Simulations predict differing phase responses to excitation vs. inhibition intheta-resonant pyramidal neurons

Rhythmic activity is ubiquitous in neural systems, with theta-resonant pyramidal neurons integrating rhythmic inputs in manycortical structures. Impedance analysis has been widely used to examine frequency-dependent responses of neuronal mem-branes to rhythmic inputs, but it assumes that the neuronal membrane is a linear system, requiring the use of small signalsto stay in a near-linear regime. However, postsynaptic potentials are often large and trigger nonlinear mechanisms (voltage-gated ion channels). The goals of this work were to1) develop an analysis method to evaluate membrane responses in thisnonlinear domain and2) explore phase relationships between rhythmic stimuli and subthreshold and spiking membranepotential (Vmemb) responses in models of theta-resonant pyramidal neurons. Responses in these output regimes were asym-metrical, with different phase shifts during hyperpolarizing and depolarizing half-cycles. Suprathreshold theta-rhythmic stim-uli produced nonstationary Vmembresponses. Sinusoidal inputs produced“phase retreat”: action potentials occurredprogressively later in cycles of the input stimulus, resulting from adaptation. Sinusoidal current with increasing amplitudeover cycles produced“phase advance”: action potentials occurred progressively earlier. Phase retreat, phase advance, andsubthreshold phase shifts were modulated by multiple ion channel conductances. Our results suggest differential responsesof cortical neurons depending on the frequency of oscillatory input, which will play a role in neuronal responses to shifts innetwork state. We hypothesize that intrinsic cellular properties complement network properties and contribute to in vivophase-shift phenomena such as phase precession, seen in place and grid cells, and phase roll, also observed in hippocam-pal CA1 neurons