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

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Abstract

Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent, and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped windows.

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Notes

  1. The stable periodic orbit corresponds to tonic spiking.

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Acknowledgements

The authors thank G. Cymbalyuk and R. Clewley for valuable discussions. We are grateful to anonymous reviewers for inspiring critique and useful suggestions. P.C. was supported by a fellowship through the GSU Brains and Behavior program; A.L.S. was supported by the GSU Brains and Behavior program and by the RFFI grant No 050100558. A.N. was supported in part by the Biomimetic Nanoscience and Nanotechnology program of Ohio University. I.F. was supported by the Faculty for the Future Fellowship awarded by the Schlumberger Foundation.

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  1. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Paul Channell & Andrey L. Shilnikov

  2. Department of Physics and Astronomy, Ohio University, Athens, OH, 45701, USA

    Ibiyinka Fuwape & Alexander B. Neiman

  3. Department of Physics, Federal University, of Technology, Akure, PMB 704, Nigeria

    Ibiyinka Fuwape

  4. The Neuroscience Institute, Georgia State University, Atlanta, GA, 30303, USA

    Andrey L. Shilnikov

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  1. Paul Channell
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Channell, P., Fuwape, I., Neiman, A.B. et al. Variability of bursting patterns in a neuron model in the presence of noise. J Comput Neurosci 27, 527–542 (2009). https://doi.org/10.1007/s10827-009-0167-1

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