Table 1.
Parameters of the network model.
Fig 1.
Cluster events and synchronization events in the modular network.
The model neural network has 5 highly connected cell clusters (left). Each of these is capable of producing population bursts of activity or “cluster events” (CE), as seen in the raster plots (right), color-coded to indicate the cluster that the cells are part of. The bottom black curve is the activity averaged 〈a〉 over all 250 cells in the population. When overlapping events occur in 3 or more clusters, 〈a〉 is above the threshold for what we refer to as a synchronization event (illustrated with gray shading) A: Without interconnections among the clusters (intraCC = 100%, interCC = 0%). B: Interconnections among the clusters, though sparse, can synchronize the cluster events (intraCC = 100%, interCC = 0.1%). We have sped up the synaptic efficacy variable to decrease the simulation time scale for producing synchronized events from hours to seconds.
Fig 2.
Synchronization events and miniature synchronization events in the modular network.
The activity time courses (the variable a) for 3 model neurons selected randomly from each of the 5 clusters. Most cells participate in some, but not all, of the synchronization events. A red X highlights an instance in which a cell did not participate, and an orange circle highlights an instance in which a cell did participate, but other cells in its cluster did not. The bottom panel shows the average activity across the network, with SEs indicated by gray bars. Arrows in the bottom panel highlight a few (but not all) instances of mini-SEs, where one cluster (light orange arrow) or two clusters (dark orange arrow) produced bursts of activity. IntraCC = 100%, interCC = 0.4%.
Fig 3.
Network connectivity parameters determines whether there are leader cells.
A: Activity time courses of 15 neurons selected from all 5 clusters during two SEs (left, SE01 and SE02). The left table shows the temporal order of firing of the 15 neurons in 8 SEs; light shading indicates that the cell fired early in an SE. The right table is a reorganization of the left table so that cells that typically fire early are placed in the top rows. The scatter plot indicates spike timing with those cells spiking early in the SEs placed on the bottom. There is a strong correlation (R = 0.84), indicating the presence of leader cells. The data points are color-coded according to the cluster that the corresponding neurons are part of. IntraCC = 55%, interCC = 0.6%. B: With a different value of the intracluster coupling parameter there is much less consistency in the temporal order of spiking during SEs (R = 0.5). IntraCC = 75%, interCC = 0.6%.
Fig 4.
Changes in coupling parameters and cell sampling can alter the consistency of temporal recruitment order.
Each element of the heat map corresponds to a specific choice of the intraCC and interCC parameters. The element value is the average of the temporal order correlation coefficient (R) for six instances of a network. Light colors indicate high R (see scale bar). A: Each panel corresponds to a different sampling of 15 cells, chosen randomly from the network. The last heat map is the average of the 5 grids of simulations. B: In this case, in each panel all 15 cells are chosen from a single cluster. The last panel is the mean of these.
Fig 5.
The number of cluster events and the degree of synchronization increases with an increase in the intercluster coupling.
A: Histograms showing the number of events in which 1, 2, …, 5 clusters fired together during simulations with 40 s duration. The interCC is increased moving from top to bottom. B: Average activity time courses of the 5 clusters during 5 s of simulation time, corresponding to the histograms with tan shading in the previous panel. The number of CEs is shown on the right. C: (left) Mean number of CEs, along with standard deviation, for the range of interCC values explored in the histograms and over simulations with 40 s duration. (right) The mean fraction of synchronization events (events with 3 or more clusters active) in which all 5 clusters are active, NCE5/NSE, along with standard deviation. IntraCC = 60%.
Fig 6.
Increasing intracluster coupling has a weak effect on the number of cluster events, and weakly decreases cluster synchronization during SEs.
A: Histograms showing the number of events in which 1, 2, …, 5 clusters fire together during simulations with 40 s duration. The intraCC is increased moving from top to bottom. B: Average activity time courses of the 5 clusters during 5 s of simulation time, corresponding to the histograms with tan shading in the previous panel. C: (left) Mean number of CEs, along with standard deviation, for the range of intraCC values explored in the histograms. (right) The mean fraction of SEs in which all five clusters participate, NCE5/NSE, and standard deviation. InterCC = 0.2%.