In silico study on structure and dynamics in bursting neuronal networks

In vitro cell cultures have been widely used as a model system for studying neuronal development and electroresponsiveness in the absence of in vivo regulation. These networks are characterized by population bursts that vary largely in both frequency and shape (Wagenaar et al., BMC Neurosci. 2000). In this work we study the interplay of structure and activity in simulated spontaneously bursting networks. The computational approach is useful due to the difficulty of gaining enough control on the structure in in vitro experiments, although promising attempts are being made in cultured neuronal networks (Wheeler, Proc. IEEE 2010). Recently, the effect of network structure on activity has been analyzed through, e.g., the degree distribution width (Roxin, Front. Comp. Neurosci. 2011) and occurrence of second-order connections (Zhao et al. 2011, Front. Comp. Neurosci. 2011). In the present work we apply a set of graph measures to a wide set of different networks in order to determine which of the structural measures are relevant in the prediction of the bursting network activity. The network activity is quantified using standard measures such as number of bursts and burst duration.
We use two neuron models that are applicable to small (N=100) spontaneously bursting networks, namely, an integrate-and-fire model with short-term plasticity (Tsodyks et al., J. Neurosci. 2000) and a more detailed point-neuron model with four ionic and three synaptic currents (Golomb et al., J. Neurophysiol. 2006). We show that when the in-degree is sharp (binomial), the network activity is best predicted by using the clustering coefficient of the underlying graph. By contrast, when a broad in-degree is used (power-law), the maximum eigenvalue of the connectivity matrix becomes dominant in predicting the network activity. The results are consistent across the two neuron models. In our work the neurons are identical by their features, and no input is applied to the network, and hence all statistical difference between the compared networks is caused by the network structure and the network structure only.
The obtained results shed light on the relevance of different aspects of structure. In in vivo applications the full connectome is rarely accessible, but estimates of certain structural measures may be assessed indirectly (Vlachos et al., PLoS Comp. Biol. 2012). Extracting the structure-function relationship in neuronal networks may have implication on both the way experiments are conducted and on how biologically inspired artificial intelligence will be designed in the future.