Ion channel mechanisms underlying frequency-firing patterns of the avian nucleus magnocellularis: A computational model

We have previously shown that late-developing avian nucleus magnocellularis (NM) neurons (embryonic [E] days 19–21) fire action potentials (APs) that resembles a band-pass filter in response to sinusoidal current injections of varying frequencies. NM neurons located in the mid- to high-frequency regions of the nucleus fire preferentially at 75 Hz, but only fire a single onset AP to frequency inputs greater than 200 Hz. Surprisingly, NM neurons do not fire APs to sinusoidal inputs less than 20 Hz regardless of the strength of the current injection. In the present study we evaluated intrinsic mechanisms that prevent AP generation to low frequency inputs. We constructed a computational model to simulate the frequency-firing patterns of NM neurons based on experimental data at both room and near physiologic temperatures. The results from our model confirm that the interaction among low- and high-voltage activated potassium channels (K_LVA and K_HVA, respectively) and voltage dependent sodium channels (Na_V) give rise to the frequency-firing patterns observed in vitro. In particular, we evaluated the regulatory role of K_LVA during low frequency sinusoidal stimulation. The model shows that, in response to low frequency stimuli, activation of large K_LVA current counterbalances the slow-depolarizing current injection, likely permitting Na_V closed-state inactivation and preventing the generation of APs. When the K_LVA current density was reduced, the model neuron fired multiple APs per sinusoidal cycle, indicating that K_LVA channels regulate low frequency AP firing of NM neurons. This intrinsic property of NM neurons may assist in optimizing response to different rates of synaptic inputs.     

Ionic currents influencing spontaneous firing and pacemaker frequency in dopamine neurons of the ventrolateral periaqueductal gray and dorsal raphe nucleus (vlPAG/DRN): A voltage-clamp and computational modelling study

Dopamine (DA) neurons of the ventrolateral periaqueductal gray (vlPAG) and dorsal raphe nucleus (DRN) fire spontaneous action potentials (APs) at slow, regular patterns in vitro but a detailed account of their intrinsic membrane properties responsible for spontaneous firing is currently lacking. To resolve this, we performed a voltage-clamp electrophysiological study in brain slices to describe their major ionic currents and then constructed a computer model and used simulations to understand the mechanisms behind autorhythmicity in silico. We found that vlPAG/DRN DA neurons exhibit a number of voltage-dependent currents activating in the subthreshold range including, a hyperpolarization-activated cation current (I_H), a transient, A-type, potassium current (I_A), a background, ‘persistent’ (I_NaP) sodium current and a transient, low voltage activated (LVA) calcium current (I_CaLVA). Brain slice pharmacology, in good agreement with computer simulations, showed that spontaneous firing occurred independently of I_H, I_A or calcium currents. In contrast, when blocking sodium currents, spontaneous firing ceased and a stable, non-oscillating membrane potential below AP threshold was attained. Using the DA neuron model we further show that calcium currents exhibit little activation (compared to sodium) during the interspike interval (ISI) repolarization while, any individual potassium current alone, whose blockade positively modulated AP firing frequency, is not required for spontaneous firing. Instead, blockade of a number of potassium currents simultaneously is necessary to eliminate autorhythmicity. Repolarization during ISI is mediated initially via the deactivation of the delayed rectifier potassium current, while a sodium background ‘persistent’ current is essentially indispensable for autorhythmicity by driving repolarization towards AP threshold.     

Functional role of the activity of ATP-sensitive potassium channels in electrical behavior of hippocampal neurons: experimental and theoretical studies

ATP-sensitive K⁺ (K_ATP) channels are distributed in a variety of cell types, including hippocampal neurons. These channels provide a link between electrical activity of cell membranes and cellular metabolism. The activity of K_ATP channels in hippocampal H19-7 neurons treated with or without short interfering RNAs (siRNAs) directed against Kir6.2 mRNA was investigated in this study. In single-channel recordings, cell exposure to diazoxide (30 μM) significantly prolonged the mean open time of K_ATP channels; however, neither closed-time kinetics nor the single-channel conductance of the channel was altered by this compound. However, in cells transfected with Kir6.2 siRNAs, diazoxide-stimulated activity of K_ATP channels was abolished. Based on single-channel recordings, the activity of K_ATP channels was mathematically constructed in a Markovian manner. The simulated activity of single K_ATP channels was incorporated in a modeled hippocampal neuron to assess how any changes in K_ATP-channel activity affect burst firing of action potentials (APs). The modeled neuron was adopted from the model of Xu and Clancy (2008). Specifically, to mimic the action of diazoxide, the baseline value of open time (τ_bas) of K_ATP channels was arbitrarily elevated, while varying number of active channels (N_O) was set to simulate electrical behavior of Kir6.2 siRNAs-transfected cells. The increase of either N_O or τ_bas depressed membrane excitability of modeled neuron. Fast-slow analysis of AP bursting from this modeled neuron also revealed that the increased K_ATP-channel activity shifted the voltage nullcline in an upward direction, thereby leading to a reduction of the repetitive spike regime. Taken together, it is anticipated that the increased activity of K_ATP channels caused by increasing N_O or τ_bas contributes to or is responsible for burst firing of APs in hippocampal neurons if similar results occur in vivo.     

Spontaneous action potential generation due to persistent sodium channel currents in simulated carotid body afferent fibers.

The mechanism by which action potentials (APs) are generated in afferent nerve fibers in the carotid body is unknown, but it is generally speculated to be release of an excitatory transmitter and synaptic depolarizing events. However, previous results suggested that Na(+) channels in the afferent nerve fibers play an important role in this process. To better understand the potential mechanism by which Na(+) channels may generate APs, a mathematical model of chemoreceptor nerve fibers that incorporated Hodgkin-Huxley-type Na(+) channels with kinetics of activation and inactivation, as determined previously from recordings of petrosal chemoreceptor neurons, was constructed. While the density of Na(+) channels was kept constant, spontaneous APs arose in nerve terminals as the axonal diameter was reduced to that in rat carotid body. AP excitability and pattern were similar to those observed in chemoreceptor recordings: 1) a random pattern at low- and high-frequency discharge rates, 2) a high sensitivity to reductions in extracellular Na(+) concentration, and 3) a variation in excitability that increased with AP generation rate. Taken together, the results suggest that an endogenous process in chemoreceptor nerve terminals may underlie AP generation, a process independent of synaptic depolarizing events.     

Electrical excitability of taste cells. Mechanisms and possible physiological significance

Neuronal, muscle and some endocrine cells are electrically excitable. While in muscle and endocrine cells AP stimulates and synchronizes intracellular processes, neurons employ action potentials (APs) to govern discontinuous synapses located distantly. Meanwhile, such axonless sensory cells as photoreceptors and hair cells exemplify afferent output, which is not driven by APs; instead, gradual receptor potentials elicited by sensory stimuli control the release of afferent neurotransmitter glutamate. Mammalian taste cells of the type II and type III are electrically excitable and respond to stimulation by firing APs. Since taste cells also have no axons, physiological significance of the electrical excitability for taste transduction and encoding sensory information is unclear. Perhaps, AP facilitates transmitter release, ATP in type II cells and 5-HT in type III cells, although via different mechanisms. The ATP release is mediated by connexin hemichannels, does not require a Ca²⁺ trigger, and largely gated by membrane voltage. 5-HT secretion is driven by intracellular Ca²⁺ and involves VG Ca²⁺ channels. Here, we discuss ionic mechanisms of excitability of taste cells and speculate on a likely role of APs in mediating their afferent output.     

A small fraction of strongly cooperative sodium channels boosts neuronal encoding of high frequencies

Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction [Formula: see text] of sodium channels expressing cooperativity and the strength of coupling between cooperative channels [Formula: see text]. We show that starting at a critical value of the coupling strength [Formula: see text], the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.     

First node of Ranvier facilitates high-frequency burst encoding

In central neurons the first node of Ranvier is located at the first axonal branchpoint, ～ 100 μm from the axon initial segment where synaptic inputs are integrated and converted into action potentials (APs). Whether the first node contributes to this signal transformation is not well understood. Here it was found that in neocortical layer 5 axons, the first branchpoint is required for intrinsic high-frequency (≥ 100 Hz) AP bursts. Furthermore, block of nodal Na(+) channels or axotomy of the first node in intrinsically bursting neurons depolarized the somatic AP voltage threshold (～ 5 mV) and eliminated APs selectively within a high-frequency cluster in response to steady currents or simulated synaptic inputs. These results indicate that nodal persistent Na(+) current exerts an anterograde influence on AP initiation in the axon initial segment, revealing a computational role of the first node of Ranvier beyond conduction of the propagating AP.     

Control of action potential-driven calcium influx in GT1 neurons by the activation status of sodium and calcium channels

An analysis of the relationship between electrical membrane activity and Ca2+ influx in differentiated GnRH-secreting (GT1) neurons revealed that most cells exhibited spontaneous, extracellular Ca(2+)-dependent action potentials (APs). Spiking was initiated by a slow pacemaker depolarization from a baseline potential between -75 and -50 mV, and AP frequency increased with membrane depolarization. More hyperpolarized cells fired sharp APs with limited capacity to promote Ca2+ influx, whereas more depolarized cells fired broad APs with enhanced capacity for Ca2+ influx. Characterization of the inward currents in GT1 cells revealed the presence of tetrodotoxin-sensitive Na+, Ni(2+)-sensitive T-type Ca2+, and dihydropyridine-sensitive L-type Ca2+ components. The availability of Na+ and T-type Ca2+ channels was dependent on the baseline potential, which determined the activation/inactivation status of these channels. Whereas all three channels were involved in the generation of sharp APs, L-type channels were solely responsible for the spike depolarization in cells exhibiting broad APs. Activation of GnRH receptors led to biphasic changes in cytosolic Ca2+ concentration ([Ca2+]i), with an early, extracellular Ca(2+)-independent peak and a sustained, extracellular Ca(2+)-dependent phase. During the peak [Ca2+]i response, electrical activity was abolished due to transient hyperpolarization. This was followed by sustained depolarization of cells and resumption of firing of increased frequency with a shift from sharp to broad APs. The GnRH-induced change in firing pattern accounted for about 50% of the elevated Ca2+ influx, the remainder being independent of spiking. Basal [Ca2+]i was also dependent on Ca2+ influx through AP-driven and voltage-insensitive pathways. Thus, in both resting and agonist-stimulated GT1 cells, membrane depolarization limits the participation of Na+ and T-type channels in firing, but facilitates AP-driven Ca2+ influx.     

Amplitude-dependent spike-broadening and enhanced Ca(2+) signaling in GnRH-secreting neurons

In GnRH-secreting (GT1) neurons, activation of Ca(2+)-mobilizing receptors induces a sustained membrane depolarization that shifts the profile of the action potential (AP) waveform from sharp, high-amplitude to broad, low-amplitude spikes. Here we characterize this shift in the firing pattern and its impact on Ca(2+) influx experimentally by using prerecorded sharp and broad APs as the voltage-clamp command pulse. As a quantitative test of the experimental data, a mathematical model based on the membrane and ionic current properties of GT1 neurons was also used. Both experimental and modeling results indicated that inactivation of the tetrodotoxin-sensitive Na(+) channels by sustained depolarization accounted for a reduction in the amplitude of the spike upstroke. The ensuing decrease in tetraethylammonium-sensitive K(+) current activation slowed membrane repolarization, leading to AP broadening. This change in firing pattern increased the total L-type Ca(2+) current and facilitated AP-driven Ca(2+) entry. The leftward shift in the current-voltage relation of the L-type Ca(2+) channels expressed in GT1 cells allowed the depolarization-induced AP broadening to facilitate Ca(2+) entry despite a decrease in spike amplitude. Thus the gating properties of the L-type Ca(2+) channels expressed in GT1 neurons are suitable for promoting AP-driven Ca(2+) influx in receptor- and non-receptor-depolarized cells.     

Interactions of glutamate and dopamine in a computational model of the striatum

A network model of simplified striatal principal neurons with mutual inhibition was used to investigate possible interactions between cortical glutamatergic and nigral dopaminergic afferents in the neostriatum. Glutamatergic and dopaminergic inputs were represented by an excitatory synaptic conductance and a slow membrane potassium conductance, respectively. Neuronal activity in the model was characterized by episodes of increased action potential firing rates of variable duration and frequency. Autocorrelation histograms constructed from the action potential activity of striatal model neurons showed that reducing peak excitatory conductance had the effect of increasing interspike intervals. On the other hand, the maximum value of the dopamine-sensitive potassium conductance was inversely related to the duration of firing episodes and the maximal firing rates. A smaller potassium conductance restored normal firing rates in the most active neurons at the expense of a larger proportion of neurons showing reduced activity. Thus, a homogeneous network with mutual inhibition can produce equally complex dynamics as have been proposed to occur in a striatal network with two neuron populations that are oppositely regulated by dopamine. Even without mutual inhibition it appears that increased dopamine concentrations could partially compensate for the effects of reduced glutamatergic input in individual neurons.     

Channel currents during spontaneous action potentials in embryonic chick heart cells. The action potential patch clamp.

Single-channel currents were recorded with the cell-attached patch-clamp technique from small clusters (2-20 cells) of spontaneously beating 7-d embryo ventricle cells. Because the preparation was rhythmically active, the trans-patch potential varied with the action potential (AP). The total current through the patch membrane was the patch action current (AC). ACs and APs could be recorded simultaneously, with two electrodes, or sequentially with one electrode. Channel activity, which varied depending on the number and type of channels in the patch, was present during normal cell firing. This method can reveal the kinetics and magnitudes of the specific currents that contributed to the AP, under conditions that reflect not only the time and voltage dependence of the channels, but also environmental factors that may influence channel behavior during the AP.     

Mechanisms of Gain Control by Voltage-Gated Channels in Intrinsically-Firing Neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.     

Contribution of non-inactivating Na+ current induced by oxidizing agents to the firing behavior of neuronal action potentials: experimental and theoretical studies from NG108-15 neuronal cells

The effects of chemical injury with oxidizing agents on voltage-gated Na+ current (I(Na)) in differentiated NG108-15 neuronal cells were investigated in this study. In whole-cell patch-clamp recordings, the challenge of these cells with t-butyl hydroperoxide (t-BHP; 1 mM) decreased the peak amplitude of I(Na) with no modification in the current-voltage relationship. It caused a slowing of current inactivation, although there was no alteration in the activation time course of I(Na). Cell exposure to t-BHP also increased a non-inactivating I(Na) (I(Na(NI)) elicited by long-lasting ramp pulses. The t-BHP-induced increase of I(Na(NI)) was reversed by a further application of riluzole (10 microM) or oxcarbazepine (10 microM). When I(Na) was elicited by simulated waveforms of action potentials (APs), during exposure to t-BHP, the amplitude of this inward current was diminished, accompanied by a reduction in inactivation/deactivation rate and an increase in current fluctuations. Under current-clamp recordings, addition of t-BHP (0.3 mM) enhanced AP firing in combination with clustering-like activity and sub-threshold membrane oscillations. In the simulation study, when the fraction of non-inactivating Na(v) channels was elevated, the simulated window component of I(Na) in response to a long-lasting ramp pulse was reduced; however, the persistent I(Na) was markedly enhanced. Moreover, when simulated firing of APs was generated from a modeled neuron, changes of AP firing caused by the increased fraction of non-inactivating Na(v) channels used to mimic the t-BHP actions were similar to the experimental observations. Taken together, it is anticipated that the effects of oxidizing agents on I(Na(NI)) could be an important mechanism underlying their neurotoxic actions in neurons or neuroendocrine cells occurring in vivo.     

Near Poisson-type firing produced by concurrent excitation and inhibition

The effect of inhibition on the firing variability is examined in this paper using the biologically-inspired temporal noisy-leaky integrator (TNLI) neuron model. The TNLI incorporates hyperpolarising inhibition with negative current pulses of controlled shapes and it also separates dendritic from somatic integration. The firing variability is observed by looking at the coefficient of variation (C(V)) (standard deviation/mean interspike interval) as a function of the mean interspike interval of firing (delta tM) and by comparing the results with the theoretical curve for random spike trains, as well as looking at the interspike interval (ISI) histogram distributions. The results show that with 80% inhibition, firing at high rates (up to 200 Hz) is nearly consistent with a Poisson-type variability, which complies with the analysis of cortical neuron firing recordings by Softky and Koch [1993, J. Neurosci. 13(1) 334-530]. We also demonstrate that the mechanism by which inhibition increases the C(V) values is by introducing more short intervals in the firing pattern as indicated by a small initial hump at the beginning of the ISI histogram distribution. The use of stochastic inputs and the separation of the dendritic and somatic integration which we model in TNLI, also affect the high firing, near Poisson-type (explained in the paper) variability produced. We have also found that partial dendritic reset increases slightly the firing variability especially at short ISIs.     

Responses of neurons in somatosensory cortical area II of cats to high-frequency vibratory stimuli during iontophoresis of a GABA antagonist and glutamate

Areas in the second somatic sensory cortex (SII) of cats that responded vigorously to low-amplitude, high-frequency vibratory stimulation were mapped with respect to the surrounding somatotopic organization. Neurons with these properties were found in the posterior and medial parts of the distal forelimb zone and were judged as receiving input from Pacinian mechanoreceptors. The responses of these neurons to sinusoidal vibrotactile stimulation were studied during iontophoretic administration of glutamate or bicuculline methiodide (BMI) to determine if the temporal fidelity of these cortical neurons was controlled by inhibitory circuits that used gamma-aminobutyric acid (GABA) as a neurotransmitter. The data from 19 Pacinian-sensitive neurons were analyzed for changes in the mean firing rate, the percentage of entrainment, and the pattern of periodicity as revealed by autocorrelograms and interval histograms. Iontophoresis of BMI or glutamate caused significant increases in mean firing rates during low- and high-frequency vibratory stimulation. The pattern of increased activity produced by BMI was characterized by a small, yet significant, reduction in the percentage of entrainment, whereas glutamate caused smaller and fewer significant changes in this measure. Analysis of autocorrelation and interval histograms suggested that BMI increased the probability of firing on consecutive stimulus cycles in small segments of the stimulus duration.     

Elementary and compound postsynaptic potentials in the defensive command neurons of Helix lucorum

The present communication concerns with the analysis of elementary and the compound excitatory postsynaptic potentials (eEPSPs and cEPSPs) recorded by intracellular microelectrode from an identified defensive command neuron of the snail Helix lucorum. The eEPSPs were evoked by single presynaptic action potentials (APs) elicited by cationic current injection into one of the identified sensory neurons synapsing on the respective command neuron. The cEPSPs were elicited by local brief tactile stimuli on the skin or internal organs. It was shown that the cEPSPs amplitudes depend mainly on the number of activated sensory neurons. Compound EPSPs depend also on frequency and the number of APs in the bursts occurring in a single neuron. Presynaptic APs having frequency 2-10 Hz evoke high frequency depression of that eEPSPs after an interval is followed by post-tetanic potentiation of single eEPSPs. Preceding stimulation of a pneumostom area facilitates the cEPSPs elicited by repeated stimulation of viscera. The eEPSPs from the same visceral area demonstrate no heterosynaptic facilitation in experiments with double parallel intracellular recording from responsive sensory and command neurons. The different types of the eEPSPs plasticity are discussed according to their contribution cEPSPs plastic changes.     

Fast calcium wave propagation mediated by electrically conducted excitation and boosted by CICR

We have investigated synchronization and propagation of calcium oscillations, mediated by gap junctional excitation transmission. For that purpose we used an experimentally based model of normal rat kidney (NRK) cells, electrically coupled in a one-dimensional configuration (linear strand). Fibroblasts such as NRK cells can form an excitable syncytium and generate spontaneous inositol 1,4,5-trisphosphate (IP(3))-mediated intracellular calcium waves, which may spread over a monolayer culture in a coordinated fashion. An intracellular calcium oscillation in a pacemaker cell causes a membrane depolarization from within that cell via calcium-activated chloride channels, leading to an L-type calcium channel-based action potential (AP) in that cell. This AP is then transmitted to the electrically connected neighbor cell, and the calcium inflow during that transmitted AP triggers a calcium wave in that neighbor cell by opening of IP(3) receptor channels, causing calcium-induced calcium release (CICR). In this way the calcium wave of the pacemaker cell is rapidly propagated by the electrically transmitted AP. Propagation of APs in a strand of cells depends on the number of terminal pacemaker cells, the L-type calcium conductance of the cells, and the electrical coupling between the cells. Our results show that the coupling between IP(3)-mediated calcium oscillations and AP firing provides a robust mechanism for fast propagation of activity across a network of cells, which is representative for many other cell types such as gastrointestinal cells, urethral cells, and pacemaker cells in the heart.     

Interaction of NMDA Receptor and Pacemaking Mechanisms in the Midbrain Dopaminergic Neuron

Dopamine neurotransmission has been found to play a role in addictive behavior and is altered in psychiatric disorders. Dopaminergic (DA) neurons display two functionally distinct modes of electrophysiological activity: low- and high-frequency firing. A puzzling feature of the DA neuron is the following combination of its responses: N-methyl-D-aspartate receptor (NMDAR) activation evokes high-frequency firing, whereas other tonic excitatory stimuli (-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate receptor (AMPAR) activation or applied depolarization) block firing instead. We suggest a new computational model that reproduces this combination of responses and explains recent experimental data. Namely, somatic NMDAR stimulation evokes high-frequency firing and is more effective than distal dendritic stimulation. We further reduce the model to a single compartment and analyze the mechanism of the distinct high-frequency response to NMDAR activation vs. other stimuli. Standard nullcline analysis shows that the mechanism is based on a decrease in the amplitude of calcium oscillations. The analysis confirms that the nonlinear voltage dependence provided by the magnesium block of the NMDAR determine its capacity to elevate the firing frequency. We further predict that the moderate slope of the voltage dependence plays the central role in the frequency elevation. Additionally, we suggest a repolarizing current that sustains calcium-independent firing or firing in the absence of calcium-dependent repolarizing currents. We predict that the ether–a-go-go current (ERG), which has been observed in the DA neuron, is the best fit for this critical role. We show that a calcium-dependent and a calcium-independent oscillatory mechanisms form a structure of interlocked negative feedback loops in the DA neuron. The structure connects research of DA neuron firing with circadian biology and determines common minimal models for investigation of robustness of oscillations, which is critical for normal function of both systems.     

Modeling the spontaneous activity in suprachiasmatic nucleus neurons: Role of cation single channels

A population of interconnected neurons of the mammalian suprachiasmatic nuclei (SCN) controls circadian rhythms in physiological functions. In turn, a circadian rhythm of individual neurons is driven by intracellular processes, which via activation of specific membrane channels, produce circadian modulation of electrical firing rate. Yet the membrane target(s) of the cellular clock have remained enigmatic. Previously, subthreshold voltage-dependent cation (SVC) channels have been proposed as the membrane target of the cellular clock responsible for circadian modulation of the firing rate in SCN neurons. We tested this hypothesis with computational modeling based on experimental results from on-cell recording of SVC channel openings in acutely isolated SCN neurons and long-term continuous recording of activity from dispersed SCN neurons in a multielectrode array dish (MED). The model reproduced the circadian behavior if the number of SVC channels or their kinetics were modulated in accordance with protein concentration in a model of the intracellular clock (Scheper et al., 1999. J. Neurosci. 19, 40-47). Such modulation changed the average firing rate of the model neuron from zero (“subjective-night” silence) up to 18 Hz (“subjective-day” peak). Furthermore, the variability of interspike intervals (ISI) and the circadian pattern of firing rate (i.e. silence-to-activity ratio and shape of circadian peaks) are in reasonable agreement with experimental data obtained in dispersed SCN neurons in MED. These results suggest that the variability of ISI in intact SCN neurons is mostly due to stochastic single-channel openings, and that the circadian pattern of the firing rate is specified by threshold properties of dependence of the spontaneous firing rate on the number of single channels (R-N relationship). This plausible mathematical modeling supports the hypothesis that SVC channels could be a critical element in circadian modulation of firing rate in SCN neurons.