Linear Response of General Observables in Spiking Neuronal Network Models

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Network Dynamics

Background:

• Spiking neuronal networks exhibit complex dynamics influenced by intrinsic properties and network connectivity.
• Understanding how external stimuli modulate these dynamics, particularly spike train statistics, is crucial.
• Existing models often struggle with the long-range temporal dependencies (unbounded memory) present in neural activity.

Purpose of the Study:

• To establish a general linear response framework for spiking neuronal networks with unbounded memory.
• To provide a method for predicting the impact of time-dependent stimuli on spatio-temporal spike correlations.
• To elucidate the relationship between stimuli, neuronal dynamics, network connectivity, and spike train statistics.

Main Methods:

• Developed a general linear response relation based on memory chains.
• Utilized spontaneous network statistics (without external stimuli) to predict responses.
• Employed numerical simulations on a discrete-time integrate-and-fire model for illustration.

Main Results:

• Established a predictive relationship between weak external stimuli and spatio-temporal spike correlations.
• Demonstrated that the linear response is explicitly determined by the interplay of stimuli, intrinsic neuronal properties, and network connectivity.
• Quantified the influence of network memory on the response characteristics.

Conclusions:

• The developed linear response framework offers a powerful tool for analyzing stimulus-evoked activity in complex neuronal networks.
• This approach simplifies the prediction of network responses by leveraging readily available spontaneous activity data.
• The findings highlight the critical role of network memory and connectivity in shaping neural responses to external perturbations.