Differences in Visual-Spatial Input May Underlie Different Compression Properties of Firing Fields for Grid Cell Modules in Medial Entorhinal Cortex
Fig 4
Illustrates the influence of bias-free and biased Gaussian noise on the location estimates and grid cell firing.
(A-D) shows the temporal integration without a transform from polar to Cartesian coordinates (Eq 9). Here the of estimated radial distance and angle based on the integrated linear velocity and rotational velocity follows a Brownian motion model for the bias-free noise and biased noise. (A) Squared distance error for the linear velocity for bias-free noise and (B) squared angular error for the rotational velocity for bias-free noise. (C) Squared distance error and (D) and squared angular error for biased noise. The legend in (A) applies to all panels (A-D). In (D) the blue (model) and black line (data) overlap. (E-F) Euclidean error computed from integration of position in Cartesian coordinates (Eq 9). The Euclidean error between the estimated and ground-truth location for bias-free noise is small in both the moving feature system (E) and in the static feature system (F). (G-H) For biased noise the error increases rapidly due to the error accumulation in the moving feature system (G), but the error stays almost constant for biased-free noise in the static feature system because no error accumulation happens (H). For panels (E-H) the statistics includes 100 trials, where the black line shows the mean and the shaded gray area +-1 STD. Panels (I-L) are analogous to panels (E-H) but provide data for a single trial. (M-P) The corresponding firing patterns of that single trial from the velocity controlled oscillator model are shown for: (M) bias-free noise and the moving feature system; (N) bias-free noise and the static feature system; (O) biased noise and the moving feature system; and (P) biased noise and the static feature system.