A Grid & Place Cell Model of Path Integration Utilizing Phase Precession Versus Theta Neil Burgess 12* , Caswell Barry 123 , Kathryn J Jeffery 3 , John O’Keefe 2 13Hz 7Hz 23Hz 1m Grid cells in dorsomedial Entorhinal cortex fire in a strikingly regular array of locations as a rat explores (Hafting et al., 2005). Nearby grid cells have similar orientation and scale, but shifted to tile the environment B 1m Grid scale increases as recording site moves from dorsal to ventral dorsal ventral Grid orientation follows sensory cues Does the cyclical firing pattern reflect interference? 1: Institute of Cognitive Neuroscience; 2: Department of Anatomy; 3: Department of Psychology; University College London, U.K. * Correspondence to: n.burgess@ucl.ac.uk. Supported by the Medical Research Council, U.K. Theta-phase of place cell firing precesses from late to early as the rat runs through the place field: Phase of firing correlates better with position than time in field. 0 0.4 0.8 1.2 1.6 2 360 0 theta: dendrite: sum: phase: time/s If MPO is voltage-controlled and input ~speed, interference peaks correlate with position (& more so than with time). See also Lengyel et al., 2003; O’Keefe & Burgess (2005). O’Keefe & Recce, 1993 ‘place field’ Firing rate: This may reflect interference of theta with a dendritic membrane potential oscillation (MPO): w d =w θ +βscos(ø-ø d ) w θ ø d high s low s phase difference ~ distance travelled in preferred direction ø d } v s =cos(w θ t θ ) v d =cos(w d t+φ d ) f = Θ(v d + v s ) ø s = speed ø = heading 1-D interference: ‘band cells’ (could be cells or dendritic sub-units) Straight runs from (0,0), ø d =0 Combining band cells to make grid cells (taking product of firing) 2 band cells (90 o & 30 o ) or 3 band cells (150 o , 90 o & 30 o ) will do But 3 band cells => 60 o /120 o separation for max firing of grid cell: Straight runs from (0,0) 10mins real trajectory Most frequent ‘winner’/100 random selections of 3 band cell orientations: Least frequent ‘winner’/100: smoothed plots 3 band cells require phase reset at a location for correct alignment and correction of error in path integration (PI). mis-aligned at start Example coherent phase alignments to θ at start 5% cumulative error in s & ø Perfect PI (i.e. s, ø) 5% err, band cells reset to θ phase at start location (41x) start = (0, 0, 0) (180, 180, 0) (180, 0, 180) (0, 180, 180) (0, 0, 180) smoothed plots start = (0, 0, 0) Alignment of grid to environment: phase reset of band cells by place cells Place cell at peak rate (MPO in phase with θ) Grid cell driving place cell (1 of many) Band cells phase- reset by place cell (MPOs in phase with θ) sensory input Firing fields θ synchronised in hippocampus & EC Reset at a single location divorces grid scale from environmental scale: Data Grid position is determined by reset location: grid spacing Local sets of grid cells which tile environment may result from sets of phase-shifted band cells: (0,0) 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 Phase shifts: (0,0,0) (90,90,0) (90,0,270) (0,90,90) (180,180,0) (180,0,180) (0,180,180) (270,270,0) (270,0,90) (0,270,270) Hafting et al Model is consistent with place fields ‘remapping’ while grids shift Trial:5 Max Rate:1.3 Trial:6 Max Rate:1.6 Trial:7 Max Rate:2.6 Trial:9 Max Rate:1.7 Trial:10 Max Rate:3.5 Trial:11 Max Rate:1.1 1.2 1.7 1.7 1.1 1.7 3.5 2.6 1.3 1.6 Trial:5 Max Rate:4.4 Trial:6 Max Rate:4.2 Trial:7 Max Rate:0.1 Trial:9 Max Rate:1.5 Trial:10 Max Rate:2.6 Trial:11 Max Rate:1.5 0.2 2.0 0.2 4.4 4.2 0.1 1.5 2.6 1.5 Trial:5 Max Rate:8.8 Trial:6 Max Rate:3.4 Trial:7 Max Rate:0.3 Trial:9 Max Rate:1.5 Trial:10 Max Rate:0.9 Trial:11 Max Rate:8.5 0.3 2.4 1.5 8.8 3.4 0.3 8.5 0.9 1.5 Place fields from overlapping grid cells Simulate 600 grid cells:: 60 local sets (12 orientations, 5 scales, 60 reset points) of 10 grid cells with different offsets. Thresholded sum of 60 randomly chosen grid cells gives realistic looking place fields: 1 grid cell shifts in dark, while 2 simultaneously recorded place cells ‘switch on’. Data, Barry et al., in prep. 20 40 60 20 40 60 20 40 60 20 40 60 References: Hafting T et al. (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436 801-806; Lengyel M et al. (2003) Dynamically detuned oscillations account for the coupled rate and temporal code of place cell firing. Hippocampus 13 700-714; O’Keefe J & Burgess N (2005) Dual phase & rate coding in hippocampal place cells: theoretical significance & relationship to entorhinal grid cells Hippocampus 15 853-866; O’Keefe J & Recce ML (1993) Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3 317-330.  Recurrent connections from a band cell will form predominantly to next cell with same preferred direction (ø d ) and phase diff = lag of MPO response (90 o = 25ms). Then phase will propagate correctly through the local set, only the band at start of run needing to be phase-reset, and band and grid cells will show predominantly late-early phase precession. The Boundary Vector Cell model (see Barry et al poster) is consistent with phase reset of grids by sensory input at edge of environment. Conclusion : grid cell firing could result from interference of multiple MPOs with theta, phase reset by place cells. location Once set up by interference, these connections would be support P.I. more efficiently than between place cells, as can be fine-tuned throughout environment. 0 0.4 0.8 1.2 1.6 2 eta: cell1: cell2: cell3: time theta Hafting et al., 2005 [CCNC Washington Nov 2005]