Clustered arrangement of inhibitory neurons can lead to oscillatory dynamics in a model of activity-dependent structural plasticity

The balance between excitation and inhibition in a neuronal network is considered to be an important determinant of neural excitability. Various processes are thought to maintain this balance across a range of stimuli/conditions. However, the developmental formation of this balance remains an open question, especially regarding the interplay between network blue-print (the spatial arrangement of excitatory and inhibitory neurons) and homeostatic processes. In this chapter, we use a published model of activity-dependent growth to show that the ratio between the number of excitatory and inhibitory neurons (E/I ratio) alone cannot accurately predict system behaviour but rather it is the combination of this ratio and the underlying spatial arrangement of neurons that determine both activity in, and structure of, the resulting network. In particular, we highlight the role of spatial clustering of inhibitory neurons. We develop measures that allow us to characterise the relationship between this spatial clustering and system behaviour in both the 1-dimensional (1D) and 2-dimensional (2D) forms of the model. Our results reveal that, for a given E/I ratio, networks with high levels of inhibitory spatial clustering are more likely to experience oscillatory behaviour of their connectivity and electrical activity than networks with lower levels of clustering. This instability of the network structure can be thought of as a pathological outcome. We discuss implications these results may have on future modelling studies in this field and speculate about their relationship to neuro-developmental physiology and pathophysiology.