How the brain keeps the eyes still

Abstract

The brain can hold the eyes still because it stores a memory of eye position. The brain's memory of horizontal eye position appears to be represented by persistent neural activity in a network known as the neural integrator, which is localized in the brainstem and cerebellum. Existing experimental data are reinterpreted as evidence for an "attractor hypothesis" that the persistent patterns of activity observed in this network form an attractive line of fixed points in its state space. Line attractor dynamics can be produced in linear or nonlinear neural networks by learning mechanisms that precisely tune positive feedback.

Figure 1

State space portraits and energy landscapes for the memory and read-out networks. The coordinates of the state space are the firing rates of the neurons in the network. Only two of the dimensions of state space are depicted in the plane, with the height of the energy landscape as the third dimension. The dynamical trajectories in state space correspond to trajectories down the energy landscape. (A) All trajectories in the state space of the memory network flow toward a line attractor (thick line). The corresponding trajectories on the energy landscape flow down the walls of a trough, toward a line of minimum energy at the bottom. (B) All trajectories in the state space of the read-out network flow toward a point attractor. Input to the network controls the location of the point attractor, moving it along the dashed line. A point attractor can be visualized as the minimum of a bowl-shaped energy landscape.

Figure 2

State space portraits of the memory network. Biological realizations of line attractor dynamics are inevitably imperfect, and are accompanied by various types of systematic eye position drift. In all cases, the trajectory along the oblique axis is very slow, and looks like a line of fixed points on short time scales. (A) Point attractor, corresponding to centripetal ocular drift to a null position. (B) No fixed points, corresponding to unidirectional ocular drift and no null position. (C) Saddle point, corresponding to centrifugal ocular drift. (D) Several point attractors spaced along a line, corresponding to multiple null positions.