A neural network model of spontaneous up and down transitions
Spontaneous periodic up and down transitions are considered to be a significant phenomenon that is characteristic of slow-wave sleep. We studied a neural network model of spontaneous up and down transitions based on our former study of a single-neuron model. We expanded the model by using two types of neurons—excitatory and inhibitory neurons—and redefining the connecting function between two neurons instead of assuming a constant connection, so that the model is closer to the in vivo network. Using this model, we studied the relationship between the transitions and network parameters such as size, structure and the ratio of excitatory to inhibitory neurons. We found that the network parameters have little impact on these spontaneous periodic up and down transitions. However, the intrinsic currents were found to play a leading role in the process. Then, we studied the transitions in the presence of stimulation and found that the addition of stimulation did have an effect on the network transitions. Through the observation and analysis of the findings, we have tried to explain the dynamics of up and down transitions and to lay the foundation for future work on the role of these transitions in cortex activity.
KeywordsSpontaneity Up and down transition Ionic channel Chemical synapse Subthreshold activity
This work is supported by the National Natural Science Foundation of China (No. 11232005) and The Ministry of Education Doctoral Foundation (No. 20120074110020).
- 4.Steriade, M., Nuñez, A., Amzica, F.: Intracellular analysis of relations between the slow (1 Hz) neocortical oscillation and other sleep rhythms of the electroencephalogram. J. Neurosci. 13(8), 3266–3283 (1993)Google Scholar
- 14.Wang, Q., Zheng, Y., Ma, J.: Cooperative dynamics in neuronal networks. Chaos Solions Fractals 56(7), 19–27 (2013)Google Scholar
- 21.Dickson, C.T., Magistretti, J., Shalinsky, M.H., Fransén, E., Hasselmo, M.E., Alonso, A.: Properties and role of Ih in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons. J. Neurophysiol. 83(5), 2562–2579 (2000)Google Scholar
- 28.Xu, X., Wang, R.: Neurodynamics of up and down transitions in network model. Abstr. Appl. Anal. 2013, 9 (2013). doi: 10.1155/2013/486178
- 34.Koch, C., Segev, I.: Methods in neuronal modeling: from ions to networks. MIT Press, Cambridge (1998)Google Scholar
- 37.Ermentrout, T.J., Terman, D.H.: Mathematical foundations of neuroscience. Springer, Berlin (2010)Google Scholar