We study the disynaptic effect of the hilar cells on pattern separation in a spiking neural network of the hippocampal dentate gyrus (DG). The principal granule cells (GCs) in the DG perform pattern separation, transforming similar input patterns into less-similar output patterns. In our DG network, the hilus consists of excitatory mossy cells (MCs) and inhibitory HIPP (hilar perforant path-associated) cells. Here, we consider the disynaptic effects of the MCs and the HIPP cells on the GCs, mediated by the inhibitory basket cells (BCs) in the granular layer; MC →\documentclass[12pt]{minimal}
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\begin{document}$$\rightarrow$$\end{document} BC →\documentclass[12pt]{minimal}
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\begin{document}$$\rightarrow$$\end{document} GC and HIPP →\documentclass[12pt]{minimal}
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\begin{document}$$\rightarrow$$\end{document} BC →\documentclass[12pt]{minimal}
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\begin{document}$$\rightarrow$$\end{document} GC. The MCs provide disynaptic inhibitory input (mediated by the intermediate BCs) to the GCs, which decreases the firing activity of the GCs. On the other hand, the HIPP cells disinhibit the intermediate BCs, which leads to increasing the firing activity of the GCs. In this way, the disynaptic effects of the MCs and the HIPP cells are opposite. We investigate change in the pattern separation efficacy by varying the synaptic strength K(BC,X)\documentclass[12pt]{minimal}
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\begin{document}$$K^\mathrm{(BC, X)}$$\end{document} [from the pre-synaptic X (= MC or HIPP) to the post-synaptic BC]. Thus, sparsity for the firing activity of the GCs is found to improve the efficacy of pattern separation, and hence the disynaptic effects of the MCs and the HIPP cells on the pattern separation become opposite ones. In the combined case when simultaneously changing both K(BC,MC)\documentclass[12pt]{minimal}
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\begin{document}$$K^\mathrm{(BC, MC)}$$\end{document} and K(BC,HIPP)\documentclass[12pt]{minimal}
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\begin{document}$$K^\mathrm{(BC, HIPP)}$$\end{document}, as a result of balance between the two competing disynaptic effects of the MCs and the HIPP cells, the efficacy of pattern separation is found to become the highest at their original default values where the activation degree of the GCs is the lowest. We also note that, while the GCs perform pattern separation, sparsely synchronized rhythm is found to appear in the population of the GCs. Hence, we examine quantitative association between population and individual firing behaviors in the sparsely synchronized rhythm and pattern separation. They are found to be strongly correlated. Consequently, the better the population and individual firing behaviors in the sparsely synchronized rhythm are, the more pattern separation efficacy becomes enhanced.
