Slow Oscillations of the Purkinje Cell Firing Rate Induced by Electrical Stimulation of the Locus Coeruleus in Rats

In anesthetized Wistar rats, we studied the effect of electrical stimulation of the locus coeruleus (LC) on the firing rates of Purkinje cells using spectral analysis. The frequency of extracellularly recorded activity of Purkinje cells was measured before and during the 1st, 5th, 6th, and 11th min after cessation of 10-sec-long LC stimulations. Spectral analysis of the Purkinje cell firing rates (imp./bin, the bin duration was 2^-8 sec) for 60- to 120-sec-long intervals was performed using fast Fourier transformation after digital conversion of unitary spikes. Mean power spectra of the Purkinje cell firing rates (derived from 8-sec-long consecutive epochs at a sampling rate of 256 sec^-1) showed an increase in the slow frequency range (0.1-1.0 Hz) after LC stimulation, particularly due to the slowest components (below 0.5 Hz). This effect lasted more than 1 min and usually less than 6 min after cessation of LC stimulation and could be interpreted as the development of slow oscillations in the Purkinje cell firing. Our results suggest that slow oscillations of the firing rate of cerebellar output neurons, induced by LC stimulation, reflect a specific coordination of the cerebellar neuronal activities (important for a central norepinephrine influence) in regulation of different pathological states.     

Dynamic excitation states and firing patterns are controlled by sodium channel kinetics in myenteric neurons: a simulation study

Enteric neurons located in the gastro-intestinal tract are of particular importance to control digestive functions such as motility and secretion. In our recent publication, we showed that mouse myenteric neurons exhibit 2 types of tetrodotoxin-resistant Na⁺ currents: a fast inactivating Na⁺ current produced by Nav1.5 channels, present in nearly all myenteric neurons, and a persistent Na⁺ current attributed to Nav1.9 channels, restricted to the intrinsic primary afferent neurons (IPANs). By combination of experimental recording and computer simulation we found that Nav1.5 contributed to the upstroke velocity of action potentials (APs), whereas Nav1.9 opposed AP repolarization. Here, we detailed the Na⁺, Ca²⁺ and K⁺ currents used in our computational model of IPAN. We refined the prototype cell to reproduce the sustained firing pattern recorded in situ. As shown in experimental conditions we demonstrated that Nav1.9 channels critically determine the up-state life-time and thus, are essential to sustain tonic firing.     

Homeostatic regulation mechanism of spontaneous firing determines glutamate responsiveness in the midbrain dopamine neurons

Autonomous tonic firing of the midbrain dopamine neuron is essential for maintenance of ambient dopamine level in the brain, in which intracellular Ca²⁺ concentration ([Ca²⁺]c) plays a complex but pivotal role. However, little is known about Ca²⁺ signals by which dopamine neurons maintain an optimum spontaneous firing rate. In the midbrain dopamine neurons, we here show that spontaneous firing evoked [Ca²⁺]c changes in a phasic manner in the dendritic region but a tonic manner in the soma. Tonic levels of somatic [Ca²⁺]c strictly tallied with spontaneous firing rates. However, manipulatory raising or lowering of [Ca²⁺]c with caged compounds from the resting firing state proportionally suppressed or raised spontaneous firing rate, respectively, suggesting presence of the homeostatic regulation mechanism for spontaneous firing rate via tonic [Ca²⁺]c changes of the soma. More importantly, abolition of this homeostatic regulation mechanism significantly exaggerated the responses of tonic firings and high-frequency phasic discharges to glutamate. Therefore, we conclude that this Ca²⁺-dependent homeostatic regulation mechanism is responsible for not only maintaining optimum rate of spontaneous firing, but also proper responses to glutamate. Perturbation of this mechanism could cause dopamine neurons to be more vulnerable to glutamate and Ca²⁺ toxicities.     

Dynamic excitation states and firing patterns are controlled by sodium channel kinetics in myenteric neurons: a simulation study

Enteric neurons located in the gastro-intestinal tract are of particular importance to control digestive functions such as motility and secretion. In our recent publication, we showed that mouse myenteric neurons exhibit 2 types of tetrodotoxin-resistant Na⁺ currents: a fast inactivating Na⁺ current produced by Nav1.5 channels, present in nearly all myenteric neurons, and a persistent Na⁺ current attributed to Nav1.9 channels, restricted to the intrinsic primary afferent neurons (IPANs). By combination of experimental recording and computer simulation we found that Nav1.5 contributed to the upstroke velocity of action potentials (APs), whereas Nav1.9 opposed AP repolarization. Here, we detailed the Na⁺, Ca²⁺ and K⁺ currents used in our computational model of IPAN. We refined the prototype cell to reproduce the sustained firing pattern recorded in situ. As shown in experimental conditions we demonstrated that Nav1.9 channels critically determine the up-state life-time and thus, are essential to sustain tonic firing.     

An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory

We have developed a firing rate network model for working memory that combines Mexican-hat-like synaptic coupling with intrinsic or cellular dynamics that are conditionally bistable. While our approach is in the spirit of Camperi and Wang (1998) we include a specific and plausible mechanism for the cellular bistability. Modulatory neurotransmitters are known to activate second messenger signaling systems, and our model includes an intracellular Ca²⁺ handling subsystem whose dynamics depend upon the level of the second messenger inositol 1,4,5 trisphosphate (IP3). This Ca²⁺ subsystem endows individual units with conditional intrinsic bistability for a range of IP3. The full “hybrid” network sustains IP3-dependent persistent (“bump”) activity in response to a brief transient stimulus. The bump response in our hybrid model, like that of Camperi-Wang, is resistant to noise – its position does not drift with time. Action Editor: Upinder Bhalla     

The Sodium-Potassium Pump Controls the Intrinsic Firing of the Cerebellar Purkinje Neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na⁺/K⁺ pump activity sets the Purkinje cell''s operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na⁺/K⁺ pump. The model can replicate these recordings. We propose that Na⁺/K⁺ pump activity controls the intrinsic firing mode of cerbellar Purkinje cells.     

Spike-Frequency Adaptation of a Generalized Leaky Integrate-and-Fire Model Neuron

Although spike-frequency adaptation is a commonly observed property of neurons, its functional implications are still poorly understood. In this work, using a leaky integrate-and-fire neural model that includes a Ca²⁺-activated K⁺ current (I _AHP), we develop a quantitative theory of adaptation temporal dynamics and compare our results with recent in vivo intracellular recordings from pyramidal cells in the cat visual cortex. Experimentally testable relations between the degree and the time constant of spike-frequency adaptation are predicted. We also contrast the I _AHP model with an alternative adaptation model based on a dynamical firing threshold. Possible roles of adaptation in temporal computation are explored, as a a time-delayed neuronal self-inhibition mechanism. Our results include the following: (1) given the same firing rate, the variability of interspike intervals (ISIs) is either reduced or enhanced by adaptation, depending on whether the I _AHP dynamics is fast or slow compared with the mean ISI in the output spike train; (2) when the inputs are Poisson-distributed (uncorrelated), adaptation generates temporal anticorrelation between ISIs, we suggest that measurement of this negative correlation provides a probe to assess the strength of I _AHP in vivo; (3) the forward masking effect produced by the slow dynamics of I _AHP is nonlinear and effective at selecting the strongest input among competing sources of input signals.     

Analysis of spontaneous electrical activity in cerebellar Purkinje cells acutely isolated from postnatal rats

Whole-cell patch recording techniques were used to analyze spontaneous electrical activity in cerebellar Purkinje cells acutely isolated from postnatal rats. Spontaneous activity was present in 65% of the cells examined, and it included simple and complex firing patterns which persisted under conditions that eliminated residual or reformed synaptic contacts. Under voltage clamp, both spontaneous and quiescent cells displayed similar voltage-dependent conductances. Inward current was carried by Na⁺ through tetrodotoxin (TTX)-sensitive channels and by Ca²⁺ through P-type and T-type Ca channels. P-type current was present in all cells examined. T-type current was found in <50%, and it did not correlate with spontaneous activity. We found no evidence of a transient (A-type) potassium current or hyperpolarization-activated cationic current in either spontaneous or quiescent cells. Spontaneous activity did correlate with a lower activation threshold of the Na current, resulting in substantial overlap of the activation and inactivation curves. TTX reduced the holding current of spontaneous cells clamped between −50 and −30 mV, consistent with the presence of a Na "window" current. We were unable, however, to measure a persistent component of the Na current using voltage steps, a result which may reflect the complex gating properties of Na channels. An Na window current could provide the driving force underlying spontaneous activity, as well as plateau potentials, in Purkinje cells. © 1997 John Wiley & Sons, Inc. J Neurobiol 33: 18–32, 1997     

Dynamics of Intrinsic Dendritic Calcium Signaling during Tonic Firing of Thalamic Reticular Neurons

The GABAergic neurons of the nucleus reticularis thalami that control the communication between thalamus and cortex are interconnected not only through axo-dendritic synapses but also through gap junctions and dendro-dendritic synapses. It is still unknown whether these dendritic communication processes may be triggered both by the tonic and the T-type Ca²⁺ channel-dependent high frequency burst firing of action potentials displayed by nucleus reticularis neurons during wakefulness and sleep, respectively. Indeed, while it is known that activation of T-type Ca²⁺ channels actively propagates throughout the dendritic tree, it is still unclear whether tonic action potential firing can also invade the dendritic arborization. Here, using two-photon microscopy, we demonstrated that dendritic Ca²⁺ responses following somatically evoked action potentials that mimic wake-related tonic firing are detected throughout the dendritic arborization. Calcium influx temporally summates to produce dendritic Ca²⁺ accumulations that are linearly related to the duration of the action potential trains. Increasing the firing frequency facilitates Ca²⁺ influx in the proximal but not in the distal dendritic compartments suggesting that the dendritic arborization acts as a low-pass filter in respect to the back-propagating action potentials. In the more distal compartment of the dendritic tree, T-type Ca²⁺ channels play a crucial role in the action potential triggered Ca²⁺ influx suggesting that this Ca²⁺ influx may be controlled by slight changes in the local dendritic membrane potential that determine the T-type channels’ availability. We conclude that by mediating Ca²⁺ dynamic in the whole dendritic arborization, both tonic and burst firing of the nucleus reticularis thalami neurons might control their dendro-dendritic and electrical communications.     

Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.     

Rhythmic activities of hypothalamic magnocellular neurons: Autocontrol mechanisms

Electrophysiological recordings in lactating rats show that oxytocin (OT) and vasopressin (AVP) neurons exhibit specific patterns of activities in relation to peripheral stimuli: periodic bursting firing for OT neurons during suckling, phasic firing for AVP neurons during hyperosmolarity (systemic injection of hypertonic saline). These activities are autocontrolled by OT and AVP released somato-dentritically within the hypothalamic magnocellular nuclei. In vivo, OT enhances the amplitude and frequency of bursts, an effect accompanied with an increase in basal firing rate. However, the characteristics of firing change as facilitation proceeds: the spike patterns become very irregular with clusters of spikes spaced by long silences; the firing rate is highly variable and clearly oscillates before facilitated bursts. This unstable behaviour dramatically decreases during intense tonic activation which temporarily interrupts bursting, and could therefore be a prerequisite for bursting. In vivo, the effects of AVP depend on the initial firing pattern of AVP neurons: AVP excites weakly active neurons (increasing duration of active periods and decreasing silences), inhibits highly active neurons, and does not affect neurons with intermediate phasic activity. AVP brings the entire population of AVP neurons to discharge with a medium phasic activity characterised by periods of firing and silence lasting 20–40 s, a pattern shown to optimise the release of AVP from the neurohypophysis. Each of the peptides (OT or AVP) induces an increase in intracellular Ca²⁺ concentration, specifically in the neurons containing either OT or AVP respectively. OT evokes the release of Ca²⁺ from IP3-sensitive intracellular stores. AVP induces an influx of Ca²⁺ through voltage-dependent Ca²⁺ channels of T-, L- and N-types. We postulate that the facilitatory autocontrol of OT and AVP neurons could be mediated by Ca²⁺ known to play a key role in the control of the patterns of phasic neurons.     

A model of the electrophysiological properties of nucleus reticularis thalami neurons.

A model of the electrophysiological properties of rodent nucleus reticularis thalami (NRT) neurons of the dorsal lateral thalamus was developed using Hodgkin-Huxley style equations. The model incorporated voltage-dependent rate constants and kinetics obtained from recent voltage-clamp experiments in vitro. The intrinsic electroresponsivity of the model cell was found to be similar to several empirical observations. Three distinct modes of oscillatory activity were identified: 1) a pattern of slow rhythmic burst firing (0.5-7 Hz) usually associated with membrane potentials negative to approximately -70 mV which resulted from the interplay of ITs and IK(Ca); 2) at membrane potentials from approximately -69 to -62 mV, rhythmic burst firing in the spindle frequency range (7-12 Hz) developed and was immediately followed by a tonic tail of single spike firing after several bursts. The initial bursting rhythm resulted from the interaction of ITs and IK(Ca), with a slow after-depolarization due to ICAN which mediated the later tonic firing; 3) with further depolarization of the membrane potential positive to approximately -61 mV, sustained tonic firing appeared in the 10-200-Hz frequency range depending on the amplitude of the injected current. The frequency of this firing was also dependent on the maximum conductance of the leak current, IK(leak), and an interaction between the fast currents involved in generating action potentials, INa(fast) and IK(DR), and the persistent Na+ current, INa(P). Transitions between different firing modes were identified and studied parametrically.     

Ghostbursting: A Novel Neuronal Burst Mechanism

Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish have been observed to produce high-frequency burst discharge with constant depolarizing current (Turner et al., 1994). We present a two-compartment model of an ELL pyramidal cell that produces burst discharges similar to those seen in experiments. The burst mechanism involves a slowly changing interaction between the somatic and dendritic action potentials. Burst termination occurs when the trajectory of the system is reinjected in phase space near the ghost of a saddle-node bifurcation of fixed points. The burst trajectory reinjection is studied using quasi-static bifurcation theory, that shows a period doubling transition in the fast subsystem as the cause of burst termination. As the applied depolarization is increased, the model exhibits first resting, then tonic firing, and finally chaotic bursting behavior, in contrast with many other burst models. The transition between tonic firing and burst firing is due to a saddle-node bifurcation of limit cycles. Analysis of this bifurcation shows that the route to chaos in these neurons is type I intermittency, and we present experimental analysis of ELL pyramidal cell burst trains that support this model prediction. By varying parameters in a way that changes the positions of both saddle-node bifurcations in parameter space, we produce a wide gallery of burst patterns, which span a significant range of burst time scales.     

A hemicord locomotor network of excitatory interneurons: a simulation study

Locomotor burst generation is simulated using a full-scale network model of the unilateral excitatory interneuronal population. Earlier small-scale models predicted that a population of excitatory neurons would be sufficient to produce burst activity, and this has recently been experimentally confirmed. Here we simulate the hemicord activity induced under various experimental conditions, including pharmacological activation by NMDA and AMPA as well as electrical stimulation. The model network comprises a realistic number of cells and synaptic connectivity patterns. Using similar distributions of cellular and synaptic parameters, as have been estimated experimentally, a large variation in dynamic characteristics like firing rates, burst, and cycle durations were seen in single cells. On the network level an overall rhythm was generated because the synaptic interactions cause partial synchronization within the population. This network rhythm not only emerged despite the distributed cellular parameters but relied on this variability, in particular, in reproducing variations of the activity during the cycle and showing recruitment in interneuronal populations. A slow rhythm (0.4–2 Hz) can be induced by tonic activation of NMDA-sensitive channels, which are voltage dependent and generate depolarizing plateaus. The rhythm emerges through a synchronization of bursts of the individual neurons. A fast rhythm (4–12 Hz), induced by AMPA, relies on spike synchronization within the population, and each burst is composed of single spikes produced by different neurons. The dynamic range of the fast rhythm is limited by the ability of the network to synchronize oscillations and depends on the strength of synaptic connections and the duration of the slow after hyperpolarization. The model network also produces prolonged bouts of rhythmic activity in response to brief electrical activations, as seen experimentally. The mutual excitation can sustain long-lasting activity for a realistic set of synaptic parameters. The bout duration depends on the strength of excitatory synaptic connections, the level of persistent depolarization, and the influx of Ca²⁺ ions and activation of Ca²⁺-dependent K⁺ current.     

Analysis of models for crustacean stretch receptors

 The mechanisms underlying the diverse responses to step current stimuli of models [Edman et al. (1987) J Physiol (Lond) 384: 649–669] of lobster slowly adapting stretch receptor organs (SAO) and fast-adapting stretch receptor organs (FAO) are analyzed. In response to a step current, the models display three distinct types of firing reflecting the level of adaptation to the stimulation. Low-amplitude currents evoke transient firing containing one to several action potentials before the system stabilizes to a resting state. Conversely, high-amplitude stimulations induce a high frequency transient burst that can last several seconds before the model returns to its quiescent state. In the SAO model, the transition between the two regimes is characterized by a sustained pacemaker firing at an intermediate stimulation amplitude. The FAO model does not exhibit such a maintained firing; rather, the duration of the transient firing increases at first with the stimulus intensity, goes through a maximum and then decreases at larger intensities. Both models comprise seven variables representing the membrane potential, the sodium fast activation, fast inactivation, slow inactivation, the potassium fast activation, slow inactivation gating variables, and the intra cellular sodium concentration. To elucidate the mechanisms of the firing adaptations, the seven-variable model for the lobster stretch receptor neuron is first reduced to a three-dimensional system by regrouping variables with similar time scales. More precisely, we substituted the membrane potential V for the sodium fast activation equivalent potential V _m , the potassium fast inactivation V _n for the sodium fast inactivation V _h , and the sodium slow inactivation V _l for the potassium slow inactivation V _r . Comparison of the responses of the reduced models to those of the original models revealed that the main behaviors of the system were preserved in the reduction process. We classified the different types of responses of the reduced SAO and FAO models to constant current stimulation. We analyzed the transient and stationary responses of the reduced models by constructing bifurcation diagrams representing the qualitatively distinct dynamics of the models and the transitions between them. These revealed that (1) the transient firings prior to reaching the stationary state can be accounted for by the sodium slow inactivation evolving more slowly than the other two variables, so that the changes during the transient firings reflect the bifurcations that the two-dimensional system undergoes when the sodium slow inactivation, considered as a parameter, is varied; and (2) the stationary behaviors of the models are captured by the standard bifurcations of a two-dimensional system formed by the membrane potential and the potassium fast inactivation. We found that each type of firing and the transitions between them is due to the interplay between essentially three variables: two fast ones accounting for the action potential generation and the post-discharge refractoriness, and a third slow one representing the adaptation. Received: 28 February 2000 / Accepted in revised form: 4 October 2000     

藜芦碱和乌头碱在受损背根节神经元诱发不同的放电模式

为了研究钠通道失活门阻断后受损背根节神经元放电模式的变化特征,在大鼠背根节慢性压迫模型上采用单纤维技术记录A类神经元的自发放电。藜芦碱和乌头碱是钠通道失活门的抑制剂,但二者作用于不同的位点,前者结合于D2-S6,后者结合于D3-S6。我们比较了这两种试剂引发的放电模式。结果发现,在同一神经元,藜芦碱(1．5～5．0μmol／L)可以引起放电峰峰间期的慢波振荡,即峰峰间期由大逐渐减小,然后又逐渐增大,形成重复的振荡波形,每个振荡持续约数十秒至数分钟：而乌头碱(10～200μmol／L)则引起强直性放电,即峰峰间期逐渐减小,然后维持在一个稳定的水平。这两种不同的放电模式不因背景放电或试剂浓度的不同而发生明显的改变。实验结果表明,藜芦碱和乌头碱在受损的背根节神经元可以引发不同的放电模式,这可能与它们结合于钠通道上不同位点的抑制作用有关。     

Fast Na+ channels and slow Ca2+ current in smooth muscle from pregnant rat uterus

Summary Smooth muscle cells normally do not possess fast Na²⁺ channels, but inward current is carried through two types of Ca²⁺ channels: slow (L-type) Ca²⁺ channels and fast (T-type) Ca²⁺ channels. Using whole-cell voltage clamp of single smooth muscle cells isolated from the longitudinal layer of 18-day pregnant rat uterus, depolarizing pusles, applied from a holding potential of –90 mV, evoked two types of inward current, fast and slow [8]. The fast inward current decayed within 30 ms, depended on [Na]₀, and was inhibited by TTX (K_0.5 = 27 nM). The slow inward current decayed slowly, was dependent on [Ca]₀, and was inhibited by nifedipine. These results suggest that the fast inward current is a fast Na²⁺ channel current, and that the slow inward current is a Ca²⁺ channel current was not evident. Thus, the ion channels which generate inward currents in pregnant rat uterine cells are TTX-sensitive fast Na⁺ channels and dihudropuridine-sensitive slow Ca²⁺ channels. The number of fast Na⁺ channels increased during gestation [9]. The averaged current density increased from 0 on day 5, to 0.19 on day 9, to 0.56 on day 14, to 0.90 on day 18, and to 0.86 pA/pF on day 21. This almost linear increase occurs because of an increase in the fraction of cells which possess fast Na²⁺ channels, and it suggested that the fast Na⁺ current may be involved in spread of excitation. The Ca²⁺ channel current density also was higher during the latter half of gestation. These results indicate that the fast Na⁺ channels and Ca²⁺ slow channels in myometrium become more numerous as term approaches, and may facilitate parturition. Isoproterenol (beta-agonist) did not affect either I_Ca(s) or I_Na(f), whereas Mg²⁺ (K_0.5 of 12 mM) and nifedipine (K_0.5 of 3.3 nM) depressed I_Ca(s). Oxytocin had no effect on I_Na(f) and actually depressed I_Ca(s) to a small extect. Therefore, the tocolytic action of beta-agonists cannot be explained by an inhibition of I_Ca(s), whereas that of Mg²⁺ can be so explained. The stimulating action of oxytocin on uterine contractions is not due to stimulation of I_Ca(s).     

Frequency-dependent response properties of adapting spiking neurons

The dynamics of a population of integrate and fire (IF) neurons with spike-frequency adaptation (SFA) is studied. Using a population density approach and assuming a slow dynamics for the variable driving SFA, an equation for the emission rate of a finite set of uncoupled neurons is derived. The system dynamics is then analyzed in the neighborhood of its stable fixed points by linearizing the emission rate equation. The information transfer properties are then probed by perturbing the system with a sinusoidal input current: despite the low-pass properties of the dynamical variable associated with SFA, the adapting IF neuron behaves as a band-pass device and a phase-lock condition appears at a frequency related to the characteristic time constants of both neuronal and SFA dynamics. When a finite set of neurons is considered, the power spectral density of the pooled firing rates shows for intermediate omega a rich pattern of resonances. Theoretical predictions are successfully compared to numerical simulations.     

Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials

Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo. We use a three-compartment model calibrated to reproduce DA neuron responses to several pharmacological manipulations to uncover mechanisms of frequency limitation. The model exhibits a slow oscillatory potential (SOP) dependent on the interplay between the L-type Ca²⁺ current and the small conductance K⁺ (SK) current that is unmasked by fast Na⁺ current block. Contrary to previous theoretical work, the SOP does not pace the steady spiking frequency in our model. The main currents that determine the spontaneous firing frequency are the subthreshold L-type Ca²⁺ and the A-type K⁺ currents. The model identifies the channel densities for the fast Na⁺ and the delayed rectifier K⁺ currents as critical parameters limiting the maximal steady frequency evoked by a depolarizing pulse. We hypothesize that the low maximal steady frequencies result from a low safety factor for action potential generation. In the model, the rate of Ca²⁺ accumulation in the distal dendrites controls the transient initial frequency in response to a depolarizing pulse. Similar results are obtained when the same model parameters are used in a multi-compartmental model with a realistic reconstructed morphology, indicating that the salient contributions of the dendritic architecture have been captured by the simpler model.     

p75 Regulates Purkinje Cell Firing by Modulating SK Channel Activity through Rac1

p75 is expressed among Purkinje cells in the adult cerebellum, but its function has remained obscure. Here we report that p75 is involved in maintaining the frequency and regularity of spontaneous firing of Purkinje cells. The overall spontaneous firing activity of Purkinje cells was increased in p75^−/− mice during the phasic firing period due to a longer firing period and accompanying reduction in silence period than in the wild type. We attribute these effects to a reduction in small conductance Ca²⁺-activated potassium (SK) channel activity in Purkinje cells from p75^−/− mice compared with the wild type littermates. The mechanism by which p75 regulates SK channel activity appears to involve its ability to activate Rac1. In organotypic cultures of cerebellar slices, brain-derived neurotrophic factor increased RacGTP levels by activating p75 but not TrkB. These results correlate with a reduction in RacGTP levels in synaptosome fractions from the p75^−/− cerebellum, but not in that from the cortex of the same animals, compared with wild type littermates. More importantly, we demonstrate that Rac1 modulates SK channel activity and firing patterns of Purkinje cells. Along with the finding that spine density was reduced in p75^−/− cerebellum, these data suggest that p75 plays a role in maintaining normalcy of Purkinje cell firing in the cerebellum in part by activating Rac1 in synaptic compartments and modulating SK channels.