Analyzing spike trains with circular statistics

Daisuke Takeshita, University of Missouri-St. Louis
John T. Gale, Massachusetts General Hospital
Erwin B. Montgomery, University of Wisconsin School of Medicine and Public Health
Sonya Bahar, University of Missouri-St. Louis
Frank Moss, University of Missouri-St. Louis

Abstract

In neuroscience, specifically electrophysiology, it is common to replace a measured sequence of action potentials or spike trains with delta functions prior to analysis. We apply a method called circular statistics to a time series of delta functions and show that the method is equivalent to the power spectrum. This technique allows us to easily visualize the idea of the power spectrum of spike trains and easily reveals oscillatory and stochastic behavior. We provide several illustrations of the method and an example suitable for students, and suggest that the method might be useful for courses in introductory biophysics and neuroscience. © 2009 American Association of Physics Teachers.