A geometric attractor mechanism for self-organization of entorhinal grid modules

Abstract

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated by ratios in the range 1.2-2.0. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

Dynamic and reversible remapping of network representations in an unchanging environment

“…Alternative mechanisms for maintaining multiple maps, such as correlated ring attractor manifolds (Romani and Tsodyks, 2010) , might also be investigated. Finally, the attractor model presented here does not account for the reality that many MEC neurons have multiple spatial firing fields, and does not consider the possibility of more sophisticated interactions between landmark and grid cells (Campbell et al, 2018;Kang and Balasubramanian, 2019;Ocko et al, 2018) .…”

Evaluating state space discovery by persistent cohomology in the spatial representation system

“…In addition, we explore different relative orientations between the modules by generating different orientations for module 2. Notably, these scale ratios and orientation differences are not chosen such that the two rhombic unit cells would share a simple geometric relationship with each other [27], which would limit their possible overlap configurations. As we include more neurons from both modules into our dataset, we see that four persistent 1-cocycles eventually emerge from the points close to the diagonal that represent sampling noise (Fig.…”

A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

“…The variability can arise from inhomogeneities in the synaptic connections from place cell to grid cells which are unrelated to the embedding of multiple maps ( Dunn et al, 2017 ). Alternately, it can arise from sensory inputs, or from synaptic inputs from different modules ( Ismakov et al, 2017 ; Kang and Balasubramanian, 2019 ). Instead, we identified a mechanism which naturally produces this variability, at least in part, simply by the process of embedding multiple spatial maps in the connectivity and is independent from sensory inputs.…”