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.

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

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.

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.

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.

scholarly journals Phase-response curves and synchronized neural networks

2010 ◽  
Vol 365 (1551) ◽  
pp. 2407-2422 ◽  
Author(s):  
Roy M. Smeal ◽  
G. Bard Ermentrout ◽  
John A. White
Keyword(s):  
Spike Timing ◽  
Phase Response ◽  
Neural Oscillator ◽  
Response Curves ◽  
Linear Summation ◽  
Phase Response Curves ◽  
New Methods ◽  
Common Drive ◽  
Noise Tolerant ◽  
Adaptation Limits

We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.

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.

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