Spiking dynamics of individual neurons reflect changes in the structure and function of neuronal networks.

Brain networks exhibit diverse topological structures to adapt and support brain functions. The changes in neuronal network architecture can lead to alterations in neuronal spiking activity, yet how individual neuronal behavior reflects network structure remains unexplored. Therefore, mathematical tools to decode and infer neuronal network structure and role from spiking behavior need to be developed to relate the neuronal firing activity with topology and goal of underlying network. Toward this end, we perform a comprehensive multifractal analysis of the neuronal interspike intervals to characterize their non-linear, non-stationary and non-Markovian dynamics. We explore the relationship of neuronal network connectivity with the multifractal spiking pattern and show that such a measure is sensitive to network structure while relatively consistent to stimulus. In addition, we reveal that the observed multifractal profile is not influenced by the activity of unobserved neuronal ensembles. To mimic neurons performing specific functions, we further train spiking neural networks to generate goal-directed architectures and demonstrate that multifractal analysis also enables differentiating networks with diverse tasks.