A Simple Probabilistic and Point-process Response Model for Predicting Every Spike in Optogenetics

Abstract

Optogenetics is a new tool to stimulate genetically targeted neuronal circuits using light flashes that can be delivered at high frequencies. It has shown promise for studying neural circuits that are critically involved in normal behavior as well as neuropsychiatric disorders. The data from experiments in which circuits are stimulated by optogenetics presents the statistical challenge of modeling a high frequency point process (neuronal spikes) while the input is another high frequency point process (light flashes). We propose a new simple probabilistic approach to model the relationships between two point processes which employs additive point-process response functions on the logit scale. The resulting model, Point-process Responses for Optogenetics (PRO), provides explicit nonlinear transformations to link the input point process with the output one. Such response functions may provide important and interpretable scientific insights into properties of the biophysical process that govern neural spiking in response to optogenetics stimulation. We validate the PRO model via out-of-sample prediction on a large dataset from optogenetics experiments. Compared with other statistical and biophysical models, the PRO model yields a superior area-under-the-curve value as high as 93% for predicting every future spike within a 5ms interval. Another advantage of the PRO model is its efficient computation via standard logistic regression procedures. We also demonstrate by simulation that the PRO model performs well for neurons following the classical Leaky Integrate and Fire (LIF) model. A spline extension of the PRO approach is also illustrated. Finally, the PRO model outputs a few simple parameters summarizing how neurons integrate specific patterns of light inputs.