The dendrite impacts the phase of entrainment to rhythmic inputs.

A: Perforated patch recording of a spontaneously spiking neuron with an average perturbed firing rate fp. A cosine shaped stimulation delivered in the proximal illumination condition entrained the discharge of the cell. The spike tends to occur near the peak of the stimulation, corresponding to phases near 0.5. Left arrow indicates -30 mV. B: Simulated (Eq 5) plot of the perturbed period (Tp) as a function of the effective phase of the preceding spike (for θp = 0.9). C: Iterative map of ψn+1 versus ψn generated based on the simulated plot shown in B. The map (red) crosses the diagonal (blue), achieving a stable fixed point at phase 0.537, as demonstrated by the Cobweb plot (black arrows). Yellow box highlights stable fixed point. D: The probability distribution of effective phases shows a peak at approximately 0.5, in accordance with the raw data shown in A. E: Same as A for full-field illumination. Spikes occur slightly after peak of cosine stimulation. Left arrow indicates 0 mV. F: Same as B for full-field illumination (for θf = 0.75). G: Same as C for full-field illumination. The map (green) crosses the diagonal (blue), generating a stable fixed point at phase 0.6. Phase locking induced by full-field stimulation occurs at a delayed phase compared to proximal stimulation (shown in A-D). H: Same as D for full-field illumination. The phase of the peak in the probability distribution is later than that corresponding to proximal illumination and shown in D. I: Distribution of circular variances of effective phases (each calculated from a corresponding probability distribution of effective phases as in panels D and H) for various stimulation frequencies (2.5-21Hz) in n = 6 cells, under three stimulation conditions: proximal illumination (red), somatic current injection (purple) and full-field illumination (green). Mean vectors are shown in black. Proximal illumination and somatic current injection induce locking in a similar range of phases, but current injection is more effective in entraining the neuron’s spiking. Phase locking generated by full-field illumination is shifted rightward compared to proximal illumination and current injection by 0.072–0.104. Yellow insets are zoomed-in versions of panels C and G that show that the shift in the model of the empirical distribution of locked phases agrees with the phase model simulations. See Materials and Methods for derivation of P-values.