Conversion of a phase‐ to a rate‐coded position signal by a three‐stage model of theta cells, grid cells, and place cells

Abstract

ABSTRACT:As a rat navigates through a familiar environment, its position in space is encoded by firing rates of place cells and grid cells. Oscillatory interference models propose that this positional firing rate code is derived from a phase code, which stores the rat's position as a pattern of phase angles between velocity-modulated theta oscillations. Here we describe a three-stage network model, which formalizes the computational steps that are necessary for converting phase-coded position signals (represented by theta oscillations) into rate-coded position signals (represented by grid cells and place cells). The first stage of the model proposes that the phase-coded position signal is stored and updated by a bank of ring attractors, like those that have previously been hypothesized to perform angular path integration in the head-direction cell system. We show analytically how ring attractors can serve as central pattern generators for producing velocity-modulated theta oscillations, and we propose that such ring attractors may reside in subcortical areas where hippocampal theta rhythm is known to originate. In the second stage of the model, grid fields are formed by oscillatory interference between theta cells residing in different (but not the same) ring attractors. The model's third stage assumes that hippocampal neurons generate Gaussian place fields by computing weighted sums of inputs from a basis set of many grid fields. Here we show that under this assumption, the spatial frequency spectrum of the Gaussian place field defines the vertex spacings of grid cells that must provide input to the place cell. This analysis generates a testable prediction that grid cells with large vertex spacings should send projections to the entire hippocampus, whereas grid cells with smaller vertex spacings may project more selectively to the dorsal hippocampus, where place fields are smallest. V

Functional correlates of the lateral and medial entorhinal cortex: objects, path integration and local–global reference frames

“…The combination of these factors (spatial signals and movement signals) has propelled the notion that these areas are a major constituent of the path integration circuitry of the brain. The major classes of models of grid cells (the continuous attractor models and the oscillatory interference models) are both explicitly path integration models [63][64][65][66]. That is, they both rely on the integration of a velocity vector (speed and direction) over time to produce a periodic position signal.…”

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

“…These phase interference models resemble the model of grid cells based on Moire interference of higher spatial frequency grids (Blair et al, 2007(Blair et al, , 2008. The initial Moire interference model did not use the integration of speed-modulated head direction to map from temporal oscillations to spatial periodicity.…”

“…The initial Moire interference model did not use the integration of speed-modulated head direction to map from temporal oscillations to spatial periodicity. However, a new version of this model has been presented with an alternate mechanism that updates frequency of subcortical oscillators based on running velocity (Blair et al, 2008).…”

“…This created a matrix of synaptic connectivity W EH allowing the 75 entorhinal cells with activity g(t) to cause spiking in 400 hippocampal cells with activity p(t) as follows: p t ð Þ ¼ W EH g t ð Þ. Many other papers have explored how convergent input from grid cells causes place cell activity (O'Keefe and Solstad et al, 2006;Blair et al, 2007Blair et al, , 2008Franzius et al, 2007;Hayman and Jeffery, 2008).…”

Computation by oscillations: Implications of experimental data for theoretical models of grid cells

“…Several computational models of grid cell formation in the entorhinal cortex have been developed (O'Keefe and Burgess, 2005;Blair et al, 2006;Blair et al, 2008;Fuhs and Touretzky, 2006;McNaughton et al, 2006;Burgess et al, 2007). Computational models of grid cell formation include two types, oscillatory interference models Hasselmo et al, 2007) and attractor-dynamic models (Fuhs and Touretzky, 2006;McNaughton et al, 2006;Welinder and Flete, 2008).…”