Grid cell hexagonal patterns formed by fast self‐organized learning within entorhinal cortex

Abstract

Grid cells in the dorsal segment of the medial entorhinal cortex (dMEC) show remarkable hexagonal activity patterns, at multiple spatial scales, during spatial navigation. How these hexagonal patterns arise has excited intense interest. It has previously been shown how a selforganizing map can convert firing patterns across entorhinal grid cells into hippocampal place cells that are capable of representing much larger spatial scales. Can grid cell firing fields also arise during navigation through learning within a self-organizing map? A neural model is proposed that converts path integration signals into hexagonal grid cell patterns of multiple scales. This GRID model creates only grid cell patterns with the observed hexagonal structure, predicts how these hexagonal patterns can be learned from experience, and can process biologically plausible neural input and output signals during navigation. These results support a unified computational framework for explaining how entorhinal-hippocampal interactions support spatial navigation.

Cosine Directional Tuning of Theta Cell Burst Frequencies: Evidence for Spatial Coding by Oscillatory Interference

“…In a population of ring oscillators with different velocity inputs, the nth ring oscillator serves as a multiphase VCO that performs translational path integration along its own preferred vector, d n . This ring oscillator model of translational path integration is quite similar to hypothetical ring attractor models of angular path integration by head-direction cells (Skaggs et al, 1995;Redish et al, 1996;Zhang, 1996;Song and Wang, 2005), raising the possibility that translational and angular path integration might both be performed by similar ring attractor circuits (Blair et al, 2008;Mhatre et al, 2010). Figure 7C illustrates a hypothetical arrangement of ring oscillators within a structured matrix of VCOs that contains a distributed population of theta cells from which many different spatial tuning functions can be synthesized.…”

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.…”

“…It is this separation that has remained unexplained. In 2010, Mhatre et al proposed a model in which, instead of using interference of theta and a velocity-dependent oscillation, they used ring attractors to generate stripe-like responses 116 . They showed, through computer simulations, that when the stripes do not share the same phase or orientation, grid cells can be generated by choosing stripes separated from each other by 60 degrees through a self-organizing process.…”

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

“…This property was first described in [22], and refined in [23]. It controls the sets of coactive stripe cells, for a given spatial scale, that the grid cell layer experiences as the space is traversed.…”

“…Models of grid cells can be divided into three classes: SOM [17,22,23], continuous attractor [12,102 -104] and oscillatory interference models [35,36,105]. Zilli [106] reviews some basic properties of these models.…”