Fig. 2.

(A) A ring of east velocity selective cells has outgoing connections onto the attractor ring that are biased in the clockwise direction. Such cells also receive unbiased incoming connections from attractor network cells (not shown). Thus, these east velocity selective cells will fire conjunctively if the animal is moving east and the attractor bump is nearby on the ring. When these cells fire, the biased outgoing connections to the attractor network will then excite cells clockwise relative to the current attractor bump and inhibit cells active in the bump. Thus, the attractor bump will move in the clockwise direction. (B) Similarly, when the animal moves west, the firing of west-conjunctive cells with counterclockwise biased connections will cause the attractor pattern to move counterclockwise. (C) As the animal moves east, the phase of the attractor bump rotates clockwise at a rate proportional to the velocity (Eq. 2). The firing rate of an individual cell (shaded gray) then becomes a periodic function of position (Eq. 3). The firing rates of all other attractor cells are also periodic functions of position with the same period but different phases, yielding a module of 1D grid cells. (D) Schematic of a landmark cell correcting the attractor bump phase (Eq. 4). A single landmark cell can provide excitation that is centered at a certain location on the attractor network ring. When this landmark cell fires, its efferent synapses provide excess excitation to this location, thereby pulling the phase of the attractor bump toward the peak of the landmark cell’s efferent synaptic strength profile.