The emergence of grid cells: Intelligent design or just adaptation?

Abstract

ABSTRACT:Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that appears to be essentially invariant across environments, modulo simple transformations, in contrast to multiple, rapidly acquired hippocampal maps; it may therefore be established gradually during rodent development. We explore with a simplified mathematical model the possibility that the self-organization of multiple grid fields into a triangular grid pattern may be a single-cell process, driven by firing rate adaptation and slowly varying spatial inputs. A simple analytical derivation indicates that triangular grids are favored asymptotic states of the self-organizing system, and computer simulations confirm that such states are indeed reached during a model learning process, provided it is sufficiently slow to effectively average out fluctuations. The interactions among local ensembles of grid units serve solely to stabilize a common grid orientation. Spatial information, in the real mEC network, may be provided by any combination of feedforward cortical afferents and feedback hippocampal projections from place cells, since either input alone is likely sufficient to yield grid fields. V V C 2008 Wiley-Liss, Inc. KEY WORDS:hippocampus; entorhinal cortex; firing rate adaptation; attractor network; memory DO GRIDS STEM FROM ATTRACTORS OR FROM OSCILLATIONS?Among the complex memory processes operating within the medial temporal lobe (see e.g., Eichenbaum and Lipton, 2008), the core contribution of the hippocampus may be its capacity to retrieve multiple arbitrary representations, a capacity that has been associated to the 'collateral effect' (Marr, 1971). McNaughton and Morris (1987) and Rolls (1989) proposed that the collateral effect is implemented by the recurrent connections of the CA3 region, which led to the insight that the CA3 network may 'compute' just by following attractor dynamics (Amit, 1989), as described by the simplified Hopfield (1982) model. The striking demonstration of abrupt global remapping, indicative of attractor dynamics, in rat place cells (Wills et al., 2005) has reinforced the notion that attractors are a key to understanding hippocampal memory computation. The concurrent discovery of grid cells in neighboring medial entorhinal cortex (mEC;Fyhn et al., 2004;Hafting et al., 2005) has led to the attractor idea reverberating into mEC networks: grid cells have been interpreted as the stable attractor states of spinglass-like interactions among pyramidal cells, mediated by recurrent connections (Fuhs and Touretzky, 2006). Unlike the multiple representations in CA3, however, which require global remapping transitions from one to the other (Leutgeb et al., 2005), local ensembles of mEC grid cells seem to demonstrate a single representation, which shifts and rotates coherently in different environments (Fyhn et al., 2007). If so, and if attractor computation were its core design principle, what the recurrent network in mEC would produce is merely the recovery of this single representation, e....

Grid cell mechanisms and function: Contributions of entorhinal persistent spiking and phase resetting

“…The simulations presented here demonstrate how context-dependence could arise from resetting the phase of persistent spiking at specific locations (e.g., stopping locations, reward locations, or turning locations), either by shifting the phase of one population, or turning off the current population and turning on a new population of persistent spiking neurons. These contextdependent responses would also need to be addressed by network models of grid cells (Fuhs and Touretzky, 2006;McNaughton et al, 2006;Kropff and Treves, 2008).…”

“…The simulation of both field size and spacing with the same parameter differs from recurrent attractor models of grid cells that model grid field size with the pattern of synaptic connectivity, but model spacing with the gain of velocity input. As an alternate mechanism, the biophysical time scale of adaptation has been shown to account for differences in grid cell spatial scaling (Kropff and Treves, 2008).…”

“…This avoids the problem of head direction input with specific preference angle relationships, but replaces it with the requirement of specific synaptic connectivity. An alternate network model avoids the need for specific recurrent connectivity by obtaining hexagonal patterns of synaptic input by selforganization of afferent input regulated by the time course of neuronal adaptation (Kropff and Treves, 2008).…”

A metric for space

“…Because the connections are bidirectional, it is conceivable that grid cells are driven by place cells, just as much as place cells are driven by grid cells. The maintenance of grid patterns during the first minutes after inactivation of the hippocampus (Hafting et al, 2008a) speaks against a direct role for place cells in maintaining firing, but place cells may nonetheless be instrumental in forming the grids initially (Kropff and Treves, 2008).…”

Grid alignment in entorhinal cortex

“…This hypothesis is in part supported by recent findings that the spatial periodicity of grid cells is susceptible to the suppression of theta oscillations by pharmacological silencing of the medial septum 21,22 . The third class of models on grid cell formation argues that grid fields may not require detailed ad hoc mechanisms like structured connectivity or theta oscillations, rather they may emerge spontaneously from a general feature of cortical cell activity, like firing rate adaptation 23 or, equivalently, other types of temporal modulation 24 . Such temporal modulation is shown in computer simulations to sculpt the spatial modulation of grid cells through a self-organization process that, averaged over a long developmental time of one or two weeks 25,26 , leaves as a footprint on each unit the regular periodicity found in real grid cells.…”