Figure 4. Analytically predicted Φ–I curves for variations in oscillation parameters (amplitude and frequency) and intrinsic cell properties (R_in and τ_m).

Analytically derived Φ–I curves for a passive point neuron model with the following parameters, except where otherwise stated: R_in= 150 MΩ, τ_m= 20 ms, I_osc= 40 pA, oscillation frequency = 5 Hz (these default values shown by the red traces). A, increasing oscillation amplitude leads to horizontal stretch of the f–I curve, symmetrical about its midpoint. B, increasing oscillation frequency leads to an upward and rightward shift of the Φ–I curve, along with an increase in its slope. C, decreasing R_in leads to a rightward shift of the Φ–I curve, with no effect on curve slope or phase lag. D, changing τ_m has an effect identical to proportional changes in oscillation frequency. E, parallel changes in R_in and τ_m (as seen with, e.g. a change in net synaptic drive to a cell) yield a simple combination of the effects of independent changes in R_in and τ_m. Specifically, increased τ_m and R_in yields a left shift of the curve, with increased phase lag and an increase in slope. In the lower panel of E, Φ–I curves have been horizontally aligned by the midpoint (dashed line), emphasizing that substantial changes in conductance state of the cell could yield surprisingly small changes in the shape of Φ–I curve (dependent on specific parameters; see text for details).