Phase Resetting Curves Predict Network Activity in Networks of Neural Oscillators

Abstract

Event Abstract Back to Event Phase Resetting Curves Predict Network Activity in Networks of Neural Oscillators A phase response curve (PRC) characterizes the change in cycle period of an otherwise stable oscillator to perturbations applied by precisely timed stimuli. Networks of model neurons were constructed and their activity was predicted using an iterated map based solely on the phase resetting curves (PRCs). The predictions were quite accurate provided that the resetting to simultaneous inputs was calculated using the sum of the simultaneously active conductances, obviating the need for weak coupling assumptions. Fully synchronous activity was observed only when the slope of the PRC at a phase of zero, corresponding to spike initiation, was positive. A novel stability criterion was developed and tested for all to all networks of identical, identically connected neurons. When the PRC generated using N-1 simultaneously active inputs becomes too steep, the fully synchronous mode loses stability in a network of N model neurons. Therefore, the stability of synchrony can be lost by increasing the slope of this PRC either by increasing the network size or the strength of the individual synapses. Existence and stability criteria were also developed and tested for the splay mode in which neurons fire sequentially. Finally, N/M synchronous sub-clusters of M neurons were predicted using the intersection of parameters that supported both between cluster splay and within cluster synchrony. Surprisingly, the splay mode between clusters could enforce synchrony on sub-clusters that were incapable of synchronizing themselves. Although all to all networks were used as examples for simplicity, these methods can be extended to heterogenous networks in two ways. First, the results for the homogeneous network apply approximately to slightly heterogenous networks, and second, the procedure of using the PRCs to predict which firing patterns will be exhibited can be applied to arbitrary circuits that contain both inhibition and excitation with network topologies that are not all to all. When heterogeneity is introduced by allowing variability in the intrinsic frequency or coupling conductances, the solution structure of the homogeneous network is perturbed, such that exact synchrony within a cluster becomes near synchrony, and a symmetric splay mode between clusters, such as the antiphase mode, becomes a near antiphase mode. For the parameter ranges examined in this study, the PRCs of component neural oscillators were demonstrated to contain all the information necessary to predict network activity in heterogeneous networks of oscillatory neurons as well. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Phase Resetting Curves Predict Network Activity in Networks of Neural Oscillators. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.113 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 02 Feb 2009; Published Online: 02 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.