TY - JOUR

T1 - Linear noise approximation for oscillations in a stochastic inhibitory network with delay

AU - Dumont, Grégory

AU - Northoff, Georg Franz Josef

AU - Longtin, André

N1 - Cited By :2
Export Date: 11 May 2016
CODEN: PLEEE
Funding Details: HDRF, Hope for Depression Research Foundation
Funding Details: NSERC, Hope for Depression Research Foundation
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PY - 2014

Y1 - 2014

N2 - Understanding neural variability is currently one of the biggest challenges in neuroscience. Using theory and computational modeling, we study the behavior of a globally coupled inhibitory neural network, in which each neuron follows a purely stochastic two-state spiking process. We investigate the role of both this intrinsic randomness and the conduction delay on the emergence of fast (e.g., gamma) oscillations. Toward that end, we expand the recently proposed linear noise approximation (LNA) technique to this non-Markovian "delay" case. The analysis first leads to a nonlinear delay-differential equation (DDE) with multiplicative noise for the mean activity. The LNA then yields two coupled DDEs, one of which is driven by additive Gaussian white noise. These equations on their own provide an excellent approximation to the full network dynamics, which are much longer to integrate. They further allow us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations of the full network dynamics, for the large range of parameters where both the intrinsic stochasticity and the conduction delay are necessary for the occurrence of oscillations. The intrinsic noise arises from the probabilistic description of each neuron, yet it is expressed at the system activity level, and it can only be controlled by the system size. In fact, its effect on the fluctuations in system activity disappears in the infinite network size limit, but the characteristics of the oscillatory activity depend on all model parameters including the system size. Using the Hilbert transform, we further show that the intrinsic noise causes sporadic strong fluctuations in the phase of the gamma rhythm. © Published by the American Physical Society.

AB - Understanding neural variability is currently one of the biggest challenges in neuroscience. Using theory and computational modeling, we study the behavior of a globally coupled inhibitory neural network, in which each neuron follows a purely stochastic two-state spiking process. We investigate the role of both this intrinsic randomness and the conduction delay on the emergence of fast (e.g., gamma) oscillations. Toward that end, we expand the recently proposed linear noise approximation (LNA) technique to this non-Markovian "delay" case. The analysis first leads to a nonlinear delay-differential equation (DDE) with multiplicative noise for the mean activity. The LNA then yields two coupled DDEs, one of which is driven by additive Gaussian white noise. These equations on their own provide an excellent approximation to the full network dynamics, which are much longer to integrate. They further allow us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations of the full network dynamics, for the large range of parameters where both the intrinsic stochasticity and the conduction delay are necessary for the occurrence of oscillations. The intrinsic noise arises from the probabilistic description of each neuron, yet it is expressed at the system activity level, and it can only be controlled by the system size. In fact, its effect on the fluctuations in system activity disappears in the infinite network size limit, but the characteristics of the oscillatory activity depend on all model parameters including the system size. Using the Hilbert transform, we further show that the intrinsic noise causes sporadic strong fluctuations in the phase of the gamma rhythm. © Published by the American Physical Society.

KW - Computation theory

KW - Differential equations

KW - Neural networks

KW - Power spectrum

KW - Stochastic systems

KW - Additive Gaussian white noise

KW - Delay differential equations

KW - Infinite network size limit

KW - Intrinsic randomness

KW - Linear noise approximation

KW - Population activities

KW - Probabilistic descriptions

KW - Theoretical expression

KW - Low noise amplifiers

KW - biological model

KW - cytology

KW - nerve cell

KW - nerve cell inhibition

KW - nerve cell network

KW - physiology

KW - statistical model

KW - statistics

KW - Linear Models

KW - Models, Neurological

KW - Nerve Net

KW - Neural Inhibition

KW - Neurons

KW - Stochastic Processes

U2 - 10.1103/PhysRevE.90.012702

DO - 10.1103/PhysRevE.90.012702

M3 - Article

C2 - 25122330

SN - 1539-3755

VL - 90

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 1

ER -