(A) Rasterplot of excitatory (1–700) and inhibitory (701–900) neurons recorded in the simulation experiment. (B) Rows are sorted such that neurons with similar rate modulations appear together. Evidently, a subgroup of neurons fires action-potentials in a correlated manner during certain epochs in time (short black lines near bottom of the frame). (C) Schematic depiction of the underlying network from which neural activity was sampled. (D) The same network reorganized graphically using a force vector algorithm (cf. Methods) to reveal its modular structure. Note that in this Gedankenexperiment the big subnetwork controls the arm movement.

Example of a toy-network illustrating that the degree to which any given metric of neuron embeddedness predicts the neurons' impact on the population response may depend on single neuron properties. The small numbers next to each node indicate the corresponding k-shell-out index. (A,B) Neurons exhibited regular firing behavior. (A) A sufficiently strong input activating neuron 5 will yield propagation of activity to neurons 7–14. (B) If the same stimulus arrives in neuron 1, activity will only spread to neurons 2–4 and 6. In this case, the out-degree correctly predicts that the impact of neuron 5 is bigger than that of neuron 1. (C) Neurons exhibited bursting behavior. As previously, neuron 1 will activate neurons 2–4 and 6. However, the bursting response of these neurons may be sufficient to activate their post-synaptic targets as well, leading to spreading of activity over the entire network. Here, the impact of neuron 1 is clearly larger than that of neuron 5. This effect is not grasped by the widely used out-degree measure. However, higher-order network metrics, like the k-shell-out index, correctly assign a higher value to neuron 1, as compared to neuron 5. (D) Total network response in the three cases depicted in panels A–C. Note the higher impact of neuron 1 under some conditions (curve C), compared to that of neuron 5 (curve A).

(A) Network response (PSTH) for identical stimulation of 30 different subpopulations of 250 neurons each (thin blue lines) in one example network. Observe that peak, onset, and rise times of responses of each subpopulation differ greatly. The thick blue lines depict the smallest and the biggest response, respectively. (B) Rasterplot of the network when the subpopulation of neurons with the lowest degree of embeddedness was stimulated. Light blue dots denote spikes from all neurons, dark blue dots those from stimulated ones. Inset: Magnified cut-out around 600 ms for neurons 4000–6000. Activation of weakly embedded neurons does not spread much in the network. (C) As in (B), but now the subpopulation with the highest average degree of embeddedness was stimulated, leading to a much bigger impact on the network activity. Activation of these strongly embedded neurons lead to a spreading of activity throughout the network. Moreover, feedforward inhibition suppressed the network activity entirely. (D) Response of all stimulated subpopulations (250 neurons each) and all networks pooled together (pale blue dots). On average, there was a positive correlation between out-degree and total network activity (  = 0.84). Two networks with small-world properties are highlighted (dark blue, light amber dots). The five random networks (filled gray triangles) did not exhibit high out-degree variance, and therefore the variance of their population response was small compared to that of the small-world networks. (E) Average correlation coefficient (sorted) between population response and degree of embeddedness as measured by out-degree and k-shell-out index. Both metrics had a high predictive power, with out-degree maintaining high prediction rates for most of the graphs. However, the predictive power of topology measures depended also on additional criteria (cf. main text and Figure 3).