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.     

Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling

Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as “fold/limit cycle” type of bursting, then anti-phase continuous spiking, followed by the “fold/torus” type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate “fold/Hopf” bursting via “fold/fold” hysteresis loop; whereas, the chemically coupled cells generate “fold/subHopf” bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast–slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.     

Conflicting effects of excitatory synaptic and electric coupling on the dynamics of square-wave bursters

Using two-cell and 50-cell networks of square-wave bursters, we studied how excitatory coupling of individual neurons affects the bursting output of the network. Our results show that the effects of synaptic excitation vs. electrical coupling are distinct. Increasing excitatory synaptic coupling generally increases burst duration. Electrical coupling also increases burst duration for low to moderate values, but at sufficiently strong values promotes a switch to highly synchronous bursts where further increases in electrical or synaptic coupling have a minimal effect on burst duration. These effects are largely mediated by spike synchrony, which is determined by the stability of the in-phase spiking solution during the burst. Even when both coupling mechanisms are strong, one form (in-phase or anti-phase) of spike synchrony will determine the burst dynamics, resulting in a sharp boundary in the space of the coupling parameters. This boundary exists in both two cell and network simulations. We use these results to interpret the effects of gap-junction blockers on the neuronal circuitry that underlies respiration.     

The structure and size of sensory bursts encode stimulus information but only size affects behavior

Cricket ultrasound avoidance is a classic model system for neuroethology. Avoidance steering is triggered by high-firing-rate bursts of spikes in the auditory command neuron AN2. Although bursting is common among sensory neurons, and although the detailed structure of bursts may encode information about the stimulus, it is as yet unclear whether this information is decoded. We address this question in two ways: from an information coding point of view, by showing the relationship between stimulus and burst structure; and also from a functional point of view by showing the relationship between burst structure and behavior. We conclude that the burst structure carries detailed temporal information about the stimulus but that this has little impact on the behavioral response, which is affected mainly by burst size.     

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.     

State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment.During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the model's biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting.During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable.We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neuron's complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.     

Development and modulation of endogenous bursting in identified neuron R15 of juvenile Aplysia

Evidence from a variety of both vertebrate and invertebrate preparations has demonstrated that modulation of the intrinsic firing patterns of individual neurons can have a dramatic effect on the functional output of a neural circuit. Although the mechanisms underlying the production and modulation of intrinsic firing patterns have been extensively studied in adult nervous systems, relatively little is known about how these two features of intrinsically active neurons develop. To address these issues, we have examined the development of endogenous bursting and its modulation by neuropeptides in the identified cell R15 of juvenile Aplysia. Confirming Ohmori (1981), we found that the mature parabolic bursting pattern of R15 is absent in early juvenile stages and develops only gradually over the last stage of juvenile development. We have then analyzed the modulatory effects of extracts made from the neurosecretory bag cells of Aplysia on the immature firing pattern of juvenile R15 cells. In the adult, neuroactive peptides released from the bag cells are known to intensify bursting. In juveniles, we have found that bag cell extract (BCE) can induce bursting prematurely as well as intensify immature bursts, whereas control extracts have no effect on the firing pattern of R15. These results show that the ionic currents necessary for the generation of endogenous bursting in R15 are present and can be modulated before the normal developmental expression of the burst pattern.     

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.     

Improving noise resistance of intrinsic rhythms in a square-wave burster model

The square-wave burster (Wang and Rinzel, 2003) is a class of autonomous bursting cells that share a bifurcation structure. It is known that this class of cells is involved in the generation of various life-supporting rhythms. In our research to realize an electronic circuit that mimics the rhythm generating mechanism in the square-wave burster, our circuit experimentally exhibited severe fluctuations in its rhythmic activity. We have found a noise-sensitive region in the phase portrait of the ideal model and have proposed modifications of the model that can reduce this fluctuation. A possible modification to ionic-conductance neuron models (Kohno and Aihara, 2011) was inspired by them. This modification, however, cannot be applied to a group of square-wave bursters, including the Butera–Rinzel–Smith model (0010 and 0050), which is a model of the pre-Bötzinger complex bursting neuron that plays a crucial role in the generation of respiration rhythms, because this modification premises that the slow dynamics originates from an activation gate variable of a hyperpolarizing ionic current. However, in some square-wave bursters, they are controlled by an inactivation gate variable of a depolarizing ionic current. In this study, we proposed a similar modification with a completely different mechanism that can be applied to this group of square-wave bursters. In the presence of noises, the modified Butera–Rinzel–Smith model can generate rhythmic activity that is more stable and similar to biological observations than the original model. The mechanisms underlying this modification are explained with noisy bifurcation diagrams.     

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).     

Ghostbursting: A Novel Neuronal Burst Mechanism

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

On the dynamics of the spontaneous activity in neuronal networks

Most neuronal networks, even in the absence of external stimuli, produce spontaneous bursts of spikes separated by periods of reduced activity. The origin and functional role of these neuronal events are still unclear. The present work shows that the spontaneous activity of two very different networks, intact leech ganglia and dissociated cultures of rat hippocampal neurons, share several features. Indeed, in both networks: i) the inter-spike intervals distribution of the spontaneous firing of single neurons is either regular or periodic or bursting, with the fraction of bursting neurons depending on the network activity; ii) bursts of spontaneous spikes have the same broad distributions of size and duration; iii) the degree of correlated activity increases with the bin width, and the power spectrum of the network firing rate has a 1/f behavior at low frequencies, indicating the existence of long-range temporal correlations; iv) the activity of excitatory synaptic pathways mediated by NMDA receptors is necessary for the onset of the long-range correlations and for the presence of large bursts; v) blockage of inhibitory synaptic pathways mediated by GABA(A) receptors causes instead an increase in the correlation among neurons and leads to a burst distribution composed only of very small and very large bursts. These results suggest that the spontaneous electrical activity in neuronal networks with different architectures and functions can have very similar properties and common dynamics.     

Network bursts in cortical cultures are best simulated using pacemaker neurons and adaptive synapses

One of the most specific and exhibited features in the electrical activity of dissociated cultured neural networks (NNs) is the phenomenon of synchronized bursts, whose profiles vary widely in shape, width and firing rate. On the way to understanding the organization and behavior of biological NNs, we reproduced those features with random connectivity network models with 5,000 neurons. While the common approach to induce bursting behavior in neuronal network models is noise injection, there is experimental evidence suggesting the existence of pacemaker-like neurons. In our simulations noise did evoke bursts, but with an unrealistically gentle rising slope. We show that a small subset of ‘pacemaker’ neurons can trigger bursts with a more realistic profile. We found that adding pacemaker-like neurons as well as adaptive synapses yield burst features (shape, width, and height of the main phase) in the same ranges as obtained experimentally. Finally, we demonstrate how changes in network connectivity, transmission delays, and excitatory fraction influence network burst features quantitatively.     

High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

Flexibility in neuronal circuits has its roots in the dynamical richness of their neurons. Depending on their membrane properties single neurons can produce a plethora of activity regimes including silence, spiking and bursting. What is less appreciated is that these regimes can coexist with each other so that a transient stimulus can cause persistent change in the activity of a given neuron. Such multistability of the neuronal dynamics has been shown in a variety of neurons under different modulatory conditions. It can play either a functional role or present a substrate for dynamical diseases. We considered a database of an isolated leech heart interneuron model that can display silent, tonic spiking and bursting regimes. We analyzed only the cases of endogenous bursters producing functional half-center oscillators (HCOs). Using a one parameter (the leak conductance ()) bifurcation analysis, we extended the database to include silent regimes (stationary states) and systematically classified cases for the coexistence of silent and bursting regimes. We showed that different cases could exhibit two stable depolarized stationary states and two hyperpolarized stationary states in addition to various spiking and bursting regimes. We analyzed all cases of endogenous bursters and found that 18% of the cases were multistable, exhibiting coexistences of stationary states and bursting. Moreover, 91% of the cases exhibited multistability in some range of . We also explored HCOs built of multistable neuron cases with coexisting stationary states and a bursting regime. In 96% of cases analyzed, the HCOs resumed normal alternating bursting after one of the neurons was reset to a stationary state, proving themselves robust against this perturbation.     

<Emphasis Type="BoldItalic">In vivo</Emphasis> conditions influence the coding of stimulus features by bursts of action potentials

The functional role of burst firing (i.e. the firing of packets of action potentials followed by quiescence) in sensory processing is still under debate. Should bursts be considered as unitary events that signal the presence of a particular feature in the sensory environment or is information about stimulus attributes contained within their temporal structure? We compared the coding of stimulus attributes by bursts in vivo and in vitro of electrosensory pyramidal neurons in weakly electric fish by computing correlations between burst and stimulus attributes. Our results show that, while these correlations were strong in magnitude and significant in vitro, they were actually much weaker in magnitude if at all significant in vivo. We used a mathematical model of pyramidal neuron activity in vivo and showed that such a model could reproduce the correlations seen in vitro, thereby suggesting that differences in burst coding were not due to differences in bursting seen in vivo and in vitro. We next tested whether variability in the baseline (i.e. without stimulation) activity of ELL pyramidal neurons could account for these differences. To do so, we injected noise into our model whose intensity was calibrated to mimic baseline activity variability as quantified by the coefficient of variation. We found that this noise caused significant decreases in the magnitude of correlations between burst and stimulus attributes and could account for differences between in vitro and in vivo conditions. We then tested this prediction experimentally by directly injecting noise in vitro through the recording electrode. Our results show that this caused a lowering in magnitude of the correlations between burst and stimulus attributes in vitro and gave rise to values that were quantitatively similar to those seen under in vivo conditions. While it is expected that noise in the form of baseline activity variability will lower correlations between burst and stimulus attributes, our results show that such variability can account for differences seen in vivo. Thus, the high variability seen under in vivo conditions has profound consequences on the coding of information by bursts in ELL pyramidal neurons. In particular, our results support the viewpoint that bursts serve as a detector of particular stimulus features but do not carry detailed information about such features in their structure.     

Discrete Pattern of Burst Stimulation in the Ventrobasal Thalamus for Anti-Nociception

The thalamus has been proposed to play a role in sensory modulation via switching between tonic and burst dual firing of individual neurons. Of the two firing modes, altered burst firing has been repeatedly implicated with pathological pain conditions, which suggests that maintaining a certain form of thalamic burst could be crucial for controlling pain. However, specific elements of burst firing that may contribute to pain control have not yet been actively investigated. Utilizing the deep brain stimulation (DBS) technique, we explored the effects of bursting properties in pain control by electrically stimulating the ventrobasal (VB) thalamus in forms of burst patterned to test different aspects of bursts during the formalin induced nociception in mice. Our results demonstrated that electrical stimulations mimicking specific burst firing properties are important in producing an anti-nociceptive effect and found that the ≤3 ms interval between burst pluses (intra-burst-interval: IntraBI) and ≥3 pulses per burst were required to reliably reduce formalin induced nociceptive responses in mice. Periodicity of IntraBI was also suggested to contribute to anti-nociception to a limited extent.     

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。     

Firing synchronization and temporal order in noisy neuronal networks

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.     

Anti-phase,asymmetric and aperiodic oscillations in excitable cells—I. Coupled bursters

I seek to explain phenomena observed in simulations of populations of gap junction-coupled bursting cells by studying the dynamics of identical pairs. I use a simplified model for pancreatic β-cells and decompose the system into fast (spike-generating) and slow subsystems to show how bifurcations of the fast subsystem affect bursting behavior. When coupling is weak, the spikes are not in phase but rather are anti-phase, asymmetric or quasi-periodic. These solutions all support bursting with smaller amplitude spikes than the in-phase case, leading to increased burst period. A key geometrical feature underlying this is that the in-phase periodic solution branch terminates in a homoclinic orbit. The same mechanism also provides a model for bursting as an emergent property of populations; cells which are not intrinsic bursters can burst when coupled. This phenomenon is enhanced when symmetry is broken by making the cells differ in a parameter.     

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.