Selforganization of modular activity of grid cells

Abstract

A unique topographical representation of space is found in the concerted activity of grid cells in the rodent medial entorhinal cortex. Many among the principal cells in this region exhibit a hexagonal firing pattern, in which each cell expresses its own set of place fields (spatial phases) at the vertices of a triangular grid, the spacing and orientation of which are typically shared with neighboring cells. Grid spacing, in particular, has been found to increase along the dorso‐ventral axis of the entorhinal cortex but in discrete steps, that is, with a modular structure. In this study, we show that such a modular activity may result from the self‐organization of interacting units, which individually would not show discrete but rather continuously varying grid spacing. Within our “adaptation” network model, the effect of a continuously varying time constant, which determines grid spacing in the isolated cell model, is modulated by recurrent collateral connections, which tend to produce a few subnetworks, akin to magnetic domains, each with its own grid spacing. In agreement with experimental evidence, the modular structure is tightly defined by grid spacing, but also involves grid orientation and distortion, due to interactions across modules. Thus, our study sheds light onto a possible mechanism, other than simply assuming separate networks a priori, underlying the formation of modular grid representations.

Partial coherence and frustration in self‐organizing spherical grids

“…The simulation of our adaptation model, allowing for collateral interactions among the units, indicates a radically different nature of the grid code on the sphere. The same interactions which on a plane suppress fluctuations and lead to a collapse into a smooth continuous attractor recruiting all units with the same or similar grid spacing (Si et al, ; Urdapilleta, Si, & Treves, ), on a sphere lead to a hierarchy of effects on single‐unit maps that are distorted from the available symmetric “soccer ball” field arrangement are forced into clusters of units with approximately overlapping fields remap to a different sphere with only partial coherence, even within clusters. …”

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

“…Nevertheless, because grid orientation depends on the boundary conditions, it remains difficult to compare the distributions obtained here with the ones observed experimentally [1, 93, 99, 100]. Finally, in order to explain grid alignment across cells and/or environments [1, 93], collateral interactions between developing grid cells may be required [50, 51, 101] (see also Sec Recurrent dynamics).…”

“…However, because adaptation was found to be stronger ventrally than dorsally, Yoshida et al [71] interpreted their results as evidence against grid-cell models based on adaptation. Yet the critical variable controlling the grid scale is not the strength of adaptation, but rather its temporal dynamics (Fig 7), which was not systematically analyzed [71]; see also [101] for a similar discussion on this point.…”

“…However, because excitatory and inhibitory recurrent circuits have been described in the mEC [19, 20, 112, 113, 138], grid cells are likely to be mutually coupled [139, 140]. Such recurrent connections could explain the modular organization of grid-cell properties [93, 101] and their coherent responses to environmental changes [139]. Feedback interactions within a module may also amplify an initially broad grid-tuning given by the feed-forward inputs, similarly to the sharpening of receptive fields in visual cortex [141, 142].…”

Inter- and intra-animal variation of integrative properties of stellate cells in the medial entorhinal cortex

“…Our data argue against models that explain this relationship through single cell computations (Burgess, 2008;Giocomo et al, 2007) , as in this case modularity of integrative properties of SCs is required to generate modularity of grid firing. A continuous dorsoventral organisation of electrophysiological properties of SCs could support modular grid firing generated by self-organising maps (Grossberg and Pilly, 2012) , or by synaptic learning mechanisms (Kropff and Treves, 2008;Urdapilleta et al, 2017) . It is less clear how a continuous gradient would affect predictions of grid firing from continuous attractor network models (Shipston-Sharman et al, 2016;Widloski and Fiete, 2014) , which can account for modularity by limiting synaptic interactions between modules.…”