From spiking neuron models to linear-nonlinear models.

Area of Science:

• Computational Neuroscience
• Neural Modeling
• Systems Neuroscience

Background:

• Neurons process time-varying inputs into stochastic action potentials.
• Linear-nonlinear (LN) cascade models simplify this input-output mapping.
• Biophysical details of spiking neurons are often omitted in simplified models.

Purpose of the Study:

• To determine if biophysically realistic spiking neuron models can be reduced to a simple LN cascade.
• To investigate the accuracy of LN cascade models for leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF), and Wang-Buzsáki models.
• To develop improved firing rate models for spiking neurons.

Main Methods:

• Utilized analytic results for LIF, EIF, and Wang-Buzsáki models to derive parameter-free linear filters and nonlinearities.
• Employed reverse correlation analysis to determine linear filters and nonlinearities.
• Compared LN cascade model outputs with numerical simulations of spiking neurons under varying input and noise conditions.
• Introduced an adaptive timescale rate model.

Main Results:

• LN cascade models accurately estimate firing rates for EIF and Wang-Buzsáki models across most parameter spaces.
• The LN cascade for EIF and Wang-Buzsáki models can be reduced to a firing rate model with an analytically determined timescale.
• The adaptive timescale rate model significantly enhances the accuracy of instantaneous firing rate estimations.

Conclusions:

• LN cascade models offer a robust framework for approximating the firing rates of complex spiking neurons.
• Analytic derivations provide a parameter-free approach to defining LN components for specific neuron models.
• Adaptive timescale models represent a significant advancement in accurately capturing neural firing dynamics.