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

Area of Science:

• Computational neuroscience
• Theoretical neuroscience
• Neural network dynamics

Background:

• Neural variability presents a significant challenge in neuroscience.
• Understanding the mechanisms generating neural oscillations, such as gamma rhythms, is critical.

Purpose of the Study:

• To investigate the roles of intrinsic stochasticity and conduction delays in generating fast neural oscillations (gamma) in a globally coupled inhibitory neural network.
• To extend the linear noise approximation (LNA) to model non-Markovian systems with delays.

Main Methods:

• Developed a theoretical framework using computational modeling and the linear noise approximation (LNA).
• Derived nonlinear delay-differential equations (DDEs) with multiplicative and additive noise to approximate network dynamics.
• Computed the power spectrum of population activity analytically and compared it with numerical simulations.

Main Results:

• The extended LNA accurately approximates the full network dynamics, reducing computational load.
• Analytical power spectrum results closely match numerical simulations across a wide parameter range.
• Both intrinsic noise and conduction delays are essential for the emergence of oscillations.
• Intrinsic noise, dependent on network size, influences oscillatory characteristics and causes phase fluctuations in gamma rhythms.

Conclusions:

• The study provides a robust analytical method for studying neural oscillations in complex networks.
• Intrinsic noise and conduction delays are identified as key drivers of gamma oscillations.
• The findings offer insights into the origins of neural variability and rhythmic activity.