Organization of Excitable Dynamics in Hierarchical Biological Networks

Abstract

This study investigates the contributions of network topology features to the dynamic behavior of hierarchically organized excitable networks. Representatives of different types of hierarchical networks as well as two biological neural networks are explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrate that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach also shows that the dynamic behavior of the cerebral cortical systems network in the cat is dominated by the network's modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. These findings indicate the interaction of multiple topological features and dynamic states in the function of complex biological networks.

The effect of individual variation on the structure and function of interaction networks in harvester ants

“…Thus, variation among individuals in connectivity can facilitate rapid information flow without increasing the total number of interactions. Networks with variation among individuals in interaction frequency have faster information flow than uniform networks because the highly interactive individuals reduce the number of interactions required to connect distant nodes [1,3,31,32,34]. The speed of information flow was similar in the two models (Uniform and Changing) with a Poisson degree distribution, in which there was no or little variation among individuals in interaction frequency, and a similar total number of interactions.…”

Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

“…At the same time, these theories (or classes of models) are well embedded in the broader framework of self-organization. Very much in the light of [57] and [34] our principal goal is to understand what the network equivalents of classical spatiotemporal patterns are, and how, e.g., the presence of loops and feedbacks in networks relate the processes behind spatiotemporal patterns to the theory of complex systems.…”

“…The principal goal of discussing CA on graphs [15] is to explore the relationship between network architecture and dynamics from the perspective of pattern formation (and, more specifically, the Wolfram classes [27,28], as a way of characterizing observed dynamic behaviors). In a series of numerical studies we have employed this framework and related systems to analyze discrete dynamical processes on graphs [16,[32][33][34]. Furthermore, the concept of probing real networks with binary dynamics has been formulated for assessing the regularizing capacity of networks and, conversely, its ability to display complex dynamics [16].…”

Cortico-cortical Communication Dynamics

“…For instance, it can be shown with multi-scale models as well as simple excitable nodes (akin to cellular automata) that topological features of brain networks strongly shape brain dynamics. For instance, modular and hub features of biological neural networks induce a modular and target wave-like propagation of excitation, respectively (Zhou et al, 2006;Müller-Linow et al, 2008; 1 www.humanbrainproject.eu Lohmann et al, 2010). "Nodes" in these models correspond to neural elements ranging in scope from individual cells to largescale populations (e.g., cortical areas).…”