Distance-dependent connectivity in the brain facilitates high dynamical and structural complexity.

Recent experiments have revealed that the inter-regional connectivity of the cerebral cortex exhibits strengths spanning over several orders of magnitude and decaying with distance. We demonstrate this to be a fundamental organizing feature that fosters high complexity in both connectivity structure and network dynamics, achieving an advantageous balance between integration and differentiation of information. This is verified through analysis of a multi-scale neuronal network model with nonlinear integrate-and-fire dynamics, incorporating inter-regional connection strengths decaying exponentially with spatial separation at the macroscale as well as small-world local connectivity at the microscale. Through numerical simulation and optimization over the model parameterspace, we show that inter-regional connectivity over intermediate spatial scales naturally facilitates maximally heterogeneous connection strengths, agreeing well with experimental measurements. In addition, we formulate complementary notions of structural and dynamical complexity, which are computationally feasible to calculate for large multi-scale networks, and we show that high complexity manifests for each over a similar parameter regime. We expect this work may help explain the link between distance-dependence in brain connectivity and the richness of neuronal network dynamics in achieving robust brain computations and effective information processing.