Abstract
Recent evidence suggests that Golgi cells in the cerebellar granular layer are densely connected to each other with massive gap junctions. Here, we propose that the massive gap junctions between the Golgi cells contribute to the representational complexity of the granular layer of the cerebellum by inducing chaotic dynamics. We construct a model of cerebellar granular layer with diffusion coupling through gap junctions between the Golgi cells, and evaluate the representational capability of the network with the reservoir computing framework. First, we show that the chaotic dynamics induced by diffusion coupling results in complex output patterns containing a wide range of frequency components. Second, the long non-recursive time series of the reservoir represents the passage of time from an external input. These properties of the reservoir enable mapping different spatial inputs into different temporal patterns.
Highlights
Broad distribution of the interspike interval caused by gap junctions First, we show that introducing diffusion coupling causes chaotic dynamics, which in turn results in a broad distribution of interspike interval (ISI) of a neuron in the model
We investigated the computational role of the gap junction between Golgi cells in the cerebellar granular layer
We showed that introducing gap junctions in the model induces chaotic dynamics that enables the reservoir to output complex patterns containing a wide range of frequency components (Figs. 2-5)
Summary
Recent experimental studies have revealed that neighboring Golgi cells in the granular layer of the cerebellar cortex are densely interconnected with gap junctions that allow direct diffusion of ions between neuronal intracellular spaces (Dugue et al (2009); Vervaeke et al (2010)). Vervaeke et al (2010) reported that more than 80 % of neighboring neuron pairs are interconnected with gap junctions, and that each Golgi cell is connected to approximately 10 other Golgi cells via gap junctions. Vast amount of evidence supports the fact that the cerebellum acquires the desired map to return a specific spatiotemporal pattern to a specific input To explain this computation of the cerebellum, Buonomano & Mauk (1994) proposed a model of the granular layer consisting of sparse reciprocally connected granule cells and Golgi cells that are capable of representing the passage of time from the onset of an external sensory stimulus. In their model, mossy fiber excitation conveying the information of external tone stimulus elicits activity of the granule cells and the Golgi cells, with different sub-populations activated at different times. Considering the facts that chaotic activity is related to the performance of the reservoir (Jaeger (2001); Bertschinger & Natschlager (2004); Natschlager et al (2005); Sussillo & Abbott (2009); Yildiz et al (2012); Laje & Buonomano (2013)) and that gap junction often induces chaotic activity (Yamada & Kuramoto (1976); Fujii & Tsuda (2004); Tsuda et al (2004); Schweighofer et al (2004); Katori et al (2010); Tokuda et al (2010); Tadokoro et al (2011); Tokuda et al (2019)), it is necessary to elucidate how the gap junctions affect the computational performance of the granular layer as the reservoir, especially in terms of the effect of chaotic dynamics it may produce
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