Figure 1.

A: Dual oscillator interference model of phase precession, showing the sum of an oscillatory somatic input (v_s) at 10Hz, and an oscillatory dendritic input at 11.5 Hz (v_d). That is, v_s+ v_d, where v_s=a_scos(w_s t), v_d = a_dcos(w_d t+φ_d), with w_s =10×2π, w_d=11.5×2π, a_s = a_d = 1, φ_d = 0. The sum of the two oscillations is an interference pattern comprising a high frequency “carrier” oscillation (frequency 10.75Hz) modulated by a low frequency “envelope” (frequency 0.75Hz; rectified amplitude varies at 1.5Hz). B: Schematic showing a cell whose firing rate is the rectified sum of both inputs (Θ is the Heaviside function). The top row of A represents the phase at which peaks of the interference pattern occur – i.e. peaks of the overall membrane potential when summing the dendritic and somatic inputs and thus likely times for the firing of an action potential.