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Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks
- Source :
- PLoS Computational Biology, PLoS Computational Biology, Vol 12, Iss 6, p e1004963 (2016)
- Publication Year :
- 2016
- Publisher :
- Public Library of Science, 2016.
-
Abstract
- The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.<br />Author Summary Many biological phenomena can be viewed as dynamical processes on a graph. Understanding coordinated activity of nodes in such a network is of some importance, as it helps to characterize the behavior of the complex system. Of course, the topology of a network plays a pivotal role in determining the level of coordination among its different vertices. In particular, correlations between triplets of events (here: action potentials generated by neurons) have recently garnered some interest in the theoretical neuroscience community. In this paper, we present a decomposition of an average measure of third-order coordinated activity of neurons in a spiking neuronal network in terms of the relevant topological motifs present in the underlying graph. We study different network topologies and show, in particular, that the presence of certain tree motifs in the synaptic connectivity graph greatly affects the strength of third-order correlations between spike trains of different neurons.
- Subjects :
- Computer and Information Sciences
Leaves
Neural Networks
Physiology
Models, Neurological
Action Potentials
Neurophysiology
Plant Science
Network Motifs
Membrane Potential
Infographics
Animal Cells
Medicine and Health Sciences
Animals
lcsh:QH301-705.5
Neurons
Covariance
Plant Anatomy
Data Visualization
Biology and Life Sciences
Computational Biology
Random Variables
Cell Biology
Probability Theory
Electrophysiology
lcsh:Biology (General)
Cellular Neuroscience
Physical Sciences
Cellular Types
Nerve Net
Graphs
Network Analysis
Mathematics
Research Article
Neuroscience
Subjects
Details
- Language :
- English
- ISSN :
- 15537358 and 1553734X
- Volume :
- 12
- Issue :
- 6
- Database :
- OpenAIRE
- Journal :
- PLoS Computational Biology
- Accession number :
- edsair.pmid.dedup....952d3c721488b446a545d3960831ed3d