Matthew H. Higgs, Charles J. Wilson J Neurosci Methods. 289:23-30.

Background: The phase resetting curve (PRC) is a primary measure of a rhythmically firing neuron's responses to synaptic input, quantifying the change in phase of the firing oscillation as a function of the input phase. PRCs provide information about whether neurons will synchronize due to synaptic coupling or shared input. However, PRC estimation has been limited to in vitro preparations where stable intracellular recordings can be obtained and background activity is minimal, and new methods are required for in vivo applications.
New method: We estimated PRCs using dense optogenetic stimuli and extracellular spike recording. Autonomously firing neurons in substantia nigra pars reticulata (SNr) of Thy1-channelrhodopsin 2 (ChR2) transgenic mice were stimulated with random barrages of light pulses, and PRCs were determined using multiple linear regression.
Results: The PRCs obtained were type-I, showing only phase advances in response to depolarizing input, and generally sloped upward from early to late phases. Secondary PRCs, indicating the effect on the subsequent ISI, showed phase delays primarily for stimuli arriving at late phases. Phase models constructed from the optogenetic PRCs accounted for a large fraction of the variance in ISI length and provided a good approximation of the spike-triggered average stimulus.
Comparison with existing methods: Compared to methods based on intracellular current injection, the new method sacrifices some temporal resolution. However, it should be much more widely applicable in vivo, because only extracellular recording and optogenetic stimulation are required.
Conclusions: These results demonstrate PRC estimation using methods suitable for in vivo applications.

Figure 1: ChR2 current responses to optogenetic barrage stimulation. A. 9 s stimulus barrage (top, blue trace) and current response (bottom trace) in an SNr neuron (V = -80 mV). The baseline holding current was subtracted from the trace.
B. Expanded view of stimulus barrage and steady-state response, showing the summated fluctuations produced by individual stimulus pulses. C. Mean (bottom, black line) and SD (top, gray line) of stimulus current measured in 1 s bins (n = 6 cells). D. Average current response to a stimulus pulse in the example cell during the steady-state period. The average response rises from a non-zero baseline resulting from the decay of responses to previous stimulus pulses. The fitted function (red line) is the convolution of a double exponential, I0 + A exp(-t / rise) - A exp(-t / decay), with the square-pulse waveform of an individual stimulus pulse. For this cell, rise = 1.23 ms and decay = 6.13 ms.

Figure 2: Spike responses to optogenetic barrage stimulation. A. Optogenetic pulse barrage (top, blue trace) and corresponding spike response of an SNr neuron recorded in the on-cell voltage-clamp mode (bottom, black trace). Top panel shows the autonomous firing before stimulus onset (up to 1 s) and the initial response. Bottom panel includes a portion of the steady-state response, showing the sustained increase in firing rate and variability of ISIs. B. ISIs of this cell during this barrage. C. Effect of optogenetic barrages on mean firing rate (steady-state) (n = 18 cells). D. Effect of optogenetic barrages on CVISI.
Figure 3: Primary and secondary PRCs measured by optogenetic barrage stimulation. A. PRC of an example SNr neuron. The primary PRC is the portion to the right of the vertical axis (phases of 0-1), and the secondary PRC is the portion to the left of the axis. Typical features seen in this cell are the upward slope and lack of a negative region in the primary PRC and the relatively small negativity in the secondary PRC. Error bars are smaller than the size of the symbols. B. Primary and secondary PRCs of 18 SNr neurons. The PRC from panel A is shown in red.

Figure 4: Prediction of individual ISI lengths by phase models with experimental PRCs. A. A subset of phase trajectories generated by the model for the example cell. The individual stimulus pulses produce rapid phase increases, with the largest increases occurring where the phase corresponds to the peak of the PRC. The curvature of the intervening phase trajectories results from a below-average stimulus (where the average includes pulses and inter-pulse intervals) interacting with the PRC and thereby slowing the rate of phase advance.
B. Individual model-generated ISIs compared to the corresponding real ISIs of the example neuron. For this test, the model phase was set to 0 at the beginning of each ISI. In this cell, r = 0.883.

Figure 5: Prediction of the spike-triggered average stimulus by phase models with experimental PRCs. A. Free-running model prediction of spike response to stimulus barrage. Red marks indicate model spike times. Black trace is spike response of SNr neuron with the PRC used to generate the model. B. Probability density of model phase at real spike times. Note the large peak around phases of 0/1, showing substantial correspondence between model and cell oscillations. C. Spike-triggered average stimuli for the example cell (blue trace) and the corresponding model (red trace).