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1Neuroscience Center of Excellence, 2Department of Ophthalmology, Louisiana State University Health Sciences Center; and 3Department of Physics, University of New Orleans, New Orleans, Louisiana
Submitted 7 July 2006; accepted in final form 29 July 2006
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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), schizophrenia (Weinberger 1987), and drug abuse (Koob et al. 1987). The firing pattern in these neurons determines the amount of dopamine released in the projection areas, and a bursting firing pattern releases more dopamine than a tonic one (Chergui et al. 1996; Gonon 1988). Therefore an understanding of dopaminergic signaling must include an understanding of how the firing pattern is regulated. Dopamine neurons in vivo can exhibit one of several firing modes (Grace and Bunney 1984a,b; Hyland et al. 2002): silence, regular single-spike firing, irregular single-spike firing, and bursting. In a bursting cell, the percentage of spikes fired in bursts is variable. DA neurons also exhibit interesting activity in the context of a behavioral task. Recordings from awake, behaving monkeys during reward-mediated learning (Schultz 1998) show that dopamine neurons fire a population burst in response to the delivery of an unexpected primary reward or to a reward-predicting stimulus. Correlation between pattern and rate
The definition of a burst in midbrain dopamine neurons in vivo is based on experimental observations (Grace and Bunney 1984b). The criterion is that a burst begins with an interspike interval (ISI) <80 ms but terminates when the ISI exceeds 160 ms. The spikes identified by this criterion as occurring within a burst are consistent with the perception of bursts on visual inspection; not only the original investigators, but essentially all subsequent ones use the same definition except that some studies consider a doublet to be a burst, whereas others stipulate a minimum of three spikes. Based on the operational definition of a burst, an increase in frequency might reasonably be expected to increase the fraction of spikes occurring in bursts without increasing the tendency to cluster. Because an increase in frequency decreases the average ISI, the probability that an ISI <80 ms would occur and be followed by an ISI <160 ms might be increased by this mechanism alone.
When a single parameter (such as levels of iontophoresis of glutamate or haloperidol) is manipulated in a single neuron while holding all other parameters constant (Grace and Bunney 1984b), the correlation between rate and pattern (fraction of spikes fired in bursts) is excellent (r = 0.99). On the other hand, several studies (Grace and Bunney 1984b; Hyland et al. 2002; Paladini and Tepper 1999) found only a weak correlation (r = 0.14–0.38) between pattern and rate across a population of DA neurons. Furthermore, in one study, burst firing was increased by pressure ejection of bicucculine, and the correlation across the population between changes in the pattern and changes in frequency in the same neuron before and after the manipulation was very low (r = 0.14) (Paladini and Tepper 1999).
These findings and others (Charlety et al. 1991; Overton and Clark 1992) suggest that the rate and pattern can be modulated independently in dopamine neurons, consistent with some independence of the mechanisms generating baseline firing rates and bursts (Hyland et al. 2002). However, if only cells firing >6 Hz are examined, a positive linear relationship emerges between rate and pattern (Hyland et al. 2002; Smith and Grace 1992; Zhang et al. 1994). This relationship seems to be an artifact of the definition of bursting using intervals forburst initiation and termination that are unusual at the range of firing rates usually observed (Hyland et al. 2002) but not necessarily at higher rates. Therefore one challenge was to separate the effects of chance increases in bursting due to increases in frequency and of increases due to enhancing burst firing selectively.
In this study, we examine two different types of modulations. The two modulations were to increase the 
-amino-3-hydroxy-5-methylisoxazole-4-proprionate (AMPA) conductance and to block the small-conductance (SK) Ca2+-activated K+ channel conductance. In the model, increasing AMPA modulates rate and pattern concurrently but blocking SK modulates the firing pattern in a manner that is largely independent of the rate.
Rationale for examining the effect of doubling the AMPA conductance
A doubling of the AMPA component of the synaptic current evoked by glutamate is an example of plasticity that has been observed in dopamine neurons in response to the administration of drugs of abuse, both in vivo (Zhang et al. 1997) and in vitro (Borgland et al. 2004). The ratio of the peak excitatory postsynaptic current (EPSC) evoked by the stimulation of AMPA and N-methyl-D-aspartate (NMDA) receptors can be measured by blocking all other synaptic currents pharmaceutically, voltage clamping the cell to +40 mV, then stimulating the slice. Under these conditions, the ratio of the peak AMPA EPSC to the peak NMDA EPSC can be increased from 0.38 to 0.75 by a single injection of cocaine (Ungless et al. 2001). An increase in the AMPA component was responsible for this change. The AMPA/NMDA ratio was positively correlated with locomotor activity, and Jones and Bonci (2005) speculated that an increase in the synaptic AMPA response could result in an enhancement of the response of dopamine neurons to reward related stimuli. In addition, iontophoretic administration of AMPA has been shown to increase both the frequency and the fraction of spikes fired in bursts in chloral hydrate anesthetized rats (Christoffersen and Meltzer 1995).
Rationale for examining the effect of blocking the SK conductance
Hyland et al. (2002) found a greater intra-burst frequency for bursts in the context of a task within operant behavior experiments than for those occurring at other times. They suggested that a reduction of spike afterhyperpolarization, similar to that produced by the application of the SK blocker apamin, may be involved in the mechanism of inducing bursts in behaving animals. SK channel blockers have been shown to facilitate bursting in vivo in rats under chloral hydrate anesthesia (Ji and Shepard 2006; Waroux et al. 2005). The proportion of spikes fired in three or more spike bursts in the VTA was increased from 20 to 52% with only a slight if any increase in rate. In addition, differential expression of the small-conductance, calcium-activated potassium channel SK3 accounts for differences in the regularity of firing in dopaminergic midbrain neurons (Wolfart et al. 2001). The SK3 subtype is preferentially expressed in the monoamine cell group regions, and some studies have found an association between abnormalities in the SK3 channel gene and schizophrenia (Liegeois et al. 2003). The SK3 channel is not known to be directly modulated, but there are several known modulators of the second-messenger cascades that release calcium from internal stores that can activate the SK channel (Fiorillo and Williams 1998). Acetylcholine (Fiorillo and Williams 2000), norepinephrine, dopamine (Paladini et al. 2001), and serotonin (Brodie et al. 1999) have all been postulated to reduce the access of the SK channel to calcium activation in dopamine neurons, hence these modulators may act to reduce current flow through the SK channel in vivo.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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The three-compartment model of Komendantov et al. (2004) was used with a few modifications (see Fig. 1). Computation was minimized by using a stylized, symmetric model neuron with a soma, four primary, and eight secondary dendrites. Using symmetry, only one compartment of each type was integrated and the electrotonic currents were scaled accordingly (Canavier 1999). All compartments contain a fast sodium current (INa), a delayed rectifying potassium channel (IK,DR), a transient outward potassium current (IK,A), a leak current (IL), and a sodium pump (INaP). Each compartment is capable of spiking (Hausser et al. 1995). All compartments contain sodium dynamics and a sodium balance. The soma also contains calcium dynamics and a calcium balance that includes the voltage-activated T-, N-, and L-type calcium currents (ICa,T, ICa,N, and ICa,L), a calcium component of the leak current (IL,Ca), and a calcium pump (ICaP). Calcium entry in the soma activates the SK channel current (IK,SK). The glutamatergic synapses that produce the AMPA and NMDA currents (IAMPA and INMDA) are located exclusively on the dendrites, and the GABAergic synaptic conductance that produces the GABAergic current (IGABA,A) is located primarily on the soma. As in Komendantov et al. (2004), some IGABA,A is located on the dendrites, but the conductance is 1/10 that on the soma and is not shown in Fig. 1 in order to emphasize that the bulk of the inhibitory input in the model is on the soma.
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; Wilson and Callaway 2000). The model also emulates NMDA-induced burst firing based on an oscillation in dendritic sodium concentration that in the model is driven by the interplay between sodium entering via the voltage-dependent NMDA receptor channel and exiting via the electrogenic sodium pump. The value of the SK conductance was changed from the 900 µS/cm2 reported in Komendantov et al. (2004) to 800 µS/cm2 to obtain robust pacemaker firing, and the axial resistance (Ra) was changed to 400 
cm. Full equations and parameters are given in APPENDIX A. Glutamatergic synaptic current dynamics
A two-state kinetic scheme was used for both AMPA and NMDA receptor dynamics. The rate constants and 
for binding and unbinding, respectively for AMPA (1100 s–1mM–1, 190 s–1) and NMDA (72 s–1mM–1, 6.6 s–1) were taken from Table 1 of Destexhe et al. (1995). Assuming the law of mass action, the explicit solution for the fraction of the population of receptors activated at a synapse is
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is the steady-state value [T]/([T] + ) in the presence of transmitter concentration [T], and 
is the time constant during the pulse, 1/([T] + ). A 1-mM, 1-ms pulse in glutamate concentration in the cleft ([T]) was presumed to occur at the time of a synaptic event. During most simulations, r(tn) was assumed to be zero, hence the potential unavailability of receptors due to a previous recent input at the same synapse was not considered. To take this potential unavailability into account, one would have to assume a fixed number of synapses and generate a dedicated input train for each input. For the simulations of transient inputs, we did assume that a fixed number of synapses were activated; however, we assumed a common input train for all synapses that was the result of a reward-related stimulus, and r(tn) was calculated for each input in the train.
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) generated using a strong stimulus that presumably activated a number of glutamatergic synapses. The model EPSCs (see Fig. 2) were measured under simulated somatic voltage clamp to +40 mV to mimic the conditions in Fig. 1B of Borgland et al. (2004). The delayed rectifier conductance (gK,DR) was set to zero because the patch-clamp electrodes contained TEA, and both internal and external TEA block this current (Lenaeus et al. 2005). Using the kinetic parameters given in the preceding text, the AMPA conductance (gAMPA) and the NMDA receptor channel permeability (PNMDA) to sodium were scaled to match the ratio of the peak AMPA EPSC to peak NMDA EPSC in Fig. 1B of Borgland et al. (2004) that was 0.38 under control conditions and 0.75 after exposure to cocaine. In the absence of precise knowledge of how many synapses were activated, we assumed that ten minimal synaptic events were simultaneously activated by the stimulus during the voltage-clamp simulation.
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The Nernst potential for sodium was allowed to vary based on internal cytosolic concentration to calculate the contribution of IAMPA,Na to the sodium balance. The apparent conductance of the NMDA receptors in the model was estimated by measuring the slope of the linear portions of the current-voltage (I-V) curve generated using the Goldman Hodgkin Katz (GHK) equation for this current. Because the internal sodium and calcium are variable, the slope conductance of the NMDA current associated with a minimal event varies somewhat but is 
100–150 µS/cm2 in the concentration ranges observed during simulations, with a reversal potential near 0 mV. The total AMPA conductance (sodium plus potassium) that we assumed for a minimal event is 6.05 µS/cm2. To determine that the values chosen for a minimal event, the actual conductances were calculated from the densities. The area of the proximal compartment is 14.1 x 10–6 cm2 and that of the distal compartment is 16.5 x 10–6 cm2, for a total dendritic surface area of 188.5 x 10–6 cm2. Thus the minimum distributed synaptic conductance is 1.140 nS for AMPA and 28.275 nS for NMDA. However, to match the peak conductance ratios for the EPSC generated in response to a single strong input, the scaling by the peak r(t) achieved during a pulse of transmitter must be taken into account: the peak r(t) for AMPA is 0.618 compared with only 0.069 for NMDA, resulting in peak conductances for a single input of 705 and 1951 pS, respectively. A recent study (Dalby and Mody 2003) using spontaneous EPSCs in rat dentate gyrus cells estimated the single-channel conductance of an NMDA receptor as 60 pS, and the number of channels open as 4, for a minimum event conductance of 240 pS. Hence, the minimum synaptic input to the model corresponds to about eight spontaneous events as measured in dentate gyrus. The magnitude of the smallest synaptic event in the model, distributed across the 12 conceptual compartments, seems reasonable in view of the simplicity of the model and the lack of precise knowledge regarding the convergence and coherence of the glutamatergic inputs to dopamine neurons. In simulations of the drug-induced plasticity described in the Introduction in which the AMPA/NMDA ratio increased from 0.38 to 0.75, both components of gAMPA were doubled.
Glutamatergic synaptic event statistics
The interevent intervals for the glutamatergic synaptic events were selected using a simulated Poisson process. The input was symmetrically distributed between the proximal and distal compartments. Each event generated a 1 ms pulse of transmitter at a synapse. The output r(t) from all prior events were summed at each time point to produce the cumulative receptor activation R(t). A maximum time step of 0.1 ms was used with the integration package CVODE. The first 90 s of each simulation was discarded to allow the system to equilibrate, and data analysis was performed on the next 90 s of simulated data. The same 90 s of random receptor activation history was used for the discarded 90 s and the 90 s that was analyzed. To speed computation, this input was precomputed and discretized at 0.1 ms and used for all simulation runs at a given average PNMDA regardless of the value of the GABA and SK conductances or the AMPA/NMDA ratio.
In this study, the relative background levels of activation of AMPA and NMDA depend on the average interevent interval (IEI) given in ms. Because we have assumed that a given synapse is not activated often enough to saturate, there is an approximately linear relationship between the average level of NMDA receptor activation (RNMDA) and the reciprocal of the mean interevent interval, [RNMDA] = 10.503 /[IEI], where [ ] indicates the average value. If this relationship is multiplied by the permeability of a single synapse to sodium, we obtain an expression for the average total permeability to sodium, [PNMDA x 10–6 cm/s] = 2.4157 x 10–9 cm /[IEI]. The relationship is different for AMPA, which has a faster time constant, such that [RAMPA ] = 3.626 /[IEI] and [g,AMPA] = 21.937 ms µS/cm2 /[IEI]. Figure 3A plots the average value and SD of the synaptic activation of both AMPA and NMDA receptors calculated from a simulation. The linear relationship is evident. NMDA receptor activation summates much more effectively than AMPA especially as the frequency of the synaptic events is increased. An example at an IEI of 1.6981 ms (588 Hz) is given in Fig. 3B. As stated in the preceding text, the same set of random event times was used for all values of the GABAA conductance at a given average value of PNMDA.
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A spike was counted when the somatic potential became more depolarized than –30 mV. Occasionally a spike would have two peaks very close together due to electrical coupling of compartments with a slightly different spike time. These false doublets were eliminated by requiring a hyperpolarization below –30 mV between spikes. A burst was initiated by an ISI of 80 ms and terminated by an ISI of <160 ms. These criteria were based on the experimental literature (Grace and Bunney 1984b). Our previous study (Komendantov et al. 2004) used a similar definition but required a 5-mV hyperpolarization between bursts. To make a better comparison with in vivo data in this study, a minimum hyperpolarization between bursts was not required.
Probabilistic algorithm for random insertion of spikes into the firing pattern
The number of spikes that occur in bursts, which in this analysis have a minimum of three spikes, can be increased in several ways. The most obvious is to add a spike during a burst. In addition, a spike that occurs <80 ms prior to, or <160 ms after, an existing burst will be counted as occurring within a burst and will extend the burst duration. A doublet, or two spikes separated by <80 ms, can be converted to a new three-spike burst by a spike occurring before, during, or after the doublet. Finally, spikes in bursts can be added by concatenation of bursts or doublets. Two bursts are separated >160 ms by definition, and if they are separated by an interval between 160 and 320 ms, a spike occurring in a window equal to the interval less 160 ms can concatenate the two bursts. A spike is added to the bursting fraction in the process. Similarly, two doublets are separated by >80 ms by definition and can be concatenated in a similar fashion. New doublets can be created if a spike is inserted within 80 ms of an existing spike. A probabilistic algorithm was developed that took as its input the number of bursts, the number of doublets, the number of single spikes, the cumulative duration of the bursts, the cumulative duration of the doublets, and the number of spikes added by the manipulation.
A constant probability density for spike occurrence is assumed throughout the interval except that a refractory period is assumed after each spike. Thus the probability of a spike occurring during a burst or a doublet or immediately before or after is the fraction of the total nonrefractory duration of the train comprised by the relevant interval. For the purposes of calculating the probability of concatenations, each pair of events was assumed to have its interevent intervals distributed evenly over the entire interval. To obtain pairs of events, the largest integer smaller than the current expectation value for the number of events was used. In an actual trial, a spike is added to one category to the exclusion of all others, but in the probabilistic algorithm, the expectation value of spikes in each category was computed instead. Therefore the actual values when plotted against the values predicted by the probabilistic algorithm should scatter evenly above and below the diagonal if the increase in spikes that occur within a burst is a result of the random insertion of spikes. The complete algorithm is given in APPENDIX B.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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In contrast to doubling gAMPA, setting gK,SK to zero in Fig. 4B3 causes a pronounced increase in the tendency of spikes to cluster into bursts that are frequently followed by relatively long hyperpolarized intervals. Note that the same manipulation in the presence of a tonic level of receptor activation converts singlet firing to periodic doublets (Fig. 4A3) rather than bursts, underestimating the actual increase in bursting observed in the presence of noisy synaptic input pattern. The noise causes unpredictable switches between the hyper- and depolarized phases, resulting in singlets and bursts in addition to doublets. However, the underlying mechanism is the same. The SK current usually generates a hyperpolarizing current in response to a depolarization, and blocking this current allows the subthreshold oscillation to increase in the amplitude and duration so that not just one but two spikes occur on each cycle. The slower frequency of the subthreshold oscillation in Fig. 4A3 compared with Fig. 4A1 results from the increased amplitude of the subthreshold oscillation (see explanation of intrinsic mechanisms in Fig. 5).
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To more clearly delineate this interaction, Fig. 6 illustrates the response of a quiescent model neuron to a weak transient input. The idea is to predict the alteration in response to a coherent, reward-related activation of glutamatergic receptors. A train of three excitatory postsynaptic potentials (EPSPs) was applied with an IEI of 50 ms, assuming that the inputs were received concurrently at 10 synapses activated as described in METHODS. Under control conditions (Fig. 6A1), only the second input elicits an action potential. The current elicited by stimulation of the NMDA receptors (blue trace Fig. 6B) summates and is opposed by an increase in IK,SK (green trace in Fig. 6B) and the sodium pump current (black trace in Fig. 6B). The first EPSP does not elicit an action potential because temporal summation is required to reach threshold in this instance, and the third does not elicit and action potential because IK,SK has become strong enough to prevent it. The current elicited by stimulation of the AMPA receptor is short-lived (red trace in Fig. 6B). Doubling gAMPA (Fig. 6A2) allows the first EPSP to elicit an action potential in addition to the second by allowing a subthreshold EPSP to become supratheshold. Setting gK,SK to zero (Fig. 6A3) instead allows the third EPSP to elicit an action potential in addition to the second.
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Figure 8D summarizes the effect of both manipulations on the pattern, showing the fraction of spikes fired in bursts after each manipulation as a function of the spikes fired in bursts under control conditions. Doubling gAMPA (red) produces a modest increase in the fraction of spikes fired in bursts, whereas the effect of setting gK,SK to zero (green) is a much more pronounced and variable increase. Figure 8E shows the average frequency under control conditions across the parameter space, and F summarizes the effect of each manipulation on frequency. The effect of doubling gAMPA (red) on frequency seems similar to the effect on pattern, whereas the effect of setting gK,SK to zero (green) is quite small at low frequencies and increases at higher frequencies, which often correspond to high bursting rates. The banded appearance of the green symbols in F is an artifact of the sampling grid in E and can be made to appear continuous by reducing the grid spacing (not shown).
Figure 9 shows more examples of the effects of these manipulations on the firing pattern. On the left-hand side, doubling gAMPA (A2) inserts a few spikes into the control single spike pattern shown in A1, including one that produces a doublet. Setting gK,SK to zero (A3) converts numerous single spike into doublets, including a pair that are concatenated into a burst. As stated in the preceding text, because there are significant intrinsic dynamics at work in addition to the synaptic dynamics, an explanation based solely on random spike insertion is clearly an oversimplification, but in the case of manipulating the AMPA conductance, it appears to be a reasonable starting point. On the right-hand side, the control pattern (B1) is already quite bursty, with over half its spikes in bursts of three or more spikes and nearly a quarter in doublets. Once again, doubling gAMPA (B2) appears to insert a few spikes into the control pattern, but here setting gK,SK to zero (B3) results in longer bursts with more spikes, to the near exclusion of single spikes and doublets.
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) except that the switches between spiking and quiescence appear random rather than periodic due to the random nature of the synaptic input. Increasing the relative contribution of nonlinear regenerative currents (such as INMDA) favors a larger-amplitude oscillation in the underlying slow variable (such as accumulation of sodium in the dendrites) with a slower frequency. On the other hand, increasing the linear currents dampens the oscillation causing a decrease in amplitude and a concomitant increase in frequency. Hence increasing the linear IAMPA current (Fig. 10B) produces more and shorter bursts, whereas blocking the SK current (Fig. 10C) produces fewer and longer bursts. Blocking SK exerts its effects by removing its opposition to the regenerative INMDA. The larger depolarization experienced in the larger amplitude bursts reduces the amplitude of the spikes. A similar reduction of spike amplitude during bursts has been observed in vitro (Wang et al. 1994) in the presence of 30 µM NMDA.
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. On the other hand, Fig. 11A2 shows that for lower values of PNMDA, the total number of bursts in a 90-s simulation consistently decreases as gGABA,A is increased, whereas for higher values, there is an initial increase followed by a decrease. The increase occurs in the continuously bursting regime by decreasing the amplitude and increasing the frequency of bursts analogously to the effect of increasing gAMPA in Fig. 10. As gGABA,A continues to increase, the amplitude of some bursts is decreased to the point that they no longer can sustain burst firing. Figure 11B shows an example of blocking the SK current at high levels of gGABA,A. The top trace (B1) shows control conditions, and the bottom trace (B2) shows SK block. Three additional spikes are inserted, two of them in bursts, but the effect is not as dramatic as at lower values of gGABA,A (Figs. 4 and 9).
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We used the probabilistic algorithm described in METHODS and in APPENDIX B to test whether the addition of spikes randomly throughout the spike train can explain the effects of modulating gAMPA or gK,SK and to quantify whether the rate and pattern are truly being modulated differentially. The main assumption is that the probability of a spike being inserted anywhere in the spike train is uniform except during the refractory period. Figure 13 plots the actual number of spikes added in bursts compared with the predicted number of spikes added in bursts. A perfect prediction would fall along the diagonal line (slope = 1). For doubling gAMPA (Fig. 13A), the slope of the best fit line was 1.06 (r = 0.93), whereas for blocking the SK current (Fig. 13B), it was 2.56 (r = 0.89). These slopes are significantly different because their 95% confidence intervals do not overlap. It is evident from Fig. 13A that the increase in spike frequency can reasonably account for the increased number of spikes in bursts caused by doubling gAMPA, and it is equally evident from Fig. 13B that when gK,SK is set to zero, the change in pattern is far greater than the change in that is expected simply due to an increase in frequency. To make an appropriate comparison between the two manipulations, only simulations in which blocking SK added <200 spikes in bursts were used in the analysis shown in Fig. 13. However, in every case when gK,SK was set to zero, the observed values were greater then the predicted values. A potential confound for the algorithm are the extreme bursting cases in which there are clear up and down states because the probability of a spike occurring during the down state is very low. Eliminating these extreme cases in which 95% or more spikes were fired in bursts made little difference to the analysis, however; for doubling gAMPA we obtained a slope of 1.07 (r = 0.95) and a slope of 2.53 (r = 0.90) for setting gK,SK to zero.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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In the absence of intracellular membrane potential recordings, it is not possible to confirm the presence of a depolarizing wave underlying bursting and often extending beyond the last spike in a burst (Grace and Bunney 1984b). Instead, an operational definition of a burst (Grace and Bunney 1984b) that relies only on successive ISIs is employed. Although rhythmic bursting has been observed under certain conditions in vitro, it is the exception in vivo (Freeman et al. 1985, Fig. 3B), and most burst episodes are transient and intermixed with single spikes in vivo. If the firing rate is increased, then more spikes occur in a fixed time interval. For burst firing to be modulated truly independently of the rate, then more spikes should be added in bursts than one would expect by random insertion of spikes regardless of the firing pattern. To our knowledge, this type of analysis has not yet been applied to physiological data. However, in the model presented in this study, the assumption of random insertion accounts for most of the effects of the modulation of the AMPA conductance but not the SK conductance. Therefore rate and pattern are modulated concurrently in the first instance but independently in the second. The results of this modeling study suggest that the increases in burst firing caused by increasing gAMPA are mostly due to increasing the tendency for EPSPs to summate above threshold, with the EPSPs that are promoted from sub- to suprathreshold located nearly uniformly throughout the spike trains. There may be a small bias toward clustering spikes in bursts because the confidence interval for the slope of the best fit line between actual and predicted values based on the assumption of random insertion did not include 1. On the other hand, the SK current is activated by depolarization with a delay so that it directly suppresses bursts but not single spikes, therefore blocking this current modulates pattern preferentially by facilitating the underlying burst mechanism. This mechanism is consistent with recent data (Ji and Shepard 2006) showing that apamin-treated DA neurons in vivo have more bursts with three or more spikes and fewer doublets than control cells.
A linear correlation analysis between pattern and rate is not particularly helpful because the dependency of pattern on rate increases is highly nonlinear, and a linear correlation analysis does not directly address whether the proportion of spikes fired in bursts is changed by chance or by modulating the underlying mechanisms for burst generation. Even in the cases that the increase in rate was used to predict the change in pattern, changes in pattern and rate were weakly correlated (Table 1). The dependence of pattern on rate as a single parameter is changed in the same neuron is linear in both physiological (Grace and Bunney 1984b) and model dopamine neurons (see RESULTS) but becomes decorrelated as more than one parameter is varied simultaneously. This explains the weak correlation between pattern and observed across a population of physiological (Grace and Bunney 1984b; Hyland et al. 2002; Paladini and Tepper 1999) or model neurons (see Table 1). One study (Zhang et al. 1994) obtained an r = 0.68 for the correlation between pattern and rate; this is close to the values obtained in the model in physiological frequency ranges. The correlation between changes in pattern and rate in the model is a close match to the data of Paladini and Tepper (1999). The model predicts that blocking SK will tighten the correlation between pattern and rate (Table 1) by eliminating the low bursters that occur at many frequencies and also predicts that high levels of tonic GABAergic receptor activation could occlude the effects of blocking the SK channel.
How do the statistics of the model compare with real dopamine neurons?
At least 70% of identified dopamine neurons were spontaneously active in chloral hydrate-anesthetized and gallamine paralyzed rats (Grace and Bunney 1984a), and more active DA neurons per track were identified in freely moving rats (Freeman et al. 1985) than in paralyzed or anesthetized rats, consistent with an enhancement of GABAergic transmission and an inhibition of glutamate-mediated excitation by chloral hydrate anesthesia (Fa et al. 2003). DA neurons in awake, freely moving rats fired an average of 46% (range: 1–81%) of their spikes in bursts (Freeman et al. 1985). In freely moving rats, 20% of all spikes were fired in bursts but nearly half of these occurred as doublets (Hyland et al. 2002). A subset of high bursters had 45% of their spikes in bursts. In chloral hydrate anesthetized rats (Grace and Bunney 1984b), 55% of the spontaneously firing neurons fired on average 30% of their spikes in bursts of two or more spikes but usually six or less. A recent study (Fa et al. 2003) found that the proportion of spikes fired in bursts in the conscious, head-restrained rat was 23% compared with 13% in rats lightly anesthetized with choral hydrate and only 0.5% in deeply anesthetized rats. Based on the statistics given above, most physiological dopamine neurons fall in the region of the colored diagonal bands in Fig. 8A, in which spontaneous activity ranging from single spike firing to 
75% burst firing is observed. The implication is that in vivo the excitatory and inhibitory inputs to the dopamine neurons are balanced.
Comparison to other models
Recently, Kuznetsov et al. (2006) proposed a multicompartmental model of transient burst firing in dopamine neurons. Our results are in agreement with those of Kuznetsov et al. (2006) in that the activation of the dendritic NMDA receptors is essential for the transient bursting in both models. The restriction of calcium dynamics to the soma in the model in this study is an oversimplification, and it has been suggested that dendritic calcium dynamics drive pacemaking (Chan et al. 2005). However, dopamine neurons with only small stumps of dendrites remaining after trituration (Cardozo and Bean 1995) still fire regularly at 3 Hz, as do acutely isolated neurons (Silva et al. 1990). The model in this paper, unlike the model of Kuznetsov et al. (2006), does not depend on the dendritic calcium entry and activation of the SK current alone to prevent depolarization block at high rates of firing because our model produces increased bursts in the presence of SK blockers, consistent with experimental evidence (Ji and Shepard 2006; Waroux et al. 2005).
The model presented in this paper is an extension of a previous model (Komendantov et al. 2004) that simulated the situation in vivo with constant levels of both glutamatergic and GABAergic input. The results of the previous paper underestimated the effects of blocking SK because the deterministic model could only burst or fire in single spikes. In contrast, the stochastic model with realistic synaptic dynamics presented in this study can burst transiently like real dopamine neurons. The effects of SK channel blockers in promoting burst firing are more prominent in the presence of synaptic noise (see Fig. 4C). The effects of increasing AMPA are fundamentally different as well (see Fig. 4B).
Theoretical framework
The mechanisms of burst firing in dopamine neurons are not fully understood. The regenerative, nonlinear inward current mediated by NMDA receptors has been implicated in burst firing both in vivo (Chergui et al. 1993) and in vitro (Johnson et al. 1992; Mereu et al. 1997; Prisco et al. 2002; Wang et al. 1994). SK channel blockers facilitated NMDA-induced bursting in several studies (Johnson et al. 1992; Prisco et al. 2002; Seutin et al. 1993). Recently, Johnson and Wu (2004) were able to generate both NMDA-dependent and -independent burst firing experimentally. The latter was induced by the application of the SK blocker apamin alone, is analogous to similar bursting observed previously by Ping and Shepard (1996), and is probably dependent on the L-type calcium channel because it is abolished in the presence of nifedipine. In the model in this study, the NMDA receptor current and other nonlinear, regenerative, inward currents, such as the L-type calcium current, can contribute to the depolarizations underlying spike and burst firing in our model. Their regenerative nonlinearity enables repetitive oscillations, and both linear currents (Canavier 1999) and the nonlinear SK channel current tend to reduce the amplitude of these oscillations. In addition to a process that produces a regenerative depolarization, a delayed repolarizing process is required to produce an oscillation such as that underlying bursting or repetitive single spike firing. The SK channel current provides a repolarizing force, and in its absence, the model sodium pump provides much of the repolarizing drive. Other, as yet unidentified currents, may also contribute in physiological dopamine neurons.
The underlying nonlinear dynamics of the model provide a theoretical framework for understanding the effects of pharmacological manipulations on the firing rate. The effect of GABA to reduce the number of spikes per burst (Fig. 11A1) until there are no bursts can be explained in terms of the linear dampening (Canavier 1999) that removes any region of positive feedback or negative conductance associated with the regenerative inward currents from the steady state IV curve. Blocking SK has the opposite effect (Fig. 12B), which is even more pronounced because SK has a supralinear dependence on voltage, that is, the hyperpolarization becomes more pronounced with increasing depolarization than one would expect from an increase in driving force alone because calcium entry is voltage-activated. In general, a large negative conductance excursion in the I-V curve results in a large amplitude oscillation with a long period, thus effects on amplitude also change the period (Fig. 10).
Effect on reward-related responses
Increasing gAMPA in the model has little if any effect on the train of strong inputs in Fig. 7 that were meant to simulate reward-related synaptic inputs signaling reward-related stimuli received by dopamine neurons. Because increasing gAMPA also increases the background firing rate and percent spikes fired in bursts (Fig. 8), such transient stimuli might seemed weaker than normal rather than enhanced as hypothesized by Jones and Bonci (2005). However, increasing gAMPA also lowers the threshold for stimuli to evoke a response in model DA cells. Behaviorally, the implications might be to cause a small subset of stimuli that would otherwise be ignored to elicit an expectation of reward. On the other hand, a reduction in the SK conductance is predicted to consistently intensify the response to reward-mediated stimuli by increasing the duration of bursts and the intra-burst frequency, resulting in a larger release of dopamine in the projection areas. Hyland et al. (2002) observed a greater intra-burst frequency in bursts related to reward compared with bursts in a context unrelated to reward, so we suggest that modulation of the SK current may convey reward-related information.
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APPENDIX A: EQUATIONS AND PARAMETERS FOR COMPARTMENTAL MODEL |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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NMDA-induced current:
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AMPA current:
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GABA current:
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Linear leakage current:
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Sodium pump current:
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Sodium balance:
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Calcium pump current:
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Calcium balance:
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Fast sodium current:
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Calcium currents:
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Delayed rectifier current:
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Transient outward potassium current:
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SK potassium current:
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Interneuronal coupling currents:
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Parameters
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APPENDIX B |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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N, number of total additional spikes due to manipulation
Nb[n], number of bursts
Nd[n], number of doublets
Nsb[n], number of spikes in bursts
Nsd[n], number of spikes in doublets
Nss[n], number of single spikes that are not in a burst or a doublet
r, refractory period (0.030 s)
T, total time (90 s)
Tb[n], sum of time periods in which an additional spike would become part of an existing burst
Td[n], sum of time periods in which an additional spike would convert a doublet to a burst
Ts[n], sum of time periods in which an additional spike would be a singlet
Tbr [n], Tb[n] corrected for refractory period
Tdr[n], Td[n] corrected for refractory period
Tsr[n], Ts[n] corrected for refractory period
Nb[n], change in the expected number of bursts due to addition of spike n
Nbs[n], change in the expected number of spikes in bursts due to addition of spike n
Nd[n], change in the expected number of doublets due to addition of spike n
Nss[n], change in the expected number of single spikes due to addition of spike n
ISIb, expected duration added to a burst by a spike occurring just before or just after a burst or doublet
ISId, expected interspike interval within a new doublet
Cb[n], expected number of concatenated bursts- includes for each pair of bursts the probability that the interval between them will be in the range 0.160 to 0.320 and the probability that the spike will occur in the right part of that interval so that the interval between the spike and each burst is <0.160
Cd[n], expected number of concatenated doublets
Cbs[n], expected number of spikes concatenated into bursts
Cds[n], expected number of spikes concatenated into doublets
Cbd[n], expected number of doublets concatenated into bursts
dd[n], expected doublet duration
db[n], expected burst duration
w = 0.160 ms or Ts[n]/Nss[n], whichever is smaller, for the expected interval between single spikes
ISIb = 0.080/6 + 0.0160/3
ISId = 0.080/2
Input to algorithm: Nb[0], d[0], Nsb[0], Nss[0], Tb[0], Td[0], N
Algorithm; repeat N times
Nsd[n] = 2 Nd[n]
Tbr[n] = Tb[n] – Nb[n] r
Tdr[n] = Td[n] – Nd[n] r
Ts[n] = 1 -Tb[n] – Td[n]
Tsr[n] = Ts[n] – Nss[n] r
dd[n] = Td[n]/Nd[n]
db[n] = Tb[n]/Nb[n]
Nsb[n] = Tbr[n]/(Tsr[n] + Tdr[n] + Tbr[n])
Nb[n] = Tdr[n]/(Tsr[n] + Tdr[n] + Tbr[n])
Nd[n] = Nss[n] (w[n] – 2 r)/(Tsr[n] + Tdr[n] + Tbr[n])
Nss[n] = Tsr[n]/(Tsr[n] + Tdr[n] + Tbr[n]) – Nd[n]
Cb[n] = Nb[n] (Nb[n] – 1) (0.160)/(T – 2 db[n]) (0.080/(Tsr[n] + Tdr[n] + Tbr[n]))
Cd[n] = Nd[n] (Nd[n] – 1) (0.160)/(T – 2 dd[n]) (0.080/(Tsr[n] + Tdr[n] + Tbr[n]))
Cbd[n] = Nb[n] Nd[n] (0.160)/(T – db[n] – dd[n]) (0.080/(Tsr[n] + Tdr[n] + Tbr[n]))
Cbs[n] = Nb[n] Ns[n] (0.120)/(T – db[n]) (0.060/(Tsr[n] + Tdr[n] + Tbr[n]))
Cbs[n] = Nb[n] Ns[n] (0.120)/(T - db[n]) (0.060/(Tsr[n] + Tdr[n] + Tbr[n]))
Nsb[n + 1] = Nsb[n] + Nsb[n] +3 Nb[n] +5 Cd[n] + Cb[n] +3 Cbd[n] +2 Cbs[n] +4 Cds[n]
Nb[n + 1] = Nb[n] + Nb[n] – Cb[n] + Cd[n]
Nd[n + 1] = Nd[n] + Nd[n] – Nb[n] – 2 Cd[n] – Cbd[n] – Cds[n]
Tb[n + 1] = Tb[n] + Nd[n] (2 ISIb +0.080 + 0.160) + Nb[n] ISIb (0.240/(Tsr[n] + Tdr[n] + Tbr[n]))
Td[n + 1] = Td[n] + ISId Nd[n] – dd[n] (Nb[n] +2 Cd[n] + Cbd[n] + Cds[n])
Nsd[n + 1] = 2 Nd[n + 1]
Nss[n + 1] = Nss[n] + Nss[n] – Nd[n] – Cd[n] – Cb[n] – Cbd[n] – 2 Cbs[n] – 2 Cds[n]
Output, predicted increase in number of spikes in bursts is Nsb[N] – Nsb[0]
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GRANTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
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FOOTNOTES |
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1 In Fig. 2A2 of Komendantov et al. (2004), it is stated that all concentrations were equilibrated at –60 MV before each step, but we have since noticed equilibrium was not reached in all cases. Also, the voltage dependence of the NMDA receptor current was called instantaneous in that paper, but in the model, it had a 1-ms time constant. The relative permeability of the NMDA channel to Ca2+ over monovalent ions was changed from 10.6 to 2.65 (Schneggenberger 1998), which was not mentioned. Other omissions and typographical errors in the equations and parameters have been corrected in APPENDIX A. 
Address for reprint requests and other correspondence: C. C. Canavier, Neuroscience Center of Excellence, LSU Health Sciences Center, 2020 Gravier St., Suite D, New Orleans, LA 70112 (E-mail: ccanav{at}lsuhsc.edu)
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REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIX A: EQUATIONS AND...APPENDIX BGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
Bernheimer H, Birkmayer W, Hornykiewicz, Jellinger K, and Seitelberger F. Brain dopamine and the syndromes of Parkinson and Huntingdon. Clinical, morphological, and neurochemical correlations. J Neurosci 20: 415–455, 1973.
Borgland SL, Malenka RC, and Bonci A. Acute and chronic cocaine-induced potentiation of synaptic strength in the ventral tegmental area: electrophysiological and behavioral correlates in individual rats. J Neurosci 24: 7482–7490, 2004.
Brodie MS, McElvain MA, Bunney EB, and Appel SB. Pharmacological reduction of small conductance calcium activated potassium current (SK) potentiates the excitatory effect of ethanol on ventral tegmental area dopamine neurons. J Phamacol Exp Ther 290: 325–333, 1999.
Canavier CC. Sodium dynamics underlying burst firing and putative mechanisms for the regulation of the firing pattern in midbrain dopamine neurons: a computational approach. J Comput Neurosci 6: 49–69, 1999.[CrossRef][Web of Science][Medline]
Cardozo DL and Bean BP. Voltage-dependent calcium channels in rat midbrain dopamine neurons: modulation by dopamine and GABAB receptors. J Neurophysiol 74: 1137–1148, 1995.
Chan CS, Wokosin DL, Rick CE, and Surmeier DJ. Dendritic Cav1.3 L-type calcium channels drive pacemaking in substantia nigra pars compacts dopaminergic neurons. Soc Neurosci Abstr 738.16 2005.
Charlety PJ, Grenhoff J, Chergui K, Svensson TH, and Chouvet G. Burst firing of mesencephalic dopamine neurons is inhibited by somatodendritic application of kynurenate. Acta Physiol Scand 142: 105–112, 1991.[Web of Science][Medline]
Chergui K, Charlety PJ, Akaoka H, Saunier CF, Brunet J-L, Buda M, Svensson TH, and Chouvet G. Tonic activation of NMDA receptors causes spontaneous burst discharge of rat midbrain neurons in vivo. Eur J Neurosci 5: 137–144, 1993.[CrossRef][Web of Science][Medline]
Chergui K, Nomikos GG, Methe JM, Gonon FG, and Svensson TH. Burst stimulation of the medial forebrain bundle selectively increases fos-like immunoreactivity in the limbic forebrain of the rat. Neuroscience 72: 141–156, 1996.[CrossRef][Web of Science][Medline]
Christoffersen CL and Meltzer LT. Evidence for N-methyl-D-aspartate and AMPA subtypes of the glutamate receptor on substantia nigra dopamine neurons: possible preferential role for N-methyl-D-aspartate receptors. Neuroscience 67: 373–381, 1995.[CrossRef][Web of Science][Medline]
Dalby NO and Mody I. Activation of NMDA receptors in rat dentate gyrus granule cells by spontaneous and evoked transmitter release. J Neurophysiol 90: 786–797, 2003.
Destexhe A, Mainen ZF, and Sejnowski TJ. Fast kinetic models for simulating AMPA, NMDA, GABAA and GABAB receptors. In: The Neurobiology of Computation, edited by Bower, J and Norwell, MA. Dordrecht: Kluwer Academic, 1995, p. 9–14.
Fa M, Mereu G, Ghiglieri V, Meloni A, Salis P, and Gessa GL. Electrophysiological and pharmacological characteristics of nigral dopaminergic neurons in the conscious, head-restrained rat. Synapse 48: 1–9, 2003.[CrossRef][Web of Science][Medline]
Fiorillo CD and Williams JT. Glutamate mediates an inhibitory postsynaptic potential in dopamine neurons. Nature 394: 19–21, 1998.[CrossRef][Medline]
Fiorillo CD and Williams JT. Cholinergic inhibition of ventral midbrain dopamine neurons. J Neurosci 20: 7855–7860, 2000.
Freeman AS, Meltzer LT, and Bunney BS. Firing properties of substantia nigra dopaminergic neurons in freely moving rats. Life Sciences 36: 1983–1994, 1985.[CrossRef][Web of Science][Medline]
Gonon FG. Nonlinear relationship between impulse flow and dopamine release by rat midbrain dopaminergic neurons as studied by in vivo electrochemistry. Neuroscience 24: 19–28, 1988.[CrossRef][Web of Science][Medline]
Grace AA and Bunney BS. The control of firing pattern in nigral dopamine neurons: single spike firing. J Neurosci 4: 2866–2876, 1984a.[Abstract]
Grace AA and Bunney BS. The control of firing pattern in nigral dopamine neurons: burst firing. J Neurosci 4: 2877–2890, 1984b.[Abstract]
Hausser M, Stuart G, Racca C, and Sakmann B. Axonal initiation and active dendritic propagation of action potentials in substantia nigra neurons. Neuron 15: 637–647, 1995.[CrossRef][Web of Science][Medline]
Hyland BI, Reynolds JNJ, Hay J, Perk CG, and Miller R. Firing modes of midbrain dopamine cells in the freely moving rat. Neuroscience 114: 475–492, 2002.[CrossRef][Web of Science][Medline]
Ji H and Shepard PD. SK Ca2+-activated K+ channel ligands alter the firing pattern of dopamine-containing neurons in vivo. Neuroscience 140: 623–633, 2006.[CrossRef][Web of Science][Medline]
Johnson SW, Seutin V, and North RA. Burst-firing in dopamine neurons induced by N-methyl-D-aspartate: role of electrogenic sodium pump. Science 258: 665–667, 1992.
Johnson SW and Wu Y-N. Multiple mechanisms underlie burst firing in rat midbrain dopamine neurons in vitro. Brain Res 1019:293–296, 2004.[CrossRef][Web of Science][Medline]
Jones S and Bonci A. Synaptic plasticity and drug addiction. Curr Opin Pharmacol 5: 20–25, 2005.[CrossRef][Web of Science][Medline]
Komendantov AO, Komendantova OG, Johnson SW, and Canavier CC. A modeling study suggests complimentary roles for GABAA and NMDA receptors and the SK channel in regulating the firing pattern in midbrain dopamine neurons. J Neurophysiol 91: 346–357, 2004.
Koob GF, Vaccarino FJ, Amalric M, and Bloom FE. Positive reinforcement properties of drugs: search for neural substrates. In: Brain Reward Systems and Abuse, edited by Engel J and Oreland L. New York: Raven, 1987, p. 35.
Kuznetsov AS, Kopell, NJ, and Wilson CJ. Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron. J Neurophysiol 95: 932–947, 2006.
Lenaeus MJ, Vamvouka M, Focia PJ, Gross A. Structural basis of TEA blockade in a model potassium channel. Nat Struct Mol Biol 12: 454–459. 2005.[CrossRef][Web of Science][Medline]
Liegeois J-F, Mercier F, Graulich A, Graulich-Lorge F, Scuvee-Moreau J, and Seutin V. Modulation of a small conductance calcium-activated potassium (SK) channels: a new challenge in medicinal chemistry. Curr Med Chem 10: 625–647, 2003.[CrossRef][Web of Science][Medline]
Mereu G, Lilliu V, Casula A, Vargiu PF, Diana M, Musa A, and Gessa GL. Spontaneous bursting activity of dopaminergic neurons in midbrain slices from immature rats: role of N-methyl-D-aspartate receptors. Neuroscience 77: 1029–1036, 1997.[CrossRef][Web of Science][Medline]
Overton P and Clark D. Iontophoretically administered drugs acting at the N-methyl-D-aspartate receptor to modulate burst firing in A9 dopamine neurons in the rat. Synapse 10: 131–140, 1992.[CrossRef][Web of Science][Medline]
Paladini CA, Fiorillo CD, Morikawa H, and Williams JT. Amphetamine selectively blocks inhibitory glutamate transmission in dopamine neurons. Nat Neurosci 4: 275–281, 2001.[CrossRef][Web of Science][Medline]
Paladini CA and Tepper JM. GABAA and GABAB antagonists differentially affect the firing pattern of substantia nigra dopaminergic neurons in vivo by decreasing input resistance. Synapse 32: 165–176, 1999.[CrossRef][Web of Science][Medline]
Ping HX and Shepard PD. Apamin-sensitive Ca2+-activated K+ channels regulate pacemaker activity in nigral dopamine neurons. Neuroreport 7: 809–814, 1996.[Web of Science][Medline]
Prisco S, Natoli S, Bernardi G, and Mercuri NB. Group I metabotropic receptors activate burst firing in rat midbrain dopaminergic neurons. Neurophamacology 42: 289–296, 2002.[CrossRef][Web of Science][Medline]
Schneggenberger R. Altered voltage dependence of fractional Ca2+ current in N-methyl-D-aspartate channel pore mutants with decreased Ca2+ permeability. Biophys J 74: 1790–1794, 1998.[Web of Science][Medline]
Schultz W. Predictive reward signal of dopamine neurons. J Neurophysiol 80: 1–27, 1998.
Seutin V, Johnson SW, and North RA. Apamin increases NMDA-induced burst firing of rat mesencephalic dopamine neurons. Brain Res 630: 341–4, 1993.[CrossRef][Web of Science][Medline]
Silva NL, Pechura CM, and Barker JL. Postnatal rat nigrostriatal dopaminergic neurons exhibit five types of potassium conductances. J Neurophysiology 64: 262–272, 1990.
Smith ID and Grace AA. Role of the subthalamic nucleus in the regulation of nigral dopamine neuron activity. Synapse 12: 287–303, 1992.[CrossRef][Web of Science][Medline]
Ungless MA, Whistler JL, Malenka RC, and Bonci A. Single cocaine exposure in vivo induces long-term potentiation in dopamine neurons. Nature 411: 583–586, 2001.[CrossRef][Medline]
Wang T, O’Connor WT, Ungerstedt U, and French ED. N-methyl-D-aspartic acid biphasically regulates the biochemical and electrophysiological response of A10 dopamine neurons in the ventral tegmental area: in vivo microdialysis and in vitro electrophysiological studies. Brain Res 666: 255–262, 1994.[CrossRef][Web of Science][Medline]
Waroux O, Massotte L, Alleva L, Graulich A, Thomas E, Liegeois JF, Scuvee-Moreau J, and Seutin V. SK channel control the firing pattern of midbrain dopaminergic neurons in vivo. E J Neurosci 22: 3111–3121, 2005.[CrossRef][Web of Science][Medline]
Weinberger DR. Implications of normal brain development for the pathogenesis of schizophrenia. Arch Gen Psychiatry 44: 660–669, 1987.
Wilson CJ and Callaway JC. Coupled oscillator model of the dopaminergic neuron of the substantia nigra. J Neurophysiol 83: 3084–3100, 2000.
Wolfart J, Neuhoff H, Franz O, and Roeper J. Differential expression of the small-conductance, calcium activated potassium channel SK3 is critical for pacemaker control in dopaminergic midbrain neurons. J Neurosci 21: 3443–3456, 2001.
Zhang HF, Hu HT, White FJ, and Wolf ME. Increased responsiveness of ventral tegmental area dopamine neurons to glutamate after repeated administration of cocaine or amphetamine is transient and selectively involves AMPA receptors. J Pharmacol Exp Ther 281: 699–706, 1997.
Zhang J, Chiodo LA, and Freeman AS. Influence of excitatory amino acid receptor subtypes on the electrophysiological activity of dopaminergic and nondopaminergic neurons in rat substantia nigra. J Pharmacol Exp Ther 269: 313–321, 1994.
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3 that did not appear under control conditions. B1: control firing with several doublets and most spikes in bursts of [mtequ3. B2: once again, increasing adds some spikes and shifts the timing of others. B3: longer bursts with larger interburst intervals than under control conditions.
