A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability
- Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Israel
- Racah Institute of Physics, The Hebrew University of Jerusalem, Israel
Figures
Figure 1
Schematic illustration: possible architectures of grid cell and place cell connectivity.
(a) Two hypotheses on connectivity, with hierarchical relationship between grid cells and place cells. Left: feed-forward connectivity from grid cells to place cells. Right: feed-forward …
Figure 2
Examples of simulation results, demonstrating joint persistent states of place cells and grid cells.
(a) One persistent state of the network (state 1). In each panel, cells are ordered according to their preferred firing locations in one environment. In each grid cell module, positions displaced by …
Figure 3 with 5 supplements
Quantitative mapping of the persistent states expressed by the joint network.
In all panels, the system is placed at 500 initial conditions of three types (a-d: ‘consistent’, e-h: ‘inconsistent’, i-l: ‘all random’). Its state is then analyzed after a 1 s delay period. (a-d) …
Figure 3—figure supplement 1
Analysis of persistent states following initial conditions of type (4).
(a-d) Similar to Figure 3a–d but for ‘Grid cells - random, Place cells - bump’ initial conditions: grid cells were initially set to have random rates, while place cells were set to encode a specific …
Figure 3—figure supplement 2
Bump score dynamics of persistent states.
(a) Bump score dynamics in the ‘consistent’ initial condition, corresponding to all realizations shown in Figure 3a–d. Error bars correspond to ±1 std. (b) Same as (a) but in the ‘inconsistent’ …
Figure 3—video 1
Dynamics under ‘consistent’ initial condition.
Firing rates of place cells (black) and grid cell modules (red, green, and blue) during a single 1 s simulation, in which the network was initialized in a ‘consistent’ state in map 1. Left: neurons …
Figure 3—video 2
Dynamics under ‘inconsistent’ initial condition.
Firing rates of place cells (black) and grid cell modules (red, green, and blue) during a single 1 s simulation, in which the network was initialized in an ‘inconsistent’ state in map 1. Left: …
Figure 3—video 3
Dynamics under ‘all random’ initial condition.
Firing rates of place cells (black) and grid cell modules (red, green, and blue) during a single 1 s simulation, in which the network was initialized in an ‘all random’ state. Left: neurons are …
Figure 4 with 1 supplement
Velocity integration in grid cells can update the place cell representation.
(a) Readout of place cell bump location (black) while grid cell modules (green, red, and blue) integrate a velocity profile (dashed orange line). (b) Mean absolute distance between measured location …
Figure 4—figure supplement 1
Bump score dynamics for each of the embedded maps, corresponding to the realization shown in Figure 4a.
Figure 5
Place cells coordinate the representations of position in distinct grid cell modules.
(a) The need for coupling. Top panel: blue- and red-shaded areas represent schematically the posterior likelihood for the animal’s position in 2-d, obtained from the activity of all grid cells in …
Figure 6
Spontaneously emerging variability of individual grid cell firing rates across firing fields.
(a) Simultaneous firing rates of place cells (black) and grid cells from one module (module #3, blue), shown at three different persistent states that represent periodic locations of module #3. Even …
Figure 7 with 4 supplements
Emergence of persistent mixed states under depolarization but not under hyperpolarization of grid cells.
(a) Histogram showing bump score distributions for all embedded maps under grid cell hyperpolarization. In each simulation, the system is placed in a ‘consistent’ initial condition, and …
Figure 7—figure supplement 1
Persistent mixed state examples, and maintenance of grid cell firing location but not firing rate under grid cell depolarization.
(a) Firing rates of place cells (black) and grid cells (different modules shown in green, red and blue), shown 2.25 s after starting from a ‘Consistent’ initial condition at a specific location (24 …
Figure 7—figure supplement 2
Bump score dynamics under grid cell hyperpolarization and depolarization.
(a) Bump score dynamics for each of the embedded maps and for unembedded maps (gray) under grid cell hyperpolarization, corresponding to the realizations shown in Figure 7a–b. Scores for all maps …
Figure 7—figure supplement 3
Mixed states can be induced or suppressed by changing the connectivity between grid cells and place cells.
(a-b) Same analysis as Figure 7a–b but while doubling the bi-directional synaptic strengths between grid cells and place cells. Mixed states emerge under this manipulation, without grid cell …
Figure 7—video 1
Dynamics under grid cell depolarization.
Firing rates of place cells (black) and grid cell modules (red, green, and blue) during a single 2.5 s simulation (shown also in Figure 7—figure supplement 1a–d), in which the network was …
Figure 8 with 2 supplements
Artificial remapping of place cells following depolarization, but not hyperpolarization of grid cells.
(a-g) Firing rate maps of seven representative place cells during locomotion without (blue) and with (orange) grid cell depolarization. Rate maps show that under grid cell depolarization place cells …
Figure 8—figure supplement 1
Place cell population activity patterns observed while traversing the environment using path integration.
(a) Place cell firing rates vs. spatial location under grid cell depolarization and grid cell integration of velocity input that produces one complete cycle through the environment. Color bar: place …
Figure 8—figure supplement 2
Altered firing rate relationship between individual grid fields is observed during grid cell depolarization.
(a) Spearman rank correlation before and after grid cell depolarization is shown for a varied number of embedded maps. Perturbation was applied persistently 10 ms after starting from a ‘consistent’ …
Appendix 1—figure 1
Covariances of place cell inputs across sub-populations vanish.
(a) Simulation results (blue dots) showing the covariance of place cell inputs arising from activities of pairs of different grid cell modules. A common scaling factor determines the number of …
Appendix 1—figure 2
Variance of place cell inputs.
(a) Simulation results (blue dots) showing the variance of place cell inputs arising from place cell activities. A common scaling factor determines the number of place cells and grid cells in …
Appendix 1—figure 3
Variance of grid cell inputs.
(a) Simulation results (blue dots) showing the variance of grid module 1 inputs arising from place cell activities. A common scaling factor determines the number of place cells and grid cells in …
Appendix 1—figure 4
Capacity dependence on grid to place coupling parameter.
Bump score vs the total number of embedded maps for three different values of (circle, triangle and square) when starting from a ‘consistent’ initial condition in map #1. Blue curves show the …
Tables
Table 1
| Parameter | Value | Units |
|---|---|---|
-
*In all Figures we simulated the same networks using , except for Figure 6b (where was also set to 1 and 2), and Figure 8—figure supplement 2 (where was also set to 1, 2 and 4).
