Topological Reinforcement as a Principle of Modularity Emergence in Brain Networks

Modularity is a ubiquitous topological feature of structural brain networks at various scales. While a variety of potential mechanisms have been proposed, the fundamental principles by which modularity emerges in neural networks remain elusive. We tackle this question with a plasticity model of neural networks derived from a purely topological perspective. The topological reinforcement (TR) model acts by enhancing the topological overlap (TO) between nodes. Specifically, the TR rule iteratively connects a randomly selected node to a non-neighbor with the highest TO, while pruning another network link at random, hence preserving graph density. The topological reinforcement reliably evolves synthetic random networks toward a modular architecture. Additionally, the final modular structure reflects features of the initial networks, particularly, local density variations (‘proto-modules’), thus allowing to predict the modules of the evolved graph. Subsequently, we show that this topological selection principle when implemented biologically is equivalent to the classic Hebbian rule. Concretely, we explore a simple model of excitable dynamics, the SER model, in which the activity of network nodes is described by discrete susceptible, excited and refractory states. In this case, the plasticity rule acts in a Hebbian-like fashion, i.e., based on the functional connectivity (FC) between nodes represented by co-activations. Results produced by the SER-based model are consistent with TR, showing a consistent final network configuration. Our findings suggest that the selective reinforcement of topological overlap may be a fundamental mechanism by which brain networks evolve toward modular structure.