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

Rhythmic activity is ubiquitous in neural systems, with theta-resonant pyramidal neurons integratingrhythmic inputs in many cortical structures. Impedance analysis has been widely used to examinefrequency-dependent responses of neuronal membranes to rhythmic inputs, but it assumes that the neuronalmembrane is a linear system, requiring the use of small signals to stay in a near-linear regime. However,postsynaptic potentials are often large and trigger nonlinear mechanisms (voltage-gated ion channels). Thegoals of this work were to 1. develop an analysis method to evaluate membrane responsesin this nonlinear domain and 2. explore phase relationships between rhythmic stimuli and subthreshold and spiking membrane potential (V_memb) responses in models of theta-resonant pyramidal neurons. Responses in these output regimes were asymmetrical, with different phase shifts during hyperpolarizing and depolarizing half-cycles.Suprathreshold theta-rhythmic stimuli produced nonstationary Vmemb responses .Sinusoidal inputs produced phase retreat: action potentials occurred progressively later in cycles of theinput stimulus, resulting from adaptation. Sinusoidal current with increasing amplitude overcycles produced phase advance: action potentials occurred progressively earlier. Phase retreat,phase advance, and subthreshold phase shifts were modulated by multiple ion channel conductances. Our results suggest differential responses of cortical neurons depending on the frequency of oscillatory input, which will play a role inneuronal responses to shifts in network state. We hypothesize that intrinsic cellular properties complementnetwork properties and contribute to in vivo phase-shift phenomena such as phase precession, seen in placeand grid cells, and phase roll, also observed in hippocampal CA1 neurons.