The oscillatory interference model of grid cell firing and theta
I review the oscillatory interference model of grid cell firing (Burgess et al., 2005; Burgess et al., 2007; Burgess 2008). Path integration is performed by “velocity-controlled oscillators” (VCOs): An intrinsic theta-band membrane potential oscillation (MPO) increases in frequency from baseline in response to depolarization by synaptic input varying as a cosine function of running direction and linearly in running speed. The phase of the VCO relative to baseline tracks displacement along the “preferred direction” of the cosine tuning. Multiple VCOs with different preferred directions (in different dendrites or in different neurons) combine to drive the firing of grid cells, providing a system for path integration. Preferred directions differing by multiples of 60 o and the common orientation of grids implies unsupervised learning during development and recurrent connectivity. In comparison to the continuous attractor model, both models benefit from the stability of (symmetric) lateral interactions between grid cells, but provide different mechanisms for path integration (asymmetric lateral interactions vs VCOs).
Tested predictions of the model include the relationships between the modulation frequency of grid cell firing, grid scale and running speed (Jeewajee et al., 2008), and between the rate of increase of MPO frequencies in stellate cells in mEC layer II and (inferred) grid scale (Giocomo et al., 2008). Unconfirmed predictions include the presence of individual velocity-controlled oscillators as dendritic oscillators or as neurons (see also Hasselmo, 2008) and evidence that grids comprise multiple linear interference patterns.
Predictions were also made for the local field potential theta rhythm (Burgess, 2008). The slope and intercept of the relationship between theta frequency and running speed reflect distinct mechanisms of theta generation: Type I “movement-related” mechanisms reflect the increasing frequency of VCOs with running speed; type II “arousal-related” mechanisms reflect the baseline frequency of the septo-hippocampal circuit. I present evidence supporting this dissociation from manipulations of environmental novelty and neuropharmacology (Wells et al., in prep.).
We also suggested that grids are stabilized relative to the environment by feedback from place cells (O’Keefe and Burgess, 2005), via phase-resetting of VCOs (Burgess et al., 2005; 2007). Place cells are stabilized by environmental input from “boundary-vector cells” (Lever et al., 2009), while also receiving path integrative input from grid cells. This predicts that: (a) self-location combines both visual and path integrative representations; (b) inactivation of place cells causes spatial instability of grids; (c) place cell firing only depends on grid cell input for its path integrative properties; (d) grids respond to manipulation of the environmental boundary (e) changing grid scale will cause a mis-match with environmental inputs, triggering place cell remapping. (d) was shown by Barry et al., (2007). I will present evidence that (a) is true in humans, even during the path-integration task of triangle-completion in darkness (Tcheang et al., in prep.).
Barry C, Hayman R, Burgess N, Jeffery K(2007) Experience-dependent rescaling of entorhinal grids. Nature Neuroscience, 10, 682 - 684.
Burgess N, Barry C, Jeffery KJ, O’Keefe J (2005) A Grid & Place Cell Model of Path Integration Utilizing Phase Precession Versus Theta. Poster at CCNC Washington 2005:
Burgess N, Barry C, O'Keefe J (2007)An oscillatory interference model of Grid cell firing. Hippocampus 17, 801-812.
Burgess N (2008) Grid cells and theta as oscillatory interference: Theory and predictions. Hippocampus 18 1157-1174.
Giocomo LM, Hasselmo ME (2008) Computation by oscillations: Implications of experimental data for theoretical models of grid cells. Hippocampus 18: 1186-99.
Hasselmo ME (2008) Grid cell mechanisms and function: contributions of entorhinal persistent spiking and phase resetting. Hippocampus. 18:1213-29.
Jeewajee A, Barry C, O'Keefe J, Burgess N. (2008) Grid cells and theta as oscillatory interference: electrophysiological data from freely moving rats. Hippocampus 18:1175-85.
Lever C, Burton S, Jeewajee A, O'Keefe J, Burgess N. (2009) Boundary vector cells in the subiculum of the hippocampal formation. J Neurosci. 29 9771-7.
O'Keefe J, Burgess N (2005) Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 15 853-866.
Tcheang L, Bülthoff H, Burgess N (in prep) Visual influences on path integration in darkness suggest a cognitive map.
Wells CE, Jeewajee A, Douchamps V, Burton S, Rodges J, O’Keefe J, Burgess N, Lever C (in prep) Pharmacology, novelty and running speed dissociate two components of the hippocampal theta rhythm.