Reduced spatial spread of nodes in geometric network models improves topology associated with increased computational capabilities

Abstract

Biological neural networks are characterized by short average path lengths, high clustering, and modular and hierarchical architectures. These complex network topologies strike a balance between local specialization and global synchronization via long-range connections, resulting in highly efficient communication. Efficient network organization and information processing are directly affected after network perturbation, e.g., as a result of trauma or neurodegenerative disease. Here, we used a spatial network model combining changes to spatial constraints on neuron placement with different wiring probabilities to investigate the effects of wiring cost principles on network complexity for different spatial conformations. By combining different wiring probabilities with varying levels of spatial clustering, we aimed to understand how alterations to mechanisms such as the neurons ability to group together, leading to different levels of clustering, in combination with altered axon outgrowth and branching, change network topology. Through targeted pruning of the networks we further aimed to understand how these topologies changed due to perturbations, resulting in a breakdown of function. We found that both long-range and intermediate wiring probabilities only conform to small-world architectures for neurons in dense spatial clusters due to a decrease in wiring cost within clusters. Furthermore, both small-worldness and modularity were reduced in systems with long-range connections caused by a reduction in network clustering. The presence of long-range connections were found to improve global information transmission, especially in networks with strong spatial clustering. In addition, these connections were shown to have a protective effect on the networks during targeted pruning, maintaining global connectivity even with high levels of pruning. Combining spatial clustering with wiring cost principles allows for novel insights into mechanisms underlying adaptive or maladaptive network alterations, explaining how specific interactions may lead to observed changes in networks. Our findings corroborate previous work showing that both wiring probability and spatial distributions play a key role in neural network development and response to perturbations, and increase our understanding of how maladaptive responses may lead to increased strain on local circuitry while negatively impacting global communication. Author summaryBiological neural networks organize into networks capable of performing a variety of complex tasks in a cost-efficient manner. In networks where neurons are subject to neuropathological disease or perturbations, the mechanisms leading to these networks are disrupted, resulting in changes to the computational capabilities of the networks which can be challenging to elucidate. In this study, we combine spatial network models with different wiring costs used to establish connections between nodes of the network to gain an understanding of how changes to the wiring cost and spatial distribution of nodes in a network impacts the resulting topologies. We find that irrespective of wiring cost, sufficient spatial clustering is required for the emergence of network capabilities related to onset and maintenance of activity found in biological neural networks. Furthermore, we find that a balance between local connectivity and long-range connections improve outcomes when networks are subject to targeted perturbations of these connections. To summarize, spatial models prove an efficient method for understanding how changes related to wiring cost and targeted deletion of connections may change topologies of networks, allowing us to understand how specific changes to networks may arise and manifest in in vitro and in vivo cases.