Adaptive rewiring based on diffusion balances stability and plasticity in weighted networks while evolving ‘brain-like’ structure
Authors: Rentzeperis Ilias , van Leeuwen Cees 
Published: August 2019

Activity dependent plasticity is the brain’s mechanism for reshaping neural connections. Representing activity by graph diffusion, we model plasticity as adaptive rewiring. The rewiring involves adding shortcut connections where diffusion on the graph is intensive while pruning underused ones. This process robustly steers initially random networks to high-levels of structural complexity reflecting the global characteristics of brain anatomy: modular or centralized small world topologies, depending on overall diffusion rate. We extend this result, known from binary networks, to weighted ones in order to evaluate the flexibility of their evolved states. Both with normally- and lognormally-distributed weights, networks evolve modular or centralized topologies depending on a single control parameter, the diffusion rate, representing a global homeostatic or normalizing regulation mechanism. Once settled, normally weighted networks lock into their topologies, whereas lognormal ones allow flexible switching between them, tuned by the diffusion rate. For a small range of diffusion rates networks evolve the largest variety of topologies: modular, centralized or intermediate. Weighted networks in the transition range show topological but not weighted rich-club structure matching empirical data in the human brain. The simulation results allow us to propose adaptive rewiring based on diffusion as a parsimonious model for activity-dependent reshaping of the brain’s connections.

Author Summary

The brain is adapting continuously to a changing environment by strengthening or adding new connections and weakening or pruning existing ones. This forms the basis of flexible and adaptable behaviors. On the other hand, uncontrolled changes to the wiring can compromise the stability of the brain as an adaptive system. We used an abstract model to investigate how this basic problem could be addressed from a graph-theoretical perspective. The model adaptively rewires an initially randomly connected network into a more structured one with properties akin to the human brain, such as small worldness and rich club structure. The adaptive changes made to the network follow the heat diffusion, an abstract representation of brain functional connectivity. Moreover, depending on a parameter of the model, the heat diffusion rate, either modular or centralized connectivity patterns emerge, both found across different regions of the brain. For a narrow range of intermediate heat diffusion rates, networks develop a full range from modular to centralized connectivity patterns. Once settled into a connectivity pattern networks with normally distributed weights lock into that state, whereas networks with lognormally distributed weights show greater flexibility to adjust, while maintaining their small-world and rich club properties. Networks with lognormally distributed weights, therefore, show the combination of stability and flexibility needed to address the fundamental requirements of adaptive networks.