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Noise-Induced Synchronization and Antiresonance in Interacting Excitable Systems: Applications to Deep Brain Stimulation in Parkinson’s Disease

Jonathan D. Touboul, Charlotte Piette, Laurent Venance, and G. Bard Ermentrout
Phys. Rev. X 10, 011073 – Published 27 March 2020
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Abstract

We study the nonlinear dynamics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate levels of noise. This noise-induced synchronization, distinct from classical stochastic resonance, is fundamentally collective in nature. Indeed, we show that, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel antiresonance phenomenon in this regime: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range (high relative to the spontaneous activity). In that antiresonance regime, the system is optimal for measures of information transmission. This observation provides a new hypothesis accounting for the efficiency of high-frequency stimulation therapies, known as deep brain stimulation, in Parkinson’s disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with specific coupling and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel antiresonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson’s disease.

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  • Received 23 May 2019
  • Revised 17 January 2020
  • Accepted 12 February 2020

DOI:https://doi.org/10.1103/PhysRevX.10.011073

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsPhysics of Living SystemsNetworks

Authors & Affiliations

Jonathan D. Touboul1,*, Charlotte Piette1,2, Laurent Venance2, and G. Bard Ermentrout3

  • 1Department of Mathematics and Volen National Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02453, USA
  • 2Center for Interdisciplinary Research in Biology (CIRB), College de France, CNRS, INSERM, PSL Research University, Paris 75005, France
  • 3Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15213, USA

  • *jtouboul@brandeis.edu

Popular Summary

From nerve cells to gene networks and laser emission, excitable systems subject to noise are ubiquitous. Such systems sit at an equilibrium in the absence of stimulations, and sufficiently large perturbations lead to large excursions. We show that, when coupled together, these systems may respond to random fluctuations by showing highly synchronized periodic oscillations where elements activate in unison. We explore possible applications to neuroscience, particularly in the context of Parkinson’s disease, where an increased excitability of neurons arises and abnormal oscillations emerge.

An important treatment for Parkinson’s disease is deep brain stimulation, a therapy in which high-frequency periodic electrical signals stimulate deep nuclei of the brain. This results in a dramatic reduction of symptoms and abnormal oscillations. We demonstrate a similar antiresonance phenomenon in coupled systems of excitable elements where the network is optimal in processing information.

Our result suggests a novel interpretation of the mechanism of action of deep brain stimulation in Parkinson’s disease that sharply contrasts with classical theories of “information lesion,” which hypothesize that deep brain stimulation reduces communication between pathological regions and other brain regions. We also show that these mechanisms of synchronization and antiresonance are universal in a class of coupled excitable systems subject to stochastic fluctuations.

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Vol. 10, Iss. 1 — January - March 2020

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