Latent Oscillation in Spike Train (LOST)

Kensuke Arai and Robert E. Kass

Inferring oscillatory modulation in neural spike trains (2017)

Introduction

The timing of spikes in a neural spike train are sometimes observed to fire preferentially at certain phases of oscillatory components of brain signals such as the LFP or EEG, ie may be said to have an oscillatory modulation. However, the temporal relationship is not exact, and there exists considerable variability in the spike-phase relationship. Because the spikes themselves are often temporally sparse, assessing whether the spike train has oscillatory modulation, is challenging. Further, the oscillatory modulation may not be uniformly present throughout the entire experiment. We therefore developed a method to detect and also infer the instantaneous phase of the oscillation in the spike train, and also detection for non-stationarity in the modulation of the spikes.

Run LOST on Google Colab directly by following links in this repository.

LOST can be run entirely on Colab without having to download or install the software following the links in this repository. We provide several example datasets and analysis results, as the inference results require some interpretation. The examples will illustrate how to interpret the results, and also some guidelines in the choice of parameters that can affect the inferred oscillations. Notebooks are found in the Notebooks directory above, as are the example data. In particular, here are the parameters and settings that most influence the fit:

• 1. AR(p) innovation variance Generally, allowing the innovation variance to be too large can result in a model of spiking probability that is near 0 where there are no spikes, and nearly 1 at spike times. The probability of observing a spike in the tth timebin is . x is the oscillation at time t and o is the offset. Because of the nonlinearity of the link function, if x has large fluctuations and o is a large, negative number, it is possible that the probability of a spike to be very near 1 only near the spikes, and near 0 everywhere else, even if x is a relatively smoothly varying signal in time. To avoid this the hyperparameters of the AR innovation variance should be changed, either by decreasing the location parameter or by increasing the shape parameter.

• 2. Timescale and knot locations of the post-spike history dependence Both an oscillation and post-spike history explain the history dependence of the spiking probability, but we included both mechanisms in the model to explain history dependence in the spiking arising from different biological mechanisms. We included the post-spike history to account for the refractory period, a property of the neuron and its membrane excitability itself - something that can be observed in isolated electrophysiological experiments. The oscillation we believe to be a network effect. We implement the post-spike history as a function of of lag from the last spike time. There is overlap in the observed spiking probability that these two terms can explain. We assume that the refractory effect is a relatively short-term effect that quickly reaches an asymptotic value following fast function following a spike, and that the oscillation is a longer timescale phenomenon that is smooth in time. The post-spike history function is implemented as cubic splines, and in the example data, we provide some rules of thumb about how to choose the timescale and location and number of knots used. We also illustrate resulting fits for cases where it is difficult to infer an oscillation or post-spike refractory period from the data.