A single-cell spiking model for the origin of grid-cell patterns

Abstract

Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity.

Coding advantage of grid cell orientation under noisy conditions

“…Many open issues remain for a more general understanding of the dynamics and functions of grid cells during spatial navigation. For example, how does the activity of place cells in the hippocampus relate to the orientation of grid cells [47][48][49][50]? How do grid cells modulate the coding scheme for two separate spaces when the two spaces are being merged into a single space [51][52]?…”

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

“…It is also straightforward to produce grid-cell like responses by combining synaptic inputs from multiple place cells. Moreover, theoretical studies have demonstrated that plasticity mechanisms, acting between place cells and their post-synaptic partners in the MEC, can give rise to synaptic connectivity that produces gridcell like spatial tuning (D'Albis and Kempter, 2017;Dordek et al, 2016;Kropff and Treves, 2008;Monsalve-Mercado and Leibold, 2017;Stepanyuk, 2015;Weber and Sprekeler, 2018).…”

“…One such difficulty arises from the observation that place cell activity patterns remap in different environments (Muller and Kubie, 1987). If grid cell responses emerge under activity dependent plasticity of feedforward synapses from place cells to grid cells (D'Albis and Kempter, 2017;Dordek et al, 2016;Kropff and Treves, 2008;Monsalve-Mercado and Leibold, 2017;Stepanyuk, 2015;Weber and Sprekeler, 2018), it is difficult to explain why they remain grid-like across familiar and novel environments, and why phase relationships between grid cells within a module are tightly preserved (Gardner et al, 2019;Trettel et al, 2019;Yoon et al, 2013). Furthermore, grid cells maintain their correlation structure under hippocampal inactivation (Almog et al, 2019), indicating that the low dimensionality of activity within each grid cell module is independent of hippocampal inputs.…”

Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity

“…The cellular and network mechanisms that give rise to each of these firing patterns are subject to extensive experimental and theoretical research. Several computational models have been suggested to explain the emergence of grid cells ( Fuhs and Touretzky, 2006 ; McNaughton et al, 2006 ; Franzius et al, 2007a ; Burak and Fiete, 2009 ; Couey et al, 2013 ; Burgess et al, 2007 ; Kropff and Treves, 2008 ; Bush and Burgess, 2014 ; Castro and Aguiar, 2014 ; Dordek et al, 2016 ; Stepanyuk, 2015 ; Giocomo et al, 2011 ; Zilli, 2012 ; D'Albis and Kempter, 2017 ; Monsalve-Mercado and Leibold, 2017 ), place cells ( Tsodyks and Sejnowski, 1995 ; Battaglia and Treves, 1998 ; Arleo and Gerstner, 2000 ; Solstad et al, 2006 ; Franzius et al, 2007b ; Burgess and O'Keefe, 2011 ; Franzius et al, 2007a ) and head direction cells ( McNaughton et al, 1991 ; Redish et al, 1996 ; Zhang, 1996 ; Franzius et al, 2007a ). Most of these models are designed to explain the spatial selectivity of one particular cell type and do not consider invariances along other dimensions, although the formation of invariant representations is a non-trivial problem ( DiCarlo and Cox, 2007 ).…”