Mechanism of bistability: Tonic spiking and bursting in a neuron model

Shilnikov, Andrey; Calabrese, Ronald L.; Cymbalyuk, Gennady

doi:10.1103/physreve.71.056214

Cited by 140 publications

(81 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A saddle periodic orbit is a generic component of a number of mechanisms supporting bistability in the dynamics of single neurons [6,17,19,30,32,36,37]. Its stable manifold acts as a threshold between the two regimes; and different perturbations of the state of the model could induce crossing the threshold and a switch from one regime to the other.…”

Section: Discussionmentioning

confidence: 99%

Bistability of bursting and silence regimes in a model of a leech heart interneuron

2011

Self Cite

View full text Add to dashboard Cite

Bursting is one of the primary activity regimes of neurons. Our study is focused on determining a generic biophysical mechanism underlying the co-existence of the bursting and silent regimes observed in a neuron model. We show that the main ingredient for this mechanism is a saddle periodic orbit. The stable manifold of the orbit sets a threshold between the regimes of activity. Thus, the range of the controlling parameters, where the co-existence is observed, is limited by the bifurcations' values at which the saddle orbit appears and disappears. We show that it appears through the sub-critical Andronov-Hopf bifurcation, where the equilibrium representing the silent regime loses stability, and disappears at the homoclinic bifurcation. Correspondingly, the bursting regime disappears in close proximity to the homoclinic bifurcation.

show abstract

Section: Discussionmentioning

confidence: 99%

Bistability of bursting and silence regimes in a model of a leech heart interneuron

2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…This should be contrasted to situations when adding more noise leads to broadening of peaks already existing in a probability distribution to begin with. For example, in a bistable situation of coexisting tonic spiking and bursting regimes in a neuron (Shilnikov et al 2005), the type of output can be realized by proper choice of initial conditions. Each regime may be associated with a peak in a probability distribution.…”

Section: Discussionmentioning

confidence: 99%

“…Some neurons demonstrate coexistent tonic and bursting modes, which can be switched by external stimulation. Examples include pyramidal cells in the electrosensory system of weakly electric fish (Oswald et al 2004), LGN (lateral geniculate nucleus) cells (Lesica and Stanley 2004;Reinagel et al 1999), and leech heart interneurons (Shilnikov et al 2005). …”

Section: Dynamics Of Burstingmentioning

confidence: 99%

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

Neiman¹,

Yakusheva²,

Russell³

2007

Journal of Neurophysiology

View full text Add to dashboard Cite

Neiman AB, Yakusheva TA, Russell DF. Noise-induced transition to bursting in responses of paddlefish electroreceptor afferents. J Neurophysiol 98: [2795][2796][2797][2798][2799][2800][2801][2802][2803][2804][2805][2806] 2007. First published September 12, 2007; doi:10.1152/jn.01289.2006. The response properties of ampullary electroreceptors of paddlefish, Polyodon spathula, were studied in vivo, as single-unit afferent responses to external electrical stimulation with varied intensities of several types of noise waveforms, all Gaussian and zero-mean. They included broadband white noise, Ornstein-Uhlenbeck noise, low-or high-frequency band-limited noise, or natural noise recorded from swarms of Daphnia zooplankton prey, or from individual prey. Normally the afferents fire spontaneously in a tonic manner, which is actually quasiperiodic due to embedded oscillators. 1) Weak noise stimuli increased the variability of afferent firing, but it remained tonic. 2) In contrast, stimulation with less-weak broadband noise led to a qualitative change of the firing patterns, to parabolic bursting, even though the mean firing rate was scarcely affected.3) The transition to afferent bursting was marked by the development of two well-separated timescales: the fast frequency of spiking inside bursts at Յ250 spikes/s and the slow frequency of burst occurrences at about 9 (range 5-13) bursts/s. These two timescales were manifested as two regimes in afferent power spectra, bimodal interspike interval histograms, return maps, and autocorrelation functions of afferent spike trains. 4) The stochastic approximately 9-Hz bursts were not simply driven by similar-frequency components of noise stimuli because bursts could be dissociated from stimulus waveforms using high-pass filtered noise, or a 0.1-Hz sine-wave stimulus. 5) Arrhenius plots showed that the threshold noise intensity required to elicit bursting depended on the frequency content of a noise stimulus, being lowest, about 1.2 V/cm, for stimuli matching the 1-to 20-Hz best response band of these cathodally excited ampullary electroreceptors. This is only slightly higher than previous behavioral estimates of the electrosensory threshold as 0.5 V/cm. 6) Comparable threshold values for bursting came from an alternate analytical approach, based on correlation times of spike trains. 7) Simultaneous recordings from pairs of afferents showed that their bursting frequencies (bursts/s) always converged as the amplitude of a noise stimulus was raised. Thus the slow timescale of bursting is similar for different electroreceptors, even though their mean spiking rates can differ. In conclusion, the ampullary electroreceptors of paddlefish have two distinct modes of operation: their spontaneous tonic firing is modulated by the weakest stimuli, but they switch to bursting output for less-weak stimuli. We propose that afferent bursting may mediate close-range tracking of planktonic prey.

show abstract

“…Slow transitions between a slow-wave state and a fast-wave state were also observed in the olfactory cortex (Murakami et al, 2005). Coexistence of bursting and tonic spiking regimens is not limited to vertebrates (Lechner et al, 1996;Turrigiano et al, 1996;Shilnikov et al, 2005). Different levels of synaptic excitatory drive, activation of intrinsic conductances by neuromodulation, and changes in the extracellular ionic environment control the state-dependent oscillatory regimen (McCormick, 1992;Gil et al, 1997;Steriade and McCarley, 2005).…”

Section: Introductionmentioning

confidence: 99%

Slow State Transitions of Sustained Neural Oscillations by Activity-Dependent Modulation of Intrinsic Excitability

Fröhlich

Bazhenov

Timofeev

et al. 2006

Journal of Neuroscience

View full text Add to dashboard Cite

Little is known about the dynamics and mechanisms of transitions between tonic firing and bursting in cortical networks. Here, we use a computational model of a neocortical circuit with extracellular potassium dynamics to show that activity-dependent modulation of intrinsic excitability can lead to sustained oscillations with slow transitions between two distinct firing modes: fast run (tonic spiking or fast bursts with few spikes) and slow bursting. These transitions are caused by a bistability with hysteresis in a pyramidal cell model. Balanced excitation and inhibition stabilizes a network of pyramidal cells and inhibitory interneurons in the bistable region and causes sustained periodic alternations between distinct oscillatory states. During spike-wave seizures, neocortical paroxysmal activity exhibits qualitatively similar slow transitions between fast run and bursting. We therefore predict that extracellular potassium dynamics can cause alternating episodes of fast and slow oscillatory states in both normal and epileptic neocortical networks.

show abstract

Mechanism of bistability: Tonic spiking and bursting in a neuron model

Cited by 140 publications

References 39 publications

Bistability of bursting and silence regimes in a model of a leech heart interneuron

Bistability of bursting and silence regimes in a model of a leech heart interneuron

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

Slow State Transitions of Sustained Neural Oscillations by Activity-Dependent Modulation of Intrinsic Excitability

Contact Info

Product

Resources

About