapses and allowing spontaneous activity to recover. This compensatory increase in the excitability of the remaining network reflects the progressive increase in synaptic efficacy that occurs in the absence of activity. Therefore, the mechanism responsible for the episodic nature of the activity automatically renders this activity robust to network disruptions. The results are presented using the framework of our computational model of spontaneous activity in the developing cord. Specifically, we show how they follow logically from a bistable network with a slow activity-dependent depression switching periodically between the active and inactive states.

Dynamics of low-threshold spike activation in relay neurons of the cat lateral geniculate nucleus.

The low-threshold spike (LTS), generated by the transient Ca(2+) current I(T), plays a pivotal role in thalamic relay cell responsiveness and thus in the nature of the thalamic relay. By injecting depolarizing current ramps at various rates to manipulate the slope of membrane depolarization (dV/dt), we found that an LTS occurred only if dV/dt exceeded a minimum value of approximately 5-12 mV/sec. We injected current ramps of variable dV/dt into relay cells that were sufficiently hyperpolarized to de-inactivate I(T) completely. Higher values of dV/dt activated an LTS. However, lower values of dV/dt eventually led to tonic firing without ever activating an LTS; apparently, the inactivation of I(T) proceeded before I(T) could be recruited. Because the maximum rate of rise of the LTS decreased with slower activating ramps of injected current, we conclude that slower ramps allow increasing inactivation of I(T) before the threshold for its activation gating is reached, and when the injected ramps have a sufficiently low dV/dt, the inactivation is severe enough to prevent activation of an LTS. In the presence of Cs(+), we found that even the lowest dV/dt that we applied led to LTS activation, apparently because Cs(+) reduced the K(+) "leak" conductance and increased neuronal input resistance. Nonetheless, under normal conditions, our data suggest that there is neither significant window current (related to the overlap of the inactivation and activation curves for I(T)), rhythmogenic properties, nor bistability properties for these neurons. Our theoretical results using a minimal model of LTS excitability in these neurons are consistent with the experimental observations and support our conclusions. We suggest that inputs activating very slow EPSPs (i.e., via metabotropic receptors) may be able to inactivate I(T) without generating sizable I(T) and a spurious burst of action potentials to cortex.

Self-organized synchronous oscillations in a network of excitable cells coupled by gap junctions.

Recent evidence suggests that electrical coupling plays a role in generating oscillatory behaviour in networks of neurons; however, the underlying mechanisms have not been identified. Using a cellular automata model proposed by Traub et al (Traub R D, Schmitz D, Jefferys J G and Draguhn A 1999 High-frequency population oscillations are predicted to occur in hippocampal pyramidal neural networks interconnected by axo-axonal gap junctions Neuroscience 92 407-26), we describe a novel mechanism for self-organized oscillations in networks that have strong, sparse random electrical coupling via gap junctions. The network activity is generated by random spontaneous activity that is moulded into regular population oscillations by the propagation of activity through the network. We explain how this activity gives rise to particular dependences of mean oscillation frequency on network connectivity parameters and on the rate of spontaneous activity, and we derive analytical expressions to approximate the mean frequency and variance of the oscillations. In doing so, we provide insight into possible mechanisms for frequency control and modulation in networks of neurons.

The dynamic activation of colicin Ia channels in planar bilayer lipid membrane.

Dynamic activation of ion channels formed by colicin Ia incorporated into a planar bilayer lipid membrane (BLM) was investigated by the voltage clamp technique using different step voltage stimuli. We have demonstrated a critical resting interval, Deltat(c), between two identical successive voltage pulses. If the second pulse is applied within Deltat(c), it produces a predictable current response. On the contrary, if the second pulse is applied after Deltat(c), the current response cannot be reliably predicted. Computer simulations based on an idealized mathematical model, developed in this paper, qualitatively reproduce the system's dynamic responses to stimulus trains. The behavior of the ion channels, when the resting period exceeds Deltat(c), may be interpreted as a transient gain or loss or resetting of memory, as revealed by a specific sequence of electrical pulses used for stimulation.

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons.

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.

Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model.

We performed intracellular recordings of relay neurons from the lateral geniculate nucleus of a cat thalamic slice preparation. We measured responses during both tonic and burst firing modes to sinusoidal current injection and performed Fourier analysis on these responses. For comparison, we constructed a minimal "integrate-and-fire-or-burst" (IFB) neuron model that reproduces salient features of the relay cell responses. The IFB model is constrained to quantitatively fit our Fourier analysis of experimental relay neuron responses, including: the temporal tuning of the response in both tonic and burst modes, including a finding of low-pass and sometimes broadband behavior of tonic firing and band-pass characteristics during bursting, and the generally greater linearity of tonic compared with burst responses at low frequencies. In tonic mode, both experimental and theoretical responses display a frequency-dependent transition from massively superharmonic spiking to phase-locked superharmonic spiking near 3 Hz, followed by phase-locked subharmonic spiking at higher frequencies. Subharmonic and superharmonic burst responses also were observed experimentally. Characterizing the response properties of the "tuned" IFB model leads to insights regarding the observed stimulus dependence of burst versus tonic response mode in relay neurons. Furthermore the simplicity of the IFB model makes it a candidate for large scale network simulations of thalamic functioning.

Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network.

Spontaneous episodic activity is a general feature of developing neural networks. In the chick spinal cord, the activity comprises episodes of rhythmic discharge (duration 5-90 sec; cycle rate 0.1-2 Hz) that recur every 2-30 min. The activity does not depend on specialized connectivity or intrinsic bursting neurons and is generated by a network of functionally excitatory connections. Here, we develop an idealized, qualitative model of a homogeneous, excitatory recurrent network that could account for the multiple time-scale spontaneous activity in the embryonic chick spinal cord. We show that cycling can arise from the interplay between excitatory connectivity and fast synaptic depression. The slow episodic behavior is attributable to a slow activity-dependent network depression that is modeled either as a modulation of cellular excitability or as synaptic depression. Although the two descriptions share many features, the model with a slow synaptic depression accounts better for the experimental observations during blockade of excitatory synapses.

Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons.

A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Bötzinger complex (pre-BötC) in mammals. Two minimal models of these neurons are proposed. In model 1, bursting arises via fast activation and slow inactivation of a persistent Na+ current INaP-h. In model 2, bursting arises via a fast-activating persistent Na+ current INaP and slow activation of a K+ current IKS. In both models, action potentials are generated via fast Na+ and K+ currents. The two models have few differences in parameters to facilitate a rigorous comparison of the two different burst-generating mechanisms. Both models are consistent with many of the dynamic features of electrophysiological recordings from pre-BötC oscillatory bursting neurons in vitro, including voltage-dependent activity modes (silence, bursting, and beating), a voltage-dependent burst frequency that can vary from 0.05 to >1 Hz, and a decaying spike frequency during bursting. These results are robust and persist across a wide range of parameter values for both models. However, the dynamics of model 1 are more consistent with experimental data in that the burst duration decreases as the baseline membrane potential is depolarized and the model has a relatively flat membrane potential trajectory during the interburst interval. We propose several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.

Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations Of coupled pacemaker neurons.

We have proposed models for the ionic basis of oscillatory bursting of respiratory pacemaker neurons in the pre-Bötzinger complex. In this paper, we investigate the frequency control and synchronization of these model neurons when coupled by excitatory amino-acid-mediated synapses and controlled by convergent synaptic inputs modeled as tonic excitation. Simulations of pairs of identical cells reveal that increasing tonic excitation increases the frequency of synchronous bursting, while increasing the strength of excitatory coupling between the neurons decreases the frequency of synchronous bursting. Low levels of coupling extend the range of values of tonic excitation where synchronous bursting is found. Simulations of a heterogeneous population of 50-500 bursting neurons reveal coupling effects similar to those found experimentally in vitro: coupling increases the mean burst duration and decreases the mean burst frequency. Burst synchronization occurred over a wide range of intrinsic frequencies (0.1-1 Hz) and even in populations where as few as 10% of the cells were intrinsically bursting. Weak coupling, extreme parameter heterogeneity, and low levels of depolarizing input could contribute to the desynchronization of the population and give rise to quasiperiodic states. The introduction of sparse coupling did not affect the burst synchrony, although it did make the interburst intervals more irregular from cycle to cycle. At a population level, both parameter heterogeneity and excitatory coupling synergistically combine to increase the dynamic input range: robust synchronous bursting persisted across a much greater range of parameter space (in terms of mean depolarizing input) than that of a single model cell. This extended dynamic range for the bursting cell population indicates that cellular heterogeneity is functionally advantageous. Our modeled system accounts for the range of intrinsic frequencies and spiking patterns of inspiratory (I) bursting cells found in the pre-Bötzinger complex in neonatal rat brain stem slices in vitro. There is a temporal dispersion in the spiking onset times of neurons in the population, predicted to be due to heterogeneity in intrinsic neuronal properties, with neurons starting to spike before (pre-I), with (I), or after (late-I) the onset of the population burst. Experimental tests for a number of the model's predictions are proposed.

Current clamp and modeling studies of low-threshold calcium spikes in cells of the cat's lateral geniculate nucleus.

Current clamp and modeling studies of low-threshold calcium spikes in cells of the cat's lateral geniculate nucleus. All thalamic relay cells display a voltage-dependent low-threshold Ca2+ spike that plays an important role in relay of information to cortex. We investigated activation properties of this spike in relay cells of the cat's lateral geniculate nucleus using the combined approach of current-clamp intracellular recording from thalamic slices and simulations with a reduced model based on voltage-clamp data. Our experimental data from 42 relay cells showed that the actual Ca2+ spike activates in a nearly all-or-none manner and in this regard is similar to the conventional Na+/K+ action potential except that its voltage dependency is more hyperpolarized and its kinetics are slower. When the cell's membrane potential was hyperpolarized sufficiently to deinactivate much of the low-threshold Ca2+ current (IT) underlying the Ca2+ spike, depolarizing current injections typically produced a purely ohmic response when subthreshold and a full-blown Ca2+ spike of nearly invariant amplitude when suprathreshold. The transition between the ohmic response and activated Ca2+ spikes was abrupt and reflected a difference in depolarizing inputs of <1 mV. However, activation of a full-blown Ca2+ spike was preceded by a slower period of depolarization that was graded with the amplitude of current injection, and the full-blown Ca2+ spike activated when this slower depolarization reached a sufficient membrane potential, a quasithreshold. As a result, the latency of the evoked Ca2+ spike became less with stronger activating inputs because a stronger input produced a stronger depolarization that reached the critical membrane potential earlier. Although Ca2+ spikes were activated in a nearly all-or-none manner from a given holding potential, their actual amplitudes were related to these holding potentials, which, in turn, determined the level of IT deinactivation. Our simulations could reproduce all of the main experimental observations. They further suggest that the voltage-dependent K+ conductance underlying IA, which is known to delay firing in many cells, does not seem to contribute to the variable latency seen in activation of Ca2+ spikes. Instead the simulations indicate that the activation of IT starts initially with a slow and graded depolarization until enough of the underling transient (or T) Ca2+ channels are recruited to produce a fast, "autocatalytic" depolarization seen as the Ca2+ spike. This can produce variable latency dependent on the strength of the initial activation of T channels. The nearly all-or-none nature of Ca2+ spike activation suggests that when a burst of action potentials normally is evoked as a result of a Ca2+ spike and transmitted to cortex, this signal is largely invariant with the amplitude of the input activating the relay cell.

The role of dendrites in auditory coincidence detection.

Coincidence-detector neurons in the auditory brainstem of mammals and birds use interaural time differences to localize sounds. Each neuron receives many narrow-band inputs from both ears and compares the time of arrival of the inputs with an accuracy of 10-100 micros. Neurons that receive low-frequency auditory inputs (up to about 2 kHz) have bipolar dendrites, and each dendrite receives inputs from only one ear. Using a simple model that mimics the essence of the known electrophysiology and geometry of these cells, we show here that dendrites improve the coincidence-detection properties of the cells. The biophysical mechanism for this improvement is based on the nonlinear summation of excitatory inputs in each of the dendrites and the use of each dendrite as a current sink for inputs to the other dendrite. This is a rare case in which the contribution of dendrites to the known computation of a neuron may be understood. Our results show that, in these neurons, the cell morphology and the spatial distribution of the inputs enrich the computational power of these neurons beyond that expected from 'point neurons' (model neurons lacking dendrites).

Propagating activity patterns in large-scale inhibitory neuronal networks.

The propagation of activity is studied in a spatially structured network model of gamma-aminobutyric acid-containing (GABAergic) neurons exhibiting postinhibitory rebound. In contrast to excitatory-coupled networks, recruitment spreads very slowly because cells fire only after the postsynaptic conductance decays, and with two possible propagation modes. If the connection strength decreases monotonically with distance (on-center), then propagation occurs in a discontinuous manner. If the self- and nearby connections are absent (off-center), propagation can proceed smoothly. Modest changes in the synaptic reversal potential can result in depolarization-mediated waves that are 25 times faster. Functional and developmental roles for these behaviors and implications for thalamic circuitry are suggested.

Mechanisms of spontaneous activity in the developing spinal cord and their relevance to locomotion.

The isolated lumbosacral cord of the chick embryo generates spontaneous episodes of rhythmic activity. Muscle nerve recordings show that the discharge of sartorius (flexor) and femorotibialis (extensor) motoneurons alternates even though the motoneurons are depolarized simultaneously during each cycle. The alternation occurs because sartorius motoneuron firing is shunted or voltage-clamped by its synaptic drive at the time of peak femorotibialis discharge. Ablation experiments have identified a region dorsomedial to the lateral motor column that may be required for the alternation of sartorius and femorotibialis motoneurons. This region overlaps the location of interneurons activated by ventral root stimulation. Wholecell recordings from interneurons receiving short latency ventral root input indicate that they fire at an appropriate time to contribute to the cyclical pause in firing of sartorius motoneurons. Spontaneous activity was modeled by the interaction of three variables: network activity and two activity-dependent forms of network depression. A "slow" depression which regulates the occurrence of episodes and a "fast" depression that controls cycling during an episode. The model successfully predicts several aspects of spinal network behavior including spontaneous rhythmic activity and the recovery of network activity following blockade of excitatory synaptic transmission.

Low-amplitude oscillations in the inferior olive: a model based on electrical coupling of neurons with heterogeneous channel densities.

The mechanism underlying subthreshold oscillations in inferior olivary cells is not known. To study this question, we developed a single-compartment, two-variable, Hodgkin-Huxley-like model for inferior olive neurons. The model consists of a leakage current and a low-threshold calcium current, whose kinetics were experimentally measured in slices. Depending on the maximal calcium and leak conductances, we found that a neuron model's response to current injection could be of four qualitatively different types: always stable, spontaneously oscillating, oscillating with injection of current, and bistable with injection of current. By the use of phase plane techniques, numerical integration, and bifurcation analysis, we subdivided the two-parameter space of channel densities into four regions corresponding to these behavioral types. We further developed, with the use of such techniques, an empirical rule of thumb that characterizes whether two cells when coupled electrically can generate sustained, synchronized oscillations like those observed in inferior olivary cells in slices, of low amplitude (0.1-10 mV) in the frequency range 4-10 Hz. We found that it is not necessary for either cell to be a spontaneous oscillator to obtain a sustained oscillation. On the other hand, two spontaneous oscillators always form an oscillating network when electrically coupled with any arbitrary coupling conductance. In the case of an oscillating pair of electrically coupled nonidentical cells, the coupling current varies periodically and is nonzero even for very large coupling values. The coupling current acts as an equalizing current to reconcile the differences between the two cells' ionic currents. It transiently depolarizes one cell and/or hyperpolarizes the other cell to obtain the regenerative response(s) required for the synchronized oscillation. We suggest that the subthreshold oscillations observed in the inferior olive can emerge from the electrical coupling between neurons with different channel densities, even if the inferior olive nucleus contains no or just a small proportion of spontaneously oscillating neurons.

Sensing and refilling calcium stores in an excitable cell.

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ mobilization leads to depletion of the endoplasmic reticulum (ER) and an increase in Ca2+ entry. We show here for the gonadotroph, an excitable endocrine cell, that sensing of ER Ca2+ content can occur without the Ca2+ release-activated Ca2+ current (Icrac), but rather through the coupling of IP3-induced Ca2+ oscillations to plasma membrane voltage spikes that gate Ca2+ entry. Thus we demonstrate that capacitative Ca2+ entry is accomplished through Ca(2+)-controlled Ca2+ entry. We develop a comprehensive model, with parameter values constrained by available experimental data, to simulate the spatiotemporal behavior of agonist-induced Ca2+ signals in both the cytosol and ER lumen of gonadotrophs. The model combines two previously developed models, one for ER-mediated Ca2+ oscillations and another for plasma membrane potential-driven Ca2+ oscillations. Simulations show agreement with existing experimental records of store content, cytosolic Ca2+ concentration ([Ca2+]i), and electrical activity, and make a variety of new, experimentally testable predictions. In particular, computations with the model suggest that [Ca2+]i in the vicinity of the plasma membrane acts as a messenger for ER content via Ca(2+)-activated K+ channels and Ca2+ pumps in the plasma membrane. We conclude that, in excitable cells that do not express Icrac, [Ca2+]i profiles provide a sensitive mechanism for regulating net calcium flux through the plasma membrane during both store depletion and refilling.

Compartmental model of vertebrate motoneurons for Ca2+-dependent spiking and plateau potentials under pharmacological treatment.

In contrast to the limited response properties observed under normal experimental conditions, spinal motoneurons generate complex firing patterns, such as Ca2+-dependent regenerative spiking and plateaus, in the presence of certain neurotransmitters and ion-channel blockers. We have developed a quantitative motoneuron model, based on turtle motoneuron data, toinvestigate the roles of specific ionic currents and the effects of their soma and dendritic distribution in generating these complex firing patterns. In addition, the model is used to explore the effects of multiple ion channel blockers and neurotransmitters that are known to modulate motoneuron firing patterns. To represent the distribution of ionic currents across the soma and dendrites, the model contains two compartments. The soma compartment, representing the soma and proximal dendrites, contains Hodgkin-Huxley-like sodium (INa) and delayed rectifier K+ (IK-dr) currents, an N-like Ca2+ current (ICa-N), and a calcium-dependent K+ current [IK(Ca)]. The dendritic compartment, representing the lumped distal dendrites, contains, in addition to ICa-N and IK(Ca) as in the soma, a persistent L-like calcium current (ICa-L). We determined kinetic parameters for INa, IK-dr, ICa-N, and IK(Ca) in order to reproduce normal action-potential firing observed in turtle spinal motoneurons, including fast and slow afterhyperpolarizations (AHPs) and a linear steady-state frequency-current relation. With this parameter set as default, a sequence of pharmacological manipulations were systematically simulated. A small reduction of IK-dr [mimicking the experimental effect of tetraethylammonium (TEA) in low concentration] enhanced the slow AHP and caused calcium spiking (mediated by ICa-N) when INa was blocked. Firing patterns observed experimentally in high TEA [and tetrodotoxin (TTX)], namely calcium spikes riding on a calcium plateau, were reproduced only when both IK-dr and IK(Ca) were reduced. Dendritic plateau potentials, mediated by ICa-L, were reliably unmasked when IK(Ca) was reduced, mimicking the experimental effect of the bee venom apamin. The effect of 5-HT, which experimentally induces the ability to generate calcium-dependent plateau potentials but not calcium spiking, was reproduced in the model by reducing IK(Ca) alone. The plateau threshold current level, however, was reduced substantially if a simultaneous increase in ICa-L was simulated, suggesting that serotonin (5-HT) induces plateau potentials by regulating more than one conductance. The onset of the plateau potential showed significant delays in response to near-threshold, depolarizing current steps. In addition, the delay times were sensitive to the current step amplitude. The delay and its sensitivity were explained by examining the model's behavior near the threshold for plateau onset. This modeling study thus accurately accounts for the basic firing behavior of vertebrate motoneurons as well as a range of complex firing patterns invoked by ion-channel blockers and 5-HT. In addition, our computational results support the hypothesis that the electroresponsiveness of motoneurons depends on a nonuniform distribution of ionic conductances, and they predict modulatory effects of 5-HT and properties of plateau activation that have yet to be tested experimentally.

Modeling plasma membrane and endoplasmic reticulum excitability in pituitary cells.

The response of gonadotrophs to secretagogues involves dose-dependent, complex dynamic patterns of electrical activity and inositol 1,4,5-trisphosphate (InsP(3))-induced Ca(2+) mobilization, including pulsatility and oscillations on multiple time scales from milliseconds to minutes. Detailed in vitro experiments have enabled the identification of key mechanisms that underlie the plasma membrane (PM) electrical excitability and endoplasmic reticulum (ER) calcium excitability. We summarize these findings and review computer simulations of a biophysical model that resynthesizes and couples these components and that reproduces quantitatively the observed time courses and dose-response characteristics, as well as effects of various pharamacological manipulations. The theory suggests that cytosolic calcium is the primary messenger in coordinating the PM and ER regenerative behaviors during ER depletion and refilling.

Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons.

Burst firing of dopaminergic neurons of the substantia nigra pars compacta can be induced in vitro by the glutamate agonist N-methyl-D-aspartate. It has been suggested that the interburst hyperpolarization is due to Na+ extrusion by a ouabain-sensitive pump [Johnson et al. (1992) Science 258, 665-667]. We formulate and explore a theoretical model, with a minimal number of currents, for this novel mechanism of burst generation. This minimal model is further developed into a more elaborate model based on observations of additional currents and hypotheses about their spatial distribution in dopaminergic neurons [Hounsgaard (1992) Neuroscience 50, 513-518; Llinás et al. (1984) Brain Res. 294, 127-132]. Using the minimal model, we confirm that interaction between the regenerative, inward N-methyl-D-aspartate-mediated current and the outward Na(+)-pump current is sufficient to generate the slow oscillation (approximately 0.5 Hz) underlying the burst. The negative-slope region of the N-methyl-D-aspartate channel's current-voltage relation is indispensable for this slow rhythm generation. The time-scale of Na(+)-handling determines the burst's slow frequency. Moreover, we show that, given the constraints of sodium handling, such bursting is best explained mechanistically by using at least two spatial, cable-like compartments: a soma where action potentials are produced and a dendritic compartment where the slow rhythm is generated. Our result is consistent with recent experimental evidence that burst generation originates in distal dendrites [Seutin et al. (1994) Neuroscience 58, 201-206]. Responses of the model to a number of electrophysiological and pharmacological stimuli are consistent with known responses observed under similar conditions. These include the persistence of the slow rhythm when the tetrodotoxin-sensitive Na+ channel is blocked and when the soma is voltage-clamped at -60 mV. Using our more elaborate model, we account for details of the observed frequency adaptation in N-methyl-D-aspartate-induced bursting, the origin of multiple spiking and bursting mechanisms, and the interaction between two different bursting mechanisms. Besides reproducing several well established firing patterns, this model also suggests that new firing modes, not yet recorded, might also occur in dopaminergic neurons. This model provides mechanistic insights and explanations into the origin of a variety of experimentally observed membrane potential firing patterns in dopaminergic neurons, including N-methyl-D-aspartate-induced bursting and its dendritic origin. Such a model, capable of reproducing a number of realistic behaviors of dopaminergic neurons, could be useful in further studies of the basal ganglia-thalamocortical motor circuit. It may also shed light on bursting that involves N-methyl-D-aspartate channel activity in other neuron types.