FIGURE 1 | One-dimensional attractor map model for head direction encoding based on neural integration of head angular velocity signals.

a | Head direction cells are arranged symbolically in a circle in order of their relative head directional preferences. Each cell (coloured dots) connects with nearby cells with a synaptic strength (or connection probability) that declines as a function of distance (red and grey lines). The network is subject to global feedback inhibition (not illustrated) that limits the total neural activity. Activity in such a network has a most probable configuration in which the activity is focused at one point and declines with distance from that point (warm colours represent high activity, progressively cool colours represent progressively lower activity). Such a network would keep track of head direction if the hill or 'bump' of activity could be made to rotate around the ring in correspondence with changes in head direction. b | Rotation of the bump in the clockwise or anticlockwise directions can be achieved by an intermediate group of two types of conjunctive neuron that receive information about head angular velocity from the vestibular system (dashed arrows) and information about current head orientation from the cells immediately above them in the outer ring. The intermediate group of cells must be of two classes: cells receiving information about clockwise motion project to the right of the cells in the outer ring from which they receive input, whereas cells receiving anticlockwise vestibular signals project to the left. These hidden layer cells drive the activity bump in the corresponding direction around the ring. In the absence of motion, activation of all hidden layer cells is assumed to be below threshold. In this figure, only active connections are indicated, with the line thickness representing firing rate.

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