Low dimensional model of bursting neurons
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A computationally efficient, biophysically-based model of neuronal behavior is presented; it incorporates ion channel dynamics in its two fast ion channels while preserving simplicity by representing only one slow ion current. The model equations are shown to provide a wide array of physiological dynamics in terms of spiking patterns, bursting, subthreshold oscillations, and chaotic firing. Despite its simplicity, the model is capable of simulating an extensive range of spiking patterns. Several common neuronal behaviors observed in vivo are demonstrated by varying model parameters. These behaviors are classified into dynamical classes using phase diagrams whose boundaries in parameter space prove to be accurately delineated by linear stability analysis. This simple model is suitable for use in large scale simulations involving neural field theory or neuronal networks.
KeywordsBursting neuron Linear stability analysis Ion channel models
This work was supported by the Australian Research Council and the Westmead Millennium Institute.
Conflict of interest
The authors declare that they have no conflict of interest.
- Alligood, K., Sauer, T., Yorke, J. (1997). Chaos, an introduction to dynamical systems. New York: Springer.Google Scholar
- Chase, S.M., & Young, E.D. (2007). First-spike latency information in single neurons increases when referenced to population onset. Proceedings of the National Academy of Sciences of the United States of America, 104, 762–773.Google Scholar
- Dickenstein, A., & Emiris, I. (2005). Solving polynomial equations: foundations, algorithms, and applications (Vol. 14). Berlin: Springer.Google Scholar
- Dowling, J. (2001). Neurons and networks: an introduction to behavioral neuroscience. Cambridge: HUP.Google Scholar
- Guckenheimer, J., Tien, J., Willms, A. (2005). Bifurcations in the fast dynamics of neurons: implications for bursting. In Bursting: the genesis of rhythm in the nervous system (pp. 89–122). World Scientific.Google Scholar
- Hindmarsh, J., & Rose, R. (1984). A model of neuronal bursting using three coupled first order differential equations. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 221, 87–102.Google Scholar
- Izhikevich, E. (2007). Dynamical systems in neuroscience: the geometry of excitability and bursting. Cambridge: MIT.Google Scholar
- McCormick, D. (2004). Membrane properties and neurotransmitter actions. In The synaptic organization of the brain. Oxford Scholarship Online Monographs (pp. 39–79).Google Scholar
- Rinzel, J. (1986). A formal classification of bursting mechanisms in excitable systems. In Proceedings of the international congress of mathematicians (Vol. 1, pp. 1578–1593).Google Scholar
- Rinzel, J., Ermentrout, G. (1998). Analysis of neural excitability and oscillations. In Methods in neuronal modeling (pp. 251–292). Cambridge: MIT.Google Scholar
- Rose, R., & Hindmarsh, J. (1989).The assembly of ionic currents in a thalamic neuron i. The three-dimensional model. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237, 267–288.Google Scholar
- Sherman, A. (1996). Contributions of modeling to understanding stimulus-secretion coupling in pancreatic beta-cells. American Journal of Physiology, Endocrinology and Metabolism, 271, E362–E372.Google Scholar
- Timofeev, I., Grenier, F., Steriade, M. (1998). Spike-wave complexes and fast components of cortically generated seizures. IV. Paroxysmal fast runs in cortical and thalamic neurons. Journal of Neurophysiology, 80, 1439–1455.Google Scholar
- Wilson, H. (1999b). Spikes, decisions, and actions: the dynamical foundations of neuroscience. New York: Oxford University Press.Google Scholar