Spectral analysis of oscillatory neural circuits.

Oscillatory dynamics are found at all levels of the nervous system. The goal of our current research on the control of rhythmic motor output by the lamprey spinal cord is to determine the features of neuronal coupling that lead to stable oscillatory activity and precisely-controlled intersegmental phase. Since our experimental manipulations can greatly increase the variability of the ventral root bursting pattern, it is important for us to employ a data analysis method which remains valid independent of this variability. Traditional analysis approaches which rely on identification of burst event times do not generally satisfy this requirement. In this paper, we illustrate the application of a straightforward statistically-based method for determining important parameters of oscillatory motor circuits using Fourier spectral analysis of spike trains. The frequency, phase, and their variabilities can be quantified; and the relative strength of coupling between different parts of the circuit can be tested for statistical significance. The approach we adopt is highly convenient for neuroscientists who study oscillatory systems as it operates directly on trains of action potentials stored as lists of event times (point-processes). Basic concepts and practical issues concerning use of Fourier analysis are discussed.