Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Area of Science:

• Computational neuroscience
• Theoretical neuroscience
• Mathematical biology

Background:

• Calculating steady-state probability densities in multidimensional stochastic systems lacking detailed balance is computationally challenging.
• Stochastic neuron models are crucial for understanding neural dynamics, but incorporating adaptation complicates analysis.

Purpose of the Study:

• To analytically derive stationary probability densities for a stochastic neuron model with adaptation current.
• To investigate the effects of adaptation on the membrane potential statistics of tonically firing neurons.

Main Methods:

• Analytical derivation of stationary joint and marginal probability densities.
• Assumption of weak noise, valid for arbitrary adaptation strength and time scale.

Main Results:

• Predicted a convex shape for the membrane potential distribution.
• Showed that strong and fast adaptation increases the probability of hyperpolarized membrane potentials.
• Identified a finite adaptation time scale that maximizes variability associated with the adaptation current.

Conclusions:

• The developed analytical approach provides insights into the statistical properties of neurons with adaptation.
• Adaptation significantly shapes membrane potential statistics, including distribution shape and hyperpolarization probability.
• Adaptation time scale plays a critical role in modulating neural variability.