ArticleJournal of theoretical biology2010
Full system bifurcation analysis of endocrine bursting models.
Article in Journal of theoretical biology, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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16 citing papers in PubMed, 91 citations in OpenAlex.
- Slow negative feedback enhances robustness of square-wave bursting.Journal of computational neuroscience · 2023Article
- Classification of bursting patterns: A tale of two ducks.PLoS computational biology · 2022Review
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- Canard-induced complex oscillations in an excitatory network.Journal of mathematical biology · 2020Article
- Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study.Journal of computational neuroscience · 2020Article
- Chaotic Image Encryption Using Hopfield and Hindmarsh-Rose Neurons Implemented on FPGA.Sensors (Basel, Switzerland) · 2020Article
- Bifurcation analysis and diverse firing activities of a modified excitable neuron model.Cognitive neurodynamics · 2019Article
- When two wrongs make a right: synchronized neuronal bursting from combined electrical and inhibitory coupling.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2017Article
- From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability.Journal of computational neuroscience · 2016Article
- A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells.Journal of computational neuroscience · 2014Article
- CROSS-CURRENTS BETWEEN BIOLOGY AND MATHEMATICS: THE CODIMENSION OF PSEUDO-PLATEAU BURSTING.Discrete and continuous dynamical systems. Series A · 2012Article
- Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance.Neurological sciences : official journal of the Italian Neurological Society and of the Italian Society of Clinical Neurophysiology · 2012Article
- Dynamical systems analysis of spike-adding mechanisms in transient bursts.Journal of mathematical neuroscience · 2012Article
- A showcase of torus canards in neuronal bursters.Journal of mathematical neuroscience · 2012Article
- The dynamics underlying pseudo-plateau bursting in a pituitary cell model.Journal of mathematical neuroscience · 2011Article
- Dynamical systems theory in physiology.The Journal of general physiology · 2011Article
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Authors and funding
4 authors at 4 institutions in 3 countries.
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Abstract
Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.
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