Abstract
Using methods of geometric dynamical systems modeling, we demonstrate the mechanism through which inhibitory feedback synapses to oscillatory neurons stabilize the oscillation, resulting in a flattened phase-resetting curve. In particular, we use the concept of a synaptic phase-resetting curve to demonstrate that periodic inhibitory feedback to an oscillatory neuron locks at a stable phase where it has no impact on cycle period and yet it acts to counter the effects of extrinsic perturbations. These results are supported by data from the stable bursting oscillations in the crustacean pyloric central pattern generator.
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Notes
- 1.
\(\epsilon {v}^{{\prime}} = ({i}_{\mathrm{ext}}-{i}_{L}-{i}_{\mathrm{Ca}}-{i}_{\mathrm{syn}})/{c}_{m};\, {m}_{8}(v) = 1/(1+\exp (-(v+61)/4.2));\, {h}_{8}(v) = 1/(1+\exp ((v+88)/8.6));\, {\tau }_{h}(v) = (270/(1+\exp ((v +84)/7.3)))(\exp ((v +162)/30.0))+54;\, {i}_{\mathrm{ext}} = -0.45,\,{g}_{L} = 0.3142,\,{g}_{\mathrm{Ca}} = 1.2567,{g}_{\mathrm{syn}} = 0.0235\)(active for 219.4 ms starting at t 0 = 302 ms in each cycle), \({E}_{L} = -62.5,{E}_{\mathrm{Ca}} = 120,{E}_{\mathrm{syn}} = -80,{c}_{m} = 7,\epsilon = 1.\)
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Acknowledgements
We thank Dr. Lian Zhou for earlier ideas on this work. Supported by NIH MH-60605 (FN), NSF DMS0615168 (AB) and a Fulbright–Nehru Fellowship (AB).
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Nadim, F., Zhao, S., Bose, A. (2012). A PRC Description of How Inhibitory Feedback Promotes Oscillation Stability. In: Schultheiss, N., Prinz, A., Butera, R. (eds) Phase Response Curves in Neuroscience. Springer Series in Computational Neuroscience, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0739-3_16
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DOI: https://doi.org/10.1007/978-1-4614-0739-3_16
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