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Full system bifurcation analysis of endocrine bursting models
Copyright policy )Elsevier BVFull system bifurcation analysis of endocrine bursting models
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. For example, in insulin-secreting pancreatic β-cells, plateau bursting is characterized by well-defined spikes during the depolarized phase whereas in pituitary cells, bursting features fast, irregular, small amplitude spikes. The latter has been termed “pseudo-plateau bursting” because the spikes are transients around a depolarized steady state rather than stable oscillations in the fast subsystem. In this study we systematically investigate the bursting patterns found in endocrine cell models. We show that this class of voltage and calcium gated conductance based models can be reduced to the polynomial model of Hindmarsh and Rose (25). This reduction preserves the main properties of the biophysical class of models that we consider and allows for detailed bifurcation analysis of the full fast-slow system. Our analysis does not require decomposition of the full system into fast and slow subsystems and reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.
- University of Konstanz Germany
- University of Bristol United Kingdom
- National Institutes of Health United States
Microsoft Academic Graph classification: Bursting Mathematics Control theory Homoclinic bifurcation Biological applications of bifurcation theory Hopf bifurcation symbols.namesake symbols Bursting oscillations Bifurcation analysis Theta model Bifurcation theory Biological system
Applied Mathematics, General Agricultural and Biological Sciences, General Immunology and Microbiology, General Biochemistry, Genetics and Molecular Biology, Modeling and Simulation, General Medicine, Statistics and Probability, Animals, Biophysical Phenomena, Electrophysiological Phenomena, Endocrine Cells, Humans, Models, Neurological, Models, Theoretical, Neurons, Article, Excitable systems, Bifurcation theory, Bursting oscillations, Spike Adding, bifurcation theory, spike adding, excitable systems, endocrine cells, bursting oscillations
Applied Mathematics, General Agricultural and Biological Sciences, General Immunology and Microbiology, General Biochemistry, Genetics and Molecular Biology, Modeling and Simulation, General Medicine, Statistics and Probability, Animals, Biophysical Phenomena, Electrophysiological Phenomena, Endocrine Cells, Humans, Models, Neurological, Models, Theoretical, Neurons, Article, Excitable systems, Bifurcation theory, Bursting oscillations, Spike Adding, bifurcation theory, spike adding, excitable systems, endocrine cells, bursting oscillations
Microsoft Academic Graph classification: Bursting Mathematics Control theory Homoclinic bifurcation Biological applications of bifurcation theory Hopf bifurcation symbols.namesake symbols Bursting oscillations Bifurcation analysis Theta model Bifurcation theory Biological system
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[5] Beauvois, M. C., Merezak, C., Jonas, J.-C., Ravier, M. A., Henquin, J.-C. & cells are controlled by the membrane potential and the SERCA3 Ca2+-ATPase r c of the endoplasmic reticulum. Am J Physiol Cell Physiol, 290 (6), C1503-1511. s
[6] Belan, P., Kostyuk, P., Snitsarev, V. & Tepikin, A. (1993). Calcium clamp in isolated neurones of the snail Helix pomatia. The Journal of Physiology, 462 (1), 47-58. u [OpenAIRE]
[7] Belykh, V., Belykh, I., Colding-Jørgensen, M. & Mosekilde, nE.(2000). Homoclinic bifurcations leading to the emergence of bursting aoscillations in cell models. The European Physical Journal E, 3 (3), 205-219.
[8] Bergsten, P. (2002). Role of Oscillations in MembmranePotential, Cytoplasmic Ca2+, and Metabolism for Plasma Insulin Oscillations. Diabetes, 51 (90001), S171-176. [OpenAIRE]
[9] Berlin, J., Bassani, J. & Bers, D. (199e4). Intrinsic cytosolic calcium buffering properties of single rat cardiac myotcytes. Biophysical Journal, 67 (4), 1775- 1787. p
[10] Bertram, R., Butte, M., eKiemel, T. & Sherman, A. (1995). Topological and (3), 413-39. c phenomenological classification of bursting oscillations. Bull Math Biol, 57 c
[11] Bertram, R., Previte, J., Sherman, A., Kinard, T. & Satin, L. (2000). The phantom bAurster model for pancreatic beta-cells. Biophys J, 79 (6), 2880-92. [OpenAIRE]
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- UK Research and Innovation (UKRI)
- EP/C544048/1
- EPSRC
- University of Konstanz Germany
- University of Bristol United Kingdom
- National Institutes of Health United States
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. For example, in insulin-secreting pancreatic β-cells, plateau bursting is characterized by well-defined spikes during the depolarized phase whereas in pituitary cells, bursting features fast, irregular, small amplitude spikes. The latter has been termed “pseudo-plateau bursting” because the spikes are transients around a depolarized steady state rather than stable oscillations in the fast subsystem. In this study we systematically investigate the bursting patterns found in endocrine cell models. We show that this class of voltage and calcium gated conductance based models can be reduced to the polynomial model of Hindmarsh and Rose (25). This reduction preserves the main properties of the biophysical class of models that we consider and allows for detailed bifurcation analysis of the full fast-slow system. Our analysis does not require decomposition of the full system into fast and slow subsystems and reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.