Predicting n:1 locking in pulse coupled two-neuron networks using phase resetting theory
© Guerl Kazanci et al; licensee BioMed Central Ltd. 2008
Published: 11 July 2008
Harmonic locking has been observed between breathing and heart beat rhythms, in hippocampal slices between interneurons firing at gamma and pyramidal neurons firing at beta frequencies with missed gamma beats and in model networks between theta and gamma rhythms. Existence and stability criteria for harmonic locking modes were derived for two reciprocally pulse coupled oscillators based on their first and second order phase resetting curves (PRCs). These methods were then tested using two reciprocally inhibitory Wang and Buzsaki model neurons.
Previously, Ermentrout  derived existence and stability criteria for n:m locking assuming weak coupling using averaging theory. The methods presented here do not require the coupling to be weak and are easier to implement and apply to real neurons since only the PRCs are required. Both methods agree in the weak coupling regime (not shown), but the new method shows good agreement with the observed modes from the simulated network even in strong coupling regimes (Figure 1BC).
This project was funded by NINDs grant NS54281. Authors would like to thank Bard Ermentrout for discussions.
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