Figure 10.
Numerical simulations of how a reduction in the gain of a self-motion signal would be expected to affect relative place field size and population vector relationships if the hippocampal population vector was updated as a function of distance moved (path integration) rather than changes in external inputs. Because the head-direction signal is still operative and the lap time remains constant, reducing the linear movement signal would be equivalent to traversing a smaller circle at lower speed. The result is that fewer place fields are traversed, but those that are traversed cover a larger portion of the track. Place fields were simulated as Gaussian firing probability distributions (1 per cell), with centers distributed randomly in a unit square. The black circles in the first column represent the SD of the Gaussians, and the red circles represent the circular trajectories of the rat on the track. Simulated place fields are shown in the second column in which firing rate is represented as a gray scale value (black, 0). The vertical axis represents cell number (1:100), and the horizontal axis represents the angular coordinate (degrees). Variations in net signal-to-noise ratio (see Fig. 9) were simulated by varying the number of sampled laps, although in reality, this parameter is also affected by changes in firing probability. Notice that, as the circle diameter is reduced progressively (0.45, 0.15, and 0.05 for **A–C**, respectively), progressively fewer cells exhibit activity on the circle, but those that do exhibit activity fire over progressively larger regions of the track. The corresponding population vector overlap matrices and mean overlap versus distance (expressed in angular coordinates) functions are shown in the third and fourth columns, respectively.