Spatial synchronization codes from coupled rate-phase neurons
Fig 7
Demonstration of a 1D phaser network and target cell learning.
(A+B) We defined a set of 64 place and 64 notch tuning functions as 1D spatial inputs on the range [0, 1] (Methods). (A) Spatial inputs (top, ‘Place’-driven network; bottom, ‘Notch’-driven network) drive 128 pairs of negative (blue circles) and positive (orange circles) phasers. Inputs excite the negative phasers which suppress the positive phasers (Fig 6A). Phasers at position 0.5 are highlighted. (B) A 1-hr simulation sampled spike phase for a 1-min triangle-wave trajectory traversing the space. For the highlighted phasers in (A), joint space-phase distributions of spike timing (left) show the phaser inputs to a downstream target neuron (right). From top to bottom (input/phaser network layer): place/positive, place/negative, notch/negative, and notch/positive. (C-G) Supervised competitive learning over presynaptic phaser inputs trained a ‘target burster’ model (B, right) to follow a spatial phase code. (C) Supervised phase code for training with two modes: theta trough on the left (position 0), theta peak on the right (position 1). Black: desired activity modes; white: untrained. Inset: prior to training, the target burster randomly drifted in phase due to a stochastic input current (Eq (11); S7 Fig, panel D). (D) Competitive kWTA weights (Table 4; Methods) for connections from each of the four input/phaser network layers in (A) to the target burster. (E) Total weighted phaser network input to the target burster. (F+G) 1-hr simulations of a 1-min triangle-wave trajectory spanning the range [0, 1]. Target burster output (burst phase) is shown without (F) and with (G) intrinsic noise (σ; Table 4). Arrows: phase trajectories for rightward (F, lower arrow) or leftward (F, upper arrow) movement; gray rectangles: supervised phase code from (C); red highlight: region with minimal phaser input based on panels (D) and (E). Multiple theta cycles are shown (y-axis) for clarity.