SummaryIntracellular recording shows how differences in single cell subthreshold oscillation frequency could directly underlie the differences in spacing of grid cell firing locations shown previously in awake, behaving animals.Grid cells in layer II of entorhinal cortex fire to spatial locations in a repeating hexagonal grid with smaller spacing between grid fields for neurons in more dorsal anatomical locations. Data from in vitro whole-cell patch recordings show a corresponding difference in frequency of subthreshold membrane potential oscillations in entorhinal neurons at different positions along the dorsal to ventral axis, supporting a model of physiological mechanism for grid cell responses.The entorhinal cortex plays an important role in encoding of spatial information (1-3) and episodic memory (4). Many layer II neurons of rat entorhinal cortex are "grid cells," firing when the rat is in an array of spatial locations forming a hexagonal grid within the environment (5-7). The spacing of firing fields in the grid varies with anatomical position of the cell along the dorsal to ventral axis of entorhinal cortex, as measured by distance from the postrhinal border (5). Neurons closer to the dorsal border of entorhinal cortex have shorter distances between firing fields. Computational models explicitly predict that differences in grid field spacing should correspond to differences in intrinsic frequencies of neurons along the dorsal to ventral axis (3,8). This could provide systematic variation in the gain of a movement-speed signal for path integration (2,3,9).Subthreshold membrane potential oscillations in entorhinal cortical stellate cells (10) arise from a single-cell mechanism involving voltage-sensitive currents (11-13) and could contribute to network dynamics (14). We recorded subthreshold oscillations from 57 stellate cells in layer II of medial entorhinal cortex (Fig. S1) in slices from different anatomical positions along the dorsal to ventral axis, using whole-cell patch clamp techniques (15). The position of individual horizontal slices was measured relative to the dorsal surface of the brain (Fig. 1A).Stellate cells in dorsal entorhinal cortex show higher temporal frequencies of subthreshold membrane potential oscillations compared to lower frequencies in cells from more ventral entorhinal slices (Fig. 1B). Dorsal cells (n = 30) are defined as cells recorded in slices taken between 3.8 mm (the border with postrhinal cortex (16)) and 4.9 mm from the dorsal surface of the brain. Ventral cells (n = 27) are defined as cells recorded in slices between 4.9 and 7.1 mm from the dorsal surface. Fig. 1B shows the group means of the frequency of subthreshold oscillations recorded from these populations. Because frequency of subthreshold oscillations can depend upon the mean membrane potential voltage, we performed this analysis separately for data gathered at different approximate holding membrane potentials of −50 mV and −45 mV. The mean frequency in dorsal cells was significantly higher than the mean frequ...

Summary Medial entorhinal grid cells display strikingly symmetric spatial firing patterns. The clarity of these patterns motivated the use of specific activity pattern shapes to classify entorhinal cell- types. While this approach successfully revealed cells that encode boundaries, head direction, and running speed, it left a majority of cells unclassified, and its pre-defined nature may have missed unconventional, yet important coding properties. Here, we apply an unbiased statistical approach to search for cells that encode navigationally-relevant variables. This approach successfully classifies the majority of entorhinal cells and reveals unsuspected entorhinal coding principles. First, we find a high degree of mixed selectivity and heterogeneity in superficial entorhinal neurons. Second, we discover a dynamic and remarkably adaptive code for space that enables entorhinal cells to rapidly encode navigational information accurately at high running speeds. Combined, these observations advance our current understanding of the mechanistic origins and functional implications of the entorhinal code for navigation.

Intracellular recording and computational modelling suggest that interactions of subthreshold membrane potential oscillation frequency in different dendritic branches of entorhinal cortex stellate cells could underlie the functional coding of continuous dimensions of space and time. Among other things, these interactions could underlie properties of grid cell field spacing. The relationship between experimental data on membrane potential oscillation frequency (f) and grid cell field spacing (G) indicates a constant scaling factor H=fG. This constant scaling factor between temporal oscillation frequency and spatial periodicity provides a starting constraint that is used to derive the model of Burgess, Barry and O'Keefe (Hippocampus, in press). This model provides a consistent quantitative link between single cell physiological properties and properties of spiking units in awake behaving animals. Further properties and predictions of this model about single cell and network physiological properties are analyzed. In particular, the model makes quantitative predictions about the change in membrane potential, single cell oscillation frequency and network oscillation frequency associated with speed of movement, about the independence of single cell properties from network theta rhythm oscillations, and about the effect of variations in initial oscillatory phase on the pattern of grid cell firing fields. These same mechanisms of subthreshold oscillations may play a more general role in memory function, by providing a method for learning arbitrary time intervals in memory sequences.

Medial entorhinal grid cells fire in periodic, hexagonally patterned locations and are proposed to support path-integration-based navigation. The recursive nature of path integration results in accumulating error and, without a corrective mechanism, a breakdown in the calculation of location. The observed long-term stability of grid patterns necessitates that the system either performs highly precise internal path integration or implements an external landmark-based error correction mechanism. To distinguish these possibilities, we examined grid cells in behaving rodents as they made long trajectories across an open arena. We found that error accumulates relative to time and distance traveled since the animal last encountered a boundary. This error reflects coherent drift in the grid pattern. Further, interactions with boundaries yield direction-dependent error correction, suggesting that border cells serve as a neural substrate for error correction. These observations, combined with simulations of an attractor network grid cell model, demonstrate that landmarks are crucial to grid stability.