Predicting single spikes and spike patterns with the Hindmarsh–Rose model

Most simple neuron models are only able to model traditional spiking behavior. As physiologists discover and classify different electrical phenotypes, computational neuroscientists become interested in using simple phenomenological models that can exhibit these different types of spiking patterns. The Hindmarsh–Rose model is a three-dimensional relaxation oscillator which can show both spiking and bursting patterns and has a chaotic regime. We test the predictive powers of the Hindmarsh–Rose model on two different test databases. We show that the Hindmarsh–Rose model can predict the spiking response of rat layer 5 neocortical pyramidal neurons on a stochastic input signal with a precision comparable to the best known spiking models. We also show that the Hindmarsh–Rose model can capture qualitatively the electrical footprints in a database of different types of neocortical interneurons. When the model parameters are fit from sub-threshold measurements only, the model still captures well the electrical phenotype, which suggests that the sub-threshold signals contain information about the firing patterns of the different neurons.     

Different Ca2+ dynamics between isolated hippocampal pyramidal cells and dentate granule cells

The hippocampal formation contains a variety of neuronal types. The principal neurons are granule cells in the dentate gyrus and pyramidal cells in Ammon's horn. These two neuron types show distinct cell morphology and display a different vulnerability to ischemic injury or various neurotoxins. In order to illustrate the difference in the pathophysiological properties of these neurons, we established a method for separately culturing granule cells and pyramidal cells. They were prepared from the dentate gyrus and Ammon's horn of 3-day-old Wistar rat pups and maintained for 7–9 days in culture. After transient exposure to N-methyl-D-aspartate or glutamate, both the cultured neuron populations displayed somatic Ca²⁺ transients with similar amplitudes, but the subsequent recovery to baseline was about twice as fast in granule cells than in pyramidal cells. Similar results were obtained for K⁺ depolarization-induced Ca²⁺ elevation, suggesting that the relatively rapid Ca²⁺ clearance in granule cells is independent of Ca²⁺ influx pathways. The present study provides the first evidence for a difference in Ca²⁺ dynamics and homeostasis between granule and pyramidal cells and may represent a cellular basis for the differential vulnerability of hippocampal neurons.     

Distribution of mitochondria in pyramidal cells and boutons in hippocampal cortex

Summary The amount of mitochondria has been recorded in various parts of neurons. This was done in electron micrographs of cerebral cortex from the hippocampal region. The outlines of boutons, somata and dendrites of varying diameters were transferred to tracing paper together with the outlines of the contained mitochondria. The same was done for whole tissue for comparison. After cutting out and weighing the outlined areas, the fraction of the various tissue constituents, or of whole tissue, occupied by mitochondria was determined. The absolute values are shown in the illustrations (Figs. 4–9). The dendritic shafts of pyramidal cells, coursing through stratum radiatum of regio superior (CA 1), are particularly poor in mitochondria (about 2%). In the branches, the amount as a rule increases with decreasing diameter (to nearly 13% in stratum moleculare).Boutons were the structures richest in mitochondria, but the amount varied with location.This study was supported in part by Grant NB 02215 from the National Institute of Neurological Diseases and Blindness, U.S. Public Health Service. The authors are indebted to Mrs. J. L. Vaaland, Miss M. Johansen and Mr. B. V. Johansen for valuable technical assistance.Fellow of The Norwegian Cancer Society during part of this study.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

Interaction between the Spatiotemporal Learning Rule (STLR) and Hebb type (HEBB) in single pyramidal cells in the hippocampal CA1 Area

The spatiotemporal learning rule (STLR), proposed as a non-Hebb type by Tsukada et al. (Neural Networks 9 (1996) 1357 and Tsukada and Pan (Biol. cyberm 92 (2005) 139), 2005), consists of two distinctive factors; “cooperative plasticity without a cell spike,” and “its temporal summation”. On the other hand, Hebb (The organization of behavior. John Wiley, New York, 1949) proposed the idea (HEBB) that synaptic modification is strengthened only if the pre- and post-cell are activated simultaneously. We have shown, experimentally, that both STLR and HEBB coexist in single pyramidal cells of the hippocampal CA1 area. The functional differences between STLR and HEBB in dendrite (local)-soma (global) interactions in single pyramidal cells of CA1 and the possibility of pattern separation, pattern completion and reinforcement learning were discussed.     

Gating properties of single SK channels in hippocampal CA1 pyramidal neurons.

The activation of small-conductance calcium-activated potassium channels (SK) has a profound effect on membrane excitability. In hippocampal pyramidal neurons, SK channel activation by Ca2+ entry from a preceding burst of action potentials generates the slow afterhyperpolarization (AHP). Stimulation of a number of receptor types suppresses the slow AHP, inhibiting spike frequency adaptation and causing these neurons to fire tonically. Little is known of the gating properties of native SK channels in CNS neurons. By using excised inside-out patches, a small-amplitude channel has been resolved that was half-activated by approximately 0.6 microM Ca2+ in a voltage-independent manner. The channel possessed a slope conductance of 10 pS and exhibited nonstationary gating. These properties are in accord with those of cloned SK channels. The measured Ca2+ sensitivity of hippocampal SK channels suggests that the slow AHP is generated by activation of SK channels from a local rise of intracellular Ca2+.     

Ethanol potentiates and blocks NMDA-activated single-channel currents in rat hippocampal pyramidal cells

Single-channel currents activated by N-methyl-D-aspartate (NMDA) were characterized using the outside-out patch clamp technique in cultured hippocampal cells from the rat. Several conductance states were observed, and the main one of 47 pS was further analyzed for channel lifetime and frequency. Open times decreased with hyperpolarization of the membrane. In view of recent evidence linking NMDA receptors to central nervous system processes such as learning and memory and ethanol (EtOH) tolerance, the effects of EtOH (0.01-1%, v/v, or congruent to 1.74-174 mM) were studied in this preparation. Two effects of EtOH could be discerned: (i) at low concentrations (1.74-8.65 mM) an increase in the probability of opening (p open) of the NMDA-activated channel currents, without change in the mean channel open time, and (ii) at higher concentrations (86.5-174 mM) a decrease in p open with a concomitant decrease in the mean open time. It is suggested that EtOH, even at rather low concentrations, may affect important brain functions.     

Real-time analysis of hippocampal neural activity in the intervals between interictal spikes

Previously the electroencephalogram (EEG) was modeled as consisting of faster, smaller waves superimposed on larger, slower waves. The intent of this study is to modify the program to sample neural activity over specific intervals of time following detection of a distinct wave pattern. The use of conditional sampling is illustrated by considering wave detection following epileptic interictal spikes in the rabbit hippocampus. To create an epileptic focus, small pellets of sodium penicillin suspended in agar were placed on the rabbit hippocampus. This produced regularly recurring, spontaneous, large amplitude discharges, or interictal spikes, at the site of application. Following detection of an interictal spike, the program delayed the onset of a sample period for either 1.0 s or 6.0 s. The neural activity was then sampled for 5.1 s, and fast and slow waves were detected over the sample period. The frequency distribution of waves in four of these 5.1 s intervals was calculated. Comparison of the frequency distributions following the 1.0 s and 6.0 s delays showed no discernible differences. The data illustrate that not all types of neural activity are markedly modified by interictal spikes and suggest that hippocampal cellular populations generate similar waves 1.0 s and 6.0 s after such a spike. Moreover, this experiment illustrates adaptation of the program to sample activity over a limited period of time following detection of a specific cortical waveform.     

An online spike detection and spike classification algorithm capable of instantaneous resolution of overlapping spikes

For the analysis of neuronal cooperativity, simultaneously recorded extracellular signals from neighboring neurons need to be sorted reliably by a spike sorting method. Many algorithms have been developed to this end, however, to date, none of them manages to fulfill a set of demanding requirements. In particular, it is desirable to have an algorithm that operates online, detects and classifies overlapping spikes in real time, and that adapts to non-stationary data. Here, we present a combined spike detection and classification algorithm, which explicitly addresses these issues. Our approach makes use of linear filters to find a new representation of the data and to optimally enhance the signal-to-noise ratio. We introduce a method called “Deconfusion” which de-correlates the filter outputs and provides source separation. Finally, a set of well-defined thresholds is applied and leads to simultaneous spike detection and spike classification. By incorporating a direct feedback, the algorithm adapts to non-stationary data and is, therefore, well suited for acute recordings. We evaluate our method on simulated and experimental data, including simultaneous intra/extra-cellular recordings made in slices of a rat cortex and recordings from the prefrontal cortex of awake behaving macaques. We compare the results to existing spike detection as well as spike sorting methods. We conclude that our algorithm meets all of the mentioned requirements and outperforms other methods under realistic signal-to-noise ratios and in the presence of overlapping spikes.     

羟基马桑毒素所致的大鼠海马锥体细胞痫样放电活动

本研究采用离体海马脑片电生理研究技术,细胞外记录海马锥体细胞群体锋电位(population spike,PS),观察羟基马桑毒素(tutin)对大鼠海马脑片CA1区锥体细胞电活动的影响,探讨tutin是否具有致痛作用及其致痫机制。结果如下:(1)用40、30和20μg/ml浓度的tutin灌流海马脑片,可显著增高由顺向刺激Schaffer侧支所诱发的PS的幅度,灌流tutin 30min时,PS第一个波的幅度分别为对照的(388.7±20.1)%、(317.2±19.1)%和(180.9±11.6)%(各组n=5,P<0.05)。(2)伴随PS波幅的增高,可出现成串痫样放电波,波数4～11个不等。(3)灌流tutin后的部分脑片(n=9/34),在未刺激Schaffer侧支时也出现自发的成串、高幅痫样放电。(4)灌流CNQX阻断非NMDA受体后,再灌流tutin,PS幅度和放电波数均无显著性变化,即CNQX可完全抑制tutin所致的痫样放电;灌流AP-5阻断NMDA受体后,tutin仍可使PS幅度增高但放电波数无显著性增加,即AP-5可部分抑制tutin所致的痫样放电。上述结果表明,tutin可使海马脑片锥体细胞兴奋活动增强,具有致痫作用;兴奋性谷氨酸受体尤其是非NMDA受体可能介导tutin的致痫作用。     

Representation of objects in space by two classes of hippocampal pyramidal cells

Humans can recognize and navigate in a room when its contents have been rearranged. Rats also adapt rapidly to movements of objects in a familiar environment. We therefore set out to investigate the neural machinery that underlies this capacity by further investigating the place cell-based map of the surroundings found in the rat hippocampus. We recorded from single CA1 pyramidal cells as rats foraged for food in a cylindrical arena (the room) containing a tall barrier (the furniture). Our main finding is a new class of cells that signal proximity to the barrier. If the barrier is fixed in position, these cells appear to be ordinary place cells. When, however, the barrier is moved, their activity moves equally and thereby conveys information about the barrier's position relative to the arena. When the barrier is removed, such cells stop firing, further suggesting they represent the barrier. Finally, if the barrier is put into a different arena where place cell activity is changed beyond recognition ("remapping"), these cells continue to discharge at the barrier. We also saw, in addition to barrier cells and place cells, a small number of cells whose activity seemed to require the barrier to be in a specific place in the environment. We conclude that barrier cells represent the location of the barrier in an environment-specific, place cell framework. The combined place + barrier cell activity thus mimics the current arrangement of the environment in an unexpectedly realistic fashion.     

Excitatory amino acids: modes of action on hippocampal pyramidal cells

Recent pharmacological and biochemical evidence supports the idea that acidic amino acids act as neurotransmitters at several excitatory synapses in the hippocampus. In this paper I review work comparing certain physiological actions of N-methyl-DL-aspartate (NMA) and L-glutamate in a hippocampal slice preparation. Intracellular recordings were made from pyramidal neurons bathed in 1 microM tetrodotoxin; agonists were applied by focal ionophoresis. NMA evoked calcium spikes and produced an apparent increase in the input resistance of pyramidal cells, whereas glutamate was very weak in these respects. The depolarization and conductance change caused by NMA were voltage dependent: both could be abolished by hyperpolarizing the cell to -70 to -90 mV, but no reversal potential could be demonstrated. The results of pharmacological and ionic manipulations suggest that the primary action of NMA does not involve reduction of a conventional potassium conductance. It is suggested that N-methyl-D-aspartate (NMDA) receptor activation increases a voltage-sensitive calcium conductance leading to a transient rise in cytoplasmic calcium concentration. The significance of this event is discussed with respect to the possible synaptic functions of chemically gated, voltage-sensitive calcium channels, and in particular with respect to the possible roles that NMDA receptors might serve in the genesis of long-term potentiation of excitatory synapses in the hippocampus.     

Non-Decaying postsynaptics potentials and delayed spikes in hippocampal pyramidal neurons generated by a zero slope conductance created by the persistent Na+ current

The negative slope conductance created by the persistent sodium current (I_NaP) prolongs the decay phase of excitatory postsynaptic potentials (EPSPs). In a recent study, we demonstrated that this effect was due to an increase of the membrane time constant. When the negative slope conductance opposes completely the positive slope conductances of the other currents it creates a zero slope conductance region. In this region the membrane time constant is infinite and the decay phase of the EPSPs is virtually absent. Here we show that non-decaying EPSPs are present in CA1 hippocampal pyramidal cells in the zero slope conductance region, in the suprathreshold range of membrane potential. Na⁺ channel block with tetrodotoxin abolishes the non-decaying EPSPs. Interestingly, the non-decaying EPSPs are observed only in response to artificial excitatory postsynaptic currents (aEPSCs) of small amplitude, and not in response to aEPSCs of big amplitude. We also observed concomitantly delayed spikes with long latencies and high variability only in response to small amplitude aEPSCs. Our results showed that in CA1 pyramidal neurons I_NaP creates non-decaying EPSPs and delayed spikes in the subthreshold range of membrane potentials, which could potentiate synaptic integration of synaptic potentials coming from distal regions of the dendritic tree.     

Hippocalcin gates the calcium activation of the slow afterhyperpolarization in hippocampal pyramidal cells

In the brain, calcium influx following a train of action potentials activates potassium channels that mediate a slow afterhyperpolarization current (I(sAHP)). The key steps between calcium influx and potassium channel activation remain unknown. Here we report that the key intermediate between calcium and the sAHP channels is the diffusible calcium sensor hippocalcin. Brief depolarizations sufficient to activate the I(sAHP) in wild-type mice do not elicit the I(sAHP) in hippocalcin knockout mice. Introduction of hippocalcin in cultured hippocampal neurons leads to a pronounced I(sAHP), while neurons expressing a hippocalcin mutant lacking N-terminal myristoylation exhibit a small I(sAHP) that is similar to that recorded in uninfected neurons. This implies that hippocalcin must bind to the plasma membrane to mediate its effects. These findings support a model in which the calcium sensor for the sAHP channels is not preassociated with the channel complex.     

Involvement of mu-receptors in the opioid-induced generation of bursting discharges in hippocampal pyramidal cells

Cultured hippocampal pyramidal cells responded to field stimulation with a short latency excitation followed by a long-lasting inhibition. This sequence was transformed into a bursting response by bath application of 10(-8) M FK 33-824, 10(-6) M (D-Ala)2(D-Leu)5-enkephalin and 10(-5) M bremazocine. Bremazocine and ethylketocyclazocine stereospecifically blocked the effects of FK 33-824. The results indicate that the excitatory responses were predominantly mediated by mu-receptors.     

Cav1.2 calcium channels modulate the spiking pattern of hippocampal pyramidal cells

Ca(v)1.2 L-type calcium channels support hippocampal synaptic plasticity, likely by facilitating dendritic Ca2+ influx evoked by action potentials (AP) back-propagated from the soma. Ca2+ influx into hippocampal neurons during somatic APs is sufficient to activate signalling pathways associated with late phase LTP. Thus, mechanisms controlling AP firing of hippocampal neurons are of major functional relevance. We examined the excitability of CA1 pyramidal cells using somatic current-clamp recordings in brain slices from control type mice and mice with the Ca(v)1.2 gene inactivated in principal hippocampal neurons. Lack of the Ca(v)1.2 protein did not affect either affect basic characteristics, such as resting membrane potential and input resistance, or parameters of single action potentials (AP) induced by 5 ms depolarising current pulses. However, CA1 hippocampal neurons from control and mutant mice differed in their patterns of AP firing during 500 ms depolarising current pulses: threshold voltage for repetitive firing was shifted significantly by about 5 mV to more depolarised potentials in the mutant mice (p<0.01), and the latency until firing of the first AP was prolonged (73.2+/-6.6 ms versus 48.1+/- 7.8 ms in control; p<0.05). CA1 pyramidal cells from the mutant mice also showed a lowered initial spiking frequency within an AP train. In control cells, isradipine had matching effects, while BayK 8644 facilitated spiking. Our data demonstrate that Ca(v)1.2 channels are involved in regulating the intrinsic excitability of CA1 pyramidal neurons. This cellular mechanism may contribute to the known function of Ca(v)1.2 channels in supporting synaptic plasticity and memory.