Fig 1.
(A) The visual cortex and other cortical areas provide an image stream with optic flow and visual features. (B) Processing in cortical areas provides input to the hippocampus and allows for a mapping between the sensed image stream and the representation of spatial location. (C) In our model entorhinal cortex has two modules generated by functionally different mechanisms, estimating location through optic flow for the moving feature system or through triangulation for the static feature system. In this diagram, we also included the anatomical projection from visual cortex to entorhinal cortex, which is currently not used in our model. Therefore, we show this projection as dashed line.
Fig 2.
Shows compression influences the static feature system, while the moving feature system remains unaffected.
The box in configuration A (part A of Fig 2) is square and for configuration B (part B of Fig 2) the box is rectangular. (C) Estimated location for the moving feature system in configuration A. (D) Estimated location for the moving feature system in configuration B showing that estimates of location correctly change with compression. (E) Estimated location for the static feature system in configuration A. (F) Estimated location for the static feature system in configuration B. This shows that this static feature system inaccurately estimates location as if the box were to appear as uncompressed.
Fig 3.
Shows the compression in configuration B compared to configuration A.
(A) Simulated grid cell firing pattern from a simulated dorsal entorhinal cell for (A) configuration A (grid score 1.88) and (B) for configuration B (grid score 1.91). (C) Correlation values for different magnitudes of compression of B relative to A shows a peak correlation at a compression of ≈ 3.1%. (D) The simulated grid cell firing pattern from the ventral entorhinal cell for (D) configuration A (grid score 1.66) and (E) configuration B (grid score 1.25) based on inaccurately estimated locations in Fig 2F. (F) Correlation value for different magnitudes of compression of configuration B relative to configuration A shows that the grid cell firing in configuration B needs to be increased by a compression factor of ≈ 95.5% (about 50 cm) to obtain maximum correlation with the grid cell firing pattern from configuration A.
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.
Table 1.
Default parameter values for the synthesized trajectories, spherical camera model, and module model.
Some simulations have changed parameter values and we denoted this explicitly.
Fig 5.
Shows the geometric constraints of the model for the static feature system.
(A) Constraint for features sampled on northern or southern wall. (B) Constraint for features sampled on western or eastern wall.