Optimal Colored Noise for Estimating Phase Response Curves

Abstract

The phase response curve (PRC) is an important measure representing the interaction between oscillatory elements. To understand synchrony in biological systems, many research groups have sought to measure PRCs directly from biological cells including neurons. Ermentrout et al. andOta et al. showed that PRCs can be identified through measurement of white-noise spike-triggered averages. The disadvantage of this method is that one has to collect more than ten-thousand spikes to ensure the accuracy of the estimate. In this paper, to achieve a more accurate estimation of PRCs with a limited sample size, we use colored noise, which has recently drawn attention because of its unique effect on dynamical systems. We numerically show that there is an optimal colored noise to estimate PRCs in the most rigorous fashion.

Inferring the phase response curve from observation of a continuously perturbed oscillator

“…Recent more practical algorithms exploit weighted STA (WSTA): they imply rescaling of the input within each inter-spike interval to the same length and subsequent averaging with the weights, determined by the length of these intervals 7,10 . Another approach is to use STA with a specific optimal colored noise input 11 .…”