Literature DB >> 18764509

New dynamics in cerebellar Purkinje cells: torus canards.

Mark A Kramer1, Roger D Traub, Nancy J Kopell.   

Abstract

We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that-after a saddle node bifurcation of limit cycles-the full model dynamics temporarily follow a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical applications: torus canards.

Entities:  

Mesh：

Substances：

Year:  2008        PMID： 18764509      PMCID： PMC2662447          DOI： 10.1103/PhysRevLett.101.068103

Source DB:  PubMed          Journal:  Phys Rev Lett        ISSN： 0031-9007            Impact factor:   9.161


  13 in total

Review 1.  Bursts as a unit of neural information: selective communication via resonance.

Authors:  Eugene M Izhikevich; Niraj S Desai; Elisabeth C Walcott; Frank C Hoppensteadt
Journal:  Trends Neurosci       Date:  2003-03       Impact factor: 13.837

2.  Fast rhythmic bursting can be induced in layer 2/3 cortical neurons by enhancing persistent Na+ conductance or by blocking BK channels.

Authors:  Roger D Traub; Eberhard H Buhl; Tengis Gloveli; Miles A Whittington
Journal:  J Neurophysiol       Date:  2003-02       Impact factor: 2.714

3.  A quantitative description of membrane current and its application to conduction and excitation in nerve.

Authors:  A L HODGKIN; A F HUXLEY
Journal:  J Physiol       Date:  1952-08       Impact factor: 5.182

4.  Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe.

Authors:  Andrey Shilnikov; Gennady Cymbalyuk
Journal:  Phys Rev Lett       Date:  2005-01-31       Impact factor: 9.161

5.  Transition to bursting via deterministic chaos.

Authors:  Georgi S Medvedev
Journal:  Phys Rev Lett       Date:  2006-07-27       Impact factor: 9.161

6.  Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model.

Authors:  Jonathan Rubin; Martin Wechselberger
Journal:  Biol Cybern       Date:  2007-04-26       Impact factor: 2.086

7.  A beta2-frequency (20-30 Hz) oscillation in nonsynaptic networks of somatosensory cortex.

Authors:  Anita K Roopun; Steven J Middleton; Mark O Cunningham; Fiona E N LeBeau; Andrea Bibbig; Miles A Whittington; Roger D Traub
Journal:  Proc Natl Acad Sci U S A       Date:  2006-10-09       Impact factor: 11.205

8.  Electrophysiological properties of in vitro Purkinje cell somata in mammalian cerebellar slices.

Authors:  R Llinás; M Sugimori
Journal:  J Physiol       Date:  1980-08       Impact factor: 5.182

9.  Low-threshold potassium channels and a low-threshold calcium channel regulate Ca2+ spike firing in the dendrites of cerebellar Purkinje neurons: a modeling study.

Authors:  T Miyasho; H Takagi; H Suzuki; S Watanabe; M Inoue; Y Kudo; H Miyakawa
Journal:  Brain Res       Date:  2001-02-09       Impact factor: 3.252

10.  Canards for a reduction of the Hodgkin-Huxley equations.

Authors:  Jeff Moehlis
Journal:  J Math Biol       Date:  2005-09-29       Impact factor: 2.164
View more
  13 in total

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

Authors:  Paul Channell; Ibiyinka Fuwape; Alexander B Neiman; Andrey L Shilnikov
Journal:  J Comput Neurosci       Date:  2009-06-20       Impact factor: 1.621

2.  When two wrongs make a right: synchronized neuronal bursting from combined electrical and inhibitory coupling.

Authors:  Reimbay Reimbayev; Kevin Daley; Igor Belykh
Journal:  Philos Trans A Math Phys Eng Sci       Date:  2017-06-28       Impact factor: 4.226

3.  A sequential Monte Carlo approach to estimate biophysical neural models from spikes.

Authors:  Liang Meng; Mark A Kramer; Uri T Eden
Journal:  J Neural Eng       Date:  2011-11-04       Impact factor: 5.379

4.  Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model.

Authors:  Casey O Diekman; Peter J Thomas; Christopher G Wilson
Journal:  J Neurophysiol       Date:  2017-07-19       Impact factor: 2.714

5.  A Signal Processing Analysis of Purkinje Cells in vitro.

Authors:  Ze'ev R Abrams; Ajithkumar Warrier; Dirk Trauner; Xiang Zhang
Journal:  Front Neural Circuits       Date:  2010-05-14       Impact factor: 3.492

6.  Dynamical systems analysis of spike-adding mechanisms in transient bursts.

Authors:  Jakub Nowacki; Hinke M Osinga; Krasimira Tsaneva-Atanasova
Journal:  J Math Neurosci       Date:  2012-04-24       Impact factor: 1.300

7.  Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model.

Authors:  Roberto Barrio; Andrey Shilnikov
Journal:  J Math Neurosci       Date:  2011-07-11       Impact factor: 1.300

8.  A showcase of torus canards in neuronal bursters.

Authors:  John Burke; Mathieu Desroches; Anna M Barry; Tasso J Kaper; Mark A Kramer
Journal:  J Math Neurosci       Date:  2012-02-21       Impact factor: 1.300

9.  Signals and circuits in the purkinje neuron.

Authors:  Zéev R Abrams; Xiang Zhang
Journal:  Front Neural Circuits       Date:  2011-09-26       Impact factor: 3.492

10.  Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells.

Authors:  Alexander B Neiman; Kai Dierkes; Benjamin Lindner; Lijuan Han; Andrey L Shilnikov
Journal:  J Math Neurosci       Date:  2011-10-03       Impact factor: 1.300
View more

北京卡尤迪生物科技股份有限公司 © 2022-2023.