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Diffusive Coupling and Network Periodicity: A Computational Study

Eun-Hyoung Park ^*, Zhouyan Feng  and Dominique M. Durand ^*

^* Neural Engineering Center, Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio; and Department of Biomedical Engineering, Zhejiang University, Hangzhou, China

Correspondence: Address reprint requests to Dr. Dominique M. Durand, Room 112, Wickenden Building, Department of Biomedical Engineering, Neural Engineering Center, Case Western Reserve University, Cleveland, OH 44106. Tel.: 216-368-3974; Fax: 216-368-4872; E-mail: dxd6{at}case.edu.

Diffusive coupling (nearest-neighbor coupling) is the most common type of coupling present in many systems. Previous experimental and theoretical studies have shown that potassium lateral diffusion coupling (i.e., diffusive coupling) can be responsible for synchronization of neuronal activity. Recent in vivo experiments carried out with anesthetized rat hippocampus suggested that the extracellular potassium could play an important role in the generation of a novel type of epileptiform nonsynaptic activity. Yet, the role of potassium in the generation of seizures remains controversial. We tested the hypothesis that potassium lateral diffusion coupling is responsible for the coupling mechanisms for network periodicity in a nonsynaptic model of epilepsy in vivo using a CA1 pyramidal neuron network model The simulation results show that 1), potassium lateral diffusion coupling is crucial for establishing epileptiform activity similar to that generated experimentally; and 2), there exists a scaling relation between the critical coupling strength and the number of cells in the network. The results not only agree with the theoretical prediction, but strongly suggest that potassium lateral diffusion coupling, a physiological realization of the concept of diffusive coupling, can play an important role in entraining periodicity in a nonsynaptic neural network.