Small-world networks in neuronal populations: A computational perspective

The analysis of the brain in terms of integrated neural networks may offer insights on the reciprocal relation between structure and information processing. Even with inherent technical limits, many studies acknowledge neuron spatial arrangements and communication modes as key factors. In this perspective, we investigated the functional organization of neuronal networks by explicitly assuming a specific functional topology, the small-world network. We developed two different computational approaches. Firstly, we asked whether neuronal populations actually express small-world properties during a definite task, such as a learning task. For this purpose we developed the Inductive Conceptual Network (ICN), which is a hierarchical bio-inspired spiking network, capable of learning invariant patterns by using variable-order Markov models implemented in its nodes. As a result, we actually observed small-world topologies during learning in the ICN. Speculating that the expression of small-world networks is not solely related to learning tasks, we then built a de facto network assuming that the information processing in the brain may occur through functional small-world topologies. In this de facto network, synchronous spikes reflected functional small-world network dependencies. In order to verify the consistency of the assumption, we tested the null-hypothesis by replacing the small-world networks with random networks. As a result, only small world networks exhibited functional biomimetic characteristics such as timing and rate codes, conventional coding strategies and neuronal avalanches, which are cascades of bursting activities with a power-law distribution. Our results suggest that small-world functional configurations are liable to underpin brain information processing at neuronal level.