Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling

Abstract

The phase-resetting curve (PRC) of a neural oscillator describes the effect of a perturbation on its periodic motion and is therefore useful to study how the neuron responds to stimuli and whether it phase locks to other neurons in a network. Combining theory, computer simulations and electrophysiological experiments we present a simple method for estimating the PRC of real neurons. This allows us to simplify the complex dynamics of a single neuron to a phase model. We also illustrate how to infer the existence of coherent network activity from the estimated PRC.

Figures

FIG. 1

Estimation of phase-resetting curves in a Morris-Lecar neuron model [8]. Black lines represent the actual PRC calculated numerically from the full model. Gray lines with circles represent the estimation of the PRC from the membrane potential with our approach. (a) Type I excitability: The match between the real and the estimated PRCs is perfect. (b) Type II excitability: There is only a small mismatch at the beginning of the cycle.

FIG. 2

Experimental estimation of phase-resetting curves. (a) Traces of a neuron’s membrane potential. The effect of the perturbing current pulse can be clearly seen in each cycle at a different phase. (b) Estimated PRC (thick black line), membrane-potential cycle with a perturbation at an arbitrary phase (gray line) and odd part of the inhibitory interaction function (see text; thin line). Each curve has been rescaled to improve visualization. (c) Raw estimation of the PRC (dots) and smoothing over a 2π/3 interval (gray line) compared with the estimated PRC with our approach. Both curves match, which indicates that the raw data are consistent with a phase model. (d) Same as (c) but after shuffling the raw PRC data. The PRC is roughly flat and yields inconsistent results with the smoothing; i.e., the shuffled data cannot be described by a phase model.