Skip to main content
. 2016 May 18;116(2):868–891. doi: 10.1152/jn.00856.2015

Fig. 7.

Fig. 7.

Binding of the activity bump to space. Relatively weak external input biases the activity bump for any location in the learned space, effectively rendering the megamap a quasi-continuous attractor. A: for each of 400 trials, the initial state is set to the equilibrium state given external input with an amplitude of 0.3 centered at the animal's location (black dot). When the external input amplitude is then reduced to the value indicated for Ipeak, the preexisting activity bump persists but slowly drifts (black curve) until remaining fixed at the location encoded by the equilibrium activity bump (red dot). In the absence of external input (far left), the activity bump drifts to one of a discrete set of point attractors. As Ipeak increases, the activity bump travels a shorter distance along a similar trajectory. B: increasing the number of place cells in the megamap, which increases the density of the population's place fields, slows the drift of the activity bump. The maximum drift speed when Ipeak = 0 (solid curves) appears to follow the cumulative distribution function (CDF), F(Nact) = F0(N0/Nact)0.27 (dashed curves), where Nact is the number of place cells with at least one place field, and F0 is the CDF for a network with Nact = N0 = 9,731.This empirical power law implies that if the attractor network were to include all place cells in the CA3 (Nact = 2 × 105), then the probability that the drift speed exceeds 2 cm/s would be 0.005 (dashed red curve). The CDF for each value of Nact was constructed using the maximum drift speed for each of the 400 trials with Ipeak = 0. The exact network sizes are Nact = 9,731 (black), Nact = 19,465 (blue), and Nact = 38,756 (green). These networks correspond to one place field each 4 cm2 (black), 2 cm2 (blue), and 1 cm2 (green). The drift speed was measured as the distance traveled each second. C: increasing the input magnitude decreases both the speed of the drift and the distance traveled from the animal's location. Both measures were averaged over the 400 trials for each value of Ipeak. Dashed curves show 1 standard deviation. Since the drift from any location becomes negligible given only a weak external input (Ipeak ≥ 0.05), the megamap encodes any location within the continuous space through a stable equilibrium activity bump. For A and C, Nact = 9,731.