Hidden Food Maze and experimental setup.

A. The floor of the arena is 120cm in diameter, and the walls are 45cm tall. Note 20 cm scale bar in this panel. The home cage has a 10.5×6.5cm2 floor area. The door slides upward (mice enter without handling). The floor is washed and rotated between every trial to avoid predictable scratch marks and odor trails. The subfloor containing food is not illustrated. B. Camera view of a mouse searching for hidden food (target, pointed by the target vector). The REL of the target is marked for each entrance (from the mouse’s perspective, the displacement from the start in each quadrant to its respective REL is the same for any entrance; e.g., “70cm forward + 30cm to the left”; and it is equal to the displacement from the trained start to target). C. “Random entrances” experiment. Mice enter from any of the four entrances randomly over trials to search for food (“A”-labeled star) always in front of the X landmark. Arrows show the four possible displacements. D. “Static entrances” experiment. Mice start from the same entrance (labeled “Start”) in every trial to search for food in front of the same landmark. Blue/cyan arrows=food vector (start→food); Orange arrow=REL vector (start→REL). After training, the start position in a probe trial can be rotated (“180° Start”) to check whether mice follow idiothetic (start→REL; ignoring landmarks) or allothetic (start→A; following landmarks) cues; going via the REL vector is regarded as evidence of path integration. E. “Two food location” experiment. Mice start from a static entrance to search for food (red vector to target A). Afterwards, mice are trained to find food in a different location (blue vector to target B). After learning both targets, a probe trial (i.e., a trial without food) is designed to check whether mice can compute shortcuts from B to A (B-A vector, orange arrow).

Mouse spatial learning with random entrances.

A. Two examples of mouse search trajectories during early learning (trial 3) when the entrance changes from trial to trial. They are irregular and vary unpredictably across trials. A, B. Star = target location. Yellow Square = entrance site. B. Two examples of mouse search trajectories during late learning (trial 14) after starting from different entrances. Trajectories look as irregular as in early trials. C. (Top) Heatmap of the first 2min of a probe trial done after trial 18 (red=more time in a given region). (Bottom) Mice spent about the same time (25%) in each of the four sectors, regardless of being close to the target (blue) or to its REL (white). D. Some significant reduction in latency to reach target is seen across trials (p=0.008; N=8). D-I: Error bars = S.E. Shaded area = data range. E. Some significant increase in speed is seen (p=0.002; N=8). F. Average normalized distance traveled to reach target (dtotal/dtarget=1 is optimal; p=0.05, N=8). G. Hole-checking density (number of hole checks per distance traveled) in each half of the trajectory. The density remains constant for both halves and across trials, suggesting that mice remained uncertain as to the food location. G-inset. The S.D. of the density over the mice sample remains constant for both halves (N=8). H. The average distance of the checked holes to the food d(checks→food) remains almost constant across trials. Horizontal lines are just guides to the eye. I. The probability density of the distance of hole checks to the food d(checks→food) for the first and last learning trials (the corresponding averages over trials are in panel H). The density remains unaltered. Vertical dotted lines mark the same distances as the horizontal lines in panel H.

Mouse spatial learning with static entrances.

A. Two examples of mouse search trajectories during early learning (trial 3). They are irregular and variable similarly to those in the random entrance experiments. A, B. Star = target location. Yellow Square = entrance site. B. Two examples of mouse search trajectories during late learning (trial 14). They go directly towards the food or go along the wall before turning to the food, creating variation across mice and trials. C. (Top) Heatmap of the first 2min of a probe trial done after trial 14 (red=more time in a given region). (Bottom) Mice spent almost 50% of the time within 15cm radius of the target (blue) compared to the RELs (white). D. Latency dramatically decreases (p<10-7; N=8). D-I: Error bars = S.E. Shaded area = data range. E. Speed significantly increases during trials (p=0.0001; N=8). F. Normalized distance to reach target (dtotal/dtarget=1 is optimal) becomes almost optimal (p<10-7; N=8). G. Hole-checking density over distance in each half of the trajectory. It significantly decreases in the first half (p=0.05), and stays constant in the second. G-inset: The S.D. of the density is larger in the second half. H. The average distance of the checked holes to the food d(checks→food) decreases for both halves of the trajectory. After learning, the hole checks happen closer to the food (d(checks→food) is almost zero), although there are more checks per distance. I. The probability density of the distance of hole checks to the food d(checks→food) for the first and last trials (the corresponding averages over trials are in panel h). After learning (trial 14), the density is larger closer to the food, a feature that does not appear in the random entrance experiments.

Trajectory directionality and active sensing for random and static experiments.

Arenas on the top row (mean displacement vector – see color scale between panels b and e) correspond to the ones immediately below them (hole checking spatial distribution); the red “A” label marks the target (food site), which is pointed by the food (target) vector (purple arrow). Top row (A,B,E,F): the color and arrows indicate the most probable route taken (red=more probable; only p<0.001 displacements shown; pink arrow=inferred target position, or TEV; shaded pink sector=S.D. of TEV; see Methods, and Fig. S7). Bottom row (C,D,G,H): spatial distribution of hole-checks; size and color of circles=normalized frequency that a hole was checked (larger pink circles=higher frequency); Black ellipse (x=mean): covariance of spatial distribution. Green ellipse (+=mean): covariance of spatial distribution restricted to ≤20cm of the target. Random entrance experiments (N=8; panels A,C: trial 1; B,D: trial 14): regardless of training stage, no significant preferred routes and the TEV does not point to target (A,B); hole checks are randomly distributed throughout the arena, and shift from the walls (c) to near the center (d) after learning. Static entrance experiments (N=8; panels E,G: trial 1; F,H: trial 14): after learning (f) the TEV and significant displacements go straight to the target (although individual trajectories are variable); and hole checks align along the start-target path (h). Panel I: deviation between the TEV (pink arrow) and the target vector (purple arrow) illustrated in top panels. Directionality is quickly learned (static case). Panels J,K: hole-check area density corresponding to the spatial profiles in bottom panels. Density after learning is larger near the target (static case), supporting the path integration hypothesis. Asterisks/star: p<0.05 (paired t-test). Note the presence of more significant displacements in late learning for static entrances only, and the associated alignment of the TEV and food vector.

Changing start position after training in static protocol.

Mice are trained in the static entrance protocol to find food at the target labeled “A” (blue circle), and a probe trial is executed with mice entering from a rotated entrance after 18 trials. Panels A,B,C show the comparison between trajectories from the last learning trial (blue) versus the probe (red). The training was performed without landmarks (A: N=8, -90° rotation) and with landmarks (B: N=8, 90° rotation; c: N=8, 180° rotation). In all instances, mice ignored landmarks and went to the REL location (“REL A” label, red triangle), something that is expected under the path integration hypothesis. Panel D: trajectory directionality analysis and TEV (pink arrow; shaded sector: S.D.) show that significant paths of all mice (p<0.001; N=8; see Methods) point to the REL-A location in the same way that it pointed to the target without rotated entrance in Fig. 4F. Panel E: the spatial distribution shows that hole checks accumulate along the start-REL vector, instead of the start-target vector of the case without rotation in Fig. 4H. Black ellipse (x=mean): covariance of hole check distribution. Green ellipse (+=mean): covariance of the data within 20cm of the REL-A location. This suggests that mice follow trajectories anchored to their start location (idiothetic frame of reference).

Two food location experiment.

Panels A-D. Trajectory exemplars of four sequential stages of the experiment (all trials done with static entrance, N=8): (A) training target A (trials 1-A and 16-A for early and late learning, respectively); (B) probe A (no food is found, triggering a random search); (C) training target B (keeping A empty; trials 1-B and 8-B for early and late learning); (D) probe B-A (where both targets are trained and empty, and the mice take a shortcut from B to A; see Fig. S8 for all exemplars). Filled circles=filled target hole; empty circles=empty target. In the A and B learning stages, the trajectories evolve from random to going straight from start to the respective target. Panels E-F. Standard boxplot statistics of learning versus probe (diamonds are averages; asterisks: p<0.05 in a paired t-test comparison). Quantities are defined in Fig. S4A. Significant differences between early and late learning were observed for the traveled distance (E), heading angle (F), and distance to the food line (G). Density of hole checks (H) remained nearly constant, as expected. In all instances, the values of all quantities in the B-A probe resembled the values of the late learning trials, whereas the randomized B-A probe (gray) had values that resembled early learning, suggesting the B-A behavior is not random. In the Probe B→A trials, the “food line” is the straight line that connects B to A, along which the reference distance dtarget is measured between A and B. In the other trials, the food line is a straight line from start to the specific target, either A or B, along which dtarget is measured between start and target.

Trajectory directionality and active sensing in two food location experiment.

Arenas on the top row (mean displacement vector) correspond to the ones immediately below them (hole checking spatial distribution); the red “A” and blue “B” labels mark the targets (food sites), which are pointed by the target vector (purple arrow). Top row (A,C,D,G): the color and arrows indicate the most probable route taken (red=more probable; only p<0.001 displacements shown; pink arrow=inferred target position, or TEV; shaded pink sector=S.D. of TEV; see Methods, and Fig. S7). Bottom row (B,E,F,H): spatial distribution of hole-checks; size and color of circles=normalized frequency at which a hole was checked (larger pink circles=higher frequency); Black ellipse (x=mean): covariance of spatial distribution. Green ellipse (+=mean): covariance of spatial distribution restricted to ≤20cm of the target. Three stages of the experiment are shown (N=8; all training done in static entrance with no landmarks): after learning the target A (A,B: trial 16-A; significant routes and hole checks are observed only along the target vector, as expected); training of the target B (C,E: trial 1-B; D,F: trial 8-B; it shows the evolution of the TEV from pointing to A to pointing to B, and the hole checks distribution becomes limited to the newly learned target vector towards B); probe B-A (G,H) shows significant routes from B to A (shortcuts; N=5 out of 8 performed the route Start→B→A; see Fig. S8 for all samples); hole-checks accumulated along the B-A path suggesting that mice remember both locations. Panels I,J: TEV-target deviation and hole-check area density, respectively. Probe B-A measures are compatible with trials where trajectories have already been learned. Standard boxplot statistics. Diamond: mean. Asterisks/star: p<0.05 (t-test).

Two food location training with 180° rotated probe.

Mice (N=8) are trained to find food in the target labeled “A” (red circle, panel A), and in target labeled “B” (blue circle, panel B) afterwards; then a 180° rotated probe trial (no food; panel c) is realized to check whether the mice are able to generalize and take the shortcut from REL-B (blue triangle) to REL-A (red triangle), instead of the A and B targets. No landmarks are present. Panels A,C,E show exemplars of trajectories in three stages of the experiment, and B,D,F show their time course and hole-check locations marked with circles that increase with elapsed time. G. Trajectory directionality analysis and TEV (pink arrow; shaded sector: S.D.) show that significant paths (p<0.001; N=8; see Methods) point from REL-B to REL-A in the same way that it pointed from B to A without rotated entrance in Fig. 7G. Panel H: the spatial density shows that hole checks accumulate along the REL-B to REL-A direction, instead of the B-A direction in the case without rotation in Fig. 7H. Black ellipse (x=mean): covariance of hole check density. Green ellipse (+=mean): covariance of the same data restricted to ≤20cm of the REL-A location. This suggests that mice follow shortcut trajectories anchored to their start location (idiothetic frame of reference).