How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map

Abstract

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.

Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention and oscillations

“…Any other combination leads to dramatically different firing fields that have not been observed [36]. On the other hand, as mentioned in § §3, 5 and 6, the SOM model can self-organize hexagonal grids as well as their anatomical and neurophysiological properties along the dorsoventral axis in response to stripe cells of multiple directions, phases and scales [21].…”

“…As noted in §5, the mean frequencies of subthreshold MPOs in MEC layer II stellate cells decrease with their positions along the dorsoventral axis, and thus inversely correlate with the spatial scales of the grids [41]. Again, these data properties are not compelling evidence for oscillatory interference because they have also been simulated using the self-organized grid cells of the SOM model [21].…”

“…edu/modeldb/ShowModel.asp?model=148035. [21] demonstrates that the anatomical gradient of increasing grid spatial scales [14] can be learned by cells that respond more slowly along the dorsoventral axis (see m in equation (A 5)) [42] to their inputs from stripe cells of multiple scales, while adapting to them and undergoing refraction. The model cells also exhibit MPOs with frequencies that covary with their response rates in response to steady current injections (figure 5).…”

“…Similarly, linear velocity signals are proposed to be integrated by ring attractors that are composed of stripe cells (see §3; figure 2; and equations [41] and [44]. Simulations reproduced with permission from [21].…”

Grid cells and cortical representation

“…This has been suggested in a two-step model by Grossberg and colleagues 116,117 . In the first step, a set of ring attractors are formed upstream of the grid cells.…”