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1Departments of Neurobiology and 2Neurology, Stanford University, Stanford, California
Submitted 26 August 2007; accepted in final form 25 September 2007
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ABSTRACT |
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INTRODUCTION |
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The connections between the SC and PBN are reciprocal and topographic (Graybiel 1978
; Mufson et al. 1986
; Sherk 1979
; Tokunaga and Otani 1978
). The two areas are so densely interconnected that the PBN has been referred to as a satellite of the SC. In addition, the PBN also projects to other brain structures such as the thalamus (Harting et al. 1986
; Hashikawa et al. 1986
) and the amygdala (Usunoff et al. 2006
). Although it has been proposed that this nucleus may help orchestrate long-range excitation or inhibition spanning across the SC (Lee and Hall 2006
), it is unknown how the PBN functions to modulate neurons in the SC or in other target regions.
The properties of PBN neurons have been studied in vivo. These neurons fire at a high-frequency in response to visual input (Sherk 1979
) but also show high rates of spontaneous activity (Cui and Malpeli 2003
; Sherk 1979
). This spontaneous activity could allow the PBN to modulate SC activity both up and down. It is unknown if this spontaneous activity is due to extrinsic inputs, intrinsic connections between PBN neurons or to the biophysical properties of PBN neurons themselves. To address these possibilities, we performed cell-attached and whole cell patch-clamp recordings from PBN neurons in an acute, brain slice preparation of the rat midbrain. Here we present the first basic characterization of synaptic and intrinsic currents in PBN neurons. We report that PBN neurons in the slice fire spontaneous action potentials, even in the presence of synaptic blockers and that voltage-activated currents may play a role in regulating this spontaneous activity.
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METHODS |
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All animals were treated in accordance to institutional guidelines. Twenty-four Sprague-Dawley rats, aged p18–p23, were anesthetized with pentobarbital (50 mg/kg) and decapitated, and the brains were removed and immersed in a "cutting" solution (4°C) containing (in mM) 234 sucrose, 11 glucose, 24 NaHCO3, 2.5 KCl, 1.25 NaH2PO4, 10 MgSO4, and 0.5 CaCl2, aerated with 95% O2-5% CO2. Transverse slices (350 µm) were cut with a vibrating slicer (Leica VT1000S). Slices were incubated in oxygenated artificial cerebrospinal fluid (ACSF) containing (in mM) 126 NaCl, 26 NaHCO3, 2.5 KCl, 1.25 NaH2PO4, 2 MgSO4, 2 CaCl2, and 10 glucose (pH 7.4), initially at 32°C for 30 min and subsequently at room temperature for a minimum of 30 min before being transferred to the recording chamber. Most recordings were obtained at room temperature. In some cases, the temperature of ACSF flowing in the recording chamber was increased to 32°C by preheating the ACSF via a heat exchanger and recirculating water bath (NES Lab, GP-100).
PBN neurons were visually identified using oblique illumination and video microscopy. Neuronal density and large somatic size were used to distinguish the PBN from surrounding areas. In initial experiments, intracellular labeling with biocytin was used to confirm the morphology and location of recorded neurons. Immunostaining for choline acetyltransferase (ChAT) was used to verify the location of the PBN.
Borosilicate glass electrodes (OD: 1.5 mm, ID: 0.84 mm) were pulled with a Sutter p97 electrode puller to a tip resistance of 2–6 M
. For most cell-attached and all whole cell recordings, electrodes were filled with an intracellular solution containing (in mM) 130 K gluconate, 10 KCl, 2 NaCl, 10 HEPES, and 10 EGTA; pH = 7.3 corrected with KOH; 265–280 mosM. Biocytin (0.2%, Sigma, B4261) was included in the intracellular solution for most recordings. Electrodes were filled with ACSF for some cell-attached recordings. In whole cell recordings, the average input resistance was 116 ± 86 M
. Resting potential was not able to quantified as neurons were continually spiking.
Drugs were delivered by bath application at the following concentrations: kynurenic acid (1–2 mM, Sigma, k3375); dihydro-beta-erythroidine (DHβE, 100 nM, Sigma, D149); atropine (1 µM, Sigma, A0257); 6,7-dinitroquinoxaline-2,3-dione (DNQX, 12–25 µM, Tocris, 2312); gabazine (5–10 µM, Sigma, s106); 4-aminopyridine (4-AP, 1 and 2 mM, Sigma, A0152); and ZD-7288 (25 µM, Tocris, 1000). Signals were amplified using a Multiclamp 700A patch-clamp amplifier (Axon Instruments), filtered at 3 kHz, sampled at 10 kHz, and acquired using pClamp 9.2 (Axon Instruments). Data analysis was performed using pClamp and Matlab (Mathworks) software.
Data analysis and statistics
Values shown in text and figures are mean ± SD (not SE). Spike rates and intrinsic currents were detected and analyzed using Clampfit 9.2 software (Molecular Devices). IH was quantified in voltage-clamp recordings by calculating the difference between the average current over a 50-ms period at two time points: 50 ms after the initiation of a hyperpolarizing step and at the end of the 1-s hyperpolarizing step. To assess blockade of IH with ZD-7288, sag in potential observed in current-clamp recordings was quantified by calculating the difference between the average membrane voltage over a 100-ms period at two time points: 200 ms after the initiation of hyperpolarizing current injection and at the end of the 1-s hyperpolarizing current injection. To assess the effect of ZD-7288, traces that exhibited a similar initial hyperpolarization after a hyperpolarizing current injection in control and drug conditions were compared. The initial hyperpolarizations of control and ZD-7288 conditions were not significantly different (control: –97.0 ± 6.7 mV and ZD-7288: –99.3 ± 7.2 mV, P = 0.14, paired, 2-tailed t-test). IH deinactivation was fit to the following equation: I = 2.38 – 0.007*0.93Vm (r2 = 0.99).
The initial activation range for IA was determined by applying 100-ms membrane potential conditioning pulses to –110 mV for 100 ms to remove inactivation followed by test voltage steps to progressively more depolarized potentials until IA was observed. The steady-state IA inactivation curve was performed at the most depolarized test potential that did not cause elicit escaped action currents. The peak IA was measured starting 15 ms after returning to the activation voltage for a period of 15 ms; this time period captured the peak of the IA response. Peak IA occurred at 25 ± 3 ms after returning to the activation voltage in a sample of seven neurons. For the 4-AP experiments, a lower activation potential was required for assessing IA; after application of 1 mM 4-AP, depolarization to the most depolarized IA activation potential in control often led to spikes being generated in voltage clamp. The inactivation curve for each cell was then fit to a Boltzmann function (Origin 7, Northampton, MA).
Histology and immunostaining
Slices containing biocytin–filled neurons were immersed in 4% paraformaldehyde in phosphate-buffered saline (PBS) and kept at 4°C overnight. The following day, the paraformaldehyde was replaced with PBS, and unsectioned slices were incubated at 4°C until tissue processing. To visualize biocytin-filled neurons, slices were washed twice with PBS +0.2% Tween-20 (PBST). Avidin D conjugated to Fluorescein (Vector Labs) was added at 1/100 to the slices for 1.5 h. Sections were then washed twice in PBST, followed by a 30-min incubation with Nissl Red (Molecular Probes) at 1/100, and three more washes of PBST. Slices were washed once in PBS with no Tween, and then mounted onto slides and coverslipped using Vectashield Mounting Medium (Vector Labs).
For ChAT staining, paraformaldehyde fixed slices were washed in PBS and then placed in a solution of 30% sucrose in PBS for 1 h. Slices were resectioned at 50 µm with a freezing microtome and the sections were placed into PBS. The sections were then placed in a blocking solution of 5% goat serum in PBS for 1 h. Mouse anti-rat ChAT antibody (Chemicon, MAB305) was added at 1/100 in blocking solution for 1 day at room temperature and 2 more days at 4°C. Sections were then washed four times with PBS, and goat anti-mouse Alexa Fluor 488 (Molecular Probes, A11001) was added at 1/400 in blocking solution for 1.5 h. Sections were then washed twice in PBS, followed by a 30-min incubation with Nissl Red (Molecular Probes) at 1/100, and three more washes in PBS. Sections were mounted onto slides and coverslipped using Vectashield Mounting Medium.
Microscopy
Slices were imaged at lower power (up to x20) with a Nikon E800 upright microscope and Zeiss Axiocam and at high power (at least x40) with a Leica TCS SP2 confocal system.
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RESULTS |
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The PBN appears as a bump along the lateral wall of the midbrain, just ventral to the brachium of the inferior colliculus (Fig. 1A). It is a cell-dense region devoid of dense fiber tracts. The morphologies of biocytin-filled neurons from this region (Fig. 1B) were similar to previous descriptions of PBN neurons in Golgi studies (Tokunaga and Otani 1978
). The dendrites of most neurons were oriented toward the lateral wall of the midbrain (Fig. 1B, left neuron), although some had dendrites oriented along the dorsoventral dimension (Fig. 1B, right neuron). The latter are consistent with the "cylindrical shape" according to the classification of Tokunaga and Otani (1978)
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ChAT immunoreactivity (Fig. 1C, right). Thus our anatomical findings are in agreement with previous reports. PBN neurons fire spontaneously in vitro
In cell-attached patch recordings, PBN neurons in vitro fired spontaneous, regular action potentials (50/60 neurons, Fig. 2). The average firing rate in cell-attached recording was 2.81 ± 2.15 Hz (n = 50). Spontaneous firing persisted in most experiments (15 of 17 neurons) where cell-attached recordings were followed by whole cell voltage recordings (Fig. 2B, bottom right, mean whole cell firing rate = 3.42 ± 2.55 Hz, P > 0.45 compared with cell-attached firing rate, 2-tailed, paired t-test, n = 15 neurons). This firing was not due to disruption of the cell membrane in the sealing process or other stresses because tonic firing persisted could be detected for >20 min (Fig. 2C). Increasing the temperature of the bath increased spontaneous firing rate (Fig. 2D). The firing rate at 32°C was 169 ± 90% of the rate at 24–26°C (P < 0.01, n = 14 neurons, paired, 1-tailed t-test).
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Spontaneous activity in PBN neurons does not require fast synaptic input
The spontaneous activity of PBN neurons could be due to synaptic inputs and/or to intrinsic membrane conductances of PBN neurons. Excitatory synaptic inputs are thought to be glutamatergic based on the detection of presynaptically localized vGluT3 protein, but likely arise extrinsically to the nucleus, based on a lack of vGluT3 mRNA in the PBN (Herzog et al. 2004
). Intrinsic connections are likely to be cholinergic because most PBN neurons are thought to be cholinergic (Fig. 1C) (Mufson et al. 1986
) and the presence of
7 subunit containing nicotinic ACh receptors have been reported in the PBN (Tribollet et al. 2004
). To determine whether ionotropic input drives the activity of PBN neurons, we tested for spontaneous activity in the presence of synaptic blockers. Cell-attached recordings were made in two conditions: either in the pan-excitatory neurotransmitter receptor blocker, kynurenic acid, or in both the AMPAergic glutamate receptor antagonist, DNQX, and the GABA receptor antagonist, gabazine. Kynurenic acid blocks ionotropic glutamatergic receptors as well as alpha7-subunit containing nicotinic ACh receptors (Collingridge and Lester 1989
; Hilmas et al. 2001
). Addition of kynurenic acid to the bath blocked spontaneous excitatory postsynaptic currents in PBN neurons (Fig. 3A), indicating that these neurons receive fast, excitatory synaptic input. Regular firing persisted in recordings in which the slices were exposed to 1–2 mM kynurenic acid (mean firing rate = 1.9 ± 1.1 Hz, 9/10 neurons). Regular firing also persisted in a combination of DNQX and gabazine in 18 of 18 neurons tested (mean firing rate = 3.6 ± 2.6 Hz). Thus fast synaptic transmission is not required for the generation of rhythmic firing observed in PBN neurons.
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4β2 nicotinic blocker DHβE (100 nM), and the muscarinic ACh receptor antagonist, atropine (1 µM). Spontaneous firing rates were not significantly altered in the presence of these drugs (firing rate with drug was 107 ± 39% of that in the control period, P > 0.45; Fig. 3, B and C). In sum, these experiments indicate that fast synaptic transmission provides a minimal contribution to the spontaneous activity observed in PBN neurons in vitro. Properties of PBN neurons in response to intracellular current injection
To characterize the firing properties of PBN neurons, neurons were injected with slight hyperpolarizing current to hold the neurons just below action potential threshold and then were given hyper- or depolarizing current injections. In response to a strong hyperpolarizing currents, membrane voltage exhibited an initial hyperpolarization followed by a depolarizing "sag" (Fig. 4A, arrow). On termination of the current injection, neurons often fired rebound action potentials. Most neurons (12/14) fired two to four rebound spikes at low frequencies (4.18 ± 1.36 Hz) for several hundreds of milliseconds after the termination of the hyperpolarizing step, and a minority (2/14) fired high-frequency bursts of two to three spikes (>60 Hz) at much shorter (<50 ms) latencies. Preceding the low-frequency rebound spikes, a slow, depolarizing voltage ramp was observed that delayed the onset of spiking; this behavior is characteristic of IA (Fig. 4A, open arrowhead) (Jan and Jan 1989
; Rogawski 1985
).
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Intrinsic currents in PBN neurons: IH
Because fast synaptic transmission is not required for the spontaneous, regular firing of PBN neurons in vitro, intrinsic conductances are most likely responsible. Several currents that are implicated in rhythmic action potential generation can be elicited by membrane hyperpolarization or after the return from a hyperpolarizing step. Using whole cell patch-clamp recordings, we characterized several currents activated in response to hyperpolarizing pulses. During a 1-s, hyperpolarizing pulse, a pronounced inward current was observed (Fig. 4B, left arrow). It appeared to be an H current (IH) because it was inward, hyperpolarization-activated, and did not inactivate. IH persisted throughout the hyperpolarizing pulse, and a several-second long tail current was observed after the cell was returned to a holding potential near rest (Fig. 4B, right arrow). This current is the counterpart to the depolarizing membrane sag observed in current-clamp recordings (Fig. 4A, arrow). The activation range of IH was quite hyperpolarized as significant current was activated only with hyperpolarizations beyond –85 mV (Fig. 4C). A brief, outward current was also detected on returning the cell back to –65 mV (Fig. 4B, open arrowhead); this current will be discussed in the next section.
To test whether IH contributed to the spontaneous activity observed in PBN neurons, we monitored the spontaneous firing rate during the application of the IH blocker, ZD-7288, to the bath. These recordings were performed in the presence of DNQX and gabazine to block synaptic transmission. Application of 25 µM ZD-7288 neither prevented the spontaneous activity of PBN neurons nor did it significantly modulate the firing rate (Fig. 4D). The mean firing rate was 3.35 ± 1.53 Hz in the control condition and was 3.07 ± 1.25 Hz after application of ZD-7288 (P > 0.5, paired, 2-tailed t-test, n = 9 neurons).
To be sure that ZD-7288 was inhibiting IH, we tested whether hyperpolarization-induced membrane potential sag, indicative of IH, was affected by the application of 25 µM ZD-7288 (Fig. 4E). We tested whether an IH-related sag was reduced by ZD-7288 in eight neurons; in six of these neurons, we monitored spontaneous firing. Membrane sag after ZD-7288 application was reduced to 13.9 ± 12.2% of that in the control condition (P < 0.001, paired, 1 tailed t-test, n = 8 neurons). In sum, although ZD-7288 blocked IH, it did not alter the spontaneous firing rate in PBN neurons.
Intrinsic currents in PBN neurons: IA
The slow rise of the voltage ramp observed in current-clamp recordings between spontaneously occurring action potentials (Fig. 5A, open arrowhead) and on a termination of hyperpolarizing current pulse (Fig. 4A, open arrowhead) is indicative of A-type K+ current (IA). As mentioned previously, a transient outward current was observed in voltage-clamp recordings after a long hyperpolarizing pulse (Fig. 4B, open arrowhead). With a short (100 ms), hyperpolarizing pulse that did not activate IH significantly, IA was obtained in isolation (Fig. 5B, open arrowhead). IA peaked 25 ± 3 ms following the voltage activation step (n = 7) and lasted roughly 100–200 ms. This current was consistent with an A-type K+ current (Rogawski 1985
); it was brief, it rapidly recovered from inactivation by brief hyperpolarizing pulses and was activated by modest depolarizations to membrane potentials near –65 mV. Due to presence of active Na+ conductances in the neurons, it was not possible to adequately clamp voltage at more depolarized membrane potentials to obtain the complete activation range for IA. A steady-state inactivation voltage protocol, consisting of 100-ms conditioning steps (voltage range of –100 to –60 mV) followed by a test step to –60 or –55 mV revealed that IA was half inactivated at –97 mV and that detectable current could be activated after modest membrane hyperpolarization of –70 mV (Fig. 5C), which is near the trough voltage obtained during spontaneous firing (Fig. 5A). Thus IA is another intrinsic current that could regulate spontaneous firing of PBN neurons.
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We then tested if 4-AP blockade of IA results in a significant change in firing rate. Because 4-AP can block many types of K+ channels that affect excitability (Judge and Bever 2006
), we first assessed the effect of 1 mM 4-AP on PBN firing rate, then incremented the concentration of 4-AP to 2 mM. In this way, we hoped to control for as many of the non-IA-dependent effects of 4-AP by initially using a concentration that does not significantly affect IA, then increased the concentration of 4-AP to an IA-effective concentration. Addition of 1 mM 4-AP caused a significant increase in the firing rate of PBN neurons (Fig. 5F, left), from 2.0 ± 1.5 Hz in control conditions to 3.7 ± 2.3 Hz in 1 mM 4-AP (n = 6 neurons, P < 0.02, 2-tailed paired t-test), but further increasing the concentration from 1 to 2 mM caused highly variable effects on PBN neurons, including depolarization block in four of six cases. The net effect on firing rate in 2 mM 4-AP was not significant different from 1 mM 4-AP (3.9 ± 1.8 Hz, n = 6 neurons, 2-tailed paired t-test, P > 0.5). However, as these high concentrations of 4-AP substantially altered neuronal function independent of IA blockade, we were unable to demonstrate conclusively a role for IA in regulating the spontaneous firing.
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DISCUSSION |
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PBN neurons have been shown to be cholinergic from ChAT immunoreactivity studies (Beninato and Spencer 1986
; Mufson et al. 1986
). Consistent with previous studies, we find that the PBN contains a high proportion of ChAT immunoreactive neurons. Moreover, the morphology of biocytin filled neurons reported here (Figs. 1 and 2) are consistent with those reported in Golgi studies of PBN (Tokunaga and Otani 1978
).
The underlying mechanisms of spontaneous firing in the PBN may be similar to those demonstrated in other nuclei that exhibit spontaneous neuronal firing, such as in cerebellum (Raman and Bean 1999
), hypothalamus (Jackson et al. 2004
), striatum (Wilson 2005
), and many other nuclei (Llinas 1988
), where dynamic interactions between Na+ and K+ conductances foster ongoing activity. We found that PBN neurons have IH and IA. These currents have been shown to contribute to and/or modulate spontaneous firing in various neuronal types, so we tested their role in spontaneous firing in PBN neurons. The A-current observed in these studies (Fig. 5) is likely to be deinactivated during the spike afterhyperpolarization of the neuron. The slow depolarizing voltage ramp observed after each action potential (Fig. 5A) and after a prolonged hyperpolarization (Fig. 4D) are characteristic of IA (Connor and Stevens 1971
; Rogawski 1985
). IA has been shown to allow slow, repetitive firing of neurons (Bourdeau et al. 2007
; Nisenbaum et al. 1994
). Similarly, PBN neurons are able to fire in a slow, tonic fashion. The IA observed here is activated by membrane depolarizations to approximately –65 mV and is deinactivated by modest hyperpolarizations to –70 mV (Fig. 5C). Thus IA is active in the range of membrane voltages observed during the spike afterhyperpolarization and may participate in the generation and pacing of the spontaneous firing in PBN neurons.
However, our tests to demonstrate the role of IA in regulating PBN neuron firing with 4-AP were inconclusive. 4-AP is known to block various K+ channels, including those with A-type properties, in the submillimolar range (Judge and Bever 2006
; Rogawski 1985
; Russell et al. 1994
). Our observation that 1 mM 4-AP increased firing rate is consistent with the general increase in excitability that accompanies K+ blockade. However, 2 mM 4-AP was required to effectively reduce IA in PBN neurons. This high concentration of 4-AP severely disrupted action potential generation in a manner consistent with a persistent inactivation of Na+ channels. Moreover, the action of 4-AP may be to enhance, not inhibit, IA in response to slow voltage ramps, similar to those observed during the PBN interspike interval (A. C. Jackson, personal communication). To more completely assess the contribution of IA to spontaneous firing in these neurons, either new pharmacological agents or genetic manipulation of specific A-type K+ channels will be required. The observation that A-type current in PBN neurons is blocked by millimolar concentrations of 4-AP suggests that this current is carried by Kv 4.x subunit- containing channels, not Kv 1.x-containing channels (Coetzee et al. 1999
).
IH has been shown to contribute to pacemaking firing pattern in various groups of neurons (Chan et al. 2004
; Luthi and McCormick 1998
) and has been observed in other cholinergic nuclei (Gorelova and Reiner 1996
; Griffith and Matthews 1986
). However, the voltage range of IH activation observed here suggests that it does not contribute significantly to the spontaneous firing of PBN neurons in vitro; the activation range of the IH is significantly hyperpolarized (less than –85 mV) relative to the trough of the spike afterhyperpolarization, which was about –70 mV (Fig. 4A). Consistent with this interpretation, application of 25 µM ZD-7288, which effectively blocked IH, did not alter firing rate. These results are similar to those obtained in a subset of hippocampal interneurons that express an IH that does not appear to contribute to the rhythmic firing observed those neurons (Bourdeau et al. 2007
). Although we have not demonstrated it here, IH could play a role in repolarizing the neuron after a strong wave of GABAergic inhibition and could even induce rebound spikes.
The observation that PBN neurons fire spontaneously in vitro is consistent with prior reports of spontaneous activity in vivo. However, the rate of spontaneous firing in the rat PBN in vitro was significantly lower than that observed in cats in vivo; cat PBN neurons fired spontaneously at
15 Hz, with a range from 0 to >50 Hz (Cui and Malpeli 2003
; Sherk 1979
). This difference may be partially due to species differences but is most likely due to the effects of slicing; intrinsic properties of the neurons may be altered due to bath conditions and synaptic drive not maintained in the slice preparation that could contribute to an increased firing rate. However, our data suggest that even in the deafferented slice, in which extrinsic neuromodulatory influences are negligible, intrinsic mechanisms exist that promote continuous firing of PBN neurons.
The function of spontaneous activity in the PBN is not known, although it has been postulated that it may help PBN neurons respond very rapidly to sensory inputs (Sherk 1979
). Moreover, the presence of spontaneous activity enables neurons to represent both increases and decreases of synaptic drive to their target. Evidence of this type of push-pull regulation of firing in the PBN has been observed in vivo in response to moving visual stimuli (Cui and Malpeli 2003
). Targets moving in the appropriate hemifield elicit a high firing rate in the PBN, but targets moving in the opposite hemifield completely silence the neuron. Thus levels of ACh in SC can be dynamically regulated by controlling the activity of the PBN.
Spontaneous firing occurs frequently in neuromodulatory regions, such as the suprachiasmatic nucleus (Jackson et al. 2004
; Pennartz et al. 1997
) and in dopaminergic centers (Koyama et al. 2005
; Puopolo et al. 2007
). It is likely that the PBN is acting as a modulator of SC activity. ACh infusion depolarizes some types of principal neurons as well as affects the release of GABA onto various types of SC neurons (Endo et al. 2005
; Lee et al. 2001
; Li et al. 2004
). The finding that the PBN is spontaneously active implies that the PBN delivers a continuous, low level of ACh to the SC. However, the specific effect of PBN activity on SC circuits has not yet been established. Neurons in other cholinergic nuclei have been reported to exhibit spontaneous firing, suggesting that this tonic release of ACh may be a general mechanism for cholinergic modulation (Arrigoni et al. 2006
; Wilson 2005
).
The PBN is the mammalian analogue of the nucleus isthmi, a complex of nuclei found in nonmammalian vertebrates. In particular, PBN appears to be closely related to the nucleus isthmi pars parvocellularis (Ipc) (Wang et al. 2006
). Neurons in Ipc fire high-frequency bursts of action potentials in response to visual or auditory input; they also fire spontaneously in the absence of sensory input (Maczko et al. 2006
; Marin et al. 2005
). Moreover, Ipc activity can facilitate calcium entry into presynaptic terminals in the frog tectum, a structure analogous to mammalian SC (Dudkin and Gruberg 2003
). These observations suggest that the function of PBN and Ipc may be similar. Future work will determine the functional similarity of these structures.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: C. A. Goddard, Fairchild Bldg. D255, 299 Campus Dr., Stanford University, Stanford, CA, 94305 (E-mail: cgoddard{at}stanford.edu)
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