Changes of Firing Rate Induced by Changes of Phase Response Curve in Bifurcation Transitions

2014 ◽  
Vol 26 (11) ◽  
pp. 2395-2418 ◽  
Author(s):  
Yasuomi D. Sato ◽  
Kazuyuki Aihara
Keyword(s):  
Firing Rate ◽  
Neuron Model ◽  
Phase Response Curve ◽  
Dimensional Space ◽  
External Input ◽  
Phase Response ◽  
Input Current ◽  
Rate Curve ◽  
Response Curves ◽  
Snic Bifurcation

We study dynamical mechanisms responsible for changes of the firing rate during four different bifurcation transitions in the two-dimensional Hindmarsh-Rose (2DHR) neuron model: the saddle node on an invariant circle (SNIC) bifurcation to the supercritical Andronov-Hopf (AH) one, the SNIC bifurcation to the saddle-separatrix loop (SSL) one, the AH bifurcation to the subcritical AH (SAH) one, and the SSL bifurcation to the AH one. For this purpose, we study slopes of the firing rate curve with respect to not only an external input current but also temperature that can be interpreted as a timescale in the 2DHR neuron model. These slopes are mathematically formulated with phase response curves (PRCs), expanding the firing rate with perturbations of the temperature and external input current on the one-dimensional space of the phase [Formula: see text] in the 2DHR oscillator. By analyzing the two different slopes of the firing rate curve with respect to the temperature and external input current, we find that during changes of the firing rate in all of the bifurcation transitions, the calculated slope with respect to the temperature also changes. This is largely dependent on changes in the PRC size that is also related to the slope with respect to the external input current. Furthermore, we find phase transition–like switches of the firing rate with a possible increase of the temperature during the SSL-to-AH bifurcation transition.

scholarly journals On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro

2015 ◽  
Vol 11 (3) ◽  
pp. e1004112 ◽  
Author(s):  
João Couto ◽  
Daniele Linaro ◽  
E De Schutter ◽  
Michele Giugliano
Keyword(s):  
Firing Rate ◽  
Response Curve ◽  
Phase Response Curve ◽  
Phase Response ◽  
Purkinje Neurons ◽  
Rate Dependency

Extraretinal photoreception in the lizard Sceloporus occidentalis: phase response curve

1985 ◽  
Vol 248 (4) ◽  
pp. R407-R414
Author(s):  
H. Underwood
Keyword(s):  
Phase Response Curve ◽  
Circadian System ◽  
Phase Response ◽  
Fluorescent Light ◽  
Response Curves ◽  
Sceloporus Occidentalis ◽  
Light Pulses ◽  
Threefold Increase ◽  
Free Running ◽  
Free Running Period

All submammalian vertebrates have extraretinal photoreceptors (ERR) that can mediate entrainment of circadian rhythms to 24-h light-dark (LD) cycles. Phase response curves (PRC) for 6-h fluorescent light pulses were generated for lizards (Sceloporus occidentalis) previously subjected to sectioning of both optic nerves (ONX). The PRC for ONX lizards (only ERRs present) shows a threefold increase in the amplitude of both the advance and delay portions of the PRC compared with a PRC previously generated for sighted S. occidentalis. Also, in contrast to sighted lizards the area of the advance part of the PRC of ONX lizards is greater than the delay portion. Consistent with the shape of the respective PRCs in ONX vs. sighted lizards are the following facts. 1) The range of entrainment to LD cycles is greater in ONX lizards; some sighted lizards free-ran when exposed to LD 6:21.5 or LD 6:23.5 but entrained after ONX lizards reentrained to an 8-h shift in the phase of a LD 6:18 cycle significantly faster than sighted lizards. 3) Forty-two percent of ONX lizards showed a shorter free-running period (tau) in LL than DD, whereas 90% of sighted lizards showed a longer free-running period in LL than in DD. In those lizards in which tau LL greater than tau DD, the the average tau change in ONX lizards in was significantly less than that observed in sighted lizards. These results are consistent with the hypothesis that the eyes have an "inhibitory" role in the circadian system of S. occidentalis.

scholarly journals Phase response curves of subthalamic neurons measured with synaptic input and current injection

2012 ◽  
Vol 108 (7) ◽  
pp. 1822-1837 ◽  
Author(s):  
Michael A. Farries ◽  
Charles J. Wilson
Keyword(s):  
Firing Rate ◽  
Synaptic Input ◽  
Brain Slices ◽  
Current Injection ◽  
Phase Response ◽  
Response Curves ◽  
Phase Response Curves ◽  
Simple Description ◽  
Current Pulses ◽  
Subthalamic Neurons

Infinitesimal phase response curves (iPRCs) provide a simple description of the response of repetitively firing neurons and may be used to predict responses to any pattern of synaptic input. Their simplicity makes them useful for understanding the dynamics of neurons when certain conditions are met. For example, the sizes of evoked phase shifts should scale linearly with stimulus strength, and the form of the iPRC should remain relatively constant as firing rate varies. We measured the PRCs of rat subthalamic neurons in brain slices using corticosubthalamic excitatory postsynaptic potentials (EPSPs; mediated by both AMPA- and NMDA-type receptors) and injected current pulses and used them to calculate the iPRC. These were relatively insensitive to both the size of the stimulus and the cell's firing rate, suggesting that the iPRC can predict the response of subthalamic nucleus cells to extrinsic inputs. However, the iPRC calculated using EPSPs differed from that obtained using current pulses. EPSPs (normalized for charge) were much more effective at altering the phase of subthalamic neurons than current pulses. The difference was not attributable to the extended time course of NMDA receptor-mediated currents, being unaffected by blockade of NMDA receptors. The iPRC provides a good description of subthalamic neurons' response to input, but iPRCs are best estimated using synaptic inputs rather than somatic current injection.

scholarly journals Linear Control of Neuronal Spike Timing Using Phase Response Curves

2010 ◽  
Vol 4 (2) ◽  
Author(s):  
Tyler Stigen ◽  
P. Danzl ◽  
J Moehlis ◽  
T. I. Netoff
Keyword(s):  
Phase Response Curve ◽  
Control Function ◽  
Linear Method ◽  
Spike Timing ◽  
Phase Response ◽  
Linear Control ◽  
Least Squares Regression ◽  
Response Curves ◽  
Control Scheme

We propose a simple, robust, and linear method to control the spike timing of a periodically firing neuron. The control scheme uses the neuron’s phase response curve to identify an area of optimal sensitivity for the chosen stimulation parameters. The spike advance as a function of current pulse amplitude is characterized at the optimal phase, and a linear least-squares regression is fit to the data. The inverted regression is used as the control function for this method. The efficacy of this method is demonstrated through numerical simulations of a Hodgkin–Huxley style neuron model as well as in real neurons from rat hippocampal slice preparations. The study shows a proof of concept for the application of a linear control scheme to control neuron spike timing in vitro. This study was done on an individual cell level, but translation to a tissue or network level is possible. Control schemes of this type could be implemented in a closed loop implantable device to treat neuromotor disorders involving pathologically neuronal activity such as epilepsy or Parkinson’s disease.

Photoperiod differentially modulates photic and nonphotic phase response curves of hamsters

2004 ◽  
Vol 286 (3) ◽  
pp. R539-R546 ◽  
Author(s):  
J. A. Evans ◽  
J. A. Elliott ◽  
M. R. Gorman
Keyword(s):  
Wheel Running ◽  
Phase Response Curve ◽  
Phase Shifts ◽  
Phase Response ◽  
Cycle Phase ◽  
Phase Resetting ◽  
Response Curves ◽  
Syrian Hamsters ◽  
Light Pulses ◽  
Circadian Time

Circadian pacemakers respond to light pulses with phase adjustments that allow for daily synchronization to 24-h light-dark cycles. In Syrian hamsters, Mesocricetus auratus, light-induced phase shifts are larger after entrainment to short daylengths (e.g., 10 h light:14 h dark) vs. long daylengths (e.g., 14 h light:10 h dark). The present study assessed whether photoperiodic modulation of phase resetting magnitude extends to nonphotic perturbations of the circadian rhythm and, if so, whether the relationship parallels that of photic responses. Male Syrian hamsters, entrained for 31 days to either short or long daylengths, were transferred to novel wheel running cages for 2 h at times spanning the entire circadian cycle. Phase shifts induced by this stimulus varied with the circadian time of exposure, but the amplitude of the resulting phase response curve was not markedly influenced by photoperiod. Previously reported photoperiodic effects on photic phase resetting were verified under the current paradigm using 15-min light pulses. Photoperiodic modulation of phase resetting magnitude is input specific and may reflect alterations in the transmission of photic stimuli.

Aplysia bursting neurons as endogenous oscillators. I. Phase-response curves for pulsed inhibitory synaptic input

1977 ◽  
Vol 40 (3) ◽  
pp. 527-543 ◽  
Author(s):  
H. M. Pinsker
Keyword(s):  
Synaptic Input ◽  
Phase Response Curve ◽  
Phase Response ◽  
Linear Functions ◽  
Response Curves ◽  
Synaptic Modulation ◽  
Bursting Neuron ◽  
Bursting Neurons ◽  
Voltage Change ◽  
Inhibitory Synaptic Input

1. The left upper quadrant bursting neurons in the abdominal ganglion of Aplysia are isochronous, nonlinear oscillators. Transmembrane current and temperature are parameters of the bursting oscillator. 2. The phase-response curve (PRC) for pulsed inhibitory synaptic input from an interneuron describes the phase shift produced by synaptic input at different phases of the burst cycle. 3. The characteristic shape of the PRC consists of two linear functions that intersect at the point in the cycle where the burst of spikes ends. Whether the net effect of the synaptic input at a given phase is phase advance or phase delay depends on 1) the number of spikes inhibited, and 2) the duration of the inhibition relative to the duration of the free-run period. 4. The shape of the PRC remains constant when a stepwise change in a parameter is introduced, when the duration of the synaptic input is increased, when the fast component of the IPSP is blocked, and when a long hyperpolarizing pulse is used to mimic the slow IPSP. 5. The shape of the PRC is changed when short hyperpolarizing pulses or antidromic action potentials are used and when only the pacemaker oscillation is present in the bursting neuron. 6. Therefore, the synaptic modulation of the bursting rhythm is determined by the voltage change produced by the IPSP and its inhibition of spikes in the bursting neuron.

scholarly journals The Circadian Phase Response Curve to Light: Conservation across Seasons and Anchorage to Sunset

2021 ◽  
Author(s):  
Hannah K. Dollish ◽  
Sevag Kaladchibachi ◽  
David C. Negelspach ◽  
Fabian Fernandez
Keyword(s):  
Human Population ◽  
Phase Response Curve ◽  
Light Exposure ◽  
Phase Response ◽  
Phase Resetting ◽  
Response Curves ◽  
Light Responses ◽  
Circadian Phase ◽  
Phase Alignment ◽  
Seasonal Depression

Predictions about circadian light responses are largely based on photic phase-response curves (PRCs) generated from animals housed under seasonally agnostic equatorial photoperiods with alternating 12-hour segments of light and darkness. Most of the human population, however, lives at northerly latitudes where seasonal variations in the light-dark schedule are pronounced. Here, we address this disconnect by constructing the first high-resolution seasonal atlas for light-induced circadian phase-resetting. Testing the light responses of nearly 4,000 Drosophila at 120 timepoints across 5 seasonally relevant photoperiods, we determined that many aspects of the circadian PRC waveform are conserved with increasing daylength. Surprisingly though, irrespective of LD schedule, the start of the PRCs always remained anchored to the timing of subjective sunset, creating a differential overlap of the advance zone with the morning hours after subjective sunrise that was maximized under summer photoperiods and minimized under winter photoperiods. These data suggest that circadian photosensitivity is effectively extinguished by the early winter morning and out of optimal phase alignment with the wake schedules of many individuals. They raise the possibility that phototherapy protocols for conditions such as seasonal depression might be improved with programmed light exposure during the final hours of sleep.

scholarly journals Spectral reconstruction of phase response curves reveals the synchronization properties of mouse globus pallidus neurons

2013 ◽  
Vol 110 (10) ◽  
pp. 2497-2506 ◽  
Author(s):  
Joshua A. Goldberg ◽  
Jeremy F. Atherton ◽  
D. James Surmeier
Keyword(s):  
Pyramidal Neurons ◽  
Phase Response Curve ◽  
Numerical Models ◽  
Low Noise ◽  
Phase Response ◽  
Response Curves ◽  
Spectral Reconstruction ◽  
Cortical Pyramidal Neurons ◽  
Low Dimensional

The propensity of a neuron to synchronize is captured by its infinitesimal phase response curve (iPRC). Determining whether an iPRC is biphasic, meaning that small depolarizing perturbations can actually delay the next spike, if delivered at appropriate phases, is a daunting experimental task because negative lobes in the iPRC (unlike positive ones) tend to be small and may be occluded by the normal discharge variability of a neuron. To circumvent this problem, iPRCs are commonly derived from numerical models of neurons. Here, we propose a novel and natural method to estimate the iPRC by direct estimation of its spectral modes. First, we show analytically that the spectral modes of the iPRC of an arbitrary oscillator are readily measured by applying weak harmonic perturbations. Next, applying this methodology to biophysical neuronal models, we show that a low-dimensional spectral reconstruction is sufficient to capture the structure of the iPRC. This structure was preserved reasonably well even with added physiological scale jitter in the neuronal models. To validate the methodology empirically, we applied it first to a low-noise electronic oscillator with a known design and then to cortical pyramidal neurons, recorded in whole cell configuration, that are known to possess a monophasic iPRC. Finally, using the methodology in conjunction with perforated-patch recordings from pallidal neurons, we show, in contrast to recent modeling studies, that these neurons have biphasic somatic iPRCs. Biphasic iPRCs would cause lateral somatically targeted pallidal inhibition to desynchronize pallidal neurons, providing a plausible explanation for their lack of synchrony in vivo.

scholarly journals Biophysical basis of the phase response curve of subthalamic neurons with generalization to other cell types

2012 ◽  
Vol 108 (7) ◽  
pp. 1838-1855 ◽  
Author(s):  
Michael A. Farries ◽  
Charles J. Wilson
Keyword(s):  
Phase Response Curve ◽  
Cell Types ◽  
Phase Response ◽  
Biophysical Model ◽  
Charge Redistribution ◽  
Response Curves ◽  
Wide Range ◽  
Voltage Dependent ◽  
The Difference ◽  
Subthalamic Neurons

Experimental evidence indicates that the response of subthalamic neurons to excitatory postsynaptic potentials (EPSPs) is well described by their infinitesimal phase response curves (iPRC). However, the factors controlling the shape of that iPRC, and hence controlling the way subthalamic neurons respond to synaptic input, are unclear. We developed a biophysical model of subthalamic neurons to aid in the understanding of their iPRCs; this model exhibited an iPRC type common to many subthalamic cells. We devised a method for deriving its iPRC from its biophysical properties that clarifies how these different properties interact to shape the iPRC. This method revealed why the response of subthalamic neurons is well approximated by their iPRCs and how that approximation becomes less accurate under strong fluctuating input currents. It also connected iPRC structure to aspects of cellular physiology that could be estimated in simple current-clamp experiments. This allowed us to directly compare the iPRC predicted by our theory with the iPRC estimated from the response to EPSPs or current pulses in individual cells. We found that theoretically predicted iPRCs agreed well with estimates derived from synaptic stimuli, but not with those estimated from the response to somatic current injection. The difference between synaptic currents and those applied experimentally at the soma may arise from differences in the dynamics of charge redistribution on the dendrites and axon. Ultimately, our approach allowed us to identify novel ways in which voltage-dependent conductances interact with AHP conductances to influence synaptic integration that will apply to a wide range of cell types.

Sign in / Sign up

Export Citation Format

Share Document