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1Center for Computational Science, Tulane University, New Orleans 70118; 2Department of Psychology, University of New Orleans, New Orleans, Louisiana 70148; and 3Department of Neurology, Oregon Health Sciences University, Portland, Oregon 97201
Submitted 22 January 2003; accepted in final form 8 September 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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; Schultz 1998; Spanagel and Weiss 1999). They are also implicated in neuropsychiatric disorders including schizophrenia (Weinberger 1987), drug abuse (Koob et al. 1987), and Parkinson's disease (Obeso et al. 2000). This relatively homogenous population of neurons (but see Liss et al. 2001; Neuhoff et al. 2002) is located in the ventral tegmental area (VTA or A10), the substantia nigra pars compacta (SNC or A9), and the retrorubral area (A8).
Midbrain DA neurons in vivo exhibit at least two major firing patterns: single-spike firing, which is often irregular, and burst firing (Freeman et al. 1985; Grace and Bunney 1984a,b; Tepper et al. 1995; Wilson et al. 1977). Activation of N-methyl-D-aspartate (NMDA) receptors has been implicated in burst firing in vivo (Chergui et al. 1993). The mechanisms by which the firing pattern is regulated are of interest because the firing pattern is likely to encode information that is transmitted to target neurons. Transitions between burst firing and single-spike firing have been observed in single-neuron recordings from behaving rats (Freeman et al. 1985). The transition to bursting appeared to be correlated with an orienting response to a sensory stimulus (Freeman et al. 1985). When spikes are clustered into bursts, the increases in levels of extracellular dopamine in the projection area are much larger per spike than those observed for regularly spaced trains of action potentials at the same average frequency due to nonlinear summation as release outpaces uptake (Wightman and Zimmerman 1990). Furthermore, a bursting pattern of stimulation of the medial forebrain bundle increased the expression of one immediate early gene (cfos) (Chergui et al. 1996) and increased the mRNA expression of several immediate early genes (Chergui et al. 1997) in the dopamine-innervated brain areas of the rat, whereas a regular single-spike stimulation pattern did not.
In contrast to the activity exhibited in vivo, dopamine neurons in vitro generally fire in a regular single spike-firing pattern. Bath application of NMDA can induce burst firing in vitro under some circumstances (Johnson and North 1992), and increasing the activation of GABAA receptors in vitro by applying the appropriate agonist can convert NMDA-induced burst firing to single spike firing (Johnson and Canavier 1998; Paladini et al. 1999b). Blocking the calcium-activated small conductance (SK) potassium channel facilitates bursting in vitro (Seutin et al. 1993) and can putatively induce burst firing in the absence of NMDA (Nedergaard et al. 1993; Ping and Shepard 1996) as well. Under other conditions, an SK channel blocker such as apamin can induce irregular single-spike firing (Ping and Shepard 1996).
Spontaneous synaptic potentials from excitatory amino acid (EAA) and GABAergic inputs are not usually observed in the slice preparation, although spontaneous events that appear to be GABAA-mediated postsynaptic potentials (PSPs) can be observed if extracellular potassium concentration is increased (Johnson and North 1992). Thus the major difference between dopamine neurons in vivo versus in vitro is that the synaptic afferents are intact in vivo, leading to a much lower input resistance as measured with sharp electrodes [192 ± 12 (SE) M
(Johnson and North 1992), 183 ± 5 (SE) M (Ping and Shepard 1996), 152 ± 14 (SE) M (Scroggs et al. 2001), 292 ± 11 (SE) M (Seutin et al. 1997), and 117.5 ± 4.8 (SD) M (Yung et al. 1991) versus 31.2 ± 7.4 (SD) M (Grace and Bunney 1983)], and a shorter time constant [33 ± 2 (SE) ms (Johnson and North 1992) and 37.5 ± 1.9 (SD) ms (Yung et al. 1991) versus 12.1 ± 3.2 (SD) ms (Grace and Bunney 1983)]. We have assumed that the difference in input resistance is primarily due to the tonic activation of the GABAA receptors in vivo because 70-90% of all the inputs to the DA neurons are GABAergic (Bolam and Smith 1990; Smith and Bolam 1990). The main sources of GABAergic inputs to DA neurons originate from the substantia nigra pars reticulata, striatum, and pallidum, which all exert their effects via GABAA receptors (Celada et al. 1999).
The application of the GABAA receptor antagonists such as picrotoxin and bicuculline strongly promotes burst firing in vivo (Paladini and Tepper 1999). However, bicuculline also blocks the apamin-sensitive SK channel (Johnson and Seutin 1997), and blockade of this channel has also been recently shown to promote burst firing in vivo (Seutin et al. 2002). We used a multi-compartmental model of a DA neuron with a realistic morphological structure and electrotonic properties to explore the effects of varying the levels of activation of NMDA and GABAA receptors as well as the level of modulation of the SK current on the firing pattern because experimental data suggest that all three play a major role. Burst firing mechanisms (and oscillatory mechanisms in general) require a fast positive feedback process and a slow negative feedback process (Rinzel and Ermentrout 1998). As in previous models (Canavier 1999; Komendantov and Canavier 2002; Li et al. 1996), we assumed that the fast positive feedback process is the voltage-dependent opening and closing of NMDA receptor channels in the presence of tonic activation of those receptors, whereas the slow negative feedback is provided by the sodium activation of the sodium pump resulting from changes in sodium concentration in the dendrites due to sodium entry via NMDA receptors and sodium removal by the pump itself (Johnson and North 1992). This mechanism is controversial, but we believe it is the best available explanation of NMDA-induced burst firing in vitro and have incorporated it into our in vivo model as well, although we acknowledge that it may not be the sole bursting mechanism exhibited by these neurons (Amini et al. 1999). A preliminary report of our findings has been published in abstract form (Komendantov and Canavier 2001).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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TISSUE PREPARATION. Male Sprague-Dawley rats (150-300 g; Bantin and Kingman, Seattle, WA) were anesthetized with halothane and killed by severing major thoracic vessels. The whole brain was quickly removed and submerged in ice-cold artificial cerebral fluid (ACSF). A vibrating microtome (Lancer) was used to cut slices of midbrain (300 µm) in the horizontal plane. A slice was then placed on a nylon mesh in a recording chamber (volume: 0.5 µl) and secured by two titanium electron microscopy grids that were held in place by small pieces of platinum wire (0.5 mm diam). The slice was submerged in continuously flowing (2 ml/min) ACSF of the following composition (in mM): 126 NaCl, 2.5 KCl, 1.2 NaH2PO4, 1.2 MgCl2, 2.4 CaCl2, 10 glucose, and 18 NaHCO3; gassed with 95% O2-5% CO2, pH 7.4, at 36°C.
INTRACELLULAR RECORDINGS. Microelectrodes were made from borosilicate capillary tubing (1.0 mm OD, 0.5 mm ID; Dagan) using a P-97 Flaming-Brown micropipette puller (Sutter Instrument, Novato, CA). Microelectrodes were filled with either 2 M potassium chloride or potassium acetate with resistances of 45-150 M. Membrane voltage was amplified with an Axoclamp-2B amplifier (Axon Instruments, Foster, CA) and recorded on an IBM-compatible personal computer running Axotape (Axon Instruments) software. To ensure accurate measurement of voltage, recordings were made with an active bridge circuit that was frequently checked for proper balance by passing small (50 pA) current steps while voltage output was monitored on an oscilloscope. Membrane input resistance was calculated by measuring the change in membrane potential in response to small (20-100 pA) hyperpolarizing current pulses.
IDENTIFICATION OF DOPAMINE NEURONS. Using a dissection microscope, the VTA was identified as the region lateral to the fasciculus retroflexus and medial to the medial terminal nucleus of the accessory optic tract, whereas the SNC was located immediately rostral and caudal to the medial terminal nucleus of the accessory optic tract (Paxinos and Watson 1986). Neurons were identified as dopaminergic using well-established electrophysiological and pharmacological criteria (Grace and Onn 1989; Lacey et al. 1989; Yung et al. 1991). Briefly, dopamine-containing neurons were identified as such by their broad action potentials (>2 ms), spontaneous pacemaker-like firing pattern (1-5 Hz), by the "sag" in membrane potentials recorded during hyperpolarizing current pulses (signifying H current), and by 5- to 15-mV hyperpolarization evoked by superfusing the slice with dopamine (30 µM). Because we found no differences in results from neurons recorded in the SNC and VTA, data from these regions were pooled.
PHARMACOLOGICAL MATERIALS. All drugs were added to the superfusate. Drug solutions required 
2 min for equilibration due to the time required by pass though a heat exchanger. Bicuculline-free base (BFB) was dissolved in dimethyl sulfoxide as a stock solution, which was subsequently diluted 1:1,000 in ACSF prior to use. We have shown previously that this concentration of dimethyl sulfoxide has no effect on burst firing (Johnson and Seutin 1997). Stock solutions of all other drugs were mad in water and diluted 1:1,000 in ACSF prior to use. Bicuculline methiodine (BMI), BFB, NMDA, and isoguvacine were obtained from Research Biochemicals International (Natick, MA), whereas apamin, dopamine HCl, and tetrodotoxin (TTX) were obtained from Sigma Chemical (St. Louis, MO).
BURST FIRING. Dopamine neurons were induced to fire in bursts by perfusing the slice with NMDA (20 µM) and apamin (100 nM) as described previously (Johnson et al. 1992). Burst firing was defined as a repeating pattern in which each "burst" of action potentials, consisting of at least three spikes firing at a frequency of 
10 Hz, is separated by an interburst hyperpolarization of 5 mV (Seutin et al. 1993). A constant hyperpolarizing current (50-250 pA) was passed though the electrode as needed to prevent excessive NMDA-induced depolarization.
Modeling procedures
MODEL DEVELOPMENT. We used a modified version of compartmental model of DA neuron as described by Komendantov and Canavier (2002) but with a more realistic morphological structure, which consists conceptually of a soma and four identical branched dendrites with a single proximal and two distal branches (Fig. 1) and allowed us to use realistic values for the passive properties in intensive units, while still matching the macroscopic properties such as the input resistance and the time constant. The distal portions of the dendrites can sustain an oscillation in current even when the soma is voltage clamped (Johnson and North 1992), so the need for the distal dendritic compartment is clear. The inclusion of a proximal dendritic compartment allows the electrotonic effects of coupling between the soma and distal dendrites to be simulated more realistically with minimum computational overhead. It is certainly possible to reduce the model to two compartments, or even one, but in the case of a single compartment, direct comparison of the model with physiological data recorded from the soma would no longer be possible.
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; Preston et al. 1981; Tepper et al. 1987) and those of real DA neurons in vitro and in vivo. The electrical activity (Johnson et al. 1992; Paladini et al. 1999b; Wang et al. 1994) is also comparable to that of physiological DA neurons. The membrane potential of each compartment of the model neuron obeys the current balance equation
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; Smith et al. 1996).
Calcium dynamics were added to the soma, which is described by a calcium balance equation
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, a calcium leakage current IL,Ca,s = gL,Ca,s(Vs - ECa), and an apamin-sensitive current IK,Ca,SK = gK,Ca,SK {1/[1+ (KM,K,Ca/[Ca2+]in)4]}(Vs - EK). For all gating variables X = dT, dN, dL, fT, the dynamics of X was described by dX/dt = (X
(Vs) - X)/
x, where x is the time constant. The steady-state voltage dependence was determined using X(Vs) = 1.0/{1.0 + exp[-(Vs - Vhalf,x)/
x]}, where Vhalf,x is the half activation voltage for the gating variable X, x is the slope factor for that variable. The time constants were described by x = Ax x exp(-[(Vs - Vhalf,x)/
x]2) + Bx. For Z = fCa,L, fCa,N, the steady-state calcium dependent inactivation function was modeled as Z(Ca2+) = KM,Z/(KM,Z + [Ca2+]in). Although voltage-activated calcium channels are present on the dendrites in these neurons (Wilson and Callaway 2000), we omitted calcium dynamics in the dendrites as the simplest way of implementing the segregation of calcium entry through NMDA receptors from SK channels that is observed experimentally (Canavier and Johnson 1999; Morikawa et al. 2003). The descriptions of the calcium currents were taken from Amini et al. (1999) with a few modifications as noted in the following text. Several currents included in Amini et al. (1999) were omitted for simplicity: a high-voltage threshold calcium current, the hyperpolarization-activated cation current, and the sodium-calcium exchanger. In addition, the slow component of ICa,T described by Amini et al. (1999) was ignored, the form of the calcium-dependency of IK,Ca,SK was changed to accommodate the data presented in this paper, and some parameters of IK,DR and ICa,L were adjusted. The NMDA-induced current (INMDA) was simulated using a Goldman-Hodgkin-Katz equation (Canavier 1999; Komendantov and Canavier 2002) and an instantaneous magnesium block (p) described by p = 0.0225 + 0.9775/[1 + ([Mg]out/Km,Mg) exp(-V/q)].
Currents evoked by GABAA receptors activation were modeled as a linear leak IGABAA,i = gGABAA,i(Vi - ECl). The simulated distribution of the GABAA receptors in different compartments (soma, proximal dendrites, and distal dendrites) was based on the assumption that synapses on cell body are mainly inhibitory (Kandel and Siegelbaum 2000) and evidence of a preferential effect of GABA on the somata of dopamine neurons compared with the dendrites (Kalivas 1993). We used the following ratio between the conductances for GABAA-induced currents in all simulations: gGABAA,s:gGABAA,p:gGABAA,d = 1:0.1:0.1. The leakage current (IL) composed of calcium (IL,Ca in soma only), sodium (IL,Na), and potassium (IL,K) was adjusted along with other passive parameters to obtain better correspondence to the input resistance (215 M) (Johnson and North 1992; Ping and Shepard 1996), and time constant ( = 31 ms) (Johnson and North 1992) experimentally observable in vitro. These values were measured by applying 94 pA of hyperpolarizing current via a simulated electrode in the soma to hold the membrane potential at -66 mV to suppress the spontaneous SOP, then applying an additional 71 pA of hyperpolarizing current for 600 ms to measure the input resistance and the time constant. The dynamics of the model neuron were described by 14 first-order differential equations in the soma (V, [Na]in, [Ca]in, m, h, n, q, s, dT, fT, dN, dL, fCa,L, fCa,N) and by eight first-order differential equations each in the proximal and distal dendrites (V, [Na]in, m, h, n, p, q, and s). As in Canavier (1999), symmetry was invoked so that only a single instance of the somatic, proximal dendritic, and distal dendritic compartments was integrated. The additional currents from Amini et al. (1999) were inserted into the soma only of the single neuron model described in the appendix of Komendantov and Canavier (2002). The values of the parameters that are not the same as those given in Komendantov and Canavier (2002) or Amini et al. (1999) are presented in Table 1.
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) with a 350-ms voltage step to -30 mV from a holding potential -60 mV is shown in Fig. 2, A1. Simulated block of the SK channels eliminates the peak current of 1,200 pA with a latency of 200 ms, and the peak tail current of 450 pA.
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) using a simulated voltage clamp in the soma. The conductances for the L-type calcium current (gCa,L) and the fast sodium current (gNa,i) were set to zero to simulate the application of nifedipine and tetrodotoxin, respectively. The holding potential was -60 mV, the pulse duration was 800 ms, and the incremental voltage step was 10 mV. The control current was recorded at the end of the test potential. The series of experiments in the presence of 10 µM NMDA was reproduced with PNMDA = 0.4 · 10-6 cm/s, and the recorded current was subtracted from the control current to obtain the difference current. The ratio of PNMDA,d: PNMDA,p = 1:1 on the distal and proximal dendrites produced the best fit to the experimental data. Figure 2A2 shows that the simulated NMDA difference currents (—) closely resemble those (- · -) obtained by Wu and Johnson (1996) in 10 µM NMDA. The region of negative slope in the current-voltage curve from -90 to -50 mV causes positive feedback, which is essential to the generation of the oscillation underlying burst firing (Mereu et al. 1991; Overton and Clark 1997; Wu and Johnson 1996).
The model produces spontaneous spiking in a simulation of an in vitro preparation in normal Ringer solution (PNMDA,i = 0; gGABAA,i = 0; Fig. 2B1). The simulated application of apamin by setting gK,Ca,SK = 0 (Fig. 2B2) decreased the afterhyperpolarization (AHP) after the action potential by 15 mV and increased spike frequency, which is consistent with experimental data (Johnson and Seutin 1997; Ping and Shepard 1996; Shepard and Bunney 1991). If application of TTX is simulated instead by setting gNA,i = 0, slow oscillations in membrane potential with an amplitude of 10 mV (Fig. 2B3) result from the interaction of Ca2+ and Ca2+-dependent conductances (Kang and Kitai 1993).
MODEL IMPLEMENTATION. As in previous research (Canavier 1999; Komendantov and Canavier 2002), the simulations and programs for analysis were coded in the C programming language. Numerical integrations of simulations were performed using the Fortran implementation of an implicit Runge-Kutta method of order five with variable step size (Hairer and Wanner 1996).
ANALYSIS OF MODEL ACTIVITY. The analysis of model responses used the time courses of V and interspike intervals (ISIs); the first 30 s of a simulation was considered as a transient period and excluded. The next 20 s of simulations were recorded and analyzed. The control parameters were the permeability for the NMDA-induced current in the dendrites (PNMDA), corresponding to the level of excitation, and the conductance for the GABAA receptor current in soma (gGABAA,s), corresponding to the level of inhibition. The automated determination of the mode of activity (regular and irregular spiking, regular and irregular bursting) was made according to algorithms used for the previous model (Komendantov and Canavier 2002) with minor changes to the evaluation criteria for burst determination. Bursts were defined as groups of at least two spikes terminated by an interburst interval of 160 ms (Grace and Bunney 1984b) with hyperpolarization of 5 mV (Johnson and Seutin 1997). The selection criteria for detection of irregularity in the model activity were determined empirically and confirmed by visual observation of the membrane potential waveform in many instances.
The dependence of input resistance on gGABAA was calculated with the NMDA-induced permeability (PNMDA) set to zero using the methods described in the preceding text. The values of the conductance for the GABAA receptor currents were varied from 0 to 2,750 µS/cm2 for the soma and from 0 to 275 µS/cm2 for the dendritic compartments. We selected the range of gGABAA that produced a physiologically acceptable range of input resistance in vivo.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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We used a concentration of 100 µM isoguvacine because preliminary studies showed that this concentration of this GABAA receptor agonist is near the EC50 value for increasing conductance in DA neurons. In all dopamine neurons tested (n = 3), isoguvacine markedly inhibited NMDA-dependent burst firing and membrane oscillations, as seen in Fig. 3A.
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Simulation of effects of GABAA receptor stimulation on bursting in vitro
Figure 3B shows that the simulated addition of isoguvacine in the bath in the simulated presence of both NMDA and apamin converts burst firing to single-spike firing as in the in vitro experiments (Fig. 3A, 1 and 2). The application of isoguvacine (100 µM) was simulated by adding an ohmic GABAA receptor current that reversed at -70 mV with gGABAA,s = 350 µS/cm2, gGABAA,p = 35 µS/cm2, gGABAA,d = 35 µS/cm2. The value of the reversal potential for this current was chosen based on its correspondence to the chloride reversal potential determined experimentally in DA neuron using micropipettes filled with potassium acetate (Johnson and North 1992). GABAA receptor-mediated depolarizations in dopamine neurons have been shown to be due to the shift in the Nernst potential for chloride, which is -72 ± 4 mV with potassium acetate-filled microelectrodes but shifts to -36 ± 6 mV when potassium chloride-filled microelectrodes raise the intracellular concentration of chloride (Johnson and North 1992).
The simulated application of isoguvacine in the absence of NMDA and apamin decreases the input resistance by 63% (from its control value of 215 to 80 M), which is within the range of the decrease in input resistance (58 ± 6%) that we observed experimentally. In both experiment and simulation, a constant hyperpolarizing current of 180 pA was applied, and the average membrane potential did not change significantly.
Joint modulation of the firing pattern by the activity of NMDA and GABAA receptors
The firing pattern of DA neurons depends on the activation of both excitatory inputs and inhibitory inputs. Komendantov and Canavier (2002) investigated the dependence of the firing pattern of an in vitro model of DA neuron on the simulated level of activation of the excitatory NMDA inputs. As PNMDA was increased, the firing pattern changed from low-frequency single spiking to bursting and then to high-frequency spiking. We observed similar transitions here. An increase in PNMDA leads to an increase in the firing frequency as well as transitions from low-frequency spiking through regular and irregular bursting to high-frequency spiking. These sequences correspond to those observed in in vitro experiments as the concentration of NMDA in the bath is increased (Johnson et al. 1992; Paladini et al. 1999b; Wang et al. 1994; Wu and Johnson 2001) except that those studies show depolarization block rather than high-frequency spiking.
The conductance for IGABAA,s was also varied at a fixed value of PNMDA = 2.3 · 10-6 cm/s, which results in burst firing in the absence of GABAA receptor activation. At this fixed value of PNMDA, the different regimes may be distinguished as gGABAA,s is increased: regular bursting (Fig. 4A, 1 and 3), irregular bursting (Fig. 4A2), single spiking (Fig. 4A, 4 and 5) and a silent regime (gGABAA,s > 2,500 µS/cm2). The amplitude of the slow wave decreased as gGABAA,s was increased (Fig. 4B). On the diagram, the minima corresponding to the AHPs after action potentials were extracted using the first and second time derivatives of the membrane potentials (dVs/dt = 0, d2Vs/dt2 > 0). Of these minima, only the most and least hyperpolarized minima at each value of gGABAA,s were plotted on Fig. 4B, thus the upper branch represents the shallowest hyperpolarization during any burst and the lower branch represents the deepest hyperpolarization during any interburst interval.
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; Grace and Bunney 1984a,b).
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Calibration of the GABAergic inputs
Grace and Bunney (1983) showed that nigral dopaminergic neurons have an input resistance in vivo in the range of 18-45 M. Figure 5B shows the dependence of input resistance of model DA neuron on the value of conductance of the linear GABAA receptor current, gGABAA,s. The range of gGABAA,s from 850 to 2,750 µS/cm2 (green bar) corresponds to the range of input resistance experimentally observable in vivo (blue bar). Thus we can use Fig. 5A to explain the effects of the application of GABAA antagonists in vivo (Paladini and Tepper 1999; Paladini et al. 1999a). Every single instance of single-spike firing in the in vivo range (to the right of the dashed line) can be converted to burst firing when gGABAA,s is decreased by 41-65% of its original in vivo value, simulating the in vivo application of a GABAA channel blocker such as picrotoxin. This is consistent with the results of Paladini and Tepper (1999) that revealed that application of GABAA antagonists in vivo (picrotoxin, 200-1,000 µM, and bicuculline methiodide, 200-400 µM) "caused a robust change to a bursty pattern regardless of the baseline firing pattern," although the exact fraction of GABAA receptors blocked and the change in input resistance after the application of picrotoxin the in vivo experiments is not known precisely.
Quantitative analysis of model activity
We computed the average (Fig. 5C) spike frequency for each pair of values of the control parameters, gGABAA,s and PNMDA, for which the model demonstrated spiking or bursting spontaneous activity. Also, we counted the number spikes per burst (Fig. 5D) for each pair of the control parameters when the activity was determined as bursting. In the simulated physiological range of gGABAA,s from 850 to 2,750 µS/cm2, average spiking frequencies are always less 6.5 Hz for low-frequency single-spike firing, whereas they range from 5.0 to 16 Hz for burst firing. Thus there is some correlation between firing pattern and average frequency (Fig. 5, A and C). On each diagram C and D, the vertical dashed line bounds the area which corresponds to the putative in vivo of gGABAA,s. In in vivo experiments, the average frequency has been reported as 0-7.1 Hz (Richards et al. 1997), 0 to 7.0-7.2 Hz (Grace and Bunney 1984b), and <10 Hz (Dai and Tepper 1998); the number spikes per burst lies in the range from 2 to 10, and the maximal number spikes per burst is 23 (Grace and Bunney 1984).
Figures 6, A1 and A2, shows two possible effects of blocking the IK,Ca,SK current on the in vivo activity of DA neuron: a transition from single spiking (A1) to bursting (A2) and a transition from short bursts that contain few spikes to longer bursts containing more spikes (A, 3 and 4).
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22%, to burst firing and prolongs burst duration of the instances of burst firing. The number of instances of irregular spiking in the in vivo range of parameters increased by 60%, from 45 to 72. |
DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Dopamine neurotransmission probably operates on at least three time scales (Schultz 1998): reward responses on the order of tens and hundreds of milliseconds; the processing of a wide array of rewards, feeding, drinking, punishments, stress, and social behavior of a time scale of seconds to minutes; and an enabling function of a variety of motor, cognitive, and motivational processes on a slow, and possibly tonic, time scale. Phasic firing in DA neurons increases within 100 ms after the onset of a salient sensory event (Horvitz 2002). Our results suggest that, due to the relatively slow rate of change of sodium concentration, a DA neuron must already be biased near the bursting range in order for a transient input to cause bursting in such a short interval. The changes in firing pattern we present here are representative of persistent activity after all transients dissipate, under conditions of inputs that remain nearly constant for seconds to minutes.
Role of different receptors in the activation of glutamatergic inputs
The main sources of EAA inputs (for a review, see Kitai et al. 1999; Overton and Clark 1997) to the midbrain DA neurons are the prefrontal cortex (PFC) (Sesack and Pickel 1992), the subthalamic nucleus (STN) (Kita and Kitai 1987), and the pedunculopontine nucleus (PPN) (Tokuno et al. 1988). Minor EAA projections include the amygdala (McDonald 1996; Phillipson 1979), the laterodorsal tegmental nucleus (Clements and Grant 1990; Gould et al. 1989), and the habenula nucleus (Matsuda and Fujimara 1992). Recently a novel EAA projection from the bed nucleus of stria terminalis has been identified (Georges and Aston-Jones 2002). Although glutamate also activates non-NMDA ionotropic receptors (AMPA and kainate) and metabotropic receptors, we have chosen to focus initially on the NMDA receptor, based on the following evidence. The glutamate-induced excitation of DA neurons is more sensitive to the selective blockade of NMDA versus non-NMDA receptors because iontophoresis of glutamate and the selective NMDA receptor antagonist (±)-3-(-2-carboxypiperazin-4-yl)-propyl-1-phosphonic acid (CPP) produced an 80% reduction of the glutamate-induced increase in firing (Christoffersen and Meltzer 1995), whereas glutamate and the AMPA receptor antagonist 2,3-dihydroxy-6-nitro-7-sulfamoyl-benzo-(f)quinoxaline (NBQX) produced only a 26% inhibition of the glutamate-induced excitation. Similarly, Chergui et al. (1993) showed that bursting was blocked by the local application (iontophoresis and pressure ejection) of the NMDA receptor antagonist 2-amino-5-phosphonovaleric acid (AP-5) but not by the AMPA/kainate receptor antagonist 6-cyano-7-nitroquinoxalene-2,3-dione (CNQX) (see also Overton and Clark 1997). The duration of the excitatory postsynaptic current (EPSC) evoked by AMPA is 20 ms (Bonci and Malenka 1999), whereas that evoked by NMDA is much longer lasting (Mercuri et al. 1996; Overton and Clark 1997), on the order of 600 ms (Destexhe et al. 1998). Glutamate affinity for AMPA receptors is lower (EC50 = 19 µM) than for NMDA receptors (EC50 = 2.3 µM) (Patneau and Mayer 1990), thus lower concentrations of glutamate in the cleft are required to activate NMDA receptors, which accounts at least in part for the longer duration of the activation of these receptors. Recent simulations (Canavier and Landry 2002) suggest that only EAA afferent firing frequencies at which NMDA but not AMPA inputs summate temporally are effective in evoking burst firing. Thus modeling the activation of NMDA receptors only is a reasonable first approximation of the effects of glutamatergic inputs.
In the model, we observed high-frequency bursts with a large number of spikes per burst at high values of PNMDA that have not been observed experimentally in vivo. We hypothesize that in vivo the presence of AMPA receptors prevents this pattern of activity. Similar activity with a large number of spikes per burst was obtained in vitro using bath application of NMDA (Wu and Johnson 2001). The inclusion of AMPA receptor activation in the model as a sum of linear leaks for Na+ and K+ (see Canavier 1999) converts this high-frequency spiking into depolarization block (for example, for PNMDA = 3.4 · 10-6 cm/s, gGABAA,i = 0 µS/cm2, gAMPA,K = 30 µS/cm2, gAMPA,Na = 60 µS/cm2). We conclude that AMPA receptors play a more significant role at high levels of glutamate due to the lower affinity of AMPA receptors (Patneau and Mayer 1990) and suggest that AMPA receptors can cause depolarization block at high levels of glutamate rather than the very high-frequency spiking or bursting (28 Hz) observed in the model.
The model predicts some correlation (Fig. 5, A and C) between firing pattern and firing frequency; however, the presence of such a correlation is controversial (see Freeman et al. 1985; Grace and Bunney 1984b; Paladini and Tepper 1999). Paladini and Tepper (1999) did not observe any correlation in vivo when the application of bicucculine or picrotoxin converted single-spike firing to burst firing. Our model, with its assumption of constant parameters that correspond to activation of NMDA and GABAA receptors by the average concentration of transmitter in the cleft, cannot account for this lack of correlation. Therefore additional mechanisms must be postulated to account for it, and we hypothesize that the transient nature of the synaptic dynamics observed in vivo may provide these additional mechanisms.
Possible in vivo analogues of blockade of apamin-sensitive current
Although no endogenous neuromodulator is known to act directly on the receptor on the SK channel that binds apamin, the modulation of this current is nonetheless relevant to the modulation of the firing pattern of dopamine neurons by synaptic afferents. It is not necessary for a neuromodulator to act directly on this current to block it because reducing its access to calcium activation will effectively attenuate it. For example, muscarine (50 µM) reduces the amplitude of the slow AHP that follow action potentials in most substantia nigra DA neurons (Scroggs et al. 2001). The SK current is responsible for the AHP (Shepard and Bunney 1991), and muscarine is believed to exert its effects by reducing calcium entry. Another possible modulatory pathway involves inhibitory PSPs evoked by activation of metabotropic glutamate receptors (mGluR). This results in production of inositol triphosphate, IP3, which causes release of calcium from intracellular stores and, in turn, the activation of the SK channels (Fiorillo and Williams 1998). There is evidence that activation of 
1 adrenergic receptors or M1 muscarinic receptors interferes with the release of calcium from intracellar stores (Fiorillo and Williams 2000; Paladini et al. 2001), decreasing the amount of SK current evoked by mGluR activation. Thus both the noradrenergic afferents from the locus cerulus and the cholinergic afferents from the PPN may attenuate the apamin-sensitive SK current, and there have been suggestions (Brodie et al. 1999) that serotonin, possibly acting via IP3-coupled 5HT2 receptors, may attenuate the SK current as well, which would tend to promote burst firing. Also, dopamine, which is released somatodendritically by DA neurons, has some affinity for the 1 receptor. Thus the results of our simulations showing that blockage of Ca2+-sensitive potassium current may promote or facilitate bursting in DA neuron in vivo (Fig. 6) are probably physiologically relevant.
Recently, Wolfart and Roeper (2002) showed that in response to 20-ms hybrid-clamp depolarizations that evoked action potentials, only calcium entering via the T-type calcium channel activates the apamin-sensitive current. Thus neuromodulators that reduce the T-type calcium current would also indirectly reduce the SK current under similar circumstances. It is possible that the experimental conditions did not mimic the activation pattern of calcium channels exhibited during spontaneous, pacemaker-like firing, which has a contribution from additional calcium currents, such as the L-type calcium current (Kang and Kitai 1993; Mercuri et al. 1994; Nedergaard et al. 1993; Takada et al. 2001). On the other hand, Wolfart and Roeper have suggested that SK channels, T-type calcium channels, and intracellular calcium stores might be selectively colocalized, forming a specialized calcium-signaling complex in which T-type calcium channel influx triggers secondary calcium release that specifically activates SK channels, whereas other types of calcium influx would not. To address these issues, more detailed models that incorporate compartmentalization of calcium are required. Adding voltage-gated calcium channels and calcium dynamics to the dendritic compartments may enhance the ability of the SK channel current to suppress burst firing, as well as the ability of the model to exhibit irregular firing (Wilson and Callaway 2000) due to the desynchronization of calcium oscillations in the various compartments.
How the various manipulations induce or suppress burst firing
This is the first model in which we have combined sodium and calcium dynamics and can simulate regular, calcium-dependent spike firing as well as NMDA-induced burst firing and, as such, is our most complete model of the regulation of the firing pattern in dopamine neurons to date. This model is more focused on the interaction of the various synaptic and intrinsic currents in producing single-spike firing versus bursting than other models of dopamine neurons (Kotter and Feizelmeier 1998; Li et al. 1996; Penney and Britton 2002; Wilson and Callaway 2000). In previous papers (Canavier 1999; Komendantov and Canavier 2002), we used nullcline analyses to gain insight into the mechanisms underlying NMDA-induced burst firing. Although it is not practical to use nullcline analysis on the complex model in this paper, many of the principles from our earlier work still apply. A regenerative, nonlinear current such as the NMDA-induced current is required for a bursting oscillation, whereas linear GABAA receptor currents oppose any oscillation. Therefore the many of the modeling results presented herein are likely to be robust and not highly dependent on the precise mechanism of burst repolarization.
It has been suggested (Paladini et al. 1999b) that GABAA receptor activation prevents the observation of bursting at the soma by a shunt mechanism. If the GABAA receptor current was merely acting as a shunt, that would imply that the distal dendrites continue to oscillate as they did before the GABAA agonist was applied but that the current leaks out of the GABAA channels and so does not reach the soma. In the model, the application of the excess linear current actually suppresses the oscillation in the dendrites, so there is no burst to spread passively (or actively) to the soma. By analogy to classical mechanics, we call this alternative mechanism linear damping. There are other considerations, such as bias. A higher level of NMDA receptor activation does not always lead to more bursting. Excessive depolarization causes the neuron to leave the voltage range in which the nonlinearity is active due to positive feedback is active because all available NMDA channels are already open. Sometimes hyperpolarization that is not excessive can facilitate bursting by bringing the neuron back into the range in which the positive feedback promotes an oscillation. Finally, the spikes themselves may promote or abolish burst firing via complex nonlinear mechanisms. Therefore increases in gGABAA evoke complex nonlinear activity (Fig. 4) that eventually leads to the suppression of bursting. Whereas in general increasing glutamatergic input may promote burst firing and in general increasing GABAergic input reduces burst firing, Fig. 5 shows that the ability of a change in one input to effect a change in pattern often depends on the value of the other input. An interesting possibility is that somatic hyperpolarization promotes or actually enables burst firing in the presence of dendritic glutamatergic input by countering excessive depolarization that prevents the dendrites from bursting.
The SK channel current is known to contribute to the regularity of single-spike firing in dopamine neurons because it mediates the repolarization of the slow oscillatory potential that underlies pacemaker-like firing, thus blocking this current disrupts regular pacemaker-like firing. The nonlinearity associated with the apamin-sensitive current is not regenerative and therefore works to suppress any burst generating nonlinearity (Amini et al. 1999).
The blockade by picrotoxin of GABAA receptors is maximally effective in inducing bursting. Bicuculline blocks not only GABAA receptors, but also the SK channels, the blockage of which also promotes burst firing both in vitro (Seutin et al. 1993) and in vivo (Seutin et al. 2002), so it is not surprising that bicuculline is also maximally effective in inducing burst firing in vivo (Paladini and Tepper 1999). A salient prediction of the model is that blocking the SK channel current in vivo will facilitate bursting but not as robustly as blocking GABAA receptors. If the model is shown to underestimate this effect, the contribution of the SK channel on the dendrites must be reconsidered.
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Address for reprint requests and other correspondence: C. C. Canavier, Dept. of Psychology, University of New Orleans, New Orleans, LA 70148 (E-mail: ccanavie{at}uno.edu).
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