| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1Laboratoire de Neurobiologie des Réseaux Sensorimoteurs, Centre National de la Recherche Scientifique (CNRS)-Université René Descartes (Paris 5) Unité Mixte de Recherche (UMR) 7060, Paris, France; 2Département de Neurosciences Fondamentales, Faculté de Médecine, Université de Genève, CMU, Geneva, Switzerland; and 3Physio-Pathologie des Réseaux Neuronaux du Cycle Veille-Sommeil, CNRS-Université Lyon 1 UMR 5167, Lyon, France
Submitted 22 December 2005; accepted in final form 1 April 2006
 |
ABSTRACT |
|---|
|
25% of the population. The behavior of this subset of PHNn, referred to as type D PHNn, is clearly different from that of the medial vestibular nucleus neurons, which transmit the bulk of head velocity-related sensory vestibular inputs without integrating them. We have investigated the firing and biophysical properties of PHNn and developed data-based realistic neuronal models to quantitatively illustrate that their active conductances can produce the oscillatory behavior. Although some individual type D PHNn are able to show some features of mathematical integration, the lack of robustness of this behavior strongly suggests that additional network interactions, likely involving all types of PHNn, are essential for the neuronal integrator. Furthermore, the relationship between the impulse activity and membrane potential of type D PHNn is highly nonlinear and frequency-dependent, even for relatively small-amplitude responses. These results suggest that some of the synaptic input to type D PHNn is likely to evoke oscillatory responses that will be nonlinearly amplified as the spike discharge rate increases. It would appear that the PHNn have specific intrinsic properties that, in conjunction with network interconnections, enhance the persistent neural activity needed for their function. |
|
INTRODUCTION |
|---|
|
), division for certain inhibitory inputs (Borg-Graham et al. 1998), linear and nonlinear addition in the spinal cord or cortex (Shu et al. 2003), and finally integration of dendritic inputs for persistent memory (Polsky et al. 2004) or of an eye-velocity signal to position in the oculomotor system (Robinson 1975). The "oculomotor integrator" is thought to be the same for all oculomotor networks responsible for fixation, orientation, and stabilization (Goldman et al. 2002). It uses eye-velocity-coded saccadic commands and head-velocity vestibular signals to generate eye-position commands (Fukushima and Kaneko 1995; Moschovakis 1997). For the horizontal plane, the prepositus hypoglossi nucleus (PHN) is the principal structure of the oculomotor integrator (Mettens et al. 1994) as shown by comparison among network modeling and pharmacological for lesion experiments (Arnold et al. 1999; Cannon and Robinson 1987; Chéron and Godaux 1987; Robinson 1975; Skavenski and Robinson 1973). The PHN is in the rostral medulla (McCrea and Horn 2005), near the medial vestibular nucleus (MVN), which is one of its major inputs. Theoretical models based on intrinsic cellular properties (Egorov et al. 2002; Loewenstein and Sompolinsky 2003; Marder et al. 1996), the finding of rostrocaudal gradients for neurons showing position versus velocity signals (Delgado-Garcia et al. 1989) and extensive studies related to the oculomotor integrator of goldfish (Aksay et al. 2000, 2001, 2003a,b; Major et al. 2004a,b; Seung et al. 2000) suggest that the stability and robustness of the neuronal integrator (Galiana and Outerbridge 1984; Goldman et al. 2003; Koulakov et al. 2002) require both intrinsic properties and network interconnections (Anastasio 1998; Arnold and Robinson 1991, 1997; Blazquez et al. 2003; Cannon et al. 1983).
PHN neurons (PHNn) have been functionally characterized in vivo (Delgado-Garcia et al. 1989; Lopez-Barneo et al. 1982) and in vitro either morphologically (McCrea and Baker 1985b) or electrophysiologically with intracellular recordings (Bobker 1994; Bobker and Williams 1989–1991, 1995). The present paper links these different classifications and describes a highly oscillatory behavior shown by 25% of the PHNn and not by any MVN neuron (MVNn) (Beraneck et al. 2003; Ris et al. 2001). The whole PHN includes as well a greater percentage of phasic neurons (type B) than the MVN. In addition, it was found that the activation of N-methyl-D-aspartate (NMDA) receptors in type B PHNn leads to discrete oscillatory activity, supporting some theoretical studies showing robust neural integration in neurons having NMDA activated bistable dendrites (Goldman et al. 2003; Koulakov et al. 2002). Some of the results have been presented in abstract form (Idoux et al. 2004; Mühlethaler et al. 1996; Serafin et al. 1996a).
|
|
METHODS |
|---|
|
Experiments were carried out on pigmented guinea pigs of both genders (Animal facility of the Geneva University Medical Center and Elevage de la Garenne, Saint-Pierre d'Exideuil). Compared with rats and mice, guinea pigs are far more developed at birth and do not show as marked developmental differences during the first 5 wk after birth (Dobbing and Sands 1970; Nacher et al. 2000; Staudinger et al. 2005). To assess the potential effect of age in these animals, two groups of guinea pigs were used, one 6–9 days and the other 3–5 wk old. Unless stated otherwise, the sections of the paper referred to as qualitative analysis are from the young animals; the quantitative analysis was done on data from the older animals. The results from these two age groups showed no significant differences; nevertheless some of the results will be presented separately to indicate possible developmental differences. All intracellular recordings were done in vitro at 32°C on guinea pig 500-µm-thick brain stem coronal slices with sharp electrodes (120–150 M
). These slices were obtained and maintained using previously described procedures (Beraneck et al. 2003; Serafin et al. 1991; Vibert et al. 1999).
The viability of neurons in the brain stem slice could be improved by replacing the normal artificial cerebrospinal fluid (ACSF) by "sucrose-ACSF", i.e. an ACSF-depleted of sodium chloride and loaded with sucrose during the slice preparation. Statistical comparison of all measured parameters of PHNn between slices obtained with either ACSF showed no difference, as previously reported for lateral vestibular nucleus neurons (Uno et al. 2003). Therefore all recordings from similar age groups were pooled together.
Intracellular current-clamp experiments were done as described in Beraneck et al. (2003). The morphology, the response to neuromodulators and a qualitative determination of the cell types were done on 213 PHNn from guinea pigs <2 wk old (see Classification parameters). The quantitative classification program of Beraneck et al. (2003) was used on the remaining 110 neurons to allow a direct comparison with MVNn. Both methods led to comparable proportions of each cell type, therefore the results of all the 323 PHNn were pooled together to compare the relative distribution of cell types between the PHN and the MVN.
Classification parameters
The quantitative classification of Beraneck et al. (2003, 2004) is based on two quantitative parameters that relate to the qualitative classification used by Serafin et al. (1991): the "dAHP", which estimates the size of a double afterhyperpolarization, and the "IA", which is a measure of the rectification of the potential between spikes and possibly related to an inactivating potassium A-like current. In this paper, the IA will be termed AHPR, afterhyperpolarization rectification, because it is, like dAHP, a less ambiguous descriptive term for the membrane potential profile following the spike. Both the dAHP and the AHPR were evaluated using the first derivative of the variation of the membrane potential versus time. According to these parameters, MVNn were divided into two cell types: type A MVNn and type B MVNn. Type A MVNn were the MVNn with no dAHP (= 0 V/s) and a strong AHPR (
0.15 V/s). In contrast, type B MVNn were those with a dAHP and no AHPR or a small one (<0.15 V/s). If a neuron had both a non-null dAHP and a strong AHPR (0.15 V/s), then this cell was said to be an intermediate type C MVNn, but this class was found to be <5% of the total population of MVNn (Table 1 and Fig. 2A). To compare neuronal types within the PHN as well as with the MVN, the following parameters were determined for each neuron: dAHP, AHPR, average resting membrane potential (Vm, mV), spontaneous discharge rate (DR, spikes/s), coefficient of variation of DR (Cv, %), amplitude of the after-hyperpolarization (AHP, mV), width (ms) of the spike and finally, the concavity(Cav, mV) and convexity(Cvx, mV) of the interspike interval (see Fig. 1 in Beraneck et al. 2003).
|
|
|
Ramp stimulations over a 0.3-nA range were done both at rest and during a hyperpolarization of the neuron 10 mV below its resting potential using five slopes, so that 0.3 nA was injected within 5,000, 3,400, 1,800, 600, or 200 ms. Adaptation of the discharge was observed in most neurons and was measured, for the fourth slope, as the difference between the peak instantaneous frequency obtained when the current reached its maximal value and the steady-state value of the instantaneous frequency at the end of the plateau; this difference was called the overshoot (O600, spikes/s). The firing threshold of the neuron (FThr, mV) was computed from the lowest slope ramp (t = 5,000 ms), when initiated from a hyperpolarized value. In spontaneously active neurons, FThr is more negative than Vm. Conversely in silent neurons, FThr is positive to Vm.
In contrast to the large signal ramp stimulation, small signal discrete sinusoidal stimulation (0.07–0.09 nA) was done either individually with a set of 16 sine waves at various frequencies (0.2–50 Hz) for 5 s or with 60 sine waves applied simultaneously with random phases as a pseudo-white noise signal. These measurements were done during a hyperpolarization to abolish action potentials, at the resting potential, and at a depolarized potential (10 mV above the resting potential). Both the modulation of Vm (<10 mV) and the instantaneous frequency (IF) of action potentials were divided by the input current and shown as magnitude and phase plots of the impedance (Z, M) and instantaneous frequency transfer functions (
IF/I, spikes · s–1 · nA–1) (Ris et al. 2001), respectively. Step and sinusoidal membrane potential responses were used to construct a subthreshold electrotonic model of type D PHNn using procedures previously described (Saint-Mleux and Moore 2000a,b). Parameters used to compare the voltage-dependent intrinsic filtering properties of the neurons were obtained for the three levels of polarization: the frequency of stimulation at which the resonance occurs (peak frequency, Fpeak, Hz) and the amplitude of this resonance relative to 0.2 Hz (QR). These two parameters were calculated using the impedance during a hyperpolarization and the instantaneous frequency transfer function in the other cases. Therefore in the tables and text, a subscript related to the actual state is added, respectively H, R, and D for hyperpolarization, rest, and depolarization. For example, Fpeak-D refers to the frequency of stimulation at which the resonance occurs for the depolarized case. Means for the magnitude and phase functions were calculated for all the neurons within one cell type, except for the A PHNn, in which two cells were excluded because their discharge rate was <10 Hz, which could not be adequately modulated.
In addition to the instantaneous frequency transfer function obtained from the time intervals between each successive spike (Moore et al. 2004; Ris et al. 2001), an equivalent spectral method was used, based on the impulse functions derived from the firing times. In that case, spikes were treated as Dirac delta functions where the spike train is of the form
 |
 |
Morphological analysis
At the end of electrophysiological recordings, slices containing neurobiotin-filled neurons (1 per slice side) were immersed in an ice-cold fixative with 3% freshly depolymerized paraformaldehyde in 0.1 M phosphate buffer. Neurobiotin-filled neurons were then visualized using the avidin-biotinylated horseradish peroxydase complex reaction (Vectastain, Elite kit, Vector Laboratories, Burlingame, CA) with 3–3'-diaminobenzidine (Sigma-Aldrich) as a chromogen combined or not with nickel intensification (blue-black vs. brown reaction product). For easier microscopic observation of the morphology of the neurobiotin-filled neurons and to ensure their location within the PHN boundaries, slices were re-sectioned in 50-µm-thick sections using a cryostat. These free-floating sections were then mounted on gelatin-coated slides and counterstained with 1% Neutral Red for the PHN to be better demarcated from the adjacent medial vestibular nucleus and medullary reticular formation. The photomicrographs displayed on Fig. 1 were prepared with Adobe Photoshop 4.0.
To investigate the anatomical distribution of PHNn throughout the nucleus, the latter was first divided into three 500-µm-thick rostrocaudal levels (rostral, intermediate, and caudal levels respectively; an example of the rostral level is shown in Fig. 2B) taking the genu of the facial nerve as a rostral landmark and according to the Gstoettner's atlas of the guinea pig brain (Gstoettner and Burian 1987). At each level, the nucleus was then further subdivided into a medial (M) and a lateral (L) part and dorsoventrally into a dorsal (D), an intermediate (I) and a ventral (V) part (see Fig. 2C). Such a subdivision of the nucleus into 18 areas (6 areas per slice level: LD, LI, LV, MD, MI, and MV, respectively) of equivalent dimensions (around 150 x 150 µm) was used to map the location of 213 PHNn identified unambiguously by their intrinsic membrane properties. At least 10 cells were randomly recorded in each given area allowing the calculation of the relative proportion of each neuronal cell type with respect to the other ones in that area. More recordings were done in the medial areas because type D PHNn were found nearly exclusively in that part of the nucleus. The following is an example of calculation (repeated for each area) done to construct the boxes illustrated in Fig. 2D: in the rostral slice level (1st line in Fig. 2D) a total of 11 cells were recorded in the medioventral (MV) area, including 3 type A (3/11 = 27.3%), 2 type B (2/11 = 18.2%), 1 type B+LTS (1/11 = 9.1%), and 5 type D PHNn (5/11 = 45.4%). The cumulated percentages illustrated in Fig. 2E represent the proportion of a given neuronal cell type in a given area of the nucleus with respect to the other cell types, independently of the rostrocaudal level (in this case the 3 slice levels were merged together). Altogether, a total of 41 cells was recorded in the medioventral (MV) area through the three rostrocaudal slice levels, including 3 type A (3/41 = 7.4%), 14 type B (14/41 = 34.1%), 3 type B+LTS (14/41 = 34.1%), and 10 type D PHNn (10/41 = 24.4%).
Statistical analysis
The whole statistical analysis was done with the Systat 8.0 software (SPSS, Chicago, IL). All results are expressed as means ± SD. Normality of the distribution of each cell parameters' value was tested by a one-sample Kolmogorov-Smirnov test with usual significance threshold (P 
0.05). In case of a normal distribution and large-enough sample, parametric tests were done; otherwise the corresponding nonparametric tests were used, namely ANOVA and Kruskal-Wallis ANOVA, respectively, except for two-by-two comparisons, in which cases the Student's t-test and Mann-Whitney U test were preferred. We compared parameters' distribution both between neuronal-types (A, B, B+LTS and D) inside the PHN and between corresponding neuronal-types in MVN and PHN (type A PHNn vs. type A MVNn and type B PHNn vs. type B MVNn). When comparisons concerned the same parameters for different levels of polarization, paired tests were used, either paired parametric (ANOVA followed by paired t-test) or nonparametric tests (Friedman ANOVA followed by signed-rank tests), depending, again, on the normality of the distribution and the size of the sample. Even when the distribution was not normal, the mean and SD are given for consistency.
Neuronal models
The kinetic formulation using x as a generalized kinetic variable (Borg-Graham 1991; Moore and Buchanan 1993; Murphey et al. 1995) is
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
. Thus at the half-activation (x = 1/2) voltage, vx, sx is the slope of x and tx is the time constant, 
x. Real-time simulations were done with a soma and three dendritic compartments having a distribution of ion channels as described in each simulation. An analytical model was used (Murphey et al. 1995; Rall 1960) for all frequency domain simulations. All simulations were done with Mathematica (Wolfram Research, Champaign, Il). The analytical linearized admittance is given as
 |
 |
 |
–1 and f is the frequency in Hertz. This formulation leads to an active soma and cable (Murphey et al. 1995) having an admittance, Ya, where L is the electrotonic length
 |
 |
|
|
RESULTS |
|---|
|
The most distinctive features of PHNn in the slice compared with MVNn are their irregularity and oscillatory character. The oscillatory PHNn, referred to as type D, can be easily distinguished from all other neuronal cell types in the PHN and in the MVN by their capacity to fire in clusters of action potentials intermingled with subthreshold membrane oscillations, usually visible at rest or when depolarized (circles for the clusters and squares for the oscillations, respectively in Fig. 1D). In the PHN, the population of recorded neurons was divided into four different neuronal types, namely types A, B (with a subset of B+LTS), and D PHNn. As in the MVNn, type A PHNn (Fig. 1A) were defined qualitatively by broad action potentials and a deep monophasic AHP. Type B PHNn (Fig. 1B) had shorter-duration action potentials and a biphasic AHP. The subset of type B+LTS PHNn (Fig. 1C) were distinguished from type B neurons by bursts of spikes elicited in response to depolarizing steps while maintained hyperpolarized by DC injection and therefore named type B+LTS ("low-threshold spike") PHNn as in the MVN. The proportion of each cell type for both nuclei is summarized in Table 1.
Significantly different distributions of neuronal types within PHNn and MVNn were obtained with a 
2 test (P < 0.001). As summarized in Table 1, comparison of the proportions of each cell type found in the MVN (Beraneck et al. 2003) and PHN showed that the proportion of type B (including B+LTS neurons) increased while the proportion of type A neurons decreased. Finally, the new type D neurons accounted for 23.5% of PHNn.
As shown by Table 2, type A and B PHNn were not very different for some of their steady-state properties, namely the resting membrane potential (Vm), the spike threshold (FThr), the spontaneous discharge rate (DR) and its coefficient of variation (Cv). As indicated by Table 2, most of these parameters were different for the type D PHNn. The smaller difference between Vm and FThr is consistent with the lower spontaneous spike rate measured for the D cells.
|
|
The morphological analysis of neurobiotin-filled PHNn and their local collateralization revealed no striking differences between the neuronal types: all PHNn were variable in shape from triangular to ovoid, had medium- to large-sized somas (15–20 µm in average) with few (generally 2–5) principal dendrites (see Table 1 for values and Fig. 1 for photomicrographs). The axons of the neurons could not always be seen and could never be followed for >50–100 µm. In contrast with the hippocampus, spinal cord, or cerebellum, there are no visible anatomical substructures or cell layers within the PHN (McCrea and Horn 2005). In addition, according to McCrea and Baker (1985a), the initial trajectories of PHNn axons are very variable, and the axons often make loops and turns within the nucleus itself. Hence, it was impossible to know where outside the PHN the axons of the neurobiotin-filled PHNn might project. In a few cases, varicous axonal collaterals were observed within the PHN itself; this confirms the existence of the intra-PHN recurrent network seen by McCrea and Baker (1985a). These neurobiotin-filled neurons were used to determine the distribution of 213 of the recorded neurons as defined in the methods and illustrated in Fig. 2. In summary, type A PHNn (Fig. 2, D and E, 1st column) were slightly more frequently recorded in the medial part. Type B PHNn were present in large proportion everywhere throughout the nucleus intermingled with all other neuronal types, but they were more frequently encountered in its lateral part. Type B+LTS PHNn were rarely recorded in the rostral pole of the nucleus but were more numerous as the recording electrode was moved caudally. A large majority of these neurons were confined in the ventral part of the PHN. Finally at all three slice levels (rostral, intermediate, and caudal), type D PHNn were mainly recorded in the medial part of the nucleus close to the fourth ventricle and increased in number along a ventrodorsal gradient (Fig. 2, D and E, last column). In addition, it is noteworthy that the proportion of type D PHNn also increased in a caudorostral gradient (achieving 60% of the total neuronal population in the more rostromedial part of the nucleus). The different distribution of the four PHNn types through the nucleus (in particular that of B+LTS PHNn and D PHNn) is shown in Fig. 2E where the values in the boxes represent, independently of the rostrocaudal level, the proportion of a given neuronal type in a given area of the nucleus with respect to the other cell types (see METHODS).
Intrinsic and pharmacological properties of PHNn
Although morphologically similar, the different PHNn cell types have different intrinsic membrane properties. After brief low-intensity depolarizing current pulses (10 ms at 0.1 nA) applied to neurons slightly hyperpolarized with a steady-state current to eliminate their spontaneous activity, most of type B PHNn (n = 49/67) responded with long-lasting subthreshold plateau potentials (stars in Fig. 1B3). Such plateau potentials were observed in some type A PHNn (n = 8/18) but only in a few type D (n = 4/19) neurons. The behavior of the plateau potentials is similar to that previously described in the MVN (Serafin et al. 1991). The persistence of such plateau responses in absence of calcium ions and their total suppression following addition of 1 µM TTX (Latoxan, Rosans, France) to the bathing solution (n = 5/5, Fig. 1B3, insets) suggests that they most likely depend on a persistent sodium current similar to that reported in other neurons (Crill 1996).
High levels of 4-aminopyridine (4-AP, 1–5 mM, Sigma-Aldrich, France) suppressed an outward rectification in type A PHNn (n = 4/4, data not shown) similar to that observed in other tissues, which suggests the presence of an IA-like current in these neurons. The IA current (McCormick 1991) is a potassium outward current with fast-activating and -inactivating kinetics that is generally suppressed by 4-AP; the IA-like current is important in type A PHNn for both the typical shape of their action potential (Fig. 1A, 1 and 2) and the delay to first spike when depolarized from a hyperpolarized level (Fig. 1A3) by a step of current.
The most striking and distinctive property of type B+LTS PHNn was the presence of a potent TTX-resistant and calcium-dependent (n = 4/4, Fig. 1C3) low-threshold calcium spike evident when the neuron was released from a continuous hyperpolarization, thus removing the inactivation of low-voltage-activated T-type calcium channels (Huguenard 1996).
Type D PHNn subthreshold membrane oscillations were TTX-sensitive (n = 5/5, not shown). The frequencies of the subthreshold membrane potential oscillations and that of the action potentials within the clusters (intracluster frequency) were not fixed but co-varied in a current-dependent manner (Fig. 3B). In contrast, the frequency of occurrence of the clusters (intercluster frequency) was current-independent and remained around 4 Hz. Overall, the frequencies of the subthreshold membrane oscillations at the resting level varied from 20 to 50 Hz, whereas the intracluster frequency co-varied from 15 to 50 Hz. Another distinctive property of type D PHNn was revealed by responses to hyperpolarizing current pulses of increasing amplitude delivered from rest. Although the application of a short-lasting hyperpolarizing small-amplitude current pulse did not interfere with their generally low irregular spontaneous resting activity (Fig. 4A), a stronger hyperpolarization (20 mV) delayed the onset of activity for a long time (double arrowhead in Fig. 4B). Such behavior strongly suggested the removal of the inactivation of a slowly inactivating subthreshold current similar to the potassium ID current originally described in hippocampal neurons (Bekkers and Delaney 2001; Storm 1988) as well as other CNS neurons (Dekin and Getting 1987; Hammond and Crepel 1992; McCormick 1991; Sah and McLachlan 1992; Spain et al. 1991; Storm 1988; Surmeier et al. 1992)
|
|
) very low concentrations of 4-AP (25–100 µM) were sufficient to suppress the delay in the firing (Fig. 4C2, 8/8 cells tested). The averaged instantaneous frequencies (IF) show that the increase in IF shown in Fig. 4C3 during a constant depolarization was blocked by 4-AP (50 µM), which also increased the resting discharge rate, as would be expected from removal of an inactivating potassium current. The continuous increase in instantaneous frequency (IF) shown in Fig. 4C3 for type D PHNn was only observed in young animals and was greatly dependent on both the membrane potential and step size. It was clearly not a robust behavior that would be needed if single-cell integration could occur without network interactions. All other properties of the type D neurons were identical in young and old animals. In general, the IF was not constant over time because these neurons typically showed action potential clusters (Fig. 5A), which increased in duration with time after a current step and were interspersed with subthreshold oscillations. It appears that the increase in either cluster duration or instantaneous frequency during a step of current requires type D PHNn to be in a sufficiently hyperpolarized state to allow the ID conductance to open and then inactivate during a step depolarization.
|
; Wilson and Kawaguchi 1996). These fluctuations as well as the oscillations are not seen in the MVNn and have amplitudes well above any contribution due to instrumental noise. Because the same neuron at different times showed these slightly different fluctuation types, it is possible that the variability of the spontaneous activity of neurons often observed in the slice preparation may be due to different levels of the NMDA and AMPA activation of excitatory synapses that could be responsible for part of this variability in fluctuation behavior (Anderson et al. 2000; McCormick et al. 2003; Shu et al. 2003). Bath-applied NMDA (100 µM, Tocris) depolarized all types of PHNn but induced either oscillatory or plateau like responses only in type B and type D neurons. These oscillatory-like responses were observed in seven of eight type B neurons and two of nine type D neurons. Figure 6 illustrates the effect of NMDA on a type B neuron showing slow transitions with action potential firing in the up state and a short quiescent down state or more oscillatory responses in which spikes occur during the most depolarized phase of the oscillation. In the presence of TTX, the plateau and oscillatory fluctuation responses were clearly independent of voltage-dependent sodium conductances, contrary to those observed without NMDA in type D PHNn.
|
; Bobker and Williams 1995). In contrast, type D PHNn showed a potent hyperpolarization with exposure to noradrenalin (n = 12/13) or serotonin (n = 22/22). This hyperpolarization was likely to be responsible for the reduction of the resting membrane potential fluctuations by noradrenalin and serotonin Histamine (100 µM, Sigma-Aldrich) depolarized very clearly all cell types (4/5 type A, 17/18 type B and 7/7 type D). A cholinergic agonist (carbachol 100 µM, Sigma-Aldrich) also depolarized type A and B PHNn (9/9 and 28/29, respectively), whereas its effect on type D PHNn was more complex: 5 cells of 11 were depolarized, whereas the remaining 6 were hyperpolarized.
Responses to large ramp stimuli
Ramp currents having different slopes were applied to evaluate dynamic behavior in the time domain for comparison with frequency domain responses. Both at rest or when starting the ramp of current from a hyperpolarized level, the overshoots of all three different cell types inside the PHN illustrated in Fig. 7 are significant and show no measurable differences. This result is in contrast with those of the MVN neurons where the overshoot of type A is always inferior to that of type B MVNn. Because type A PHNn have a significantly higher overshoot than their MVNn counterparts (Table 3 and Fig. 7), the differences among type A, B, and D PHNn are minimal. Thus the PHNn are similar with regard to their ramp responses, indicating that the active membrane properties determining their phasic behavior is likely to influence the firing behavior of all PHNn.
|
IF/I) could be approximated by a linear slope, which, like the overshoot, increased in proportion to the slope of the current with time (I/t, see Fig. 7 legend for values). The ratio or sensitivity (IF/I) for the ramp stimulus from rest having a duration of 600 ms (spikes · s–1 · /nA–1, P600-R), was greater for type A PHNn than for type B or D PHNn (Table 2). This result is similar to that obtained for the magnitudes of the IF transfer function over a wide range of frequencies computed from sinusoidal current injections having periods below 1s (see Fig. 8B1). In addition, the P600-R of type B PHNn was significantly greater than that of type D PHNn (P = 0.005), which appears to be valid only at low frequencies in Fig. 8B1. Interestingly the IF transfer function data show that type D PHNn magnitudes are greater than those of type B PHNn during a depolarization. These responses represent piece-wise linear descriptions of the highly nonlinear voltage-dependent conductances present in these neurons, which provide a dynamic control of the transfer function properties that should greatly influence network activity.
|
Effect of stimulus dynamics on instantaneous frequency: frequency-dependent gate.
The dynamical properties of PHNn were investigated using small-signal sinusoidal current stimulation at frequencies from 0.2 to 50 Hz and measuring both the membrane potential (Fig. 8A) and instantaneous frequency (Fig. 8, B and C). To describe more quantitatively the physiological dynamical behavior, we have analyzed the spike rate and its dependency on the membrane potential using an empirical IF transfer function, namely the modulation of the instantaneous frequency in response to current input (IF/I) at different stimulation frequencies (Fig. 8, B and C). The IF transfer function increases with frequency to a maximal resonance, which often cannot be measured because the maximum modulation frequency is limited by the spontaneous the carrier frequency of the discharge rate. The magnitudes of the type A PHNn IF transfer functions (IF/I) are greater than observed for type D and B PHNn, which are similar at rest but diverge at depolarized potentials (Fig. 8, B and C). When the type A and D PHNn are depolarized (Fig. 8C, 1 and 2), the magnitudes of the IF transfer function increase compared with rest (Fig. 8B, 1 and 2), which is in contrast to the decrease observed in MVN neurons. As suggested in the preceding text, this could be due to the presence of steady-state negative conductances, such as small persistent sodium currents or noninactivating calcium currents, that are likely to be responsible for the oscillatory behavior of type D PHNn.
The instantaneous FM is usually seen as a relatively linear function of small currents over a relatively wide range of stimulation frequencies (du Lac and Lisberger 1995; Nelson et al. 2003; Ris et al. 2001); however, significant nonlinear responses occur in response to large currents (Ermentrout 1998; Kepecs et al. 2002; Ris et al. 2001), which themselves lead to depolarized membrane potentials and activate voltage-dependent conductances.
To estimate the relationship between firing rate and potential of resting and depolarized neurons, it is necessary to extract the sinusoidal membrane potential response in the presence of superimposed action potentials, during sinusoidal current injection. This potential has been referred to as the coarse potential (Carandini 2004) and can be estimated using spectral analysis techniques. The spectral analysis approach was done by determining the Fourier component at the stimulation frequency of the intracellular response in which the action potentials have been clipped at 10 mV above threshold. This procedure reduces the influence of the impulse modulation, which was also measured (see METHODS). In some instances the low frequency components of the after potential seriously distorted the estimation of the coarse potential, which was clearly indicated by phase functions more negative than –90° for frequencies >20 Hz. PHNn showing this behavior were not used in the analysis of the membrane potential. An action potential template subtraction method was also developed to separate the sinusoidal potential response from impulse modulation; however, the results were similar to the spectral methods. These estimates of the membrane potential response were then divided by the injected current to produce a measure of the impedance of the neuron (see Beraneck et al. 2003). These impedance measurements were used to calculate the ratio of instantaneous frequency to membrane potential (Fig. 9) and to estimate parameters for the voltage-dependent conductances responsible for the underlying coarse potential (Fig. 11).
|
|
IF/I, and Z is V/I, then the ratio SRTF/Z is IF/V. As shown in Fig. 9, this ratio clearly increases with the current stimulating frequency for any particular PHN cell type. This result quantitatively illustrates that the amplitude of the spike FM is not directly predicted by the value of the membrane potential but is also a function of the frequency of the membrane potential change in response to current stimuli, i.e., a frequency-dependent gate.
In type B and D PHNn there is a clear increase in the ratio, IF/V at each frequency when the neuron is depolarized; however, for resting and depolarized type A PHNn, the ratios are the same. These data suggest that the frequency-dependent gates of type B and D PHNn are nonlinear with respect to the membrane potential (Beierlein et al. 2002; Kepecs et al. 2002), which in type D PHN show a pronounced peak just above 10 Hz at depolarized levels and appear to be shifted to higher frequencies in type B PHNn. The average magnitude increase of the ratio, IF/V, is significantly greater for type D (254%) than type B (27%) PHNn. Thus the ratio, IF/V, appears to be a more sensitive determinant of differences between the PHNn types than IF/I alone, which shows relatively smaller effects when PHNn were depolarized (Fig. 8, B and C). This nonlinear behavior is in addition to the power law nonlinearity between firing rate and the low frequency or nearly steady-state level of the membrane potential relative to threshold observed in some cortical neurons (Carandini 2004). The power law relationship is a quantitative method to describe the increase in variability that occurs in the conversion of synaptic input to spike rate (Priebe et al. 2004). Thus the more marked nonlinearity of the type D PHNn could play a role in the irregular firing and clustering of action potentials that would even be enhanced as their frequency increases.
Although the filter properties of type D neurons of the PHN provide the most striking differences with those of the MVN, the remaining type A PHNn are also distinctly different from type A MVNn at their resting and depolarized levels, despite their hyperpolarized impedances being the same (data not shown). Interestingly type B PHNn are quite similar to type B MVNn (Fig. 10B, 1–4); however, their proportion including the LTS in the PHN is dominant (65%) and far above that found in the MVN. This gives the PHN a more type B-like or phasic character than observed in the MVN, which is further supported by the findings that instantaneous frequency transfer functions of PHN type A neurons have greater magnitudes and higher resonant frequencies than observed in the MVN (Fig. 10A, 1–4).
|
When a hyperpolarizing current was used to abolish the spontaneous pacemaker behavior, the magnitude of the impedance (Z = V/I) was greater for type D PHNn than type B PHNn for all tested frequencies (either significantly P < 0.05 or as a strong trend P < 0.10, Fig. 8A, 1 and 2). The impedance of type A PHNn was intermediate at all frequencies, and not significantly different from that of the two other cell types.
For type D neurons, the frequency range of these measurements was extended to 500 Hz to estimate their electrotonic structure as well as quantitatively characterize active conductances that were activated by hyperpolarization. The impedance functions measured during hyperpolarizations and depolarizations and at the resting potential provide accurate linear descriptions of the passive and active membrane properties and were used to estimate parameters for a subthreshold neuronal model of type D PHNn.
Figure 11B, 1 and 2, illustrates that the magnitudes of the average resting and depolarized type D PHNn impedance functions are significantly decreased compared with the superimposed hyperpolarized response. In addition, there are troughs and resonances that appear with depolarization. Thus the IF transfer function (see Fig. 8, B and C) is not linearly related to the impedance, as is clearly illustrated in Fig. 9. These profiles are not artifacts due to the averaging process because Bode plots of individual neurons show the same properties (Fig. 11A, 1 and 2). The corresponding phase functions show negative followed by more positive values, which are clearly more pronounced with depolarization. A broad and minimal resonance (Table 2 and Fig. 11B, 1 and 2, for the population average) was observed at hyperpolarized levels indicating that active voltage-dependent conductances such as h conductances are likely to be present. This was also verified by the observation of sag responses to a large hyperpolarization in 11 of 14 type D neurons, as illustrated in Figs. 3A3, 4C1, and 11D1 (dashed line).
PHN neuronal models
Nonspiking dendritic model.
The frequency domain data and real-time responses of type D PHNn provide a basis for constructing a realistic subthreshold type D dendritic model. Type A and B models have been previously constructed for neurons in the MVN (Av-Ron and Vidal 1999; Quadroni and Knöpfel 1994; Ris et al. 2001) and provide an indication of the ionic conductances needed for a type D neuronal model. Because type D neurons have dendritic trees that are likely to be involved in the process of neuronal integration, the electrotonic structure should play an important role in how membrane potential fluctuations influence and maintain the firing behavior needed for persistent activity. Thus a minimal type D nonspiking neuronal model with a Rall type analytical dendritic cylinder for impedance data and an electrotonically equivalent dendrite with three compartments for real-time simulations (Saint-Mleux and Moore 2000a,b) was constructed from membrane potential data over a range of polarizations from –90 to –40 mV. Parameter estimation techniques previously described (Saint-Mleux and Moore 2000a,b) were used to obtain active and passive neuronal parameters. Even though this is a subthreshold model, it has active conductances and describes membrane potential data underlying the action potentials as determined by the Fourier analysis described in the preceding text. This is an important point because activity alone could change the voltage-dependent conductances by alterations of intracellular modulators such as the internal calcium ion concentration. This approach to model development allows a realistic approach to the behavior of neurons in their physiological environment because the data on which the models are based were obtained during normal activity and not only under pharmacologically blocked conditions.
The experimental data required the minimal model to have three uniformly distributed voltage-dependent conductances as follows. An inactivating potassium conductance (Bekkers and Delaney 2001) was clearly needed for the increasing firing rate response as well as the trough in the impedance followed by a resonance peak. A steady-state inward current mediated by a persistent sodium conductance (Rekling and Laursen 1989) was necessary for the oscillatory effects, and finally, a hyperpolarizing h conductance (Richardson et al. 2003; Russier et al. 2003) was needed for the sag response. Although the plateau potential could not be elicited by short amplitude and duration steps (0.1 nA, 10 ms) for most type D neurons, it is likely that the persistent sodium conductance was present in all type A and D neurons because the plateau response is dependent on relative values of other conductances. The model used to fit the data had homogeneously distributed channels; however, similar results could be obtained for type D PHNn by restricting the persistent sodium channel to the dendrite. There are clearly more than three voltage-dependent conductances (Nelson et al. 2003) in the type D PHNn; however, three are sufficient to quantitatively the subthreshold behavior observed in this paper.
Consistent with their observed subthreshold oscillation frequencies, the impedance functions of type D model neurons in Fig. 11C, 1 and 2, show marked resonant peaks that shift to higher frequencies at depolarized membrane potentials. In addition to their peak resonance, these responses typically have a low frequency trough, which is a decrease in their magnitude that precedes the resonance (Fig. 11, A–C). This phenomenon requires either an inactivating D-type potassium conductance or a combination of depolarization- and hyperpolarization-activated ionic conductances (Richardson et al. 2003), all of which are present in the type D neurons. The superposition of the model and experimental data for both the frequency and time domain data in Fig. 11, C and D, show that the model assumptions provide an adequate description of the experimental features described in the preceding text.
The simulations of the real-time oscillatory behavior of Fig. 11D, 1 and 2, show that the derived model has the complexity to increase the magnitude of the oscillatory response during the applications of a step current similar to that observed in Figs. 4A and 5A. Furthermore, the initial response to the step is a large-amplitude highly damped oscillation, which could evoke action potential(s) as in Fig. 5A. After the initial large-amplitude oscillatory response, there is a decrease in the response, which then increases again with time. At lower current levels (see Fig. 11D2), the oscillatory response is preceded by an increasing depolarization of the membrane potential that eventually leads to an oscillatory response. As might be expected, the exact behavior of these oscillations is extremely sensitive to parameter values, especially those of the persistent sodium current.
Spiking dendritic model neurons
PHN type D model neuron.
To further explore the effect of the oscillatory behavior on action potential firing, a spike generating model was created by linking the above oscillatory subthreshold dendritic model with a MVN type A or B soma spike generating model previously developed that accurately describes the behavior of MVNn (Av-Ron and Vidal 1999). Figure 12 illustrates that the attachment of the type D dendrite to a MVN type A soma to form a PHN type D model produces a reasonable description of the type D neuron showing both action potential clustering and a tendency to increase in frequency during a step depolarizing current. This model behaves similar to the nonspiking model when the sodium conductance is blocked. The legend of Fig. 12 contains the specific parameter values used in all the simulations of the PHN model neurons. The clustering behavior of the PHN type D model required the presence of simulated synaptic noise, which tended to evoke random oscillatory activity. These simulations are consistent with the experimental finding that the type D neurons appear to be modified type A PHNn (see Steady state parameters in Table 2).
|
PHN type B model neuron simulations without a persistent sodium conductance (gNaP) in the dendrite (see following text) show regular firing patterns as illustrated in Fig. 12B1 consistent with experimental observations (Fig. 1B). Figure 12B2 illustrates a PHN type B hybrid model that consists of a type D dendrite connected to a MVN type B soma. This hybrid type B PHN model having gNaP in both the soma and dendrite shows spike firing synchronization with the underlying dendritic oscillations that is inconsistent with either the behavior of type B or D neurons. Thus the preferred type B PHNn spiking model (Fig. 12B1) consists of a type D dendrite without gNaP in the dendrites; although the type B soma model does have a gNaP (Av-Ron and Vidal 1999), which is consistent with our experimental results on type B PHNn (see preceding text). A distinguishing feature of type B compared with type A neurons is their oscillatory response to NMDA in both the PHN (Fig. 6) and the MVN (Serafin et al. 1992). To explore the mechanisms involved in NMDA oscillations, simulations were done with the preceding preferred PHN type B model that consisted of a MVN type B soma attached to a type D dendrite in which the sodium persistent channels of the dendritic compartments were replaced with NMDA receptor channels. Figure 12C, 1–3, illustrates PHN type B model plateau potentials in the presence and absence of action potentials similar to that experimentally observed in Fig. 6. The presence of a significant h conductance in this model leads to an increase in the frequency of plateau oscillations during a hyperpolarization (Fig. 12C2) consistent with the frequency increase observed in Fig. 6. Adding the same NMDA kinetics to a PHN type D model in the presence of the type D persistent sodium conductance did not produce NMDA oscillations (not shown). This computational result may be a partial explanation of the experimental finding that NMDA oscillations are prevalent in type B neurons, infrequently observed in type D, and not observed in type A cells, while all cell types respond with a depolarization to NMDA application in both the MVN and PHN (see preceding text and Serafin et al. 1992).
In conclusion, the analysis of the filter properties of the PHNn suggests that type B PHNn are quite similar to their MVN counterparts, whereas type A PHNn are quite different from type A MVNn as manifested by their enhanced sensitivities to current or voltage as well as their increased resonance amplitudes and frequencies. These specific features of type A PHNn make them more similar to the type D PHNn; however, the resonance of the latter appears to occur at lower stimulation frequencies. Thus all of the PHNn are relatively more phasic than tonic in their properties. Finally, the dependence of firing behavior on the different levels of polarization shows that the intrinsic membrane conductances and their modulation play an important role in the function of PHN neurons.
|
|
DISCUSSION |
|---|
|
Numerous models of the oculomotor neuronal integrator have been proposed involving both highly tuned recurrent networks and individual neuronal properties; however, there is little experimental data on the intrinsic membrane properties of neurons likely to be involved in the oculomotor integrator. The experiments reported in this paper show that intrinsic membrane properties are likely to play an important role for three reasons: type B PHNn are the main subset (65%) of PHNn and are similar to the type B MVNn, which have been shown to be the most phasic cells of the MVN; type A tonic neurons are less numerous in the PHN than in the MVN (10 vs. 50%); however, they have dynamical properties that are significantly more phasic than those of the MVN; and the remaining 25% of PHNn form a unique group of type D neurons that are highly oscillatory and clearly different from those of the MVN neurons. We have investigated the firing and biophysical properties of the type B and D neurons and developed data based models to quantitatively illustrate how active conductances produce some of the spiking and oscillatory behavior observed in these cells. We have also shown that the relationship between the membrane potential and impulse activity of type D neurons is highly nonlinear even for relatively low-amplitude responses. These results suggest that synaptic inputs to PHNn are likely to evoke responses that can be amplified in a nonlinear manner as the spike rate increases. The majority of the neurons of the PHN has NMDA receptors, which are likely to be activated during synaptic activity and, in the case of type B and some type D neurons, may provide bistable behavior (Fuentealba et al. 2005) not normally present in these neurons. NMDA receptors on type D PHNn could further enhance their intrinsic fluctuation behavior during neuronal integration as suggested by some theoretical studies (Goldman et al. 2003; Koulakov et al. 2002). The oscillatory behavior of the type D models illustrated in Figs. 11 and 12 is due to a persistent sodium negative conductance and provides a good description of the intrinsic properties of the type D PHNn. The resonant frequencies of the averaged V/I data for type D PHNn of Fig. 11B1 are similar to the mean voltage-dependent intrinsic V oscillation frequencies shown in Figs. 3 and 5; however, the averaged IF/I and IF/V amplitudes of type D PHN in Figs. 8, B1 and C1, and 9, respectively, have lower resonant frequencies. Although these comparisons suggest a relationship between evoked and spontaneous responses, it should be emphasized that linearized transfer functions, which themselves may be voltage dependent, cannot predict nonlinear spontaneous or intrinsic oscillations. Such bistable oscillations can only be obtained with a nonlinear dynamical system. NMDA-induced conductances, which also have highly voltage-dependent properties, could add to the intrinsic oscillatory character of type D PHNn and/or provide bistability in type B neurons as is clearly demonstrated in Fig. 6 as well as the simulations of Fig. 12. The findings that both type B and D PHNn as well as type B MVNn have NMDA receptors supports the hypothesis that the vestibular neural integrator utilizes network interactions within and/or between the MVN and PHN, which have neurons with either intrinsic or NMDA- induced voltage-dependent dendritic properties. Thus the bistable plateau responses induced by NMDA activation in the majority of PHNn support the hypothesis that neural integration can occur in highly connected networks having multi-state dendritic compartments (Goldman et al. 2003; Koulakov et al. 2002) that latch into an on-state depolarization that maintains a fixed firing frequency.
A network model of integration is further supported by the anatomical location of type D neurons in the rostral part of the PHN where integration has been proposed to occur (Escudero et al. 1992) as well as by the fact that type D PHNn show a rostral caudal gradient similar to that observed for position-velocity neurons recorded extracellularly (Delgado-Garcia et al. 1989; Lopez-Barneo et al. 1982). Furthermore, type D neurons are able to transform a step of current into an increase of the average firing rate (Figs. 4C1 and 5) due to their ID current, which tends to approximate mathematical integration (Storm 1988). It appears that the linear increase of firing rate seen in the young animals (Fig. 4C1) becomes dominated by the clustering or irregularity of firing (Fig. 5A), which are becoming more marked as the animal grows. There appears to be a critical level of the membrane potential for single-cell integration, which would not be sufficiently robust if there were no network connections. Thus both type B and D PHNn are likely to play a role in the neuronal integrator as an emerging property of the network organization inside the PHN. Sustained activity after a short pulse could also be enhanced by either intra-PHN collaterals (McCrea et al. 1985a,b, 2005) and/or by a synergistic effect of all PHNn, which have a more phasic behavior than their MVN counterparts and may not require bilateral connections. In addition, recent studies have shown that cooperative mechanisms (Mensh et al. 2004) involving both glutamatergic and cholinergic receptors can produce short-term potentiation (STP) of synaptic responses invoked in PHNn when stimulating the paramedian pontine reticular formation (de Dios Navarro-Lopez et al. 2005). This STP requires NMDA receptors and is likely to be involved in stabilizing eye-position signals. Our results showing that both cholinergic and NMDA receptors are present on type B PHNn support this hypothesis.
Although intrinsic properties of PHNn and their excitatory inputs have been emphasized in these experiments, it is highly likely that reciprocal inhibitory projections in the PHN across the midline (Galiana and Outerbridge 1984; McCrea et al. 1985a,b, 2005) are also necessary for the neural integration of modulated continuous activity most probably using lateral inhibition as a form of recurrent excitation (Cannon et al. 1983). It should also be noted that PHNn typically receive inputs that are not pure velocity signals and furthermore, the PHNn have both position and velocity signals depending on their rostral-caudal location in the PHN (Delgado-Garcia et al. 1989).
According to the morphological classification of PHNn by McCrea and Baker (1985b), our PHNn are likely to be their "principal cells" with relatively large neurons with a low number of dendrites. Because of the prevalence of principal cells in the PHN, our sampling of neurons may have missed other multi-dendritic or smaller neurons. In their description of the electrophysiological and pharmacological properties of PHNn, Bobker et al. (Bobker 1994; Bobker and Williams 1989–1991, 1995) have described three types of neurons in the PHN. Types I and III represent the majority of neurons and are not electrophysiologically distinguishable: they had a short-duration action potential, a spontaneous frequency between 15 and 20 Hz and they were depolarized by 30 µM serotonin sometimes with a transient hyperpolarization, which suggests that these cells are likely to be our type B PHNn. In contrast, type II neurons, mainly located in the rostral part of the PHN, showed a lower firing rate with broad spikes, each with a shoulder on the repolarizing phase, and a hyperpolarizing response to serotonin. All of these findings agree with our classification and suggest that Bobker's type II represent our type D PHNn. No type described by Bobker can be linked to type A PHNn; this might be due to facts that type A PHNn are the least frequent neurons in the PHN and Bobker's studies were focused on type I neurons, the most numerous cells in the nucleus. Similarly a recent paper on integration implying a role for acetylcholine (de Dios Navarro-Lopez et al. 2004) only considered neurons with a double AHP (our type B neurons).
We have shown that the PHNn include three neuronal types: type A, type B (including type B+LTS cells), and type D neurons, the former two being also found in the MVN. Type D neurons are specific to the PHN because of their unique discharge features, namely, subthreshold membrane potential oscillations and discharge in clusters. Furthermore, the differences observed in the type-specific criteria, namely a large decrease in AHPR and an increase in dAHP, show that the features typical of type B neurons are more pronounced in the PHN and tend to be related to the phasic dynamical behavior of the PHNn. It should also be emphasized that the type D neurons are not likely the result of injury due to electrode impalement because there were no differences in the recording durations nor in the action potential amplitudes of these neurons compared with type A and B neurons in both the PHN and the MVN. Despite their markedly phasic character, type D PHNn appear to be modified type A neurons (Fig. 12), where their IA-like rectifying current (Serafin et al. 1991) has been replaced in part by the ID current, which may assist in neuronal integration as discussed in the preceding text. Thus the finding that the phasic character of all PHN cell types is similar (for type B) or increased (for type A and D) compared with other vestibular neurons as well as the presence of a large proportion of type B and D neurons suggests that the PHN can be considered as having a more phasic character than the MVN.
The presence of comparable cell types found for both the PHN and MVN also applies to other medullary reticular neurons, namely the nucleus gigantocellularis (NGC), which are also involved in the control of gaze orientation and perhaps as well in controlling the muscle atonia associated with paradoxical sleep (Mallick et al. 2002; Serafin et al. 1996b). Typical type A and B neurons similar to those of the MVN have been described in the NGC and would seem likely to have similar functional roles.
Other roles of the PHNn
A study indicates that PHNn are involved in the regulation of REM sleep (Kaur et al. 2001). REM sleep in the guinea pig is characterized by episodes of rapid eye oscillations (Escudero and Vidal 1996) as in other mammalian species. These rapid successions of saccades, interrupted by fixation periods, are facilitated by a failure of the neuronal integrators during that state. Indeed, the interstitial nucleus of Cajal that integrates vertical and torsional eye movements and the PHN do not exhibit the tonic activity that they normally show during the waking state (Fukushima and Fukushima 1990). Altogether, these results and our in vitro data suggest that the intrinsic membrane properties of some PHNn could be instrumental in determining the type of eye movements observed during the different states of vigilance. During the waking state, type D PHNn would be hyperpolarized and could therefore show their integrative properties in part via ID conductances, namely allowing ocular fixations. Serotonin and noradrenalin could play a key role because they are released in the alert state and significantly hyperpolarize these cells. One hypothesis to explain why no bursting cells have been recorded in the PHN of awake animals (Delgado-Garcia et al. 1989; Lopez-Barneo et al. 1982) is that the massive synaptic input from all the oculomotor systems to the PHNn would be sufficient to depolarize type D PHNn out of the limited range where the clustering of action potentials can normally be seen (see Fig. 3A, 1 and 2), thus overcoming the hyperpolarizing effects of high ambient levels of noradrenalin and serotonin. Alternatively, during REM sleep, type D PHNn would be less hyperpolarized by the decrease of the concentration of these neuromodulators, explaining the failure of the neuronal integrator (inactivation of the ID conductance). The PHNn would also favor the occurrence of the rapid eye movements due to the presence of oscillations in the type D depolarized neurons. The cholinergic neurons of the pedunculopontine tegmental nucleus are likely candidates to depolarize the PHNn. This mesopontine structure, known to be active during REM sleep, has dense reciprocal projections with the PHN (Higo et al. 1990).
Thus the PHN, shown to be the principal location for oculomotor integration in the horizontal plane, possesses many properties that could contribute to the process of the integration. The complete solution to the mechanism of integration is likely to lie in the interaction between the intrinsic membrane properties and a functional network. In addition, the PHN could be considered not only for providing a position signal to the motoneurons but also as a relay in the control of the sleep wake cycle and finally as contributing to an efferent copy of the oculomotor signal in general (Cullen 2004; Hardy and Mirenowicz 1991; McCrea and Baker 1985a; Sylvestre et al. 2003).
|
|
GRANTS |
|---|
|
|
|
ACKNOWLEDGMENTS |
|---|
|
|
|
FOOTNOTES |
|---|
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Address for reprint requests and other correspondence: L. E. Moore, Laboratoire de Neurobiologie des Réseaux Sensorimoteurs, CNRS UMR 7060, 45 Rue des Saints-Pères, 75270 Paris Cédex 06, France (E-mail: moore{at}ccr.jussieu.fr)
|
|
REFERENCES |
|---|
|
Aksay E, Baker R, Seung HS, and Tank DW. Correlated discharge among cell pairs within the oculomotor horizontal velocity-to-position integrator. J Neurosci 23: 10852–10858, 2003a.
Aksay E, Gamkrelidze G, Seung HS, Baker R, and Tank DW. In vivo intracellular recording and perturbation of persistent activity in a neural integrator. Nat Neurosci 4: 184–193, 2001.[CrossRef][Web of Science][Medline]
Aksay E, Major G, Goldman MS, Baker R, Seung HS, and Tank DW. History dependence of rate covariation between neurons during persistent activity in an oculomotor integrator. Cereb Cortex 13: 1173–1184, 2003b.
Anastasio TJ. Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior. Biol Cybern 79: 377–391, 1998.[CrossRef][Web of Science][Medline]
Anderson J, Lampl I, Reichova I, Carandini M, and Ferster D. Stimulus dependence of two-state fluctuations of membrane potential in cat visual cortex. Nat Neurosci 3: 617–621, 2000.[CrossRef][Web of Science][Medline]
Arnold DB and Robinson DA. A learning network model of the neural integrator of the oculomotor system. Biol Cybern 64: 447–454, 1991.[CrossRef][Web of Science][Medline]
Arnold DB and Robinson DA. The oculomotor integrator: testing of a neural network model. Exp Brain Res 113: 57–74, 1997.[CrossRef][Web of Science][Medline]
Arnold DB, Robinson DA, and Leigh RJ. Nystagmus induced by pharmacological inactivation of the brainstem ocular motor integrator in monkey. Vision Res 39: 4286–4295, 1999.[CrossRef][Web of Science][Medline]
Av-Ron E and Vidal PP. Intrinsic membrane properties and dynamics of medial vestibular neurons: a simulation. Biol Cybern 80: 383–392, 1999.[CrossRef][Web of Science][Medline]
Beierlein M, Fall CP, Rinzel J, and Yuste R. Thalamocortical bursts trigger recurrent activity in neocortical networks: layer 4 as a frequency-dependent gate. J Neurosci 22: 9885–9894, 2002.
Bekkers JM and Delaney AJ. Modulation of excitability by alpha-dendrotoxin-sensitive potassium channels in neocortical pyramidal neurons. J Neurosci 21: 6553–6560, 2001.
Beraneck M, Hachemaoui M, Idoux E, Ris L, Uno A, Godaux E, Vidal PP, Moore LE, and Vibert N. Long-term plasticity of ipsilesional medial vestibular nucleus neurons after unilateral labyrinthectomy. J Neurophysiol 90: 184–203, 2003.
Beraneck M, Idoux E, Uno A, Vidal PP, Moore LE, and Vibert N. Unilateral labyrinthectomy modifies the membrane properties of contralesional vestibular neurons. J Neurophysiol 92: 1668–1684, 2004.
Blazquez PM, Hirata Y, Heiney SA, Green AM, and Highstein SM. Cerebellar signatures of vestibulo-ocular reflex motor learning. J Neurosci 23: 9742–9751, 2003.
Bobker DH. A slow excitatory postsynaptic potential mediated by 5-HT2 receptors in nucleus prepositus hypoglossi. J Neurosci 14: 2428–2434, 1994.[Abstract]
Bobker DH and Williams JT. Serotonin augments the cationic current Ih in central neurons. Neuron 2: 1535–1540, 1989.[CrossRef][Web of Science][Medline]
Bobker DH and Williams JT. Serotonin-mediated inhibitory postsynaptic potential in guinea pig prepositus hypoglossi and feedback inhibition by serotonin. J Physiol 422: 447–462, 1990.
Bobker DH and Williams JT. Cocaine and amphetamine interact at 5-HT synapses through distinct mechanisms in guinea-pig prepositus hypoglossi. J Neurosci 11: 2151–2156, 1991.[Abstract]
Bobker DH and Williams JT. The serotonergic inhibitory postsynaptic potential in prepositus hypoglossi is mediated by two potassium currents. J Neurosci 15: 223–229, 1995.[Abstract]
Borg-Graham LJ. Modeling the non-linear conductances of excitable membranes. In: Cellular Neurobiology: A Practical Approach, edited by Chad J and Wheal H. New-York: Oxford, 1991, p. 247–275.
Borg-Graham LJ, Monier C, and Fregnac Y. Visual input evokes transient and strong shunting inhibition in visual cortical neurons. Nature 393: 369–373, 1998.[CrossRef][Medline]
Cannon SC and Robinson DA. Loss of the neural integrator of the oculomotor system from brain stem lesions in monkey. J Neurophysiol 57: 1383–1409, 1987.
Cannon SC, Robinson DA, and Shamma S. A proposed neural network for the integrator of the oculomotor system. Biol Cybern 49: 127–136, 1983.[CrossRef][Web of Science][Medline]
Carandini M. Amplification of trial-to-trial response variability by neurons in visual cortex. PLoS Biol 2: E264, 2004.[CrossRef][Medline]
Chéron G and Godaux E. Disabling of the oculomotor neural integrator by kainic acid injections in the prepositus-vestibular complex of the cat. J Physiol 394: 267–290, 1987.
Crill WE. Persistent sodium current in mammalian central neurons. Annu Rev Physiol 58: 349–362, 1996.[CrossRef][Web of Science][Medline]
Cullen KE. Sensory signals during active versus passive movement. Curr Opin Neurobiol 14: 698–706, 2004.[CrossRef][Web of Science][Medline]
de Dios Navarro-Lopez J, Alvarado JC, Marquez-Ruiz J, Escudero M, Delgado-Garcia JM, and Yajeya J. A cholinergic synaptically triggered event participates in the generation of persistent activity necessary for eye fixation. J Neurosci 24: 5109–5118, 2004.
de Dios Navarro-Lopez J, Delgado-Garcia JM, and Yajeya J. Cooperative glutamatergic and cholinergic mechanisms generate short-term modifications of synaptic effectiveness in prepositus hypoglossi neurons. J Neurosci 25: 9902–9906, 2005.
Dekin MS and Getting PA. In vitro characterization of neurons in the ventral part of the nucleus tractus solitarius. II. Ionic basis for repetitive firing patterns. J Neurophysiol 58: 215–229, 1987.
Delgado-Garcia JM, Vidal PP, Gomez C, and Berthoz A. A neurophysiological study of prepositus hypoglossi neurons projecting to oculomotor and preoculomotor nuclei in the alert cat. Neuroscience 29: 291–307, 1989.[CrossRef][Web of Science][Medline]
Dobbing J and Sands J. Growth and development of the brain and spinal cord of the guinea pig. Brain Res 17: 115–123, 1970.[CrossRef][Web of Science][Medline]
du Lac S, and Lisberger SG. Cellular processing of temporal information in medial vestibular nucleus neurons. J Neurosci 15: 8000–8010, 1995.[Abstract]
Egorov AV, Hamam BN, Fransen E, Hasselmo ME, and Alonso AA. Graded persistent activity in entorhinal cortex neurons. Nature 420: 173–178, 2002.[CrossRef][Medline]
Ermentrout B. Linearization of F-I curves by adaptation. Neural Comput 10: 1721–1729, 1998.[CrossRef][Web of Science][Medline]
Escudero M, de la Cruz RR, and Delgado-Garcia JM. A physiological study of vestibular and prepositus hypoglossi neurones projecting to the abducens nucleus in the alert cat. J Physiol 458: 539–560, 1992.
Escudero M and Vidal PP. A quantitative study of electroencephalography, eye movements and neck electromyography characterizing the sleep-wake cycle of the guinea pig. Eur J Neurosci 8: 572–580, 1996.[CrossRef][Web of Science][Medline]
Fuentealba P, Timofeev I, Bazhenov M, Sejnowski TJ, and Steriade M. Membrane bistability in thalamic reticular neurons during spindle oscillations. J Neurophysiol 93: 294–304, 2005.
Fukushima K and Fukushima J. Activity of eye-movement-related neurons in the region of the interstitial nucleus of Cajal during sleep. Neurosci Res 9: 126–139, 1990.[CrossRef][Web of Science][Medline]
Fukushima K and Kaneko CR. Vestibular integrators in the oculomotor system. Neurosci Res 22: 249–258, 1995.[CrossRef][Web of Science][Medline]
Galiana HL and Outerbridge JS. A bilateral model for central neural pathways in vestibuloocular reflex. J Neurophysiol 51: 210–241, 1984.
Goldman MS, Kaneko CR, Major G, Aksay E, Tank DW, and Seung HS. Linear regression of eye velocity on eye position and head velocity suggests a common oculomotor neural integrator. J Neurophysiol 88: 659–665, 2002.
Goldman MS, Levine JH, Major G, Tank DW, and Seung HS. Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron. Cereb Cortex 13: 1185–1195, 2003.
Gstoettner W and Burian M. Vestibular nuclear complex in the guinea pig: a cytoarchitectonic study and map in three planes. J Comp Neurol 257: 176–188, 1987.[CrossRef][Web of Science][Medline]
Hammond C and Crepel F. Evidence for a slowly inactivating K+ current in prefrontal cortical cells. Eur J Neurosci 4: 1087–1092, 1992.[CrossRef][Web of Science][Medline]
Hardy O and Mirenowicz J. Transient increase of contraversive saccade parameters following kainic acid injection in the periparabigeminal area of guinea pig. Exp Brain Res 85: 616–620, 1991.[Web of Science][Medline]
Higo S, Ito K, Fuchs D, and McCarley RW. Anatomical interconnections of the pedunculopontine tegmental nucleus and the nucleus prepositus hypoglossi in the cat. Brain Res 536: 79–85, 1990.[CrossRef][Web of Science][Medline]
Huguenard JR. Low-threshold calcium currents in central nervous system neurons. Annu Rev Physiol 58: 329–348, 1996.[CrossRef][Web of Science][Medline]
Idoux E, Vibert N, Beraneck M, Vidal PP, and Moore LE. Static and dynamic membrane properties of prepositus hypoglossi neurons in guinea pig brainstem slices. NCM Annual Meeting, Sitges, Spain, 2004.
Kaur S, Saxena RN, and Mallick BN. GABAergic neurons in prepositus hypoglossi regulate REM sleep by its action on locus coeruleus in freely moving rats. Synapse 42: 141–150, 2001.[CrossRef][Web of Science][Medline]
Kepecs A, Wang XJ, and Lisman J. Bursting neurons signal input slope. J Neurosci 22: 9053–9062, 2002.
Koulakov AA, Raghavachari S, Kepecs A, and Lisman JE. Model for a robust neural integrator. Nat Neurosci 5: 775–782, 2002.[CrossRef][Web of Science][Medline]
Loewenstein Y and Sompolinsky H. Temporal integration by calcium dynamics in a model neuron. Nat Neurosci 6: 961–967, 2003.[CrossRef][Web of Science][Medline]
Lopez-Barneo J, Darlot C, Berthoz A, and Baker R. Neuronal activity in prepositus nucleus correlated with eye movement in the alert cat. J Neurophysiol 47: 329–352, 1982.
Major G, Baker R, Aksay E, Mensh B, Seung HS, and Tank DW. Plasticity and tuning by visual feedback of the stability of a neural integrator. Proc Natl Acad Sci USA 101: 7739–7744, 2004a.
Major G, Baker R, Aksay E, Seung HS, and Tank DW. Plasticity and tuning of the time course of analog persistent firing in a neural integrator. Proc Natl Acad Sci USA 101: 7745–7750, 2004b.
Mallick BN, Majumdar S, Faisal M, Yadav V, Madan V, and Pal D. Role of norepinephrine in the regulation of rapid eye movement sleep. J Biosci 27: 539–551, 2002.[CrossRef][Web of Science][Medline]
Marder E, Abbott LF, Turrigiano GG, Liu Z, and Golowasch J. Memory from the dynamics of intrinsic membrane currents. Proc Natl Acad Sci USA 93: 13481–13486, 1996.
McCormick DA. Functional properties of a slowly inactivating potassium current in guinea pig dorsal lateral geniculate relay neurons. J Neurophysiol 66: 1176–1189, 1991.
McCormick DA, Shu Y, Hasenstaub A, Sanchez-Vives M, Badoual M, and Bal T. Persistent cortical activity: mechanisms of generation and effects on neuronal excitability. Cereb Cortex 13: 1219–1231, 2003.
McCrea RA and Baker R. Anatomical connections of the nucleus prepositus of the cat. J Comp Neurol 237: 377–407, 1985a.[CrossRef][Web of Science][Medline]
McCrea RA and Baker R. Cytology and intrinsic organization of the perihypoglossal nuclei in the cat. J Comp Neurol 237: 360–376, 1985b.[CrossRef][Web of Science][Medline]
McCrea RA and Horn AK. Nucleus prepositus. Prog Brain Res 151: 205–230, 2005.[Web of Science][Medline]
Mensh BD, Aksay E, Lee DD, Seung HS, and Tank DW. Spontaneous eye movements in goldfish: oculomotor integrator performance, plasticity, and dependence on visual feedback. Vision Res 44: 711–726, 2004.[CrossRef][Web of Science][Medline]
Mettens P, Godaux E, Chéron G, and Galiana HL. Effect of muscimol microinjections into the prepositus hypoglossi and the medial vestibular nuclei on cat eye movements. J Neurophysiol 72: 785–802, 1994.
Moore LE and Buchanan JT. The effects of neurotransmitters on the integrative properties of spinal neurons in the lamprey. J Exp Biol 175: 89–114, 1993.[Abstract]
Moore LE, Hachemaoui M, Idoux E, Vibert N, and Vidal PP. The linear and non-linear relationships between action potential discharge rates and membrane potential in model vestibular neurons. Nonlinear Stud 11 423–447, 2004.
Moschovakis AK. The neural integrators of the mammalian saccadic system. Front Biosci 2 D552–D577, 1997.
Mühlethaler M, Vibert N, de Waele C, Vidal PP and Serafin M. Pharmacological characterization of nucleus prepositus hypoglossi neurones in guinea-pig brainstem slices. Soc Neurosci Abstr 22: 263.3, 1996.
Murphey CR, Moore LE, and Buchanan JT. Quantitative analysis of electrotonic structure and membrane properties of NMDA-activated lamprey spinal neurons. Neural Comput 7: 486–506, 1995.[Web of Science][Medline]
Nacher J, Palop JJ, Ramirez C, Molowny A, and Lopez-Garcia C. Early histological maturation in the hippocampus of the guinea pig. Brain Behav Evol 56: 38–44, 2000.[CrossRef][Web of Science][Medline]
Nelson AB, Krispel CM, Sekirnjak C, and du Lac S. Long-lasting increases in intrinsic excitability triggered by inhibition. Neuron 40: 609–620, 2003.[CrossRef][Web of Science][Medline]
Pena JL and Konishi M. Robustness of multiplicative processes in auditory spatial tuning. J Neurosci 24: 8907–8910, 2004.
Polsky A, Mel BW, and Schiller J. Computational subunits in thin dendrites of pyramidal cells. Nat Neurosci 7: 621–627, 2004.[CrossRef][Web of Science][Medline]
Priebe NJ, Mechler F, Carandini M, and Ferster D. The contribution of spike threshold to the dichotomy of cortical simple and complex cells. Nat Neurosci 7: 1113–1122, 2004.[CrossRef][Web of Science][Medline]
Quadroni R and Knöpfel T. Compartmental models of type A and type B guinea pig medial vestibular neurons. J Neurophysiol 72: 1911–1924, 1994.
Rall W. Membrane potential transients and membrane time constant of motoneurons. Exp Neurol 2: 503–532, 1960.[CrossRef][Web of Science][Medline]
Rekling JC and Laursen AM. Evidence for a persistent sodium conductance in neurons from the nucleus prepositus hypoglossi. Brain Res 500: 276–286, 1989.[CrossRef][Web of Science][Medline]
Richardson MJ, Brunel N, and Hakim V. From subthreshold to firing-rate resonance. J Neurophysiol 89: 2538–2554, 2003.
Ris L, Hachemaoui M, Vibert N, Godaux E, Vidal PP, and Moore LE. Resonance of spike discharge modulation in neurons of the guinea pig medial vestibular nucleus. J Neurophysiol 86: 703–716, 2001.
Robinson DA. Oculomotor control signals. In: Basic Mechanisms of Ocular Motility and their Clinical Implications, edited by Bach-Y-Rita P and Lennestrand G. Oxford: Pergamon, 1975, vol. 24, p. 337–374.
Russier M, Carlier E, Ankri N, Fronzaroli L, and Debanne D. A-, T-, and H-type currents shape intrinsic firing of developing rat abducens motoneurons. J Physiol 549: 21–36, 2003.
Sah P and McLachlan EM. Potassium currents contributing to action potential repolarization and the afterhyperpolarization in rat vagal motoneurons. J Neurophysiol 68: 1834–1841, 1992.
Saint-Mleux B and Moore LE. Active dendritic membrane properties of Xenopus larval spinal neurons analyzed with a whole cell soma voltage clamp. J Neurophysiol 83: 1381–1393, 2000a.
Saint-Mleux B and Moore LE. Firing properties and electrotonic structure of Xenopus larval spinal neurons. J Neurophysiol 83: 1366–1380, 2000b.
Serafin M, de Waele C, Khateb A, Vidal PP, and Mühlethaler M. Medial vestibular nucleus in the guinea-pig. I. Intrinsic membrane properties in brainstem slices. Exp Brain Res 84: 417–425, 1991.[Web of Science][Medline]
Serafin M, Khateb A, de Waele C, Vidal PP, and Mühlethaler M. Medial vestibular nucleus in the guinea-pig: NMDA-induced oscillations. Exp Brain Res 88: 187–192, 1992.[CrossRef][Web of Science][Medline]
Serafin M, Vibert N, de Waele C, Vidal PP, and Mühlethaler M. Electrophysiological properties of nucleus prepositus hypoglossi neurones in brainstem slices. Soc Neurosci Abstr 22: 263.2, 1996a.
Serafin M, Vidal PP, and Mühlethaler M. Electrophysiological study of nucleus gigantocellularis neurons in guinea-pig brainstem slices. Neuroscience 73: 797–805, 1996b.[CrossRef][Web of Science][Medline]
Seung HS, Lee DD, Reis BY, and Tank DW. Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron 26: 259–271, 2000.[CrossRef][Web of Science][Medline]
Shu Y, Hasenstaub A, Badoual M, Bal T, and McCormick DA. Barrages of synaptic activity control the gain and sensitivity of cortical neurons. J Neurosci 23: 10388–10401, 2003.
Skavenski AA and Robinson DA. Role of abducens neurons in vestibuloocular reflex. J Neurophysiol 36: 724–738, 1973.
Spain WJ, Schwindt PC, and Crill WE. Two transient potassium currents in layer V pyramidal neurones from cat sensorimotor cortex. J Physiol 434: 591–607, 1991.
Staudinger JL, Darlington RB, and Clancy B. Guinea pig neural development predicted using a statistical model. Soc Neurosci Abstr 35: 147.10, 2005.
Storm JF. Temporal integration by a slowly inactivating K+ current in hippocampal neurons. Nature 336: 379–381, 1988.[CrossRef][Medline]
Surmeier DJ, Xu ZC, Wilson CJ, Stefani A, and Kitai ST. Grafted neostriatal neurons express a late-developing transient potassium current. Neuroscience 48: 849–856, 1992.[CrossRef][Web of Science][Medline]
Sylvestre PA, Choi JT, and Cullen KE. Discharge dynamics of oculomotor neural integrator neurons during conjugate and disjunctive saccades and fixation. J Neurophysiol 90: 739–754, 2003.
Uno A, Idoux E, Beraneck M, Vidal PP, Moore LE, Wilson VJ, and Vibert N. Static and dynamic membrane properties of lateral vestibular nucleus neurons in guinea pig brain stem slices. J Neurophysiol 90: 1689–1703, 2003.
Vibert N, Bantikyan A, Babalian A, Serafin M, Mühlethaler M, and Vidal PP. Post-lesional plasticity in the central nervous system of the guinea-pig: a "top-down" adaptation process? Neuroscience 94: 1–5, 1999.[CrossRef][Web of Science][Medline]
Wilson CJ and Kawaguchi Y. The origins of two-state spontaneous membrane potential fluctuations of neostriatal spiny neurons. J Neurosci 16: 2397–2410, 1996.
This article has been cited by other articles:
|
|
 |
|
  E. Idoux, D. Eugene, A. Chambaz, C. Magnani, J. A. White, and L. E. Moore Control of Neuronal Persistent Activity by Voltage-Dependent Dendritic Properties J Neurophysiol, September 1, 2008; 100(3): 1278 - 1286. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 D. Eugene, S. Deforges, F. Guimont, E. Idoux, P.-P. Vidal, L. E. Moore, and N. Vibert Developmental regulation of the membrane properties of central vestibular neurons by sensory vestibular information in the mouse J. Physiol., September 15, 2007; 583(3): 923 - 943. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
TOP
ABSTRACT
INTRODUCTION
) that is consistent with the presence of an IA current. Application of a depolarizing current step superimposed on a steady-state hyperpolarization (here and in the following figures, 
, represent the resting membrane potential) was used to indicate the presence of an IA current as an initial short-duration lag, which delayed the firing of the cell (arrow in A3). B,1–3: type B PHNn showed tonic regular activity at rest (B1) and had a short-duration action potential (B2, inset) followed by an early fast and a delayed slower AHP (single and double 
in B2). These cells showed long-lasting sodium-dependent sub-threshold plateau potentials (B3, *) in response to a short-lasting depolarizing current pulse superimposed on a slight hyperpolarization just sufficient to eliminate their spontaneous firing. The plateau potential was still present in absence of calcium but totally suppressed by TTX at 1 µM (B3, insets). C, 1–3: type B+LTS PHNn showed tonic regular activity at rest (C1); they had a medium-duration action potential (C2, inset) followed by a biphasic afterhyperpolarization potential (AHP; single and double 
in D3) intermingled with sub-threshold membrane oscillations (closed squares in D3) when depolarized from rest. In general, such sub-threshold oscillations were also observed at the resting membrane potential (D, 1 and 2). A4–D4: photomicrographs of neurobiotin-injected PHNn of each type.
). B: steady-state current dependence (I, nA) of the frequencies (F, Hz) of subthreshold oscillations (
F = 42.0*I +18.1, R2 = 0.95) in 4 type D PHNn. In contrast, the inter-cluster frequency (
3.9, R2 = 0.00). Note that the horizontal axis is a function of current and not time.
) and type A PHNn (
). A, 1 and 2, shows a comparison of the 2 components of the transfer function (A1, magnitude, and A2, phase) at the resting level and A, 3 and 4, during a depolarization (A3, magnitude, and A4, phase). *, 