Dynamical origin for winner-take-all competition in a biological network of the hippocampal dentate gyrus

We consider a biological network of the hippocampal dentate gyrus (DG). Computational models suggest that the DG would be a preprocessor for pattern separation (i.e., a process transforming a set of similar input patterns into distinct nonoverlapping output patterns) which could facilitate pattern storage and retrieval in the CA3 area of the hippocampus. The main encoding cells in the DG are the granule cells (GCs) which receive the input from the entorhinal cortex (EC) and send their output to the CA3. We note that the activation degree of GCs is very low (∼5%). This sparsity has been thought to enhance the pattern separation. We investigate the dynamical origin for winner-take-all (WTA) competition which leads to sparse activation of the GCs. The whole GCs are grouped into lamellar clusters. In each cluster, there is one inhibitory (I) basket cell (BC) along with excitatory (E) GCs. There are three kinds of external inputs into the GCs: the direct excitatory EC input; the indirect feedforward inhibitory EC input, mediated by the HIPP (hilar perforant path-associated) cells; and the excitatory input from the hilar mossy cells (MCs). The firing activities of the GCs are determined via competition between the external E and I inputs. The E-I conductance ratio R_{E-I}^{(con)}^{*} (given by the time average of the ratio of the external E to I conductances) may represent well the degree of such external E-I input competition. It is thus found that GCs become active when their R_{E-I}^{(con)}^{*} is larger than a threshold R_{th}^{*}, and then the mean firing rates of the active GCs are strongly correlated with R_{E-I}^{(con)}^{*}. In each cluster, the feedback inhibition from the BC may select the winner GCs. GCs with larger R_{E-I}^{(con)}^{*} than the threshold R_{th}^{*} survive, and they become winners; all the other GCs with smaller R_{E-I}^{(con)}^{*} become silent. In this way, WTA competition occurs via competition between the firing activity of the GCs and the feedback inhibition from the BC in each cluster. Finally, we also study the effects of MC death and adult-born immature GCs on the WTA competition.