Part of Advances in Neural Information Processing Systems 7 (NIPS 1994)
William Skaggs, James Knierim, Hemant Kudrimoti, Bruce McNaughton
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 ofreal head direction cells. In addition it makes a number of predictions that ought to be testable by reasonably straightforward experiments.
1 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 Ranck (1984) of a population of "head direction" cells in the dorsal presubiculum (also known as the "postsubiculum") of the rat. A head direction cell
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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 maximal firing were consistently parallel, within the experimental resolution. This is difficult to explain with a simple sensory-based mechanism; it implies something more sophisticated.1
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
1 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
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if an animal 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 directional cue, a white card covering 90 degrees of the wall. During training, half of the rats were disoriented before being placed in the cylin(cid:173) der, in order to disrupt the relation between their internal sense of direction and the location of the cue card; the other half of the rats were not disoriented. Pre(cid:173) sumably, the rats that were not disoriented during training experienced the same initial relationship between their internal direction sense and 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 all rats the influence of the cue card upon the head direction system weakened gradually over the course of multiple recording sessions, and 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).