Limits...
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

Transition from tonic spiking into bursting and the evolution of the bursting waveforms.The increase of the half-inactivation voltage of the slow calcium current,  shifts  towards more hyperpolarized values of  changing the activity from tonic spiking (A) to bursting (B–D). (A) For  = 0.047 V the model exhibits a periodic tonic spiking activity. (B–D) The increase of  up to 0.048 V shifts  towards the hyperpolarized value of  thus changing the activity from tonic spiking to bursting. (C) The increase of  to 0.056 V expands the interburst interval. (D)  = 0.06 V brings the value of the interburst interval close to the targeted value. The leak current parameters are the same as in Fig. 1.  was 0.031 V for A and D. Panels (B)–(D) have the same time scale.
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pone-0021782-g002: Transition from tonic spiking into bursting and the evolution of the bursting waveforms.The increase of the half-inactivation voltage of the slow calcium current, shifts towards more hyperpolarized values of changing the activity from tonic spiking (A) to bursting (B–D). (A) For  = 0.047 V the model exhibits a periodic tonic spiking activity. (B–D) The increase of up to 0.048 V shifts towards the hyperpolarized value of thus changing the activity from tonic spiking to bursting. (C) The increase of to 0.056 V expands the interburst interval. (D)  = 0.06 V brings the value of the interburst interval close to the targeted value. The leak current parameters are the same as in Fig. 1. was 0.031 V for A and D. Panels (B)–(D) have the same time scale.

Mentions: Third, to adjust the interburst interval, we swept the half-inactivation voltage of , . The increase of prolongs the interburst interval of the bursting activity. The interburst interval grows monotonically from 0.53 sec to 3.77 sec as is swept from 0.048 V to 0.06 V (Figs. 2 and 3). The graph also shows the effect of variation of on the spike frequency within a burst (Fig. 3).


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

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

Transition from tonic spiking into bursting and the evolution of the bursting waveforms.The increase of the half-inactivation voltage of the slow calcium current,  shifts  towards more hyperpolarized values of  changing the activity from tonic spiking (A) to bursting (B–D). (A) For  = 0.047 V the model exhibits a periodic tonic spiking activity. (B–D) The increase of  up to 0.048 V shifts  towards the hyperpolarized value of  thus changing the activity from tonic spiking to bursting. (C) The increase of  to 0.056 V expands the interburst interval. (D)  = 0.06 V brings the value of the interburst interval close to the targeted value. The leak current parameters are the same as in Fig. 1.  was 0.031 V for A and D. Panels (B)–(D) have the same time scale.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0021782-g002: Transition from tonic spiking into bursting and the evolution of the bursting waveforms.The increase of the half-inactivation voltage of the slow calcium current, shifts towards more hyperpolarized values of changing the activity from tonic spiking (A) to bursting (B–D). (A) For  = 0.047 V the model exhibits a periodic tonic spiking activity. (B–D) The increase of up to 0.048 V shifts towards the hyperpolarized value of thus changing the activity from tonic spiking to bursting. (C) The increase of to 0.056 V expands the interburst interval. (D)  = 0.06 V brings the value of the interburst interval close to the targeted value. The leak current parameters are the same as in Fig. 1. was 0.031 V for A and D. Panels (B)–(D) have the same time scale.
Mentions: Third, to adjust the interburst interval, we swept the half-inactivation voltage of , . The increase of prolongs the interburst interval of the bursting activity. The interburst interval grows monotonically from 0.53 sec to 3.77 sec as is swept from 0.048 V to 0.06 V (Figs. 2 and 3). The graph also shows the effect of variation of on the spike frequency within a burst (Fig. 3).

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