Abstract
Modularity is a ubiquitous topological feature of structural brain networks at various scales. Although 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. Our topological reinforcement model acts enhancing the topological overlap between nodes, that is, iteratively allowing connections between non-neighbor nodes with high neighborhood similarity. This rule reliably evolves synthetic random networks toward a modular architecture. Such final modular structure reflects initial “proto-modules,” thus allowing to predict the modules of the evolved graph. Subsequently, we show that this topological selection principle might be biologically implemented as a Hebbian rule. Concretely, we explore a simple model of excitable dynamics, where the plasticity rule acts based on the functional connectivity (co-activations) between nodes. Results produced by the activity-based model are consistent with the ones from the purely topological rule in terms of the final network configuration and modules composition. Our findings suggest that the selective reinforcement of topological overlap may be a fundamental mechanism contributing to modularity emergence in brain networks.
Highlights
Modularity, the presence of clusters of elements that are more densely connected with each other than with the rest of the network, is a ubiquitous topological feature of complex networks and, in particular, structural brain networks at various scales of organization (Sporns & Betzel, 2016).Modularity was among the first topological features of complex networks to be associated with a systematic impact on dynamical network processes
Starting from a random network, this mechanism systematically promotes the emergence of modular architecture by enhancing initial weak proto-modules. We show that this topological selection principle can be implemented in biological neural networks through a Hebbian plasticity rule, where what “fires together, wires together” and, under proper conditions, the results are consistent between both scenarios
Random walks get trapped in modules (Rosvall & Bergstrom, 2008), the synchronization of coupled oscillators over time maps out the modular organization of a graph (Arenas, Díaz-Guilera, & Pérez-Vicente, 2006), and co-activation patterns of excitable dynamics tend to reflect the graph’s modular organization (Messé, Hütt, & Hilgetag, 2018; Müller-Linow, Hilgetag, & Hütt, 2008; Zhou, Zemanová, Zamora, Hilgetag, & Kurths, 2006)
Summary
Modularity, the presence of clusters of elements that are more densely connected with each other than with the rest of the network, is a ubiquitous topological feature of complex networks and, in particular, structural brain networks at various scales of organization (Sporns & Betzel, 2016).Modularity was among the first topological features of complex networks to be associated with a systematic impact on dynamical network processes. Modularity, the presence of clusters of elements that are more densely connected with each other than with the rest of the network, is a ubiquitous topological feature of complex networks and, in particular, structural brain networks at various scales of organization (Sporns & Betzel, 2016). Modularity in the brain is thought to be important for information processing, the balance segregation and integration, as well as system evolvability in the long temporal scale, among others (Sporns & Betzel, 2016). The modular organization of brain networks forms the substrate of functional specialization (e.g., sensory systems; Hilgetag, Burns, O’Neill, Scannell, & Young, 2000), contributes to the generation and maintenance of dynamical regimes (e.g., sustained activity; Kaiser & Hilgetag, 2010) and criticality (Wang & Zhou, 2012), and supports the development of executive functions (Baum et al, 2017). Modularity is a key component of structural brain networks with important functional consequences
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