Volume 11 Supplement 1

Nineteenth Annual Computational Neuroscience Meeting: CNS*2010

Open Access

Mutually pulse-coupled neurons that do not synchronize in isolation can synchronize via reciprocal coupling with another neural population

  • Lakshmi Chandrasekaran1Email author,
  • Srisairam Achuthan1 and
  • Carmen C Canavier1, 2
BMC Neuroscience201011(Suppl 1):P15

DOI: 10.1186/1471-2202-11-S1-P15

Published: 20 July 2010

Phase locking between similar or dissimilar clusters (synchronized groups) of neurons may be widespread in the nervous system [13]. We examine two reciprocally coupled clusters of pulse-coupled oscillatory neurons. Neurons within each cluster are presumed to be identical and identically coupled but not necessarily identical to neurons in the other cluster. We construct a discrete map using Phase Response Curves (PRCs) for a firing pattern in which the neurons within each cluster are synchronized but the two clusters fire out of phase with respect to each other. We extend this map to include a perturbation of a single neuron within one cluster and linearize about the fixed point of the original map. We derive expressions that give stability of the phase-locked cluster solution using only the slopes of the PRC at the locking points. We give an example of a cluster of inhibitory Type II excitable neurons that cannot synchronize in isolation because the absolute value of the eigenvalue that determines synchrony in the isolated cluster is greater than one. The reciprocal coupling with another cluster scales this eigenvalue such that it becomes less than one, guaranteeing stability (Figure 1). These results suggest a mechanism by which local synchronization can be induced through reciprocal coupling between brain regions via the feedback loop.
https://static-content.springer.com/image/art%3A10.1186%2F1471-2202-11-S1-P15/MediaObjects/12868_2010_Article_1721_Fig1_HTML.jpg
Figure 1

A1,A2) Cluster 1 isolated and after coupled to cluster 2. B1) Neurons in cluster 1 firing out of phase B2) Cluster 1 neurons firing synchronously. (C) Examples of characteristic shapes of first and second order phase resets with Type II inhibition. D) Qualitative stability results for two clustered solution. Black bar(observed) obtained by integrating full system of differential equations for a range of conductance values. Compared to analysis in the current study denoted by purple bar. E) Maximum eigenvalues vs. conductance. https://static-content.springer.com/image/art%3A10.1186%2F1471-2202-11-S1-P15/MediaObjects/12868_2010_Article_1721_IEq1_HTML.gif greater than one for isolated cluster (blue dots) and less than one for the coupled cluster (purple dots).

Authors’ Affiliations

(1)
Neuroscience Center of Excellence, Louisiana State University Health Sciences Center
(2)
Department of Ophthalmology, LSU Health Sciences Center

References

  1. Achuthan S, Canavier CC: Phase-locking curves determine synchronization, phase locking and clustering in networks of neural oscillators. J.Neurosci. 2009, 29 (16): 5218-5233. 10.1523/JNEUROSCI.0426-09.2009.PubMed CentralView ArticlePubMedGoogle Scholar
  2. Marder E, Calabrese R: Principles of rhythmic motor pattern generation. Physiol. Rev. 1996, 76: 687-717.PubMedGoogle Scholar
  3. Pervouchine DD, Netoff TI, Rotstein HG, White JA, Cunningham MO, Whittington WA, Kopell NJ: Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus. Neural Comput. 2006, 18: 2617-2650. 10.1162/neco.2006.18.11.2617.View ArticlePubMedGoogle Scholar

Copyright

© Chandrasekaran et al; licensee BioMed Central Ltd. 2010

This article is published under license to BioMed Central Ltd.

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