Lack of the burst firing of thalamocortical relay neurons and resistance to absence seizures in mice lacking alpha(1G) T-type Ca(2+) channels

T-type Ca(2+) currents have been proposed to be involved in the genesis of spike-and-wave discharges, a sign of absence seizures, but direct evidence in vivo to support this hypothesis has been lacking. To address this question, we generated a null mutation of the alpha(1G) subunit of T-type Ca(2+) channels. The thalamocortical relay neurons of the alpha(1G)-deficient mice lacked the burst mode firing of action potentials, whereas they showed the normal pattern of tonic mode firing. The alpha(1G)-deficient thalamus was specifically resistant to the generation of spike-and-wave discharges in response to GABA(B) receptor activation. Thus, the modulation of the intrinsic firing pattern mediated by alpha(1G) T-type Ca(2+) channels plays a critical role in the genesis of absence seizures in the thalamocortical pathway.     

The initiation of bursts in thalamic neurons and the cortical control of thalamic sensitivity

Thalamic neurons generate high-frequency bursts of action potentials when a low-threshold (T-type) calcium current, located in soma and dendrites, becomes activated. Computational models were used to investigate the bursting properties of thalamic relay and reticular neurons. These two types of thalamic cells differ fundamentally in their ability to generate bursts following either excitatory or inhibitory events. Bursts generated with excitatory inputs in relay cells required a high degree of convergence from excitatory inputs, whereas moderate excitation drove burst discharges in reticular neurons from hyperpolarized levels. The opposite holds for inhibitory rebound bursts, which are more difficult to evoke in reticular neurons than in relay cells. The differences between the reticular neurons and thalamocortical neurons were due to different kinetics of the T-current, different electrotonic properties and different distribution patterns of the T-current in the two cell types. These properties enable the cortex to control the sensitivity of the thalamus to inputs and are also important for understanding states such as absence seizures.     

Endogenous burst capability in a neuron of the gastric mill pattern generator of the spiny lobster Panulirus interruptus

The gastric system of the lobster stomatogastric ganglion has previously been thought to include no neurons capable of endogenous bursting. We describe conditions under which one of the motorneurons, the CP cell, can burst endogenously in a free-running manner in the absence of other phasic network activity. Isolated preparations of the foregut nervous system were used, and the CP bursting was either spontaneous or was activated by continuous stimulation of an input nerve. Three criteria were applied to establish the endogenous nature of such burst generation in CP: absence of phasic input, reset of the bursting pattern by pulses of current in a characteristic phase-dependent manner, and modulation of burst rate by sustained injected current. (1) The firing of other cells which are known to be related synaptically to CP was monitored in nerve records. These other cells were either silent or fired only tonically. Cross-correlograms showed that CP bursting was not ascribable to phasic activity in these other network cells. (2) A depolarizing current pulse of sufficient strength injected intracellularly between bursts triggered a burst prematurely and reset the subsequent rhythm. A hyperpolarizing pulse during a burst terminated it and reset the subsequent rhythm. Reset behavior was similar to that described for other endogenous bursters. (3) Application of a positive-going ramp current initially caused an increase in burst rate, as described for other endogenous bursters. However, further depolarization caused a slower burst rate due to lengthening of the individual bursts, although mean firing frequency continued to increase throughout the range tested. Such free-running endogenous repetitive bursting appeared to result from the CP's ability to produce slow regenerative depolarizations (“plateau potentials”). When bursting was present, so was the plateau property, as determined by I–V analysis and by the ability of brief current pulses to trigger and terminate bursts. The previous inability to observe endogenous bursting in preparations with central input removed may be due to the usual absence of the plateau property in such preparations.     

Interactive responses of a thalamic neuron to formalin induced lasting pain in behaving mice

Thalamocortical (TC) neurons are known to relay incoming sensory information to the cortex via firing in tonic or burst mode. However, it is still unclear how respective firing modes of a single thalamic relay neuron contribute to pain perception under consciousness. Some studies report that bursting could increase pain in hyperalgesic conditions while others suggest the contrary. However, since previous studies were done under either neuropathic pain conditions or often under anesthesia, the mechanism of thalamic pain modulation under awake conditions is not well understood. We therefore characterized the thalamic firing patterns of behaving mice in response to nociceptive pain induced by inflammation. Our results demonstrated that nociceptive pain responses were positively correlated with tonic firing and negatively correlated with burst firing of individual TC neurons. Furthermore, burst properties such as intra-burst-interval (IntraBI) also turned out to be reliably correlated with the changes of nociceptive pain responses. In addition, brain stimulation experiments revealed that only bursts with specific bursting patterns could significantly abolish behavioral nociceptive responses. The results indicate that specific patterns of bursting activity in thalamocortical relay neurons play a critical role in controlling long-lasting inflammatory pain in awake and behaving mice.     

Age-Dependent Changes in Intrinsic Neuronal Excitability in Subiculum after Status Epilepticus

Kainic acid-induced status epilepticus (KA-SE) in mature rats results in the development of spontaneous recurrent seizures and a pattern of cell death resembling hippocampal sclerosis in patients with temporal lobe epilepsy. In contrast, KA-SE in young animals before postnatal day (P) 18 is less likely to cause cell death or epilepsy. To investigate whether changes in neuronal excitability occur in the subiculum after KA-SE, we examined the age-dependent effects of SE on the bursting neurons of subiculum, the major output region of the hippocampus. Patch-clamp recordings were used to monitor bursting in pyramidal neurons in the subiculum of rat hippocampal slices. Neurons were studied either one or 2-3 weeks following injection of KA or saline (control) in immature (P15) or more mature (P30) rats, which differ in their sensitivity to KA as well as the long-term sequelae of the KA-SE. A significantly greater proportion of subicular pyramidal neurons from P15 rats were strong-bursting neurons and showed increased frequency-dependent bursting compared to P30 animals. Frequency-dependent burst firing was enhanced in P30, but not in P15 rats following KA-SE. The enhancement of bursting induced by KA-SE in more mature rats suggests that the frequency-dependent limitation of repetitive burst firing, which normally occurs in the subiculum, is compromised following SE. These changes could facilitate the initiation of spontaneous recurrent seizures or their spread from the hippocampus to other parts of the brain.     

Selective GABAergic control of higher-order thalamic relays

GABAergic signaling is central to the function of the thalamus and has been traditionally attributed primarily to the nucleus reticularis thalami (nRT). Here we present a GABAergic pathway, distinct from the nRT, that exerts a powerful inhibitory effect selectively in higher-order thalamic relays of the rat. Axons originating in the anterior pretectal nucleus (APT) innervated the proximal dendrites of relay cells via large GABAergic terminals with multiple release sites. Stimulation of the APT in an in vitro slice preparation revealed a GABA(A) receptor-mediated, monosynaptic IPSC in relay cells. Activation of presumed single APT fibers induced rebound burst firing in relay cells. Different APT neurons recorded in vivo displayed fast bursting, tonic, or rhythmic firing. Our data suggest that selective extrareticular GABAergic control of relay cell activity will result in effective, state-dependent gating of thalamocortical information transfer in higher-order but not in first-order relays.     

The beta subunit increases the Ca2+ sensitivity of large conductance Ca2+-activated potassium channels by retaining the gating in the bursting states

Coexpression of the beta subunit (KV,Cabeta) with the alpha subunit of mammalian large conductance Ca2+- activated K+ (BK) channels greatly increases the apparent Ca2+ sensitivity of the channel. Using single-channel analysis to investigate the mechanism for this increase, we found that the beta subunit increased open probability (Po) by increasing burst duration 20-100-fold, while having little effect on the durations of the gaps (closed intervals) between bursts or on the numbers of detected open and closed states entered during gating. The effect of the beta subunit was not equivalent to raising intracellular Ca2+ in the absence of the beta subunit, suggesting that the beta subunit does not act by increasing all the Ca2+ binding rates proportionally. The beta subunit also inhibited transitions to subconductance levels. It is the retention of the BK channel in the bursting states by the beta subunit that increases the apparent Ca2+ sensitivity of the channel. In the presence of the beta subunit, each burst of openings is greatly amplified in duration through increases in both the numbers of openings per burst and in the mean open times. Native BK channels from cultured rat skeletal muscle were found to have bursting kinetics similar to channels expressed from alpha subunits alone.     

Differential expression of T-type calcium channels in P/Q-type calcium channel mutant mice with ataxia and absence epilepsy

Mutations in P/Q-type calcium channels generate common phenotypes in mice and humans, which are characterized by ataxia, paroxysmal dyskinesia, and absence seizures. Subsequent functional changes of T-type calcium channels in thalamus are observed in P/Q-type calcium channel mutant mice and these changes play important roles in generation of absence seizures. However, the changes in T-type calcium channel function and/or expression in the cerebellum, which may be related to movement disorders, are still unknown. The leaner mouse exhibits severe ataxia, paroxysmal dyskinesia, and absence epilepsy due to a P/Q-type calcium channel mutation. We investigated changes in T-type calcium channel expression in the leaner mouse thalamus and cerebellum using quantitative real-time polymerase chain reaction (qRT-PCR) and quantitative in situ hybridization histochemistry (ISHH). qRT-PCR analysis showed no change in T-type calcium channel alpha 1G subunit (Cav3.1) expression in the leaner thalamus, but a significant decrease in alpha 1G expression in the whole leaner mouse cerebellum. Interestingly, quantitative ISHH revealed differential changes in alpha 1G expression in the leaner cerebellum, where the granule cell layer showed decreased alpha 1G expression while Purkinje cells showed increased alpha 1G expression. To confirm these observations, the granule cell layer and the Purkinje cell layer were laser capture microdissected separately, then analyzed with qRT-PCR. Similar to the observation obtained by ISHH, the leaner granule cell layer showed decreased alpha 1G expression and the leaner Purkinje cell layer showed increased alpha 1G expression. These results suggest that differential expression of T-type calcium channels in the leaner cerebellum may be involved in the observed movement disorders.     

神经放电加周期分岔中由随机自共振引起一类新节律

当改变实验性神经起步点细胞外[Ca^2 ]时,放电节律表现出从周期1节律转换为周期4节律的加周期分岔序列。其中,周期n节律转换为周期n 1节律的过程中(n=1,2,3)存在一种新的具有交替特征的节律,该新节律为周期n簇与周期n 1簇放电的交替,并且周期n 1簇的时间间隔序列呈现出整数倍特征。确定性神经放电理论模型(chay模型)只能模拟周期n节律直接到周期n 1节律的加周期分岔序列;而随机chay模型可以模拟实验中的加周期分岔过程和新节律。进一步,新节律被确认是经随机自共振机制产生的。这不仅解释了实验现象,也将随机自共振的产生区间从以前认识到的Hopf分岔点附近扩大到加周期分岔点附近,同时扩大了噪声在神经放电和神经编码中起重要作用的参数区间。     

Bursting as an Effective Relay Mode in a Minimal Thalamic Model

In recent years, accumulating evidence indicates that thalamic bursts are present during wakefulness and participate in information transmission as an effective relay mode with distinctive properties from the tonic activity. Thalamic bursts originate from activation of the low threshold calcium cannels via a local feedback inhibition, exerted by the thalamic reticular neurons upon the relay neurons. This article, examines if this simple mechanism is sufficient to explain the distinctive properties of thalamic bursting as an effective relay mode. A minimal model of thalamic circuit composed of a retinal spike train, a relay neuron and a reticular neuron is simulated to generate the tonic and burst firing modes. The integrate-and-fire-or-burst model is used to simulate the neurons. After discriminating the burst events with criteria based on inter-spike-intervals, statistical indices show that the bursts of the minimal model are stereotypic events. The relation between the rate of bursts and the parameters of the input spike train demonstrates marked nonlinearities. Burst response is shown to be selective to spike-silence-spike sequences in the input spike train. Moreover, burst events represent the input more reliably than the tonic spike in a considerable range of the parameters of the model. In conclusion, many of the distinctive properties of thalamic bursts such as stereotypy, nonlinear dependence on the sensory stimulus, feature selectivity and reliability are reproducible in the minimal model. Furthermore, the minimal model predicts that while the bursts are more frequent in the spike train of the off-center X relay neurons (corresponding to off-center X retinal ganglion cells), they are more reliable when generated by the on-center ones (corresponding to on-center X ganglion cells).     

A basic biophysical model for bursting neurons

Presented here is a basic biophysical cell model for bursting, an extension of our previous model (Av-Ron et al. 1991) for excitability and oscillations. By changing a limited set of model parameters, one can describe different patterns of bursting behavior in terms of the burst cycle, the durations of oscillation and quiescence, and firing frequency.     

Investigating the role of islet cytoarchitecture in its oscillation using a new beta-cell cluster model

The oscillatory insulin release is fundamental to normal glycemic control. The basis of the oscillation is the intercellular coupling and bursting synchronization of beta cells in each islet. The functional role of islet beta cell mass organization with respect to its oscillatory bursting is not well understood. This is of special interest in view of the recent finding of islet cytoarchitectural differences between human and animal models. In this study we developed a new hexagonal closest packing (HCP) cell cluster model. The model captures more accurately the real islet cell organization than the simple cubic packing (SCP) cluster that is conventionally used. Using our new model we investigated the functional characteristics of beta-cell clusters, including the fraction of cells able to burst f(b), the synchronization index lambda of the bursting beta cells, the bursting period T(b), the plateau fraction p(f), and the amplitude of intracellular calcium oscillation [Ca]. We determined their dependence on cluster architectural parameters including number of cells n(beta), number of inter-beta cell couplings of each beta cell n(c), and the coupling strength g(c). We found that at low values of n(beta), n(c) and g(c), the oscillation regularity improves with their increasing values. This functional gain plateaus around their physiological values in real islets, at n(beta) approximately 100, n(c) approximately 6 and g(c) approximately 200 pS. In addition, normal beta-cell clusters are robust against significant perturbation to their architecture, including the presence of non-beta cells or dead beta cells. In clusters with n(beta)> approximately 100, coordinated beta-cell bursting can be maintained at up to 70% of beta-cell loss, which is consistent with laboratory and clinical findings of islets. Our results suggest that the bursting characteristics of a beta-cell cluster depend quantitatively on its architecture in a non-linear fashion. These findings are important to understand the islet bursting phenomenon and the regulation of insulin secretion, under both physiological and pathological conditions.     

T-type Ca2+ channels and absence epilepsy

Burst firing of the thalamic neurons is driven by the low threshold Ca2+ spike generated by Ca2+ influx through T-type Ca2+ channels when these channels are activated by membrane hyperpolarization due to inhibitory inputs. The major inhibitory inputs to the thalamocortical (TC) neurons are from the GABAergic neurons in the thalamic reticular nucleus. Thalamic burst firings have long been implicated in the pathogenesis of absence epilepsy. The recent progress in genetic approaches has provided with an opportunity to examine this issue at the level of an organism. In this review I describe results primarily obtained from the analysis of the mice deficient for the alpha1G locus which is the predominant gene underlying the low threshold Ca2+ currents in the TC neurons. Current results so far demonstrate the essential role of the thalamocortical bursts in certain forms of absence seizures. Understanding of the pathophysiological mechanisms of absence epilepsy may help develop drugs to control the disease.     

Firing properties of substantia nigra dopaminergic neurons in freely moving rats

Single unit recordings were obtained from putative dopaminergic neurons in the substantia nigra of awake, freely moving rats. The cells exhibited waveforms, range of firing rates and types of firing patterns identical to those of identified DA neurons of anesthetized or paralyzed rats. Two firing patterns were observed: single spike activity and a bursting mode with spikes of progressively diminished amplitude and increased duration within each burst. The degree of burst firing varied considerably among the cells and individual cells sometimes switched from one pattern of firing (e.g. predominantly single spike) to another (e.g. bursting), although the determinants of these transitions are, at this time, unclear. Putative DA neurons were inhibited by i.v. apomorphine and excited by i.v. haloperidol. Haloperidol also reversed the apomorphine-induced inhibition of firing. Inhibitions and excitations were associated with a reduction and elevation, respectively, in burst firing. The effects of the two drugs were identical to their effects in immobilized rats. In several cases, a putative DA neuron was observed to fire all of its spikes in near coincidence with at least one other cell with identical electrophysiological characteristics. This form of interaction (i.e. presumed electrical coupling) between DA cells is only rarely observed in anesthetized or paralyzed rats and may play a significant role in the normal functioning of the nigrostriatal DA system.     

Mathematical Model of Bursting in Dissociated Purkinje Neurons

In vitro, Purkinje cell behaviour is sometimes studied in a dissociated soma preparation in which the dendritic projection has been cleaved. A fraction of these dissociated somas spontaneously burst. The mechanism of this bursting is incompletely understood. We have constructed a biophysical Purkinje soma model, guided and constrained by experimental reports in the literature, that can replicate the somatically driven bursting pattern and which hypothesises Persistent Na⁺ current (I_NaP) to be its burst initiator and SK K⁺ current (I_SK) to be its burst terminator.     

Analysis of the electrosensory pyramidal cell bursting model for weakly electric fish: model prediction under low levels of dendritic potassium conductance

Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish produce burst discharge. A Hodgkin-Huxley-type model, called ghostburster, consisting of two compartments (soma and dendrite) reproduces ELL pyramidal cell bursting observed in vitro. A previous study analyzed the ghostburster by treating Is and gDr,d as bifurcation parameters (Is: current injected into the somatic compartment and gDr,d: maximal conductance of the delayed rectifying potassium current in the dendritic compartment) and indicated that when both Is and gDr,d are set at particular values, the ghostburster shows a codimension-two bifurcation at which both saddle-node bifurcation of fixed points and saddle-node bifurcation of limit cycles occur simultaneously. In the present study, the ghostburster was investigated to clarify the bursting that occurred at gDr,d values smaller than that at the codimension-two bifurcation. Based on the number of spikes per burst, various burst patterns were observed depending on the (Is, gDr,d) values. Depending on the (Is, gDr,d) values, the burst trajectory in a phase space of the ghostburster showed either a high or a low degree of periodicity. Compared to the previous study, the present findings contribute to a more detailed understanding of ghostburster bursting.     

A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells

The electrical activity of endocrine pituitary cells is mediated by a plethora of ionic currents and establishing the role of a single channel type is difficult. Experimental observations have shown however that fast-activating voltage- and calcium-dependent potassium (BK) current tends to promote bursting in pituitary cells. This burst promoting effect requires fast activation of the BK current, otherwise it is inhibitory to bursting. In this work, we analyze a pituitary cell model in order to answer the question of why the BK activation must be fast to promote bursting. We also examine how the interplay between the activation rate and conductance of the BK current shapes the bursting activity. We use the multiple timescale structure of the model to our advantage and employ geometric singular perturbation theory to demonstrate the origin of the bursting behaviour. In particular, we show that the bursting can arise from either canard dynamics or slow passage through a dynamic Hopf bifurcation. We then compare our theoretical predictions with experimental data using the dynamic clamp technique and find that the data is consistent with a burst mechanism due to a slow passage through a Hopf.     

An analysis of the bursting behaviour of the Aplysia R15 neurone during exposure to normoxia and hypoxia with and without external calcium present

Membrane potentials (EM), interburst intervals (IBI), burst durations (BD), the numbers of spikes within a burst, and the amplitudes of the burst pacemaker potentials (BPP) were measured in two groups (N = 7 per group) of R15 neurones under conditions of 20, 10 and 5% oxygen and under nitrogen equilibration in suffusates with either Ca2+ (10 mM) or Mg2+ (10 mM) present (Groups I and II). Under normal extracellular Ca2+ conditions, EM and the amplitude of the BPP for Group I R15 neurones increased progressively during hypoxia and reoxygenation. In the absence of external calcium, the normal bursting pattern of Group II R15 neurones was interrupted. No consistent relationships were observed among BD, IBI, and the number of spikes per burst with respect to EM or BPP. Hypoxia may alter the resting permeability of R15 to potassium as well as having ephaptic effects.     

Parameter estimation for bursting neural models

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.'s (Journal of Neurophysiology 81, 382-397, 1999) model of preB?tzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070-2082, 2006). The results suggest possible modulatory mechanisms in the preB?tzinger complex, including modulation of the persistent sodium current.