Dynamics of mismatch correction in the hippocampal ensemble code for space: interaction between path integration and environmental cues

Abstract

Populations of hippocampal neurons were recorded simultaneously in rats shuttling on a track between a fixed reward site at one end and a movable reward site, mounted in a sliding box, at the opposite end. While the rat ran toward the fixed site, the box was moved. The rat returned to the box in its new position. On the initial part of all journeys, cells fired at fixed distances from the origin, whereas on the final part, cells fired at fixed distances from the destination. Thus, on outward journeys from the box, with the box behind the rat, the position representation must have been updated by path integration. Farther along the journey, the place field map became aligned on the basis of external stimuli. The spatial representation was quantified in terms of population vectors. During shortened journeys, the vector shifted from an alignment with the origin to an alignment with the destination. The dynamics depended on the degree of mismatch with respect to the full-length journey. For small mismatches, the vector moved smoothly through intervening coordinates until the mismatch was corrected. For large mismatches, it jumped abruptly to the new coordinate. Thus, when mismatches occur, path integration and external cues interact competitively to control place-cell firing. When the same box was used in a different environment, it controlled the alignment of a different set of place cells. These data suggest that although map alignment can be controlled by landmarks, hippocampal neurons do not explicitly represent objects or events.

Fig. 1.

Behavioral apparatus and analysis methods for Experiment 1. A, Linear track (to scale) with the five box locations used as the start and end point of each journey. The 188 × 8 cm track was placed across a corner of the laboratory and was surrounded by recording equipment and laboratory furniture. A 27-cm-high × 32-cm-wide × 27-cm-long cardboard box was mounted on the track. On each trial, the box was moved to one of five equally spaced locations. One food cup was mounted in the box and another was fixed at the opposite end of the track. During each trial, while the rat approached the fixed food cup, the box was moved to a new location to which the rat then returned. Box locations were randomly assigned, ensuring that all five locations were equally probable.B shows the five types of outbound journeys, labeledbox1 out, box2 out, etc. Cshows the five types of inbound journeys. D, The behavioral correlate of each cell was quantified by the slope of a line fitted to the firing profiles on the five different types of trials (the “displacement slope”). The figure shows firing profiles of an idealized cell with a displacement slope of 1.0 on the outbound journeys. This cell fires at the same distance from the box irrespective of the position of the box on the track. Theslanted dashed line represents the regression line used to calculate the displacement slope. The vertical dashed line points to the location of the peak firing on thebox1-out trials (∼0.25 for this example).E, Firing profile of an idealized cell with a displacement slope of 0.0 on the inbound journeys. The firing field of this cell remains in the same location on the track for all trial types. The vertical dashed line gives a displacement slope of 0.0 and also indicates the location of peak firing on thebox1-in trials.

Fig. 2.

Behavioral apparatus for Experiment 2. A 1.2 × 1.2 m platform was placed in the center of a room (3.5 m diameter area) surrounded by black curtains. Large white objects, serving as distal visual cues, were hung in front of the curtains (not shown). The box used in experiment 1 was also used in this task. A 5-cm-diameter, 40-cm-high landmark, which indicated the goal location (x), was also placed on the platform. A, Outbound journey originating from the middle of the Eedge of the platform, with the box opening facing W. In this trial, the landmark was placed in the northwest corner of the platform. The place of the reward is indicated by the x.B, Inbound journey of the same trial. While the rat approached the landmark to eat the chocolate sprinkles placed near it, the box was moved to the NE corner of the platform and was rotated 90° to face south. The following trial (data not shown) started from this box location. Computer software randomized box location, box orientation, and landmark location. C, Seven possible box locations and orientations (1–7) and three possible landmark locations (8) were sampled with equal probability in each recording session.

Fig. 3.

Schematic diagram showing three alignments used to analyze cell activity in both experiments. A, Three consecutive trials on the linear track. The open squaresrepresent the location of the box at the start of a trial, whereas thegray squares represent the location of the box at the end of a trial. Note that the end-box position of the previous trial becomes the start-box position for the next trial. The black lines indicate the rat’s trajectory, and the small back circles represent spikes fired by the cell. In this example, the cell fired each time the rat departed from the box.B, Each trial is shifted and aligned so that thewhite squares, representing the start-box locations, coincide. Note that, if the trials were superimposed, the spikes would form a single cluster. C, Each trial is shifted so that the end-box locations, represented by gray squares, coincide. This alignment generates multiple clusters of spikes when trials are superimposed. Thus, this idealized cell shows a single place field when the trials are aligned in the start-box frame but multiple place fields in the end-box and track frames. D, Three consecutive trials on the platform. The black,gray, and stippled lines represent the trajectory of the rat. The start-box location is indicated by the box drawn with solid lines, whereas the end-box location is drawn with dashed lines. The large black circle shows the position of the landmark in each trial, and the small black circles represent cell discharge. This idealized cell is active when the rat enters the box. E, The same three trials aligned and superimposed in the start-box frame. In this alignment, multiple clusters of spikes appear.F, The three trials aligned and superimposed in the end-box frame. This alignment gives rise to a single cluster of spikes. Thus, this cell shows a single place field when the trials are aligned in the end-box frame but multiple place fields in the start-box and platform frames.

Fig. 4.

Relationship between spatial firing properties and box location for outbound and inbound journeys. A, Firing profiles of four outbound-selective cells (1,2, 3, 4) shown for all five types of outbound journey (see Fig. 1B). The horizontal lines represent the track, and thesmall rectangles represent the box. The last 27 cm portion of the track, containing the fixed reward cup, is omitted. Cell 1 fired immediately after the rat exited the box and had a displacement slope of 0.95; cell 2 fired farther away from the box and had a displacement slope of 0.72; cell 3 fired approximately halfway between the box and the goal and had a displacement slope of 0.57; cell 4 fired close to the goal and had a displacement slope of 0.10. The maximum firing rates for cells 1, 2, 3, and 4 were 11, 30, 18, and 22 Hz, respectively. Note that the firing field of cell 2 shrunk progressively as the box moved closer to the goal. Also, the firing rate of this cell was very low on box4-out trials and vanished on box5-out trials. Cell 3 showed decreased firing rates on box3-out trials and ceased firing on box4-out and box5-out trials. No such modulation of firing rate and firing field size were seen in cell 1 or cell 4. B, Plot of the displacement slope as a function of the position of the peak firing along the track for box1-out trials (168 outbound-selective cells from eight rats). The horizontal axis represents the location of the peak firing on the track for the box1-out journeys and is scaled so that the origin corresponds to box1, and 1.0 corresponds to the fixed food cup. The vertical axisshows the displacement slope (ratio of the firing-field shift to the distance that the box was moved) representing the extent to which the box controlled cell activity. A displacement slope of 1 indicates that the cell fired at a fixed distance from the box across the five types of outbound journeys, whereas a displacement slope of 0 indicates that the cell fired at a fixed distance from the fixed reward site. This plot shows that all cells that fired on the initial part of the journey were strongly bound to the box. As the rat moved farther along the track, the displacement slope gradually declined. Near the end of the journey, the influence of the box was overridden by that of the fixed cues (displacement slope values near 0.0). Note that because a rat samples a limited region of the track on different journeys, certain combinations of slope versus peak firing along the full track are impossible. These lie at the bottom left and top right of plot B. C, Firing profiles of four inbound-selective cells (5, 6,7, 8) shown for all five types of inbound journey (see Fig. 1C). Cell 8 fired immediately after the rat departed from the fixed site and had a displacement slope of 0.0; cell 7 fired farther away and had a displacement slope of 0.0; cell 6 fired approximately halfway between the fixed food cup and the box and had a displacement slope of 0.35; cell 5 fired as the rat was entering the box and had a displacement slope of 1.06. The maximum firing rates for cells 5, 6, 7, and 8 were 32, 27, 21, and 11, respectively. Note that cells 6 and 7 ceased firing when the box was placed inside their firing fields. D, Plot of the displacement slope as a function of the position of the peak firing along the track for box1-in trials (157 inbound-selective cells from eight rats). More than half of the inbound trajectory was marked by firing fields at constant distances from the fixed reward site (displacement slopes close to 0.0). Cells with intermediate displacement slopes appeared only on the last part of the inbound journey and covered a shorter span of the inbound journey than cells with intermediate slopes did on the outbound journey. Box-related cells started to fire at a short distance before reaching the box and continued firing inside the box.

Fig. 5.

Examples of bidirectional cells. For each cell (1, 2, 3,4), the top five plots represent the outbound journeys, and the bottom five plotsrepresent the inbound journeys. Cell 1, on the outbound journeys, fired shortly after the rat left the box; on the inbound journeys (below), this cell fired at a fixed location on the track, irrespective of box location. Cell 2, on the outbound journeys, fired at a constant distance from the box and showed two peaks of firing on the box1-out and box2-out journeys; on the inbound journeys, the firing field of this cell was stable with respect to the track. Cell 3, on the outbound journeys, fired nearer to the fixed site than to the box and, hence, had a small but positive displacement slope. On the inbound journeys, this cell had a place field at almost exactly the same location, but the displacement slope was 0.0. Cell 4, on the outbound journeys, showed a shrinking of the firing field and a progressive decline in firing rate; on the inbound journeys, the firing field was fixed with respect to the track. This figure illustrates that bidirectional cells share properties with the outbound-selective cells on the outbound journeys and with the inbound-selective cells on the inbound journeys. As in Figure 4, on both journeys the firing properties of the cells are determined primarily by the landmark of origin of the journey.

Fig. 6.

Temporal cross-correlations between cells with widely separated fields on the full track and adjacent or partially overlapping fields on the shortened track. Each row corresponds to a pair of simultaneously recorded cells. In each row, the first plot shows the firing profiles of the two cells (dark gray and light gray) on all five types of journeys. The middle plot shows the temporal cross-correlation (1 sec window with 10 msec bin size) between the two spike trains. The plots on the right show the same cross-correlation but for a window of 200 msec with a bin size of 2 msec. A, Two outbound-selective cells with adjacent but nonoverlapping fields on the full track and partially overlapping fields on box5-out trials. The cross-correlations show no temporal overlap, although the fields appear to be spatially overlapping on the box5-out trials. Note that with increased distortion of the track, the sizes of the firing fields shrink, the centers of the fields converge, and the firing rates decline. B, Two outbound-selective cells with adjacent but nonoverlapping fields on the full track and partially overlapping fields on box4-out trials. This is an exceptional midtrack cell, because it fired on all five types of outbound journeys and increased its firing rate on box4-out and box5-out journeys. The cross-correlations for box1-out, box2-out, and box3-out trials show little or no temporal overlap. The cross-correlations for box4-out trials show some overlap but less than would be predicted from the spatial overlap of the firing profiles. C, Two inbound-selective cells with widely separated fields on the full track and partially overlapping fields on the box3-in and box4-in trials. The cross-correlations show little temporal overlap on these trials, although the firing profiles appear to overlap. Note that the second cell ceased firing on the box5-in trials.

Fig. 7.

Population vector correlations between the pattern of firing on the full track and on the shortened track for two rats, A and B. For each rat, population vector correlations are shown for the outbound journeys (top five plots) and inbound journeys (bottom five plots). For each correlation plot, thevertical axis corresponds to the full track, whereas thehorizontal axis corresponds to the length of the track covered by the rat in one of the five trial types (box1, box2, etc.; see Key, bottom left). Highly correlated firing patterns between one location on the full track and a second location on one of the shortened tracks are indicated in red. The first plot in each row is a spatial autocorrelation of the population vectors on the full track, which gives rise to a perfectly symmetrical pattern, with values of 1.0 along the diagonal. The more similar the firing patterns on each shortened track to those on the full track, the more closely the correlation matrix for the shortened track resembles the autocorrelation. With few exceptions, the firing pattern at each location on each shortened track was very similar to the firing pattern of some location on the full track, as indicated by the red ridge of high correlation, either continuous or broken into two pieces. The exceptions correspond to locations where the ridge is discontinuous. The regions of the ridge corresponding to the box and to the fixed food cup always had high correlations. This indicates that the population firing pattern in the vicinity of the box and fixed food cup was always similar to the corresponding patterns on the full track. Thus, the pattern of high correlation points gives a picture of the “mapping” from the shortened track to the full track (also shown in Fig. 8). A, Population vector correlations for rat A (78 cells). For both outbound and inbound journeys, the pattern of activity on the full track was highly correlated with the pattern of activity on the box2-out and box2-in trials. The correlation matrix was similar to the autocorrelation but exhibited a slight deviation from the diagonal. This deviation indicates that on box2 trials, the population activity pattern was governed primarily by the origin of the journey at early times and by the destination of the journey at later times. Beginning with the third plot (box3-out and box3-in trials), the correlation matrix shows striking differences from the autocorrelation matrix. When the track was greatly shortened, e.g., on the box4-out trials (fourth plot to the right), the pattern of activity remained correlated at the beginning of the trial when the rat is in the vicinity of the box. Then there is an area of low correlation and a sudden jump to the final part of the journey, where the activity patterns are highly correlated again, indicating that there is a discontinuous shift in the representation. B, Population vector correlations for rat B (35 cells). The same general features as for rat A are apparent, except for the correlation pattern for the shortened outbound journeys (top row). In contrast to the other seven rats, this rat showed continuous transition of the representation on all the outbound journeys. The population vector correlations on the inbound journey show discontinuity. This indicates individual differences between rats in the way the representation responds to shortening of the track.

Fig. 8.

Mappings from each shortened track to the full track, derived from the correlation plots shown in Figure 7 for rats A and B. Each black panel shows five superimposed plots, color-coded according to the box location (see Key at bottom left). For each rat, the left panel shows mappings for the outbound journeys, and the right panelshows mappings for the inbound journeys. A schematic outline of the track is drawn at the bottom of each panel, where1–5 indicate the front edge of the box. As illustrated in the key (top left) each curve shows for every point on one of the shortened journeys the point on the full journey where the hippocampal representation was most similar. In other words, the colored points correspond to the red ridges of the correlations plots in Figure 7. In each plot, thewhite dots aligned along the diagonal represent the identity mapping, associating the box1 journeys with themselves. In all cases, the red dots, representing box2 journeys, form a continuous, slightly curved line indicating a gradual transition of the representation between origin and destination. Most of the other plots, corresponding to shorter journeys, show discontinuities at some point along the journey, indicating abrupt shifts in the hippocampal representation. Note that the length of the segments in which the colored plots are parallel to the identity line reflects the distance over which the representation was dominated by the box. For some outward journeys, this was almost 1 m, even though the box was behind the rat, outside of its field of view. In contrast, for inbound journeys, the representation did not become dominated by the box until the rat was within ∼20 cm.

Fig. 9.

Examples of cells recorded both on the linear track (Experiment 1) and on the square platform (Experiment 2). Each plot is a spatial firing map in which the gray linesrepresent the superimposed trajectories of the rat, and theblack circles represent cell discharge. For the first three cells (A, B, C), thetop panels depict the firing map on the linear track obtained by superimposing all the trials, the panel below shows the same trials aligned and superimposed in the box frame (see Materials and Methods) (see Fig. 3), and the bottom panel shows the firing map for the same cell on the square platform. For cells D, E, andF, only two firing maps are shown. The fine vertical lines on the linear track correspond to the front of the five box locations. In the panels depicting the square platform, the box and goal locations correspond to three equidistant locations along the left and right edge, respectively (see Materials and Methods) (see Fig. 2).A, A cell that fired inside the box on the track and in the vicinity of the landmarks on the platform. The top panel shows that the cell fired preferentially in five equally spaced locations corresponding to the five box locations on the track. When the trials are aligned and superimposed so that the box locations coincide (below), a single cluster of firing appears, indicating that this cell fired specifically when the rat was inside the box. On the platform, the cell fired exclusively when the rat was at the three landmark (goal) locations. B, A cell that fired inside the box both on the track and on the platform. The three clusters of spikes on the right edge of the platform indicate that the cell fired on the platform when the rat was inside the box. C, This cell fired on the track just as the rat was leaving the box, and it showed very strong activity near the landmark in all three landmark locations on the platform. The trials in the middle panel are aligned on the start-box frame to show that the firing field spans the threshold of the box, indicated by a thin vertical line. D, This cell had a bidirectional place field on the track and strong fields inside the box on the platform. In the top panel, the bottom streak of spikes corresponds to the outbound journeys and the top streak to the inbound journeys. A bidirectional cell of this type is shown in Figure 5, cell 1. E, This cell had an inbound-selective place field on the track and a nondirectional place field on the platform. A second field is suggested by the small cluster of spikes near the top left corner of the platform. F, This cell was silent on the linear track but fired reliably on the platform when the rat was turning from the food cup, ready to exit the box. In general, there was no consistent relationship of cells to the box across different environments.