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Six types of multistability in a neuronal model based on slow calcium current.

Malashchenko T, Shilnikov A, Cymbalyuk G - PLoS ONE (2011)

Bottom Line: We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.We described a novel mechanism supporting the bistability of bursting and silence.This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia, United States of America.

ABSTRACT

Background: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/principal findings: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

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Related in: MedlinePlus

Bursting waveform with temporal characteristics close to experimental data.Bursting activity of the canonical 4D model at  = 0.06 V,  = 0.031 V,  = 15.2 nS and  = −0.0505 V. The burst duration is 6.0 sec, teh interburst interval is 3.0 sec, the duty cycle is 66.4%, the number of spikes is 35, the frequency is 5.7 Hz.
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pone-0021782-g004: Bursting waveform with temporal characteristics close to experimental data.Bursting activity of the canonical 4D model at  = 0.06 V,  = 0.031 V,  = 15.2 nS and  = −0.0505 V. The burst duration is 6.0 sec, teh interburst interval is 3.0 sec, the duty cycle is 66.4%, the number of spikes is 35, the frequency is 5.7 Hz.

Mentions: Our parameter sweeps of the model were concluded with the following parameters  = 0.031 V,  = 0.06 V. This adjusted model exhibits bursting activity with the burst duration of 4.5 sec, the interburst interval of 3.8 sec, the period 8.3 sec, and the duty cycle around 54.6%; the number of spikes per burst is 26, the spike frequency is 5.59 Hz (Fig. 2D). Leak current parameters are  = 15.7 nS and  = −0.0505 V. We further tuned the model by setting  = 15.2 nS, so that the temporal characteristics of bursting activity fit well to the experimental data (Fig. 4).


Six types of multistability in a neuronal model based on slow calcium current.

Malashchenko T, Shilnikov A, Cymbalyuk G - PLoS ONE (2011)

Bursting waveform with temporal characteristics close to experimental data.Bursting activity of the canonical 4D model at  = 0.06 V,  = 0.031 V,  = 15.2 nS and  = −0.0505 V. The burst duration is 6.0 sec, teh interburst interval is 3.0 sec, the duty cycle is 66.4%, the number of spikes is 35, the frequency is 5.7 Hz.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3140973&req=5

pone-0021782-g004: Bursting waveform with temporal characteristics close to experimental data.Bursting activity of the canonical 4D model at  = 0.06 V,  = 0.031 V,  = 15.2 nS and  = −0.0505 V. The burst duration is 6.0 sec, teh interburst interval is 3.0 sec, the duty cycle is 66.4%, the number of spikes is 35, the frequency is 5.7 Hz.
Mentions: Our parameter sweeps of the model were concluded with the following parameters  = 0.031 V,  = 0.06 V. This adjusted model exhibits bursting activity with the burst duration of 4.5 sec, the interburst interval of 3.8 sec, the period 8.3 sec, and the duty cycle around 54.6%; the number of spikes per burst is 26, the spike frequency is 5.59 Hz (Fig. 2D). Leak current parameters are  = 15.7 nS and  = −0.0505 V. We further tuned the model by setting  = 15.2 nS, so that the temporal characteristics of bursting activity fit well to the experimental data (Fig. 4).

Bottom Line: We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.We described a novel mechanism supporting the bistability of bursting and silence.This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia, United States of America.

ABSTRACT

Background: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/principal findings: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

Show MeSH
Related in: MedlinePlus