Self-Consistent Scheme for Spike-Train Power Spectra in Heterogeneous Sparse Networks.

Area of Science:

• Computational neuroscience
• Neural network dynamics
• Spiking neural networks

Background:

• Recurrent networks of spiking neurons exhibit an asynchronous state with low cross-correlations, mimicking cortical neuron activity.
• While spatial correlations are minimal, temporal correlations in spike trains are significant and influenced by network parameters.
• Understanding the origins of diverse temporal correlation patterns in these networks remains a challenge.

Purpose of the Study:

• To extend existing computational methods for analyzing single-cell correlations in homogeneous spiking neural networks.
• To develop a novel framework for analyzing temporal correlations in heterogeneous spiking neural networks with varying parameters and connectivity.

Main Methods:

• Extended an iterative single-neuron simulation scheme to homogeneous networks with strong inhibition and synaptic filters, using an averaging procedure.
• Developed an approximation method for heterogeneous networks, lumping neurons into classes and using a Gaussian approximation for input currents.
• Validated the approximations by comparing results with large-scale recurrent network simulations.

Main Results:

• The extended scheme successfully analyzes temporal correlations in homogeneous networks with strong inhibition.
• The novel approximation method accurately predicts correlation patterns in heterogeneous networks across various parameters.
• The findings demonstrate the method's efficacy in large-scale network simulations.

Conclusions:

• The developed computational framework effectively quantifies temporal correlations in both homogeneous and heterogeneous spiking neural networks.
• This method provides insights into how network heterogeneity shapes the asynchronous state.
• The approach offers a valuable tool for understanding neural dynamics and information processing in complex neural circuits.