Comparison of Langevin and Markov channel noise models for neuronal signal generation

TL;DR

This study compares Langevin and Markov models of neuronal channel noise, revealing that the Langevin model underestimates noise and overestimates information rates, even with many channels, questioning its accuracy for neuronal simulations.

Contribution

It provides a detailed comparison showing the limitations of the Langevin model in accurately representing channel noise compared to the Markov model.

Findings

Langevin model underestimates channel noise compared to Markov model.

Langevin model overestimates information rates in neuronal simulations.

Differences between models persist even with large channel numbers.

Abstract

The stochastic opening and closing of voltage-gated ion channels produces noise in neurons. The effect of this noise on the neuronal performance has been modelled using either approximate or Langevin model, based on stochastic differential equations or an exact model, based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either $Na^{+}$ and $K^{+}$, or only $K^{+}$ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and non-spiking membranes. Even with increasing numbers of channels the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels.