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A flexible likelihood approach for predicting neural spiking activity from oscillatory phase.



The synchronous ionic currents that give rise to neural oscillations have complex influences on neuronal spiking activity that are challenging to characterize.

New method

Here we present a method to estimate probabilistic relationships between neural spiking activity and the phase of field oscillations using a generalized linear model (GLM) with an overcomplete basis of circular functions. We first use an L1-regularized maximum likelihood procedure to select an active set of regressors from the overcomplete set and perform model fitting using standard maximum likelihood estimation. An information theoretic model selection procedure is then used to identify an optimal subset of regressors and associated coefficients that minimize overfitting. To assess goodness of fit, we apply the time-rescaling theorem and compare model predictions to original data using quantile-quantile plots.


Spike-phase relationships in synthetic data were robustly characterized. When applied to in vivo hippocampal data from an awake behaving rat, our method captured a multimodal relationship between the spiking activity of a CA1 interneuron, a theta (5-10 Hz) rhythm, and a nested high gamma (65-135 Hz) rhythm.

Comparison with existing methods

Previous methods for characterizing spike-phase relationships are often only suitable for unimodal relationships, impose specific relationship shapes, or have limited ability to assess the accuracy or fit of their characterizations.


This method advances the way spike-phase relationships are visualized and quantified, and captures multimodal spike-phase relationships, including relationships with multiple nested rhythms. Overall, our method is a powerful tool for revealing a wide range of neural circuit interactions.

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