  We investigate population and individual firing behaviors in sparsely
synchronized rhythms (SSRs) in a spiking neural network of the hippocampal
dentate gyrus (DG). The main encoding granule cells (GCs) are grouped into
lamellar 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-all
competition, leading to sparse activation of the GCs, occurs in each GC
cluster. Such sparsity has been thought to enhance pattern separation performed
in the DG. During the winner-take-all competition, SSRs are found to appear in
each population of the GCs and the BCs through interaction of excitation of the
GCs with inhibition of the BCs. Sparsely synchronized spiking stripes appear
successively with the population frequency $f_p~ (= 13$ Hz) in the raster plots
of spikes. We also note that excitatory hilar mossy cells (MCs) control the
firing activity of the GC-BC loop by providing excitation to both the GCs and
the 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 quantitatively
characterized in terms of the synchronization measures. In addition, we
investigate individual firing activity of GCs, BCs, and MCs in the SSRs.
Individual GCs exhibit random spike skipping, leading to a multi-peaked
inter-spike-interval histogram, which is well characterized in terms of the
random phase-locking degree. On the other hand, both BCs and MCs show
"intrastripe" burstings within stripes, together with "interstripe" random
spike skipping. MC loss may occur during epileptogenesis. With decreasing the
fraction of the MCs, changes in the population and individual firings in the
SSRs are also studied. Finally, quantitative association between the
population/individual firing behaviors in the SSRs and the winner-take-all
competition is discussed.
