Effect of sampling frequency on the measurement of phase-locked action potentials

Phase-locked spikes in various types of neurons encode temporal information. To quantify the degree of phase-locking, the metric called vector strength (VS) has been most widely used. Since VS is derived from spike timing information, error in measurement of spike occurrence should result in errors in VS calculation. In electrophysiological experiments, the timing of an action potential is detected with finite temporal precision, which is determined by the sampling frequency. In order to evaluate the effects of the sampling frequency on the measurement of VS, we derive theoretical upper and lower bounds of VS from spikes collected with finite sampling rates. We next estimate errors in VS assuming random sampling effects, and show that our theoretical calculation agrees with data from electrophysiological recordings in vivo. Our results provide a practical guide for choosing the appropriate sampling frequency in measuring VS.