Modeling Interactions of the Rat's Place and 
Head Direction Systems 
A. David Redish and David S. Touretzky 
Computer Science Department & Center for the Neural Basis of Cognition 
Carnegie Mellon University, Pittsburgh PA 15213-3891 
Internet: {dredJ_sh, dst:}@cs. ainu. edu 
Abstract 
We have developed a computational theory of rodent navigation that 
includes analogs of the place cell system, the head direction system, and 
path integration. In this paper we present simulation results showing how 
interactions between the place and head direction systems can account for 
recent observations about hippocampal place cell responses to doubling 
and/or rotation of cue cards in a cylindrical arena (Sharp et al., 1990). 
Rodents have multiple internal representations of their relationship to their environment. 
They have, for example, a representation of their location (place cells in the hippocampal 
formation, see Muller et al., 1991), and a location-independent representation of their 
heading (head direction cells in the postsubiculum and the anterior thalamic nuclei, see 
Taube et al., 1990; Taube, 1995). 
If these representations are to be used for navigation, they must be aligned consistently 
whenever the animal reenters a familiar environment. This process was examined in a set 
of experiments by Sharp et al. (1990). 
1 The Sharp et al., 1990 experiment 
Rats spent multiple sessions finding food scattered randomly on the floor of a black cylin- 
drical arena with a white cue card along the wall subtending 90  of arc. The animals were 
not disoriented before entering the arena, and they always entered at the same location: the 
northwest corner. See Figure 3a. Hippocampal place fields were mapped by single-cell 
recording. A variety of probe trials were then introduced. When an identical second cue 
62 A.D. REDISH, D. $. TOURETZKY 
estibular Head ] _ _ [ Lcal I 
Input   (i,e)  
Path / 
Motor Integrator[._ 
Efference  
Copy ..,/ <''Y,) l--J 
emor'y 
Visual 
Input 
Figure 1: Organization of the rodent navigation model. 
card was added opposite the first (Figure 3c), most place fields did not double.  Instead, 
the cells continued to fire at their original locations. However, if the rat was introduced into 
the double-card environment at the southeast corner (Figure 3d), the place fields rotated 
by 180  . But rotation did not occur in single-card probe trials with a southeast entry point 
(Figure 3b). When tested with cue cards rotated by +30 , Sharp et al. observed that place 
field locations were controlled by an interaction of the choice of entry point with the cue 
card positions (Figure 3f.) 
2 The CRAWL model 
In earlier work (Wan et al., 1994a; Wan et al., 1994b; Redish and Touretzky, 1996) we 
described a model of rodent navigation that includes analogs of both place cells and the head 
direction system. This model also includes a local view module representing egocentric 
spatial information about landmarks, and a separate metric representation of location which 
serves as a substrate for path integration. The existence of a path integration faculty in 
rodents is strongly supported by behavioral data; see Maurer and Seguinot (1995) for 
a discussion. Hypotheses about the underyling neural mechanismss are presently being 
explored by several researchers, including us. 
The structure of our model is shown in Figure 1. Visual inputs are represented as triples of 
form (Ti, ri, Oi), each denoting the type, distance, and egocentric bearing of a landmark. The 
experiments reported here used two point-type landmarks representing the left and right 
edges of the cue card, and one surface-type landmark representing the arena wall. For the 
latter, ri and 0i define the normal vector between the rat and the surface. In the local view 
module, egocentric bearings Oi are converted to allocentric form bi by adding the current 
value represented in the head direction system, denoted as 4ih. The visual angle ctii between 
pairs of landmarks is also part of the local view, and can be used to help localize the animal 
when its head direction is unknown. See Figure 2. 
Five of the 18 cells recorded by Sharp et al. changed their place fields over the various recording 
sessions. Our model does not reproduce these effects, since it does not address changes in place cell 
tuning. Such changes could occur due to variations in the animal's mental state from one trial to the 
next, or as a result of learning across trials. 
Modeling Interactions of the Rat's Place and Head Direction Systems 63 
Figure 2: Spatial variables used in tuning a place cell to two landmarks i and j when the 
animal is at path integrator coordinates (xp, yp). 
Our simulated place units are radial basis functions tuned to combinations of individual 
landmark bearings and distances, visual angles between landmark pairs, and path integrator 
coordinates. Place units can be driven by visual input alone when the animal is trying 
to localize itself upon initial entry at a random spot in the environment, or by the path 
integrator alone when navigating in the dark. But normally they are driven by both 
sources simultaneously. A key role of the place system is to maintain associations between 
the two representations, so that either can be reconstructed from the other. The place 
system also maintains a record of allocentric bearings of landmarks when viewed from the 
current position; this enables the local view module to compare perceived with remembered 
landmark bearings, so that drift in the head direction system can be detected and corrected. 
In computer simulations using a single parameter set, the model reproduces a variety 
of behavioral and neurophysiological results including control of place fields by visual 
landmarks, persistence of place fields in the dark, and place fields drifting in synchrony 
with drift in the head direction system. Its predictions for open-field landmark-based 
navigation behavior match many of the experimental results of Collett et al. (1986) for 
gerbils. 
2.1 Entering a familiar environment 
Upon entering a familiar environment, the model's four spatial representations (local view, 
head direction, place code, and path integrator coordinates) must be aligned with the 
current sensory input and with each other. Note that local view information is completely 
determined given the visual input and head direction, and place cell activity is completely 
determined given the local view and path integrator representations. Thus, the alignment 
process manipulates just two variables: head direction and path integrator coordinates. 
When the animal enters the environment with initial estimates for them, the alignment 
process can produce four possible outcomes: (1) Retain the initial values of both variables, 
(2) Reset the head direction, (3) Reset the path integrator, or (4) Reset both head direction 
and the path integraton 
2.2 Prioritizing the outcomes 
When the animal was placed at the northwest entry point and there were two cue cards 
(Figure 3c), we note that the orientation of the wall segment adjacent to the place field 
is identical with that in the training case. This suggests that the animal's head direction 
64 A.D. REDISH, D. S. TOURETZKY 
did not change. The spatial relationship between the entry point and place field was also 
unchanged: notice that the distance from the entry point to the center of the field is the 
same as in Figure 3a. Therefore, we conclude that the initially estimated path integrator 
coordinates were retained. Alternatively, the animal could have changed both its head 
direction (by 180 ) and its path integrator coordinates (to those of the southeast corner) and 
produced consistent results, but to the experimenter the place field would appear to have 
flipped to the other card. Because no flip was observed, the first outcome must have priority 
over the fourth. 
In panel d, where the place field has flipped to the northwest corner, the orientation of the 
segment of wall adjacent to the field has changed, but the spatial relationship between the 
entry point and field center has not. Resetting the path integrator and not the head direction 
would also give a solution consistent with this local view, but with the place field unflipped 
(as in panel b). We conclude that the second outcome (reset head direction) must have 
priority over the third (reset the path integrator). 
The third and fourth outcomes are demonstrated in Figures 3b and 3f. In panel b, the 
orientation of the wall adjacent to the place field is unchanged from panel a, but the spatial 
relationship between the entry point and the place field center is different, as evidenced by 
the fact that the distance between them is much reduced. This is outcome 3. In panel f, 
both variables have changed (outcome 4). 
Finally, the fact that place fields are stable over an entire session, even when there are 
multiple cue cards (and therefore multiple consistent pairings of head directions and path 
integrator coordinates) implies that animals do not reset their head direction or path in- 
tegrator in visually ambiguous environments as long as the current values are reasonably 
consistent with the local view. We therefore assume that outcome 1 is preferred over the 
others. 
This analysis establishes a partial ordering over the four outcomes: 1 is preferred over 4 by 
Figure 3c, and over the others by the stability of place fields, and outcome 2 is preferred 
over 3 by Figure 3d. This leaves open the question of whether outcome 3 or 4 has priority 
over the other. In this experiment, after resetting the path integrator it's always safe for the 
animal to attempt to reset its head direction. If the head direction does not change by more 
than a few degrees, as in panel b, we observe outcome 3; if it does change substantially, as 
in panel f, we observe outcome 4. 
2.3 Consistency 
The viability of an outcome is a function of the consistency between the local view and 
path integrator representations. The place system maintains the association between the 
two representations and mediates the comparison between them. 
The activity A(u) of a place unit is the product of a local view term LV(u) and a path 
integrator term C(u). LV(u) is in turn a product of five Gaussians: two tuned to bearings 
and two to distances (for the same' pair of landmarks), and one tuned to the retinal angle 
between a pair of landmarks. C(u) is a Gaussian tuned to the path integrator coordinates of 
the center of the place field. 
If the two representations agree, then the place units activated by path integrator input will 
be the same as those activated by the local view module, so the product A(u) computed 
by those units will be significantly greater than zero. The consistency t of the association 
Modeling Interactions of the Rat's Place and Head Direction Systems 65 
between path integrator and local view representations is given by:  = -u A(u)/Yu C(u). 
Because A(u) < C(u) for all place units,  ranges between 0 and 1. When the current local 
view is compatible with that predicted by the current path integrator coordinates, t will be 
high; when the two are not compatible, t will be low. 
Earlier we showed that the navigation system should choose the highest priority viable 
outcome. If the consistency of an outcome is more than t* better than all higher-priority 
outcomes, that outcome is a viable choice and higher-priority ones are not. * is an 
empirically derived constant that we have set equal to 0.04. 
3 Discussion 
Our results match all of the cases already discussed. (See Figure 3, panels a through d 
as well as f and h.) Sharp et al. (1990) did not actually test the rotated cue cards with a 
northwest entry point, so our result in panel e is a prediction. 
When the animals entered from the northwest, but only one cue card was available at 180 , 
Sharp et al. report that the place field did not rotate. In our model the place field does 
rotate, as a result of outcome 4. This discrepancy can be explained by the fact that this 
particular manipulation was the last one in the sequence done by Sharp et al. McNaughton 
et al. (1994) and Knierim et al. (1995) have shown that if rats experience the cue card 
moving over a number of sessions, they eventually come to ignore it and it loses control 
over place fields. When we tested our model without a cue card (equivalent to a card being 
present but ignored), the resulting place field was more diffuse than normal but showed no 
rotation; see Figure 3g. We thus predict that if this experiment had been done before the 
other manipulations rather than after, the place field would have followed the cue card. 
In the Sharp et al. experiment, the animals were always placed in the environment at the 
same location during training. Therefore, they could reliably estimate their initial path 
integrator coordinates. They also had a reliable head direction estimate because they were 
not disoriented. We predict that were the rats trained with a variety of entry points instead 
of just one, using an environment with a single cue card at 0  (the training environment 
used by Sharp et al.), and then tested with two cue cards at 0  and 180 , the place field 
would not rotate no matter what entry point was used. This is because when trained with a 
variable entry point, the animal would not learn to anticipate its path integrator coordinates 
upon entry; a path integrator reset would have to be done every time in order to establish the 
animal's coordinates. The reset mechanism uses allocentric bearing information derived 
from the head direction estimate, and in this task the resulting path integrator coordinates 
will be consistent with the initial head direction estimate. Hence, outcome 3 will always 
prevail. 
If the animal is disoriented, however, then both the path integrator and the head direction 
system must be reset upon entry (because consistency will be low with a faulty head 
direction), and the animal must choose one cue card or the other to match against its 
memory. So with disorientation and a variable entry point, the place field will be controlled 
by one or the other cue card with a 50/50 probability. This was found to be true in a related 
behavioral experiment by Cheng (1986). 
Our model shows how interactions between the place and head direction systems handle the 
various combinations of entry point, number of cue cards, and amount of cue card rotation. 
It predicts that head direction reset will be observed in certain tasks and not in others. In 
66 A.D. REDISH, D. S. TOURETZKY 
experiments such as the single cue card task with an entry in the southeast, it predicts the 
place code will shift from an initial value corresponding to the northwest entry point to the 
value for the southeast entry point, but the head direction will not change. This could be 
tested by recording simultaneously from place cells and head direction cells. 
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Modeling Interactions of the Rat's Place and Head Direction Systems 67 
(a) 1 cue card at 0  (East) 
entry in Northwest comer 
angle of rotation (Sharp et al.) = 2.7  
precession of HD system = 0  
(c) 2 cue cards at 0  (East) & 180  (West) 
entry in Northwest comer 
angle of rotation (Sharp et al.) = -2.3  
precession of HD system = 0  
(e) 2 cue cards at 330  & 150  
entry in Northwest comer 
not done by Sharp et al. 
precession of HD system = 331 o 
(g) 1 cue card at 180  (West) 
entry in Northwest comer 
angle of rotation (Sharp et al.) = -5.5  
precession of HD system -- 0  
(b) 1 cue card at 0  
entry in Southeast comer 
angle of rotation (Sharp et al.) = -6.00 
precession of HD system = 2  
(d) 2 cue cards at 0  & 180  
entry in Southeast comer 
angle of rotation (Sharp et al.) = 182.5  
precession of HD system = 178  
(f) 2 cue cards at 3300 & 150  
entry in Southeast comer 
angle of rotation (Sharp et al.) = 158.3  
precession of HD system = 151 o 
(h) 1 cue card at 180  
entry in Southeast comer 
angle of rotation (Sharp et al.) = 182.2  
precession of HD system = 179  
Figure 3: Computer simulations of the Sharp et al. (1990) experiment showing that place 
fields are controlled by both cue cards (thick arcs) and entry point (arrowhead). "Angle of 
rotation" is the angle at which the correlation between the probe and training case place 
fields is maximal. Because head direction and place code are tightly coupled in our model, 
precession of HD is an equivalent measure in our model. 
