Figure 3.

Synaptic connections play a major role in continuous attractor networks. For each of three 2D attractor models, we plot the activity of the sheet of neurons (top in each row) and the synaptic input to each cell caused by that activity (bottom in each row). (A) Each cell in the Fuhs and Touretzky (2006) model projects symmetrically outward in alternating rings of excitatory and inhibitory synapses. Just offset from the center, in this case downward, is an asymmetric inhibitory region (dark blue). When this cell fires, it inhibits the nearby cells except in a small region just above it where other cells are free to fire. Cells have different offset directions, so a bump of activity can form in a small group of cells that each inhibit a different direction around the bump, surrounding it in a ring of inhibition. All the cells here are driven to fire, creating new bumps spontaneously, and the excitatory ring surrounded by inhibition on each side encourages the new bumps to maintain a particular spacing. When the animal moves north, north-conjunctive cells increase in activity (producing the checker boarding of activity), increasing the inhibition on one side of each bump and causing the pattern to shift. (B) In Guanella et al. (2007) each cell has an identical synaptic output: an excitatory Gaussian bump that is inhibitory at long distances. The model has only one bump of activity, which wraps around on all sides, but with a “twist” in the up-down direction (see Figure 1A). The synapses change dynamically with velocity: e.g., when moving north the synaptic output is offset upward on the sheet of cells, which causes the bump to slide in that direction. (C) In Burak and Fiete (2009) the output of each cell is a ring of inhibition, the center offset in the direction the cell tries to move activity bumps (in this case offset two cells upward). The space inside the ring allows a bump to form, each active cell contributing to a strong ring of inhibition around the bump. The cells are driven to fire spontaneously so as many bumps form as is possible. Under the repulsive effects of the inhibitory rings, the bumps pack as tightly as possible, which is in a hexagonal grid. While moving north, north-conjunctive cells are driven strongly, slightly shifting the pattern of the synaptic drive and so shifting the bumps as well.