The Phase Oscillator Approximation in Neuroscience: An Analytical Framework to Study Coherent Activity in Neural Networks

Abstract

One of the major challenges in neuroscience today is to understand how coherent activity emerges in neural networks from the interactions between their neurons, as well as its role in normal and pathological brain function. Probably the two most relevant examples of coherent activity in the brain are synchronization and phase-locking. The phase oscillator approximation used in physics and the mathematical models based thereon provide a powerful tool to investigate the biophysical mechanisms underlying these phenomena. In particular, the experimental or numerical determination of the phase–response curve, which derives from the intrinsic properties of a real or a simulated neuron, allows one to greatly simplify the analytical treatment of their dynamics, as well as their computational modeling. In this way, it is possible to predict the existence and stability of phase-locked states and of synchronized assemblies in real and simulated neural networks with electrical or chemical synapses. The phase–response curve also determines the stability of repetitive neuronal firing thereby affecting spike-time reliability and noise-induced synchronization. Moreover, for neurons that fire repetitively, the phase–response curve is directly related to the waveform of the input that most likely precedes an action potential, i.e., to the spike-triggered average, or optimal stimulus. Here, we discuss these phenomena with special emphasis on the implications for neural function.