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Grid Cells in Rat Entorhinal Cortex Encode Physical Space with Independent firing fields and Phase Precession at the Single-Trial Level

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Grid Cells in Rat Entorhinal Cortex Encode Physical Space with Independent firing fields and Phase Precession at the Single-Trial Level Grid cells in rat entorhinal cortex encode physical space with independent firing fields and phase precession at the single-trial level Eric T. Reifensteina,b, Richard Kempterb, Susanne Schreiberb, Martin B. Stemmlera, and Andreas V. M. Herza,1 aDepartment of Biology II, Ludwig-Maximilians-Universität München, and Bernstein Center for Computational Neuroscience Munich, 82152 Planegg- Martinsried, Germany; and bInstitute for Theoretical Biology, Humboldt-Universität zu Berlin, and Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany Edited* by John J. Hopfield, Princeton University, Princeton, NJ, and approved March 08, 2012 (received for review June 14, 2011) When a rat moves, grid cells in its entorhinal cortex become active to a particular theta phase of the local field potential (LFP). There is in multiple regions of the external world that form a hexagonal also another aspect of grid-cell activity that needs to be taken into lattice. As the animal traverses one such “firing field,” spikes tend account: From one firing field to the next one visited, the discharge to occur at successively earlier theta phases of the local field po- of a single grid cell may or may not be correlated. Hence it is an open tential. This phenomenon is called phase precession. Here, we question whether the nervous system can actually make use of phase show that spike phases provide 80% more spatial information coding in mEC, notwithstanding the trends seen in pooled data or at than spike counts and that they improve position estimates from the single-run level in hippocampal place cells (13). single neurons down to a few centimeters. To understand what limits the resolution and how variable spike phases are across Results different field traversals, we analyze spike trains run by run. We Extracellularly isolated cells from layer II medial entorhinal cortex find that the multiple firing fields of a grid cell operate as inde- and the LFP were recorded by Hafting et al. (8) from rats running pendent elements for encoding physical space. In addition, phase along a linear track, and made available by E. I. Moser (Norwegian precession is significantly stronger than the pooled-run data sug- University of Science and Technology, Trondheim, Norway). Many gest. Despite the inherent stochasticity of grid-cell firing, phase cells had multiple firing fields, corresponding to different locations NEUROSCIENCE precession is therefore a robust phenomenon at the single-trial at which the cell spiked (Fig. 1A). To analyze the relationship be- level, making a theta-phase code for spatial navigation feasible. tween the timing of spikes and the background theta rhythm in the LFP, we computed an instantaneous theta phase of the LFP by neural coding | spatial representation | spike-timing code | taking the Hilbert transform of the LFP signal, band-passed be- oscillator-interference model tween 6 and 11 Hz. During the traversal of a single grid field, the firing rate first rises and then falls (Fig. 1A). At the same time, the inding and remembering paths to follow through an envi- average spike phase relative to the ongoing theta rhythm decreases Fronment relies on specialized neural circuits in which sub- (Fig. 1B). Hence, both the phase and the number of spikes within groups of neurons encode different spatial locations. A spatial athetacycleareafunctionoftherat’s position within the firing field. region that causes a cell to fire spikes defines a “firing field”; for To quantify phase precession, regression analyses were per- instance, place cells in CA1 of hippocampus often have a single formed. Because phase is a circular variable, traditional linear firing field, whereas grid cells in the medial entorhinal cortex correlation analysis, as in Hafting et al. (8), may yield slope and (mEC) have multiple, regularly spaced firing fields that are correlation estimates that do not reflect the true structure in the arranged in hexagonal grids (1–5). data (Fig. S1). Therefore, we turned to circular–linear methods Spatial location is represented not only in the firing rates of such (14, 15). Indeed, the median linear correlation for a set of 291 grid cells (Fig. 1A), but also in the timing of spikes relative to global fields from 67 cells, pooled across runs for each field, is found to rhythms in the network (Fig. 1B). A prominent 6- to 11-Hz net- be −0.28 ± 0.02, whereas the median circular–linear correlation work oscillation—the “theta rhythm”—modulates the firing pat- coefficient is only −0.05 ± 0.04. terns of nerve cells throughout the entire entorhinal–hippocampal Such weak correlations could imply that the theta phase of spikes formation during exploratory behavior and accompanies the spa- in single entorhinal grid cells is not a reliable indicator of spatial tial periodicity of rodent grid cells (6, 7). By adding up the spikes location, so we asked how well the phase of spikes relative to the recorded on many runs of the rodent through the same firing field, theta LFP predicts the rat’s position compared with the spike count. Hafting et al. (8) observed a pattern of progressively earlier phases For any single run through a given location, the number and phase relative to the theta rhythm for the spikes of layer II mEC grid of a grid cell’s spikes varies. By pooling over different runs through cells. This phenomenon is termed phase precession and was first agridfield, we map the joint probability distribution of the rat’s described in place cells from the hippocampus (9–12). position and either the spike count or the spike phase (Fig. 2 A and The observation that spatial position correlates negatively with B). Kernel density methods yield smoothed estimates for these the average phase of spikes does not answer the question of whether distributions (Materials and Methods). In the example of Fig. 2A, the animal can use this phenomenon for estimating its location at the single-run level. In fact, not only could the average, pooled be- havior mask the variability of phase precession in single runs, but Author contributions: E.T.R., R.K., S.S., M.B.S., and A.V.M.H. designed research; E.T.R. even more drastically, single-run phase precession could be un- performed research; E.T.R., M.B.S., and A.V.M.H. analyzed data; and E.T.R., R.K., S.S., related to pooled phase precession. For instance, single runs could M.B.S., and A.V.M.H. wrote the paper. exhibit no or only little phase precession, whereas pooled runs would The authors declare no conflict of interest. exhibit phase precession (Fig. 1C). The spikes on single runs could *This Direct Submission article had a prearranged editor. even recess in phase, yet still lead to phase precession in the pooled Freely available online through the PNAS open access option. data. Single-run phase precession could also be stronger than the 1To whom correspondence should be addressed. E-mail: [email protected]. D pooled runs suggest (Fig. 1 ). Moreover, runs with strong phase This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. precession could be interspersed with runs in which the spikes lock 1073/pnas.1109599109/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1109599109 PNAS | April 17, 2012 | vol. 109 | no. 16 | 6301–6306 Downloaded by guest on September 26, 2021 AB CD Fig. 1. The animal’s position within the firing field modulates both the firing rate and theta phase. (A)Averagefiring rate of a grid cell for a rat running 42 times from left to right along a linear track. (B) The phase relative to the ongoing theta rhythm of all spikes from the leftmost grid field in A.Eachdot depicts a single spike. (C and D) Hypothetical cases for which the relationship Fig. 2. The phase of spikes relative to the theta rhythm and the spike count between the spike phase and the animal’s position differs radically between per theta period convey spatial information. (A) Smoothed probability density ; single runs and pooled-run data. (C) Example in which spikes tend to be phase of the position and the spike count in a theta cycle, pX;Nðx nÞ, obtained by fi locked to the LFP oscillation, so that all subsequent spikes in later theta cycles kernel density estimation (Materials and Methods) for the grid eld depicted follow at about the same phase as the initial spike. If the phase of the initial in Fig. 1B. The probability density (color bar) is normalized relative to the spike depends on the spatial coordinate, then the pooled-run data can mimic maximum value. Observed counts are indicated by red dots. (B) Normalized phase precession. (D) Phase precession in single runs can also be stronger than joint probability density of the position and phase of spikes relative to its theta ; θ fi fi suggested by pooled data. Pooled phase precession in C and D is identical and cycle, pX;Θðx Þ, for the same grid eld. Red dots depict the phase of the rst could thus belie the phase–position relationship in single runs. spike in each theta cycle, measured across different theta cycles and different runs. The average phase decreases as a function of position, whereas the spike count’s relationship to position is inherently ambiguous: for instance, the av- erage spike count at x ≈ 20 cmðn ≈ 1:75Þ is nearly the same as that at the most likely number of spikes within a theta cycle, given that the ≈ ≈ : 8 8 grid cell spiked at all, was always one, regardless of the rat’s position x 40 cmðn 1 65Þ, whereas the (circular) average phases are 285 and 104 , respectively.
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