Figure 3.

Velocity-controlled oscillators (VCOs) could be implemented in dendrites (a, red rectangles) or neurons (b, red circles). In both cases the VCOs are driven by a speed modulated head-direction cell or population of cells (firing rates r_HDCi = v.d_i, where ν is the rat’s current velocity and d_i is the preferred direction for the i^th VCO). (a) An implementation in which dendritic VCOs (sinusoidal dendritic MPOs with frequency f_ai) sum with the baseline input (frequency f_b, blue line) and the interference patterns from different VCOs are multiplied at the grid cell soma (pale blue circle), see equation 6 and Figure 4. (b) An example in which neuronal VCOs (having sinusoidal MPOs with frequency f_ai) fire spikes with frequency f_ai. These spikes affect the membrane potential of the grid cell (modeled as a leaky-integrate and fire neuron, pale blue circle) whose membrane potential is also modulated by the baseline input (frequency f_b, blue line). Figure 3a is adapted from Burgess et al. (2007).