The Structure of Instantaneous Phase Resetting in a Neural Oscillator

A phase resetting curve (PRC) measures the transient change in the phase of a neural oscillator subject to an external perturbation. The PRC encapsulates the dynamical response of a neural oscillator and, as a result, it is often used for predicting phase-locked modes in neural networks. While phase is a fundamental concept, it has multiple definitions that may lead to contradictory results. We used the Hilbert Transform (HT) to define the phase of the membrane potential oscillations and HT amplitude to estimate the PRC of a single neural oscillator. We found that HT’s amplitude and its corresponding instantaneous frequency are very sensitive to membrane potential perturbations. We also found that the phase shift of HT amplitude between the pre- and poststimulus cycles gives an accurate estimate of the PRC. Moreover, HT phase does not suffer from the shortcomings of voltage threshold or isochrone methods and, as a result, gives accurate and reliable estimations of phase resetting.

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All Phase Resetting Curves Are Bimodal, but Some Are More Bimodal Than Others

ISRN Computational Biology ◽

10.1155/2013/230571 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 6

Author(s):

Sorinel A. Oprisan

Keyword(s):

Hopf Bifurcation ◽

Oscillatory Behavior ◽

Positive Phase ◽

Neural Oscillator ◽

Phase Resetting ◽

Invariant Circle ◽

Neural Oscillators ◽

External Stimuli ◽

Firing Period ◽

Phase Resetting Curves

Phase resetting curves (PRCs) are phenomenological and quantitative tools that tabulate the transient changes in the firing period of endogenous neural oscillators as a result of external stimuli, for example, presynaptic inputs. A brief current perturbation can produce either a delay (positive phase resetting) or an advance (negative phase resetting) of the subsequent spike, depending on the timing of the stimulus. We showed that any planar neural oscillator has two remarkable points, which we called neutral points, where brief current perturbations produce no phase resetting and where the PRC flips its sign. Since there are only two neutral points, all PRCs of planar neural oscillators are bimodal. The degree of bimodality of a PRC, that is, the ratio between the amplitudes of the delay and advance lobes of a PRC, can be smoothly adjusted when the bifurcation scenario leading to stable oscillatory behavior combines a saddle node of invariant circle (SNIC) and an Andronov-Hopf bifurcation (HB).

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Phase resetting in central and peripheral sinoatrial node cell models

Computers in Cardiology, 2004 ◽

10.1109/cic.2004.1442985 ◽

2005 ◽

Author(s):

D.G. Tsalikakis ◽

H.G. Zhang ◽

D.I. Fotiadis ◽

G.P. Kremmydas

Keyword(s):

Sinoatrial Node ◽

Phase Resetting ◽

Cell Models ◽

Sinoatrial Node Cell

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Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0070 ◽

2019 ◽

Vol 20 (3-4) ◽

pp. 257-267

Author(s):

Jiaoyan Wang ◽

Xiaoshan Zhao ◽

Chao Lei

Keyword(s):

Time Delays ◽

Single Neuron ◽

Spiking Neurons ◽

Phase Resetting ◽

Subthreshold Oscillations ◽

Weak Pulse

AbstractInputs can change timings of spikes in neurons. But it is still not clear how input’s parameters for example injecting time of inputs affect timings of neurons. HR neurons receiving both weak and strong inputs are considered. How pulse inputs affecting neurons is studied by using the phase-resetting curve technique. For a single neuron, weak pulse inputs may advance or delay the next spike, while strong pulse inputs may induce subthreshold oscillations depending on parameters such as injecting timings of inputs. The behavior of synchronization in a network with or without coupling delays can be predicted by analysis in a single neuron. Our results can be used to predict the effects of inputs on other spiking neurons.

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