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Volga Neuroscience School 2016 Astroglial control of rhythm genesis in the brain
Studying on-off Firing Patterns in the Network of Coupled Hodgkin-Huxley Neurons in the Presence of Noise
P.M. Esir*, A.Yu. Simonov, S.Yu. Gordleeva
Lobachevsky State University, Nizhny Novgorod, Russia. * Presenting e-mail: esir@neuro.nnov.ru
Abstract. Bistable dynamics is observed in various nervous systems [1], and it's considered as one of ways of organization of working memory [2]. Dynamics of single or two unidirectional coupled neurons were studied in previous works [3-4]. In our work we study dynamics of ensemble of recurrently coupled bistable Hodgkin-Huxley neurons, in the presence of noise and coupling delays. The neurons were distributed in a volume and had delays proportional to distance between them. External noise to each on neuron can evoke transitions of individual neurons from oscillatory state and steady state so named on-off firing pattern. Interesting result of our work is that such kind of on-off firing patterns is observed also in mean firing rate of whole network, Fig. 1. We found, that durations of staying in the different stable states for big time scales have exponential statistics, while for small times scales the statistics obey power law function. When the noise was switched off, the system moved to steady state in which partially synchronization between part of neurons is observed. In the case of absence of connection delays this phenomena cannot be observed, mean firing rate of whole network does not demonstrate 2 distinct states. By using Phase Response Curve generalized for 2 stimuli we explain this effect. We conclude that delays play important role in neural systems where on-off firing patterns is observed.
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Fig.1. Firing rate for different noise intensities. From up to down, noise intensity increase.
Acknowledgements
This work was supported by the Russian Science Foundation (grants 16-12-00077, 14-11-00693). References
1. Huaguang G., Zhiguo, Z., Bing, J., & Shenggen, C. (2015). Dynamics of On-Off Neural Firing Patterns and Stochastic Effects near a Sub-Critical Hopf Bifurcation. Plos One, 10(4), e0121028. http://doi.org/10.1371/journal.pone.0121028
2. Durstewite, D., Seamans, J. K., & Sejnowski, T. J. (2000). Neurocomputational models of working memory. Nature Neuroscience, 3 Suppl(november), 1184-1191. http://doi.org/10.1038/81460
3. Kazantsev, V. B., & Asatryan, S. Y. (2011). Bistability induces episodic spike communication by inhibitory neurons in neuronal networks. Physical Review E Statistical Nonlinear and Soft Matter Physics, 84(3-1), 031913. http://doi.org/10.1103/PhysRevE.84.031913
4. Simonov, A. Y., Gordleeva, S. Y., Pisarchik, A. N., & Kazantsev, V. B. (2014). Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators. JETP Letters, 98(10), 632-637. http://doi.org/10.1134/S0021364013230136
98 Opera Med Physiol 2016 Vol. 2 (S1)
