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We investigate population and individual firing behaviors in sparselysynchronized rhythms (SSRs) in a spiking neural network of the hippocampaldentate gyrus (DG). The main encoding granule cells (GCs) are grouped intolamellar clusters. In each GC cluster, there is one inhibitory (I) basket cell(BC) along with excitatory (E) GCs, and they form the E-I loop. Winner-take-allcompetition, leading to sparse activation of the GCs, occurs in each GCcluster. Such sparsity has been thought to enhance pattern separation performedin the DG. During the winner-take-all competition, SSRs are found to appear ineach population of the GCs and the BCs through interaction of excitation of theGCs with inhibition of the BCs. Sparsely synchronized spiking stripes appearsuccessively with the population frequency $f_p~ (= 13$ Hz) in the raster plotsof spikes. We also note that excitatory hilar mossy cells (MCs) control thefiring activity of the GC-BC loop by providing excitation to both the GCs andthe BCs. SSR also appears in the population of MCs via interaction with the GCs(i.e., GC-MC loop). Population behaviors in the SSRs are quantitativelycharacterized in terms of the synchronization measures. In addition, weinvestigate individual firing activity of GCs, BCs, and MCs in the SSRs.Individual GCs exhibit random spike skipping, leading to a multi-peakedinter-spike-interval histogram, which is well characterized in terms of therandom phase-locking degree. On the other hand, both BCs and MCs show"intrastripe" burstings within stripes, together with "interstripe" randomspike skipping. MC loss may occur during epileptogenesis. With decreasing thefraction of the MCs, changes in the population and individual firings in theSSRs are also studied. Finally, quantitative association between thepopulation/individual firing behaviors in the SSRs and the winner-take-allcompetition is discussed.

Population and Individual Firing Behaviors in Sparsely Synchronized Rhythms in The Hippocampal Dentate Gyrus