# How to correctly quantify neuronal phase-response curves from noisy recordings

## TL;DR

This paper investigates how to accurately estimate neuronal phase-response curves (PRCs) from noisy recordings, emphasizing the importance of stimulus strength to reflect true neuronal dynamics and avoid distortions caused by large stimuli.

## Contribution

It demonstrates that large stimuli distort PRC measurements and provides guidelines for selecting appropriate stimulus strengths to reliably infer spike-onset bifurcations.

## Key findings

- Large stimuli distort PRC estimates beyond recognition.
- Proper stimulus strength is crucial for accurate PRC estimation.
- Guidelines are provided for stimulus selection in noisy conditions.

## Abstract

At the level of individual neurons, various coding properties can be inferred from the input-output relationship of a cell. For small inputs, this relation is captured by the phase-response curve (PRC), which measures the effect of a small perturbation on the timing of the subsequent spike. Experimentally, however, an accurate experimental estimation of PRCs is challenging. Despite elaborate measurement efforts, experimental PRC estimates often cannot be related to those from modeling studies. In particular, experimental PRCs rarely resemble the generic PRC expected close to spike initiation, which is indicative of the underlying spike-onset bifurcation. Here, we show for conductance-based model neurons that the correspondence between theoretical and measured phase-response curve is lost when the stimuli used for the estimation are too large. In this case, the derived phase-response curve is distorted beyond recognition and takes on a generic shape that reflects the measurement protocol, but not the real neuronal dynamics. We discuss how to identify appropriate stimulus strengths for perturbation and noise-stimulation methods, which permit to estimate PRCs that reliably reflect the spike-onset bifurcation -- a task that is particularly difficult if a lower bound for the stimulus amplitude is dictated by prominent intrinsic neuronal noise.