A rate code for position error in a ring attractor model of path integration

Path integration is an internal computation of position by integrating velocities over time. In the absence of
external landmarks, path integration accumulates error, causing the internal representation of position to drift
relative to the external world [1,2]. In addition to the well-established role of landmarks in correcting this error,
recent experiments identified a new role of landmarks: recalibrating the path-integration gain, a factor mapping
the animal’s movement through space to an updating of position in its internal representation [3]. Here, we set
out to understand the mechanisms by which landmarks recalibrate the path-integration gain while correcting
position errors. To garner theoretical insight, we derived an expression for the path-integration gain as a function
of synaptic weights of a ring attractor model and analyzed the stability of dynamics when these weights were
tuned via Hebbian plasticity. This analysis revealed a necessary condition that the firing rates of some neurons
must change monotonously with the error in positional representation. As a preliminary test of this prediction, we
analyzed an existing dataset of place cells that were recorded during the recalibration of path-integration gain by
rotating landmarks as a function of the rat’s movement [3]. In 248/400 cells from five rats, firing rates were
correlated with the positional error, estimated by drift in firing locations relative to landmarks in each
experimental session. Across sessions, the slope of this relationship was negatively correlated with the total error
accumulated in a session. Finally, we revisited the model and modified its extrinsic connectivity to reproduce
both roles of landmarks—gain recalibration and error correction—via a rate code of the error, exhibiting the same
negative correlation between slope and total error. Our results suggest a mechanism recruiting a rate code of the
position error as a neural substrate of the interaction between landmarks and path integration.