Fluctuation-response relations for integrate-and-fire models with an absolute refractory period

Area of Science:

• Computational neuroscience
• Theoretical physics
• Mathematical modeling of neural systems

Background:

• Stochastic integrate-and-fire (IF) models are fundamental in computational neuroscience.
• Relating spontaneous fluctuations to stimulus response is crucial for understanding neural dynamics.
• Previous analyses (Lindner, 2022) simplify IF models, omitting refractory periods and spike shapes.

Purpose of the Study:

• To develop an exact fluctuation-response relation (FRR) for IF models with realistic features.
• To analyze the impact of non-vanishing refractory periods and finite spike shapes on neural response.
• To extend the applicability of FRR to more biologically plausible neuron models.

Main Methods:

• Incorporation of reset mechanisms into the IF model equation.
• Application of Rice-like averaging to stochastic differential equations.
• Utilizing the Furutsu-Novikov theorem for fluctuation analysis.
• Derivation of an exact FRR for white Gaussian noise.

Main Results:

• An exact FRR was derived for the IF model with refractory state and white Gaussian noise.
• The inclusion of refractory periods and spike shapes complicates the standard FRR derivation.
• An approximation for colored Gaussian noise was discussed.

Conclusions:

• The study provides a more accurate theoretical framework for analyzing neural responses.
• The derived FRR offers deeper insights into the dynamics of spiking neurons.
• Future work may explore more complex noise models and neuron types.