Chapter

Phase Resetting in the Presence of Noise and Heterogeneity

Srisairam Achuthan, Fred H. Sieling, Astrid A. Prinz and Carmen C. Canavier

in The Dynamic Brain

Published in print January 2011 | ISBN: 9780195393798
Published online September 2011 | e-ISBN: 9780199897049 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195393798.003.0006
Phase Resetting in the Presence of Noise and Heterogeneity

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A phase response curve (PRC) characterizes the change in cycle period of an otherwise stable neuronal oscillator to perturbations applied by precisely timed stimuli. We use PRCs to predict accurately phase locked modes in hybrid networks of one model and one biological neuron and in model networks of two identical and identically connected model neurons. In hybrid circuits, the robustness of 1:1 phase locked modes to noise is estimated by comparing the solution structure predicted using the upper/lower envelope of PRCs generated in the presence of noise in the biological neuron instead of the average PRC for predictions. If the structures are qualitatively similar, the solution is robust to noise, otherwise it is sensitive. The intrinsic periods and PRCs for neurons that comprise intact biological networks can only be approximately characterized for a given cell type, therefore we then use the model two neuron network to determine how the sensitive phase locked solutions are to deviations in frequency within the network. When heterogeneity is introduced into this network by allowing variability in the intrinsic frequency, the solution structure of the original homogeneous network is perturbed. Increasing the strength of the coupling above an abrupt threshold improves the correspondence between the original and perturbed network, offsetting the heterogeneity. PRC based methods correctly predict the location of this threshold for a given level of heterogeneity, therefore PRC based similar methods can be use to estimate the robustness to both temporal variability and variability between neurons.

Keywords: phase resetting; phase locking; synchronization; noise and heterogeneity

Chapter.  5785 words.  Illustrated.

Subjects: Neuroscience

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