A 
Model of the Neural Basis of the Rat's 
Sense of Direction 
William E. Skaggs 
bill@nsma. arizona. edu 
James J. Knierim 
jira@nsraa. arizona. edu 
Hemant S. Kudrimoti 
hemant@nsma. arizona. edu 
Bruce L. McNaughton 
bruce@nsma. arizona. edu 
APL Division of Neural Systems, Memory, And Aging 
344 Life Sciences North, University of Arizona, Tucson AZ 85724 
Abstract 
In the last decade the outlines of the neural structures subserving 
the sense of direction have begun to emerge. Several investigations 
have shed light on the effects of vestibular input and visual input 
on the head direction representation. In this paper, a model is 
formulated of the neural mechanisms underlying the head direction 
system. The model is built out of simple ingredients, depending on 
nothing more complicated than connectional specificity, attractor 
dynamics, Hebbian learning, and sigmoidal nonlinearities, but it 
behaves in a sophisticated way and is consistent with most of the 
observed properties of real head direction cells. In addition it makes 
a number of predictions that ought to be testable by reasonably 
straightforward experiments. 
I Head Direction Cells in the Rat 
There is quite a bit of behavioral evidence for an intrinsic sense of direction in 
many species of mammals, including rats and humans (e.g., Gallistel, 1990). The 
first specific information regarding the neural basis of this "sense" came with the 
discovery by Panck (1984) of a population of "head direction" cells in the dorsal 
presubiculum (also known as the "postsubiculum") of the rat. A head direction cell 
1 74 William Skaggs, James J. Knierim, Hemant S. Kudrimoti, Bruce L. McNaughton 
fires at a high rate if and only if the rat's head is oriented in a specific direction. 
Many things could potentially cause a cell to fire in a head-direction dependent 
manner: what made the postsubicular cells particularly interesting was that when 
their directionality was tested with the rat at different locations, the head directions 
corresponding to maxima] firing were consistently parallel, within the experimental 
resolution. This is difficult to explain with a simple sensory-based mechanism; it 
implies something more sophisticated. x 
The postsubicular head direction cells were studied in depth by Taube et al. 
(1990a,b), and, more recently, head direction cells have also been found in other 
parts of the rat brain, in particular the anterior nuclei of the thalamus (Mizumori 
and Williams, 1993) and the retrosplenial (posterior cingulate) cortex (Chen et 
al., 1994a,b). Interestingly, all of these areas are intimately associated with the 
hippocampal formation, which in the rat contains large numbers of "place" cells. 
Thus, the brain contains separate but neighboring populations of cells coding for 
location and cells coding for direction, which taken together represent much of the 
information needed for navigation. 
Figure 1 shows directional tuning curves for three typical head direction cells from 
the anterior thalamus. In each of them the breadth of tuning is on the order of 90 
degrees. This value is also typical for head direction cells in the postsubiculum and 
retrosplenial cortex, though in each of the three areas individual cells may show 
considerable variability. 
Figure 1: Polar plots of directional tuning (mean firing rate as a function of head 
direction) for three typical head direction cells from the anterior thalamus of a rat. 
Every study to date has indicated that the head direction cells constitute a unitary 
system, together with the place cells of the hippocampus. Whenever two head 
direction cells have been recorded simultaneously, any manipulation that caused 
one of them to shift its directional alignment caused the other to shift by the same 
amount; and when head direction cells have been recorded simultaneously with 
place cells, any manipulation that caused the head direction cells to realign either 
caused the hippocampal place fields to rotate correspondingly or to "remap" into a 
different pattern (Knierim et al., 1995). 
Head direction cells maintain their directional tuning for some time when the lights 
in the recording room are turned off, leaving an animal in complete darkness; the 
directionality tends to gradually drift, though, especially if the animal moves around 
(Mizumori and Williams, 1993). Directional tuning is preserved to some degree even 
Sensitivity to the Earth's geomagnetic field has been ruled out as an explanation of 
head-directional firing. 
A Model of the Neural Basis of the Rat's Sense of Direction 175 
if a aimal is passively rotated in the dark, which indicates strongly that the head 
direction system receives information (possibly indirect) from the vestibular system. 
Visual input influences but does not dictate the behavior of head direction cells. 
The nature of this influence is quite interesting. In a recent series of experiments 
(Knierim et al., 1995), rats were trained to forage for food pellets in a gray cylinder 
with a single salient directionM cue, a white card covering 90 degrees of the wM1. 
During training, half of the rats were disoriented before being placed in the cylin- 
der, in order to disrupt the relation between their internM sense of direction and 
the location of the cue card; the other half of the rats were not disoriented. Pre- 
sumably, the rats that were not disoriented during training experienced the same 
initial relationship between their internM direction sense axed the cue card each time 
they were placed in the cylinder; this would not have been true of the disoriented 
rats. Head direction cells in the thalamus were subsequently recorded from both 
groups of rats as they moved in the cylinder. All rats were disoriented before each 
recording session. Under these conditions, the cue card had much weaker control 
over the head direction cells in the rats that had been disoriented during training 
than in the rats that had not been disoriented. For M1 rats the influence of the cue 
card upon the head direction system weakened gradually over the course of multiple 
recording sessions, emd eventually they broke free, but this happened much sooner 
in the rats that had been disoriented during training. The authors concluded that 
a visual cue could only develop a strong influence upon the head direction system if 
the rat experienced it as stable. 
Figure 2 illustrates the shifts in alignment during a typical recording session. When 
the rat is initially placed in the cylinder, the cell's tuning curve is aligned to the 
west. Over the first few minutes of recording it gradually rotates to SSW, and there 
it stays. Note the "tail" of the curve. This comes from spikes belonging to another, 
neighboring head direction cell, which could not be perfectly isolated from the first. 
Note that, even though they come from different cells, both portions shift alignment 
synchronously. 
Figure 2: Shifts in alignment of a head direction cell over the course of a single 
recording session (one minute intervals). 
2 The Model 
As reviewed above, the most important facts to be accounted for by any model of 
the head direction system are (1) the shape of the tuning curves for head direction 
cells, (2) the control of head direction cells by vestibular input, axed (3) the stability- 
dependent influence of visual cues on head direction cells. We introduce here a 
1 76 William Skaggs, James J. Knierim, Hemant S. Kudrimoti, Bruce L. McNaughton 
model that accounts for these facts. It is a refinement of a model proposed earlier 
by McNaughton et al. (1991), the main addition being a more specific account of 
neural connections and dynamics. The aim of this effort is to develop the simplest 
possible architecture consistent with the available data. The reality is sure to be 
more complicated than this model. 
Figure 3 schematically illustrates the architecture of the model. There are four 
groups of cells in the model: head direction cells, rotation cells (left and right), 
vestibular cells (left and right), and visual feature detectors. For expository pur- 
poses it is helpful to think of the network as a set of circular layers; this does not 
reflect the anatomical organization of the corresponding cells in the brain. 
Figure 3: Architecture of the head direction cell model. 
The head direction cell group has intrinsic connections that are stronger than any 
other connections in the model, and dominate their dynamics, so that other inputs 
only provide relatively small perturbations. The connections between them are 
set up so that the only possible stable state of the system is a single localized 
cluster of active cells, with all other cells virtually silent. This will occur if there 
are strong excitatory connections between neighboring cells, and strong inhibitory 
connections between distant cells. It is assumed that the network of interconnections 
has rotation and reflection symmetry. Small deviations from symmetry will not 
impair the model too much; large deviations may cause it to have strong attractors 
at a few points on the circle, which would cause problems. 
The crucial property of this network is the following. Suppose it is in a stable state, 
with a single cluster of activated cells at one point on the circle, and suppose an 
external input is applied that excites the cells selectively on one side (left or right) 
A Model of the Neural Basis of the Rat's Sense of Direction 177 
of the peak. Then the peak will rotate toward the side at which the input is applied, 
and the rate of rotation will increase with the strength of the input. 
This feature is exploited by the mechanisms for vestibular and visual control of 
the system. The vestibular mechanism operates via a layer of "rotation" cells, 
corresponding to the circle of head direction cells (Units with a similar role were 
referred to as "H x H"' cells in the McNaughton et al. (1991) model). There 
re two groups of rotation cells, for left and right rotations. Each rotation cell 
receives excitatory input from the head direction cell at the same point on the 
circle, and from the vestibular system. The activation function of the rotation cell 
is sigmoidal or threshold linear, so that the cell does not become active unless it 
receives input simultaneously from both sources. Each right rotation cell sends 
excitatory projections to head direction cells neighboring it on the right, but not to 
those that neighbor it on the left, and contrariwise for left rotation cells. 
It is easy to see how the mechanism works. When the animal turns to the right, the 
right vestibular cells are activated, and then the right rotation cells at the current 
peak of the head direction system are activated. These add to the excitation of 
the head direction cells to the right of the peak, thereby causing the peak to shift 
rightward. This in turn causes a new set of rotation cells to become active (and 
the old ones inactive), and thence a further shift of the peak, and so on. The peak 
will continue to move around the circle as long as the vestibular input is active, 
and the stronger the vestibular input, the more rapidly the peak will move. If the 
gain of this mechanism is correct (but weak compared to the gain of the intrinsic 
connections of the head direction cells), then the peak will move around the circle 
at the same rate that the animal turns, and the location of the peak will function 
as an allocentric compass. This can only be expected to work over a limited range 
of turning rates, but the firing rates of cells in the vestibular nuclei are linearly 
proportional to angular velocity over a surprisingly broad range, so there is no 
reason .why the mechanism cannot perform adequately. 
Of course the mechanism is intrinsically error-prone, and without some sort of ex- 
ternal correction, deviations are sure to build up over time. But this is an inevitable 
feature of any plausible model, and in any case does not conflict with the available 
data, which, while sketchy, suggests that passive rotation of animals in the dark can 
cause quite erratic behavior in head direction cells (E. J. Markus, J. J. Knierim, 
unpublished observations). 
The final ingredient of the model is a set of visual feature detectors, each of which 
responds if and only if a particular visual feature is located at a particular angle 
with respect to the axis of the rat's head. Thus, these cells are feature specific 
and direction specific, but direction specific in the head-centered frame, not in the 
world frame. It is assumed that each visual feature detector projects weakly to all 
of the head direction cells, and that these connections are modifiable according to 
a Hebbian rule, specifically, 
A W = c(Wrnx f(,kpost) - W),kpre, 
where W is the connection weight, Wmx is its maximum possible value, ,kpost is the 
firing rate of the postsynaptic cell, ,Xpre is the firing rate of the presynaptic cell, and 
the function f() has the shape shown in figure 4. (Actually, the rule is modified 
slightly to prevent any of the weights from becoming negative.) The net effect of 
178 William Skaggs, James J. Knierim, Hemant S. Kudrimoti, Bruce L. McNaughton 
this rule is that the weight will only change when the presynaptic cell (the visual 
feature detector) is active, and the weight will increase if the postsynaptic cell is 
strongly active, but decrease if it is weakly active or silent. Modification rules of this 
form have previously been proposed in theories of the development of topography 
in the neocortex (e.g., Bienenstock et al., 1982), and there is considerable evidence 
for such an effect in the control of LTP/LTD (Singer and Artola, 1994). 
f(rate) 
rate 
Figure 4: Dependence of synaptic weight change on postsynaptic firing rate for 
connections from visual feature detectors to head direction cells in the model. 
To understand how this works, suppose we have a feature detecting cell that re- 
sponds to a cue card whenever the cue card is directly in front of the rat. Suppose 
the rat's motion is restricted to a small area, and the cue caxd is far away, so that it 
is always at approximately the same absolute bearing (say, 30 degrees), and suppose 
the rat's head direction system is working correctly, i.e., functioning as an absolute 
compass. Then the cell will only be active at moments when the head direction 
cells corresponding to 30 degrees are active, and the Hebbian learning process will 
cause the feature detecting cell to be linked by strong weights to these cells, but by 
vanishing weights to other head direction cells. If the absolute bearing of the cue 
card were more variable, then the connection strengths from the feature detecting 
cell would be weaker and more broadly dispersed. In the limit where the bearing 
of the cue card was completely random, all connections would be weak and equal. 
Thus the influence of a visual cue is determined by the amount of training and by 
the variability in its bearing (with respect to the head direction system). 
It can be seen that the model implements a competition between visual inputs and 
vestibular inputs for control of the head direction cells. If the visual cues are rotated 
while the rat is left stationary, then the head direction cells may either rotate to 
follow the visual cues, or stick with the inertial frame, depending on parameter 
values and, importantly, on the training regimen imposed on the network. Both 
of these outcomes have been observed in anterior thalamic head direction cells 
(McNaughton et al., 1993). 
3 Discussion 
Do the necessary types of cells exist in the brain? Cells in the brainstem vestibular 
nuclei are known to have the properties required by the model (Precht, 1978). The 
"rotation" cells would be recognizable from the fact that they would fire only when 
A Model of the Neural Basis of the Rat's Sense of Direction 179 
the rat is facing in a particular direction and turning in a particular direction, with 
rate at least roughly proportional to the speed of turning. Cells with these properties 
have been recorded in the postsubiculum (Markus e al., 1990) and retrosplenial 
cortex (Chen e al., 1994a). The visual cells would be recognizeable from the fact 
that they would respond to visual stimuli only when they come from a particular 
direction with respect to the animal's head axis. Cells with these properties have 
been recorded in the inferior parietal cortex, the internal medullary lamina of the 
thalamus, and the superior colliculus (e.g., Sparks, 1986). The superior colliculus 
also contains cells that respond in a direction-dependent manner to auditory inputs, 
thts allowing a possiblility of control of the head direction system by sound sources. 
There do not seem to be any strong direct projections from the superior colliculus 
to the components of the head direction system, but there are numerous indirect 
pathways. 
The most general prediction of the model is that the influence of vestibular input 
upon head direction cells is not susceptible to experience-dependent modification, 
whereas the influence of visual input is plastic, and is enhanced by the duration of 
experience, the richness of the visual cue array, and the distance of visual cues from 
the rat's region of travel. 
The "rotation" cells should be responsive to stimulation of the vestibular system. 
It is possible to activate the vestibular system by applying hot or cold water to 
the ears: if this is done in the dark, and head direction cells are simultaneously 
recorded, the model predicts that they will show periodic bursts of activity, with a 
frequency related to the intensity of the stimulus. 
For another prediction, suppose we train two groups of rats to forage in a cylinder 
containing a single landmark. For one group, the landmark is placed at the edge 
of the cylinder; for the other group, the same landmark is placed halfway between 
the center and the edge. The model predicts that in both cases the landmark will 
influence the head direction sytem, but the influence will be stronger and more 
tightly focused when the landmark is at the edge. 
In some respects the model is flexible, and may be extended without compromising 
its essence. For example, there is no intrinsic necessity that the vestibular system 
be the sole input to the rotation cells (other than the head direction cells). The 
performance of the system might be improved in some ways by sending the rotation 
cells input about optokinetic flow, or certain types of motor efference copy. But 
there is as yet no clear evidence for these things. 
On a more abstract level, the mechanism used by the model for vestibular control 
may be thought of as a special case of a general-purpose method for integration 
with neurons. As such, it has significant advantages over some previously proposed 
neural integrators, in particular, better stability properties. It might be worth 
considering whether the method is applicable in other situations where integrators 
are known to exist, for example the control of eye position. 
180 William Skaggs, James J. Knierim, Hemant S. Kudrimoti, Bruce L. McNaughton 
Supported by MH46823 and O.N.lq.. 
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PART III 
LEARNING THEORY AND DYNAMICS 
