The most likely voltage path and large deviations approximations for integrate-and-fire neurons.

Area of Science:

• Computational Neuroscience
• Mathematical Biology

Background:

• Noisy integrate-and-fire (IF) neurons are fundamental models in computational neuroscience.
• Understanding subthreshold voltage dynamics is crucial for interpreting neuronal activity.
• Inferring neuron behavior from spike trains is a significant challenge.

Purpose of the Study:

• To develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy IF neuron.
• To provide approximations for inferring neuron parameters and firing characteristics from observed spike trains.
• To validate the developed methods using in vitro experimental data.

Main Methods:

• Formulated the problem as finding an optimal voltage path satisfying an Euler-Lagrange equation.
• Employed analytical solutions for special cases and a numerical shooting algorithm for general cases.
• Utilized Freidlin-Wentzell theory for large deviations principles to approximate firing rate and interspike interval distributions.

Main Results:

• Developed a method to compute the most likely subthreshold voltage path for noisy IF neurons.
• Derived approximations for the likelihood of a neuron model generating observed spikes.
• Obtained approximations for the instantaneous firing rate and interspike interval distributions.
• Validated the approach by comparing computed voltage paths with in vitro recordings.

Conclusions:

• The developed methods provide a robust framework for inferring subthreshold dynamics from spiking activity.
• The approach offers valuable tools for analyzing neuronal function and characterizing neuron models.
• This work bridges theoretical advancements in stochastic processes with practical applications in neuroscience.