Short- and Long-Range Connections Differentially Modulate the Dynamics and State of Small-World Networks

Abstract

The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.