Modeling relationships between rhythmic processes and neuronal spike timing.

Neurons are embedded in complex networks, where they participate in repetitive, coordinated interactions with other neurons. Neuronal spike timing is thus predictably constrained by a range of ionic currents that shape activity at both short (milliseconds) and longer (tens to hundreds of milliseconds) timescales, but we lack analytical tools to rigorously identify these relationships. Here, we innovate a modeling approach to test the relationship between oscillations in the local field potential (LFP) and neuronal spike timing. We use kernel density estimation to relate single neuron spike timing and the phase of LFP rhythms (in simulated and hippocampal CA1 neuronal spike trains). We then combine phase and short (3 ms) spike history information within a logistic regression framework ("phaseSH models"), and show that models that leverage refractory constraints and oscillatory phase information can effectively test whether-and the degree to which-rhythmic currents (as measured from the LFP) reliably explain variance in neuronal spike trains. This approach allows researchers to systematically test the relationship between oscillatory activity and neuronal spiking dynamics as they unfold over time and as they shift to adapt to distinct behavioral conditions.