Wrestling Model of the Repertoire of Activity Propagation Modes in Quadruple Neural Networks

The spontaneous activity of engineered quadruple cultured neural networks (of four-coupled sub-networks) exhibits a repertoire of different types of mutual synchronization events. Each event corresponds to a specific activity propagation mode (APM) defined by the order of activity propagation between the sub-networks. We statistically characterized the frequency of spontaneous appearance of the different types of APMs. The relative frequencies of the APMs were then examined for their power-law properties. We found that the frequencies of appearance of the leading (most frequent) APMs have close to constant algebraic ratio reminiscent of Zipf's scaling of words. We show that the observations are consistent with a simplified "wrestling" model. This model represents an extension of the "boxing arena" model which was previously proposed to describe the ratio between the two activity modes in two coupled sub-networks. The additional new element in the "wrestling" model presented here is that the firing within each network is modeled by a time interval generator with similar intra-network Lévy distribution. We modeled the different burst-initiation zones' interaction by competition between the stochastic generators with Gaussian inter-network variability. Estimation of the model parameters revealed similarity across different cultures while the inter-burst-interval of the cultures was similar across different APMs as numerical simulation of the model predicts.