Significance of graph theoretic measures in predicting neuronal network activity

One of the most prominent patterns of activity observed in developing cortical neuronal networks in vitro is network-wide spontaneous bursting (Wagenaar et al. 2005). In this work, we study computationally the spontaneous emergence of bursts and the effect of network structure on burst shape and frequency. Recent computational structure-function approaches show the effect of, e.g., second-order connections (Zhao et al. 2011) and degree distribution widths (Roxin 2011) on activity patterns. We aim to study a wider set of graph-theoretical measures using networks with identical in-degree distributions. We apply a biophysically plausible point-neuron model of a cortical cell (Golomb et al. 2006). The model network consists of a small (N=100) number of neurons, both excitatory pyramidal neurons and inhibitory interneurons. A model of short-term depression (Golomb and Amitai 1997) is used for glutamatergic synapses. The activity simulation is run over a wide set of classes of network structure. To quantify the structure of the network, we consider graph theoretical measures such as clustering coefficient, geodesic path length, node-betweenness and occurrence of different motifs. We restrict to unweighted bidirectional graph representation, hence the synaptic weights between the neurons are uniform. We study the significance of different graph theoretic measures using a prediction framework: How well can a bursting property, such as burst duration or frequency, be estimated using various measures of structure as attributes? We show that the prediction of bursting properties is improved by taking one or more of the aforementioned measures as prediction attributes. It is best improved when the prediction is based on the clustering coefficient or occurrence of the most highly connected motifs. We confirm the results using a noise-driven LIF model with short-term depression (Tsodyks et al. 2000). We conclude that the significance of measures of clustering is prominent compared to other measures of structure.