Phase-response curves and synchronized neural networks

Smeal, Roy M.; Ermentrout, G. Bard; White, John A.

doi:10.1098/rstb.2009.0292

Cited by 198Neural dynamics and brain functionNonlinear Dynamics and Pattern Formationstochastic dynamics and bifurcation

Phase-response curves and synchronized neural networks

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Smeal, Roy M., Ermentrout, G. Bard, White, John A.·2010·Philosophical Transactions of the Royal Society B: Biological Sciences

DOI 10.1098/rstb.2009.0292PMC PMC2894948

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Abstract

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.

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One way to demonstrate that a site is involved in the tremor oscillation-generating pacemaker circuit (including its inputs), rather than in propagating already established oscillations to anterior horn cells, is to establish whether low frequency stimulation can entrain tremor through modulation of the oscillatory neural activity at the stimulation site.
“One way to demonstrate that a site is involved in the tremor oscillation-generating pacemaker circuit (including its inputs), rather than in propagating already established oscillations to anterior horn cells, is to establish whether low frequency stimulation can entrain tremor through modulation of the oscillatory neural activity at the stimulation site (Walker et al., 1982; Ermentrout, 1996; Sme”
From The nature of tremor circuits in parkinsonian and essential tremor (2014) · cites this paper as Smeal et al., 2010
Section 4 (page not provided) says perturbations shift the phase when oscillatory dynamics arise locally, but not when they are driven by a distant oscillator. This supports the proposed distinction between a rhythm-generating site and a site receiving an established rhythm. The paper does not address low-frequency stimulation of tremor or propagation to anterior horn cells. (LLM, conf=0.86)
Experimental — accuracy not yet measured
In Parkinson's disease, the entrainment of tremor through stimulation in the ventrolateral thalamus and subthalamic nucleus strongly implies that both regions are involved in the tremor pacemaker circuit of rest tremor.
“In Parkinson’s disease the entrainment of tremor through stimulation in the ventrolateral thalamus and subthalamic nucleus strongly implies that both regions are involved in the tremor pacemaker circuit of rest tremor (Hansel et al., 1995; Ermentrout, 1996; Smeal et al., 2010).”
From The nature of tremor circuits in parkinsonian and essential tremor (2014) · cites this paper as Smeal et al., 2010
The Introduction links synchronized neural activity to Parkinson’s disease and says phase-response curves can offer insight into entrainment and pacemaker mechanisms. Searches for ventrolateral thalamus, subthalamic nucleus, stimulation, and rest tremor found no passage in our copy addressing whether those regions form part of a rest-tremor pacemaker circuit. (LLM, conf=0.73)
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Stimulating at the right time: phase-specific deep brain stimulation
Cagnan, H., Pedrosa, D., Little, S., Pogosyan, A., Cheeran, B., Aziz, T., Green, A., Fitzgerald, J., Foltynie, T., Limousin, P., et al. (2017) · Brain · doi:10.1093/brain/aww286 · Cited by 270 · see citing works
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“…propagating already established oscillations to anterior horn cells, is to establish whether low frequency stimulation can entrain tremor through modulation of the oscillatory neural activity at the stimulation site (Walker et al., 1982; Ermentrout, 1996; Smeal et al., 2010; Cagnan et al., 2013).”
Background
Phase dependent modulation of tremor amplitude in essential tremor through thalamic stimulation
Cagnan, H., Brittain, J.-S., Little, S., Foltynie, T., Limousin, P., Zrinzo, L., Hariz, M., Joint, C., Fitzgerald, J., Green, A. L., et al. (2013) · Brain · doi:10.1093/brain/awt239 · Cited by 95 · see citing works

Authors: Smeal, R. M., Ermentrout, G. B., & White, J. A.
Affiliations: University of Utah (US)
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
Corresponding author: Smeal, Roy M.
ORCID: White, John A.
Venue: Philosophical Transactions of the Royal Society B: Biological Sciences
Publisher: The Royal Society
Published: 2010-08-12
Volume: 365
Issue: 1551
Pages: 2407-2422
ISSN: 0962-8436 (ISSN-L)
1471-2970
DOI: 10.1098/rstb.2009.0292
PMC: PMC2894948
OpenAlex: W2131397159
Cited by: 198
References: 177
Citations by year: 2026: 13 · 2025: 8 · 2024: 8 · 2023: 11 · 2022: 11 · 2021: 9 · 2020: 10 · 2019: 13 · 2018: 11 · 2017: 13 · 2016: 11 · 2015: 16 · 2014: 14 · 2013: 20 · 2012: 14
FWCI: 9.70
Type: journal article
Language: en
Open access: bronze
doi.org
Licence: royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
Locations: Philosophical Transactions of the Royal Society B Biological Sciences (publishedVersion)
Europe PMC (PubMed Central) (publishedVersion)
PubMed Central (publishedVersion)
PubMed (publishedVersion)
Civil War Book Review (submittedVersion)
Funders: National Institute of Mental Health (R01MH085074)
Topics: Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
Keywords: phase response curve, neuronal synchronization, neural oscillators, spike timing, spike frequency adaptation, common drive, network heterogeneity, cortical oscillations
MeSH terms: Action Potentials, Animals, Biological Clocks, Computer Simulation, Models, Neurological, Nerve Net, Neurons, Synapses

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