Ionic mechanisms underlying spontaneous CA1 neuronal firing in Ca2+-free solution

Hippocampal CA1 neurons exposed to zero-[Ca(2+)] solutions can generate periodic spontaneous synchronized activity in the absence of synaptic function. Experiments using hippocampal slices showed that, after exposure to zero-[Ca(2+)](0) solution, CA1 pyramidal cells depolarized 5-10 mV and started firing spontaneous action potentials. Spontaneous single neuron activity appeared in singlets or was grouped into bursts of two or three action potentials. A 16-compartment, 23-variable cable model of a CA1 pyramidal neuron was developed to study mechanisms of spontaneous neuronal bursting in a calcium-free extracellular solution. In the model, five active currents (a fast sodium current, a persistent sodium current, an A-type transient potassium current, a delayed rectifier potassium current, and a muscarinic potassium current) are included in the somatic compartment. The model simulates the spontaneous bursting behavior of neurons in calcium-free solutions. The mechanisms underlying several aspects of bursting are studied, including the generation of triplet bursts, spike duration, burst termination, after-depolarization behavior, and the prolonged inactive period between bursts. We show that the small persistent sodium current can play a key role in spontaneous CA1 activity in zero-calcium solutions. In particular, it is necessary for the generation of an after-depolarizing potential and prolongs both individual bursts and the interburst interval.     

Two types of independent bursting mechanisms in inspiratory neurons: an integrative model

The network of coupled neurons in the pre-Bötzinger complex (pBC) of the medulla generates a bursting rhythm, which underlies the inspiratory phase of respiration. In some of these neurons, bursting persists even when synaptic coupling in the network is blocked and respiratory rhythmic discharge stops. Bursting in inspiratory neurons has been extensively studied, and two classes of bursting neurons have been identified, with bursting mechanism depends on either persistent sodium current or changes in intracellular Ca²⁺, respectively. Motivated by experimental evidence from these intrinsically bursting neurons, we present a two-compartment mathematical model of an isolated pBC neuron with two independent bursting mechanisms. Bursting in the somatic compartment is modeled via inactivation of a persistent sodium current, whereas bursting in the dendritic compartment relies on Ca²⁺ oscillations, which are determined by the neuromodulatory tone. The model explains a number of conflicting experimental results and is able to generate a robust bursting rhythm, over a large range of parameters, with a frequency adjusted by neuromodulators.     

Intrinsic bursting enhances the robustness of a neural network model of sequence generation by avian brain area HVC

Avian brain area HVC is known to be important for the production of birdsong. In zebra finches, each RA-projecting neuron in HVC emits a single burst of spikes during a song motif. The population of neurons is activated in a precisely timed, stereotyped sequence. We propose a model of these burst sequences that relies on two hypotheses. First, we hypothesize that the sequential order of bursting is reflected in the excitatory synaptic connections between neurons. Second, we propose that the neurons are intrinsically bursting, so that burst duration is set by cellular properties. Our model generates burst sequences similar to those observed in HVC. If intrinsic bursting is removed from the model, burst sequences can also be produced. However, they require more fine-tuning of synaptic strengths, and are therefore less robust. In our model, intrinsic bursting is caused by dendritic calcium spikes, and strong spike frequency adaptation in the soma contributes to burst termination.     

Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons

Activity of neurons in the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem drives the inspiratory phase of the respiratory rhythm. Experimental results have suggested that multiple bursting mechanisms based on a calcium-activated nonspecific cationic (CAN) current, a persistent sodium (NaP) current, and calcium dynamics may be incorporated within the pre-BötC. Previous modeling works have incorporated representations of some or all of these mechanisms. In this study, we consider a single-compartment model of a pre-BötC inspiratory neuron that encompasses particular aspects of all of these features. We present a novel mathematical analysis of the interaction of the corresponding rhythmic mechanisms arising in the model, including square-wave bursting and autonomous calcium oscillations, which requires treatment of a system of differential equations incorporating three slow variables.     

Synchronous and asynchronous bursting states: role of intrinsic neural dynamics

Brain signals such as local field potentials often display gamma-band oscillations (30-70 Hz) in a variety of cognitive tasks. These oscillatory activities possibly reflect synchronization of cell assemblies that are engaged in a cognitive function. A type of pyramidal neurons, i.e., chattering neurons, show fast rhythmic bursting (FRB) in the gamma frequency range, and may play an active role in generating the gamma-band oscillations in the cerebral cortex. Our previous phase response analyses have revealed that the synchronization between the coupled bursting neurons significantly depends on the bursting mode that is defined as the number of spikes in each burst. Namely, a network of neurons bursting through a Ca(2+)-dependent mechanism exhibited sharp transitions between synchronous and asynchronous firing states when the neurons exchanged the bursting mode between singlet, doublet and so on. However, whether a broad class of bursting neuron models commonly show such a network behavior remains unclear. Here, we analyze the mechanism underlying this network behavior using a mathematically tractable neuron model. Then we extend our results to a multi-compartment version of the NaP current-based neuron model and prove a similar tight relationship between the bursting mode changes and the network state changes in this model. Thus, the synchronization behavior couples tightly to the bursting mode in a wide class of networks of bursting neurons.     

Recording site dependence of the neuronal spiking statistics

Spiking characteristics of neurons in the middle temporal (MT) area and the medial superior temporal (MST) area in the visual cortex of a monkey are compared with the ones in the principal sulcus (PS) area in the prefrontal cortex. The comparison is based on the basis of three inter-spike interval statistical measures: the coefficient of variation (CV), the skewness coefficient (SK) and the correlation coefficient of consecutive intervals (COR). Even for the spike sequences recorded from the same neuron, three coefficients computed from 100 intervals do not always exhibit similar values, but distribute rather widely. The distribution of three coefficients obtained from a single neuron in the MST area does not largely deviate from the distribution obtained from multiple neurons in MT and MST areas. Those distributions, however, largely deviate from the distribution obtained from neurons in the PS area. In this way, the distribution of those statistical coefficients reflects the nature of the recording site.     

Conversion of Phase Information into a Spike-Count Code by Bursting Neurons

Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.     

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.     

To Burst or Not to Burst?

It is well known that some neurons tend to fire packets of action potentials followed by periods of quiescence (bursts) while others within the same stage of sensory processing fire in a tonic manner. However, the respective computational advantages of bursting and tonic neurons for encoding time varying signals largely remain a mystery. Weakly electric fish use cutaneous electroreceptors to convey information about sensory stimuli and it has been shown that some electroreceptors exhibit bursting dynamics while others do not. In this study, we compare the neural coding capabilities of tonically firing and bursting electroreceptor model neurons using information theoretic measures. We find that both bursting and tonically firing model neurons efficiently transmit information about the stimulus. However, the decoding mechanisms that must be used for each differ greatly: a non-linear decoder would be required to extract all the available information transmitted by the bursting model neuron whereas a linear one might suffice for the tonically firing model neuron. Further investigations using stimulus reconstruction techniques reveal that, unlike the tonically firing model neuron, the bursting model neuron does not encode the detailed time course of the stimulus. A novel measure of feature detection reveals that the bursting neuron signals certain stimulus features. Finally, we show that feature extraction and stimulus estimation are mutually exclusive computations occurring in bursting and tonically firing model neurons, respectively. Our results therefore suggest that stimulus estimation and feature extraction might be parallel computations in certain sensory systems rather than being sequential as has been previously proposed.     

Analysis of bursting in a thalamic neuron model

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgkin-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a–c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes. Received: 18 July 1993/Accepted in revised form: 22 January 1994     

Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

The preBötzinger complex (preBötC) is a heterogeneous neuronal network within the mammalian brainstem that has been experimentally found to generate robust, synchronous bursts that drive the inspiratory phase of the respiratory rhythm. The persistent sodium (NaP) current is observed in every preBötC neuron, and significant modeling effort has characterized its contribution to square-wave bursting in the preBötC. Recent experimental work demonstrated that neurons within the preBötC are endowed with a calcium-activated nonspecific cationic (CAN) current that is activated by a signaling cascade initiated by glutamate. In a preBötC model, the CAN current was shown to promote robust bursts that experience depolarization block (DB bursts). We consider a self-coupled model neuron, which we represent as a single compartment based on our experimental finding of electrotonic compactness, under variation of g _NaP, the conductance of the NaP current, and g _CAN, the conductance of the CAN current. Varying these two conductances yields a spectrum of activity patterns, including quiescence, tonic activity, square-wave bursting, DB bursting, and a novel mixture of square-wave and DB bursts, which match well with activity that we observe in experimental preparations. We elucidate the mechanisms underlying these dynamics, as well as the transitions between these regimes and the occurrence of bistability, by applying the mathematical tools of bifurcation analysis and slow-fast decomposition. Based on the prevalence of NaP and CAN currents, we expect that the generalizable framework for modeling their interactions that we present may be relevant to the rhythmicity of other brain areas beyond the preBötC as well.     

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).     

Distinct neuronal types contribute to hybrid temporal encoding strategies in primate auditory cortex

Studies of the encoding of sensory stimuli by the brain often consider recorded neurons as a pool of identical units. Here, we report divergence in stimulus-encoding properties between subpopulations of cortical neurons that are classified based on spike timing and waveform features. Neurons in auditory cortex of the awake marmoset (Callithrix jacchus) encode temporal information with either stimulus-synchronized or nonsynchronized responses. When we classified single-unit recordings using either a criteria-based or an unsupervised classification method into regular-spiking, fast-spiking, and bursting units, a subset of intrinsically bursting neurons formed the most highly synchronized group, with strong phase-locking to sinusoidal amplitude modulation (SAM) that extended well above 20 Hz. In contrast with other unit types, these bursting neurons fired primarily on the rising phase of SAM or the onset of unmodulated stimuli, and preferred rapid stimulus onset rates. Such differentiating behavior has been previously reported in bursting neuron models and may reflect specializations for detection of acoustic edges. These units responded to natural stimuli (vocalizations) with brief and precise spiking at particular time points that could be decoded with high temporal stringency. Regular-spiking units better reflected the shape of slow modulations and responded more selectively to vocalizations with overall firing rate increases. Population decoding using time-binned neural activity found that decoding behavior differed substantially between regular-spiking and bursting units. A relatively small pool of bursting units was sufficient to identify the stimulus with high accuracy in a manner that relied on the temporal pattern of responses. These unit type differences may contribute to parallel and complementary neural codes.

Neurons in auditory cortex show highly diverse responses to sounds. This study suggests that neuronal type inferred from baseline firing properties accounts for much of this diversity, with a subpopulation of bursting units being specialized for precise temporal encoding.     

Variability of bursting patterns in a neuron model in the presence of noise

Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent, and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped windows.     

Presumed mechanisms of a long-term increase in the intrinsic excitability of cerebellar granule cells: A model study

Persistent use-dependent changes in the intrinsic neuronal excitability determine the long-term dynamics of the activity of these neurons. In synergy with the long-lasting modification of synaptic transmission, such changes in the excitability presumably contribute to the formation of a memory trace in the brain. Nevertheless, neither particular transmembrane ion conductances implicated in the intrinsic plasticity nor the mechanisms of regulation of such conductances have been identified in most neurons where this plasticity was observed. In our model study, we tried to determine those membrane conductances in cerebellar granule cells (GrCs) whose changes can result in a persistent increase in the input resistance and a decrease in the spike threshold observed after high-frequency stimulation of presynaptic neurons. For this purpose, published experimental results were simulated with the use of a slightly modified model of the electroresponsiveness of rat cerebellar GrCs. It was concluded that experimentally observed changes in the input resistance of the neuron, in the minimum current step needed to fire action potentials (APs), in the spike threshold, in the average spike frequency, and in the delay of the first spike may be caused only by changes in the background voltage-independent potassium conductance and persistent sodium conductance. Hyperpolarization-directed shifts in the activation and inactivation curves of fast sodium channels are also possible. The observed changes in the intrinsic excitability evoke the shift in the peak of the frequency-response curve in such a manner that it becomes close to the frequency of oscillations recorded in the cerebellar granular layer during realization of voluntary movements. Neirofiziologiya/Neurophysiology, Vol. 38, No. 2, pp. 119–130, March–April, 2006.     

Respiratory rhythm: an emergent network property?

We tested the hypothesis that pacemaker neurons generate breathing rhythm in mammals. We monitored respiratory-related motor nerve rhythm in neonatal rodent slice preparations. Blockade of the persistent sodium current (I(NaP)), which was postulated to underlie voltage-dependent bursting in respiratory pacemaker neurons, with riluzole (< or =200 microM) did not alter the frequency of respiratory-related motor output. Yet, in every pacemaker neuron recorded (50/50), bursting was abolished at much lower concentrations of riluzole (< or =20 microM). Thus, eliminating the pacemaker population (our statistics confirm that this population is reduced at least 94%, p < 0.05) does not affect respiratory rhythm. These results suggest that voltage-dependent bursting in pacemaker neurons is not essential for respiratory rhythmogenesis, which may instead be an emergent network property.     

Identifying Crucial Parameter Correlations Maintaining Bursting Activity

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, _Leak; a persistent K current, _K2; and of a persistent Na+ current, _P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of _Leak, _K2, and _P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Reliability of spike and burst firing in thalamocortical relay cells

The reliability and precision of the timing of spikes in a spike train is an important aspect of neuronal coding. We investigated reliability in thalamocortical relay (TCR) cells in the acute slice and also in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected into the TCR cell soma. The neuron responded with spike trains that showed trial-to-trial variability, due to amongst others slow changes in its internal state and the experimental setup. The DC current allowed to bring the neuron in different states, characterized by a well defined membrane voltage (between ?80 and ?50 mV) and by a specific firing regime that on depolarization gradually shifted from a predominantly bursting regime to a tonic spiking regime. The filtered frozen white noise generated a spike pattern output with a broad spike interval distribution. The coincidence factor and the Hunter and Milton measure were used as reliability measures of the output spike train. In the experimental TCR cell as well as the Morris-Lecar model cell the reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates. The reliability of the output of the TCR cell increases with depolarization. In hyperpolarized states bursts are more reliable than single spikes. The analytically derived relations were capable to predict several of the experimentally recorded spike features.     

A single spiking neuron that can represent interval timing: analysis,plasticity and multi-stability

The ability to represent interval timing is crucial for many common behaviors, such as knowing whether to stop when the light turns from green to yellow. Neural representations of interval timing have been reported in the rat primary visual cortex and we have previously presented a computational framework describing how they can be learned by a network of neurons. Recent experimental and theoretical results in entorhinal cortex have shown that single neurons can exhibit persistent activity, previously thought to be generated by a network of neurons. Motivated by these single neuron results, we propose a single spiking neuron model that can learn to compute and represent interval timing. We show that a simple model, reduced analytically to a single dynamical equation, captures the average behavior of the complete high dimensional spiking model very well. Variants of this model can be used to produce bi-stable or multi-stable persistent activity. We also propose a plasticity rule by which this model can learn to represent different intervals and different levels of persistent activity.