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The Journal of Neuroscience, April 22, 2009, 29(16):5218-5233; doi:10.1523/JNEUROSCI.0426-09.2009

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Behavioral/Systems/Cognitive
Phase-Resetting Curves Determine Synchronization, Phase Locking, and Clustering in Networks of Neural Oscillators

Srisairam Achuthan¹ and Carmen C. Canavier^1,2

¹Neuroscience Center of Excellence and ²Department of Ophthalmology, Louisiana State University Health Sciences Center, New Orleans, Louisiana 70112

Correspondence should be addressed to Srisairam Achuthan, Neuroscience Center of Excellence, Louisiana State University Health Sciences Center, 2020 Gravier Street, Suite D, New Orleans, LA 70112. Email: sachut{at}lsuhsc.edu

Networks of model neurons were constructed and their activity was predicted using an iterated map based solely on the phase-resetting curves (PRCs). The predictions were quite accurate provided that the resetting to simultaneous inputs was calculated using the sum of the simultaneously active conductances, obviating the need for weak coupling assumptions. Fully synchronous activity was observed only when the slope of the PRC at a phase of zero, corresponding to spike initiation, was positive. A novel stability criterion was developed and tested for all-to-all networks of identical, identically connected neurons. When the PRC generated using N – 1 simultaneously active inputs becomes too steep, the fully synchronous mode loses stability in a network of N model neurons. Therefore, the stability of synchrony can be lost by increasing the slope of this PRC either by increasing the network size or the strength of the individual synapses. Existence and stability criteria were also developed and tested for the splay mode in which neurons fire sequentially. Finally, N/M synchronous subclusters of M neurons were predicted using the intersection of parameters that supported both between-cluster splay and within-cluster synchrony. Surprisingly, the splay mode between clusters could enforce synchrony on subclusters that were incapable of synchronizing themselves. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured.

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Received Jan. 26, 2009; revised March 17, 2009; accepted March 20, 2009.

Correspondence should be addressed to Srisairam Achuthan, Neuroscience Center of Excellence, Louisiana State University Health Sciences Center, 2020 Gravier Street, Suite D, New Orleans, LA 70112. Email: sachut{at}lsuhsc.edu

This article has been cited by other articles:

				F. H. Sieling, C. C. Canavier, and A. A. Prinz Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition J Neurophysiol, July 1, 2009; 102(1): 69 - 84. [Abstract] [Full Text] [PDF]

				J. Cui, C. C. Canavier, and R. J. Butera Functional Phase Response Curves: A Method for Understanding Synchronization of Adapting Neurons J Neurophysiol, July 1, 2009; 102(1): 387 - 398. [Abstract] [Full Text] [PDF]

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