FUNCTIONAL ORGANIZATION OF THE RAT HEAD-DIRECTION CIRCUIT

Transcription

1 Chapter 9 FUNCTIONAL ORGANIZATION OF THE RAT HEAD-DIRECTION CIRCUIT Hugh T. Blair 1 and Patricia E. Sharp 2 1 Department of Psychology, University of California at Los Angeles, Los Angeles, CA Department of Psychology, Bowling Green State University, Bowling Green, OH Rats, like humans and many other animals, possess a sense of direction that helps them to plan navigational trajectories and calculate bearings to familiar objects and locations (Barlow, 1964; Mittelstaedt and Mittelstaedt, 1980; 1982; Gallistel, 1990; McNaughton, Chen, and Markus, 1991). The rat brain contains a population of neurons called head-direction (HD) cells, which are believed to provide the neural basis for this sense of direction (Ranck, 1984; Taube, 1990a,b; but see Golob, Stackman, Wong, and Taube, 2001). In this chapter, we describe the functional organization of circuitry in the rat brain that allows HD cells to compute the animal s directional heading. HEAD-DIRECTION CELLS A single HD cell fires action potentials only when the rat s head is facing in a particular direction, referred to as the cell s preferred firing direction. Each individual HD cell is tuned to have its own preferred firing direction, so that together, the entire population of HD cells provides a distributed representation of any direction that the rat faces. Figure 1 illustrates the spike activity of a typical HD cell, which was recorded from the anterior thalamus of a freely behaving rat. This cell fired whenever the rat s head faced southeast (135º), and was silent when the rat faced in other directions. Throughout this chapter, we shall denote north as 0º, east as 90º, and so on, as in Figure 1. According to this convention, degree measurements always increase in the clockwise (CW) direction, and decrease in the counterclockwise (CCW) direction. The behavior of a HD cell can be characterized by its directional tuning function, which plots the firing rate of the cell as a function of the rat s 163

2 164 The Neural Basis of Navigation 0 o N 270 o W E 90 o S 180 o 135 o = Preferred Firing Direction Time Figure 1. Spike activity of a typical HD cell, recorded from the anterior thalamus of a freely behaving rat. Overhead view shows the path of the rat s movements during a time period of about 3.5 seconds. A raster plot (bottom) shows spikes fired by the HD cell during this period. Notice that the HD cell fires spikes whenever the rat faces in the cell s preferred firing direction of southeast, or 135 degrees (gray boxes), and the cell remains silent at other times. Preferred Firing Direction = 135 o Peak Firing Rate = 54 Hz Tuning Width= 80 o Baseline Firing Rate = 0 Hz Head Direction (Degrees) Figure 2. Directional tuning function of the HD cell that was shown in Figure 1. Note that there is a prominent peak in the tuning function, centered over the cell s preferred firing direction of southeast (that is, 135 degrees). Several descriptive parameters can be derived from the tuning function.

3 H.T. Blair & P.E. Sharp 165 directional heading (Figure 2). The directional tuning function shown here is typical, in that it is roughly Gaussian, or triangular in shape. Several descriptive parameters can be derived from the HD tuning function: the preferred firing direction is computed by taking the mean value of the tuning curve on the abscissa, the tuning width is twice the standard deviation of the tuning peak, the peak firing rate is the maximum value of the tuning peak on the ordinate, and the baseline firing rate is the cell s firing rate outside of the tuning peak. It is important to note that HD cells are not influenced by the position of the rat s head with respect to its body; they are only influenced by the direction of the head relative to the surrounding environment. Furthermore, HD cell activity is modulated only by the direction of the rat s head in the horizontal plane (yaw), and not by the angle of the head in other planes, such as pitch or roll (Stackman and Taube, 1997). Establishing the Directional Reference Frame How do HD cells achieve their remarkable direction-specific firing properties? One explanation could be that, like a compass, they are sensitive to the earth s magnetic field. However, experimental evidence does not support this explanation. Unlike a compass needle, which always points toward geomagnetic north, HD cells can change their directional preference with respect to the earth s magnetic field. Indeed, a given HD cell typically has different preferred firing directions in different environments. For example, a HD cell that prefers west in one environment (such as the rat s home cage) might prefer north in another environment (such as an experiment room). Under appropriate circumstances, HD cells can even change their directional preference within a single environment. Figure 3 shows an example of how HD cells can re-establish their directional preference in a single spatial environment. An HD cell was recorded while a rat foraged for food pellets in a cylindrical chamber. The wall of the chamber was painted with an alternating series of eight black and white stripes, so that each 90º segment of the wall was visually identical (see overhead view, Figure 3). The rat was placed into the cylinder beside a white stripe, and a HD cell was then recorded for five minutes while the animal foraged. The rat was then picked up, held by the experimenter for a moment, and immediately placed back into the cylinder beside a different white stripe, so that the animal s starting position was visually identical to the previous placement, but rotated by 90º. This procedure was repeated four consecutive times, placing the rat beside a different white stripe each time, always with the right side of its body adjacent to the wall. Figure 3 shows that the HD cell s

4 166 The Neural Basis of Navigation Firing Rate (Hz) Head Direction (degrees) 4 Figure 3. The preferred firing direction of a single HD cell depends upon the rat s starting position in the environment. This cell s firing direction shifted by 90 degrees during each of four consecutive sessions in the cylinder (tuning functions, right), in exact correspondence with the difference in the rat s starting position at the beginning of the session (overhead view, left). preferred firing direction was shifted by 90º for each placement, in exact correspondence with the shift in the rat s starting position. If HD cells were able to detect the earth s magnetic field, it is unlikely that they would shift their preferred firing direction along with the rat s starting position in this way. Presumably, the HD cell in Figure 3 shifts its preferred firing direction because the four starting positions are visually identical, and the rat is unaware that the starting position has changed at each placement. In the absence of other orienting cues, HD cells use the rat s starting position in the cylinder as a reference point to establish their directional preference. However, if other sensory orienting cues are available, the HD system can use them to help establish the directional reference frame. Sensory Orienting Cues Experiments have shown that the directional reference frame of the HD system is influenced by several kinds of sensory cues. These influences provide important clues about the functional organization of the HD circuitry. Visual Cues and Landmark Learning Perhaps the easiest way to obtain directional bearings in a familiar spatial environment is by looking around for recognizable landmarks. For example, a person who is familiar with New York City knows that the Empire State Building lies to the south of Central Park. Thus, an observer in Central Park can find south by using the Empire State building as a visual landmark.

5 H.T. Blair & P.E. Sharp 167 Rodents, like people, seem to use visual landmarks for navigational orientation (Collett, Cartwright, and Smith, 1986). Supporting this, the preferred firing direction of HD cells can be influenced in predictable ways by altering the positions of familiar visual landmarks in the surrounding environment (Taube et al., 1990b; Chen, Lin, Green, Barnes, and McNaughton, 1994; Mizumori and Williams, 1993; Taube and Burton, 1995; Goodridge and Taube, 1995; Knierim, Kudrimoti, and McNaughton, 1998). For example, if a visual landmark that normally lies to the north of an experimental chamber is moved so that it lies to the east, HD cells may collectively rotate their preferred firing directions clockwise by 90º, in correspondence with the 90º shift in the position of the landmark (see the accompanying chapter by Taube et al. in this volume). However, it appears that rats must learn about the spatial position of a visual landmark before it can be used for directional orienting, because unfamiliar landmarks exert less influence over the preferred firing directions of HD cells than familiar landmarks do (McNaughton, Markus, Wilson, and Knierim, 1993; Taube and Burton, 1995; Goodridge et al., 1998). Although landmark orientation exerts a strong influence on HD cells, visual landmarks cannot be the cells only source of directional information, because once HD cells have established their preferred firing direction in an environment, they can maintain this directional firing preference even when the rat is blindfolded, or placed in complete darkness (Mizumori and Williams, 1993; Goodridge et al., 1998; see also Chapter 8). How can HD cells continue to compute the rat s directional heading in the absence of visual cues? Vestibular Signals and Angular Path Integration Once the directional reference frame has been established in a given environment, HD cells may rely on angular path integration to keep track of the rat s directional heading as it moves through that environment (McNaughton et al., 1991). To perform angular path integration, HD cells are thought to combine information about the rat s current head direction with information about the angular velocity at which the head is turning, and this combined information is then used to predict the rat s future head direction. For example, if the rat is presently facing north, and turning its head clockwise at a velocity of 360º/s, then the circuit can calculate that the rat will face northeast after 1/8 s has elapsed, and update the HD signal accordingly. To perform angular path integration, the HD circuit must receive precise information about the angular velocity of the rat s head each time the animal turns to face a new direction. Evidence indicates that the HD system relies upon vestibular signals to provide this angular velocity information (Blair and Sharp, 1996; Stackman and Taube, 1997; Knierim et al., 1998). Figure 4 shows an experiment that demonstrates how vestibular signals can exert an

6 168 The Neural Basis of Navigation influence on the preferred firing direction of HD cells (Blair and Sharp, 1996). HD cells were recorded from the anterior thalamus while a rat foraged for food pellets, in the same cylindrical chamber that was shown previously in Figure 3. After 15 minutes of recording, the entire chamber was rotated by 90 (and the rat along with it), so that the chamber remained visually unchanged before and after the rotation (since each 90º segment of the wall was visually identical). The rotation of the chamber was not signaled to the rat by any visual cues or optic flow, because the wall and floor of the cylinder appeared to remain stationary as they rotated along with the rat, and the rat could not see external cues beyond the high walls of the cylinder. 90 FAST Firing Rate (% max) PRE POST 90 SLOW Firing Rate (% max) Head Direction (degrees) Figure 4. Vestibular cues influence the preferred firing direction of HD cells. When the recording chamber is rotated quickly (top), HD cells maintain a stable directional preference, but when the chamber is rotated slowly (bottom), the directional preference rotates along with the chamber. This indicates that HD cells are sensitive to vestibular signals. The rotation of the cylinder was performed at one of two speeds: either quickly at ~60 /s, or slowly at ~1 /s. Figure 5A shows that in response to fast rotation of the cylinder, the preferred firing direction of a typical HD cell does not rotate along with the cylinder. That is, the HD cell s directional preference remains locked to the fixed environment outside the cylinder, even though the rat cannot directly perceive this external environment. By contrast, Figure 5B shows that in response to slow rotation of the chamber, an HD cell rotates its preferred firing direction along with the cylinder, and therefore fails to maintain a stable preferred firing direction.

7 H.T. Blair & P.E. Sharp 169 The main difference between the fast and slow rotations of the cylinder is that the fast rotation can be sensed by the rat s vestibular system, whereas the slow rotation cannot. Hence, the results shown in Figure 5 suggest that vestibular signals are important for updating the HD signal. Further supporting this conclusion, it has been shown that lesions of the vestibular nuclei completely abolish the HD signal (Stackman and Taube, 1997). Hence, vestibular signals appear to be essential to the functioning of the HD system. Correction of Integration Errors The results shown in Figure 5B demonstrate an important limitation of the angular path integration process: if the angular velocity of the rat s head is not measured correctly (for example, when the head rotates at a speed which is below vestibular threshold), the HD signal will become inaccurate. Even small errors in estimating the rat s head-turning velocity could cause significant errors in the accuracy of the HD signal, which would accumulate over time to make the directional signal unstable. How can such errors be prevented? It has been proposed that visual landmarks may help to solve this problem, by periodically resetting the HD signal to erase any integration errors that may have accumulated over time (Skaggs et al., 1995; Knierim et al., 1998). This proposal is supported by evidence showing that when rats are deprived of visual information, either by blindfolding them or placing them in complete darkness, the preferred direction of HD cells becomes less stable and begins to drift (Mizumori and Williams, 1993; Goodridge et al., 1998). This is exactly what would be expected if the angular path integration system relies on a visual landmark orienting system to prevent the accumulation of integration errors over time. As discussed below, this cooperation between angular path integration and landmark orienting systems may involve interactions among distinct brain circuits that perform different functions to compute the HD signal. FUNCTIONAL ANATOMY OF THE HD CIRCUIT HD cells have been found in several regions of the rat brain, including the postsubiculum (PoS; Ranck, 1984; Taube et al., 1990a), anterodorsal thalamus (AD; Blair and Sharp, 1995; Taube, 1995), laterodorsal thalamus (LD; Mizumori and Williams, 1993), striatum (Wiener, 1993), lateral mammillary nucleus (LMN; Blair et al., 1998; Stackman and Taube, 1998), retrosplenial cortex (RsC; Chen et al., 1994; Cho and Sharp, 2000), and dorsal tegmental nucleus (DTN; Sharp and Cho, 2001). Some of these regions are likely to

8 170 The Neural Basis of Navigation play an active role in generating the HD signal, while other regions may passively receive the signal from areas where it is generated. Figure 5 shows connections among several brain structures that are thought to participate in computing the HD signal. As discussed in the previous section, HD cells are believed to compute the rat s directional heading using two interacting processes: landmark orientation and angular path integration. Here, we shall argue that cortical structures containing HD cells, such as PoS and RsC, function mainly to support landmark orientation, whereas subcortical structures, such as LMN and DTN, are mostly involved in angular path integration. LANDMARK ORIENTING CORTEX Visual Cells Place Cells VCX HIP PoS/ RsC AD DTN LMN SUBCORTEX AV Cells NPH ANGULAR PATH INTEGRATION Excitation Inhibition Figure 5. Functional anatomy of the HD system. Shaded boxes denote regions that are known to contain HD cells. Abbreviations: AD, anterodorsal thalamus; DTN, dorsal tegmental nucleus; HIP, hippocampus; LMN, lateral mammillary nucleus; NPH, nucleus propositus hypoglossi; PoS, postsubiculum; RsC, retrosplenial cortex; VCX, visual cortex. Cortical HD Cells and Landmark Orientation HD cells are found abundantly within certain regions of the limbic cortex, including PoS (Ranck, 1984; Taube et al., 1990a) and RsC (Chen et al., 1994). These regions receive significant input from early visual cortex (Vogt and Miller, 1983), which could mediate the influence of visual landmarks upon

9 H.T. Blair & P.E. Sharp 171 the HD signal. Supporting this idea, RsC contains neurons that are strongly responsive to visual orienting cues (Chen, Lin, Barnes, and McNaughton, 1994). Furthermore, lesions of PoS interfere with the ability of visual landmarks to influence the preferred firing direction of HD cells recorded in AD (Goodridge and Taube, 1997). These findings suggest that cortical regions containing HD cells, such as PoS and RsC, may be involved in updating the HD signal based on visual landmarks. However, it is important to note that directional orientation using visual landmarks requires more than just the ability to visually recognize landmarks. It also requires knowledge of the spatial layout of the surrounding environment. To see why this is so, consider the example of the New Yorker who uses the Empire State Building to identify which direction is south from Central Park. What happens when this observer travels to some other location in New York City, such as Washington Square, or Penn Station? In that case, it would be necessary to know that the Empire State Building lies to the north of Washington Square, and to the east of Penn Station. That is, the same landmark indicates different directions when it is observed from different locations. Therefore, when using a visual landmark to obtain directional bearings, it is not enough to simply identify the landmark; it is also necessary to know the observer s current location within the spatial environment, and to know the directional bearing of the landmark relative to that location. For this reason, a brain system that performs landmark orientation must process more than just visual information. It must also process information about the layout of the surrounding spatial environment, and about the observer s location within that environment. Role of the Hippocampus in the HD System PoS and RsC, in addition to their visual inputs, also receive input from the hippocampus via the subiculum (van Groen and Wyss, 1990a,b). The hippocampus and subiculum contain a population of neurons called place cells that encode the rat s location in space (O'Keefe and Dostrovsky, 1971; Ranck, 1973; Sharp and Green, 1994). Place cells are thought to store a cognitive map of the spatial environment, and are probably critical for selflocalization (O Keefe and Nadel, 1978). PoS and RsC receive input from both visual cortex and the hippocampus. Hence, PoS and RsC seem anatomically well-situated to combine information about visual landmarks with information about the rat s current spatial location, and use this combined information to compute the rat s directional heading. Thus, we propose that the hippocampal system may interact with PoS and RsC to perform landmark orientation to compute the HD signal. In contradiction to this idea, Golob and Taube (1999) have proposed that the hippocampus participates primarily in angular path integration, rather than landmark orientation. These authors argue that this proposal is supported by

10 172 The Neural Basis of Navigation their finding that, in rats with hippocampal lesions (unlike normal rats), HD cells exhibit drifting of their preferred firing direction when the animal is first introduced into a novel environment. The authors claim that this is what would be expected if angular path integration were impaired. However, as explained above, the landmark orientation system is thought to periodically reset the angular path integration circuit, to prevent drifting of the HD signal that would otherwise result from the accumulation of integration errors over time (Skaggs et al., 1995). Thus, the drifting of the HD signal that was observed by Golob and Taube (1999) in hippocampal-lesioned rats is exactly what would be expected following damage to the landmark orientation system, because a primary function of the landmark system should be to prevent the HD signal from drifting. Golob and Taube (1999) found that after continued exposure to an environment, HD cells in hippocampal-lesioned rats eventually stopped drifting, and achieved stable directional firing. Once this stable directional firing was achieved, HD cells seemed to be influenced by visual landmarks, as in normal rats. Golob and Taube (1999) interpreted this result as evidence that landmark orientation is intact in rats with hippocampal lesions, since it is difficult to understand how landmarks could influence HD cells if the landmark orientation system were damaged. However, it is equally difficult to see how the preferred firing direction of HD cells could stop drifting and become stable if the angular path integration system were damaged. Hence, the effects of hippocampal lesions upon HD cells are rather confusing and difficult to interpret. Contrary to Golob and Taube s (1999) proposal, we do not think these results provide compelling evidence that the hippocampus plays a role in angular path integration. Instead, we shall argue that angular path integration occurs mainly in subcortical structures that contain HD cells. Subcortical HD Cells and Angular Path Integration HD cells are found within two subcortical regions LMN and DTN that are closely associated with the vestibular system. DTN receives direct inputs from the vestibular sensory nuclei (Lui, Chang, and Wickern, 1984), especially the nucleus prepositus hypoglossi (NPH). As shown in Figure 5, the primary ascending input to LMN comes from the DTN, and LMN sends reciprocal projections back to DTN (Liu et al., 1984; Allen and Hopkins, 1989; Gonzalo-Ruiz, Alonso, Sanz, and Llinas, 1992). The ultrastructural anatomy of the projection from DTN to LMN suggests that it is inhibitory (Hayakawa and Zyo, 1992), whereas the projection from LMN to DTN is mainly excitatory (Allen and Hopkins, 1990). For reasons to be explained below, these connections suggest that LMN and DTN are anatomically well

11 H.T. Blair & P.E. Sharp 173 positioned to participate in angular path integration (Sharp, Blair, and Cho, 2001). LMN Several lines of evidence suggest that LMN may be involved in angular path integration. First, when the rat turns its head to face a new direction, the HD signal is updated first in LMN, before it is updated in other brain areas such as AD or PoS (Blair et al., 1998; Stackman and Taube, 1998). The fact that LMN HD cells are among the first to be updated during head turns suggests that LMN may be a site where angular path integration of head-turning movement occurs. Second, bilateral lesions of LMN completely abolish the HD signal in AD (Blair et al., 1998), demonstrating that input from LMN is essential for HD cell activity in AD. Although this finding is consistent with the notion that LMN is necessary for angular path integration, the result could also be explained if LMN merely conveys the HD signal to AD from other structures where path integration takes place. Third, the tuning functions of HD cells in LMN are modulated by the angular velocity of the rat s head (Figure 6), a property that has been predicted for HD cells that participate in angular path integration (McNaughton et al., 1991; Skaggs et al., 1995; Zhang, 1996b). Firing Rate (Hz) A LEFT HEMI Head Direction (degrees from preferred) B RIGHT HEMI Figure 6. CW (solid lines) and CCW (dashed lines) tuning functions for two HD cells recorded in LMN. A: HD cell recorded from the left hemisphere of LMN has broader tuning width during CW turns, due to leftward shift of the left edge of the peak. B: HD cell in the right LMN shows the opposite pattern, with broader tuning during CCW turns, due to rightward shift of the right edge of the peak. Figure 6A shows tuning functions for a typical HD cell recorded from the left hemisphere of LMN. Two separate tuning peaks are shown for this HD cell: one that includes only spikes that occurred when the rat s head was turning CW (solid lines), and another that includes only spikes that occurred when the head was turning CCW (dashed lines). By comparing the shape of the CW and CCW tuning peaks, it is possible to see how the tuning properties of the cell differ when the head is turning in opposite directions. The left

12 174 The Neural Basis of Navigation LMN cell in Figure 6A has a broader tuning function during CW head turns than during CCW head turns, because the left edge of the CW tuning curve is shifted to the left relative to the CCW tuning curve. This is typical for HD cells recorded in the left hemisphere of LMN (Blair et al., 1998). Conversely, HD cells recorded in the right LMN have broader tuning during CCW than CW turns, due to shifting of the right edge of the curve (Figure 6B). Such hemispheric asymmetries have not been observed for HD cells recorded in AD, RsC, or PoS. DTN HD cells in DTN are also modulated by the angular velocity of the rat s head, but in a seemingly different way than LMN HD cells (Sharp, Tinkelman and Cho, 2001). Figure 7 shows tuning functions for two HD cells recorded in DTN: one from the left and the other from the right hemisphere. As in Figure 6, two separate tuning functions (CW and CCW) are shown for each DTN HD cell. DTN HD cells exhibit very broad tuning widths in comparison with HD cells in other brain regions. Notice that the left DTN cell in Figure 7A has a higher firing rate when the rat s head is turning CW than CCW, whereas the reverse is true for the right DTN cell in Figure 7B. But unlike the LMN HD cells in Figure 6, the tuning widths of DTN HD cells in Figure 7 are similar during head turns in either direction. Firing Rate (Hz) A B Head Direction (degrees from preferred) Figure 7. CW (solid lines) and CCW (dashed lines) tuning functions for two HD cells recorded in DTN. A: HD cell recorded from the left hemisphere of DTN has higher firing rate during CW turns. B: HD in the right DTN has higher firing rate during CCW turns. In addition to HD cells, DTN also contains a large number of angular velocity (AV) cells, which fire at a rate that is proportional to the angular velocity of the rat s head (Sharp, Tinkelman and Cho, 2001). AV cells fire at a constant rate when the rat s head is not turning, but increase their rate when the head turns in the cell s preferred turning direction (either CW or CCW), and decrease their rate when the head turns in the opposite, or antipreferred,

13 H.T. Blair & P.E. Sharp 175 turning direction. AV cells are found abundantly in the medial vestibular nuclei, including NPH, which projects to DTN. Hence, vestibular inputs to DTN are likely to provide the source of the AV signal. In summary, it appears that the rat s head-turning behavior exerts different modulatory effects upon HD cells in LMN and DTN. Head turns modulate the firing rate of DTN HD cells, with minimal effect on their tuning widths. Conversely, head turns seem to modulate the tuning widths of LMN HD cells, with minimal effect on their peak firing rates. This modulation of subcortical HD cells by the rat s head turning behavior may provide important clues about the computational organization of the HD circuit. A RECURRENT NETWORK MODEL The firing properties of HD cells and AV cells in LMN and DTN strongly suggest that these structures are somehow involved in angular path integration. In this section, we present a computational hypothesis to propose how these neurons might be connected together to form a neural circuit that performs angular path integration. Population Coding and Angular Path Integration Each individual HD cell is tuned to have its own preferred firing direction, so that together, the entire population of HD cells provides a distributed representation of any direction that the rat faces. This kind of distributed representation scheme is common to many brain systems, and is sometimes referred to as a neural population vector (Georgopoulos, Kalaska, Caminiti, and Massey, 1984). To understand how HD cells implement a distributed representation of the rat s directional heading, it is helpful to visualize the HD population vector as a layer of HD cells (Figure 8A), arranged so that adjacent cells have adjacent preferred firing directions (note that the layer has circular topography, so that the rightmost neuron in the layer is adjacent to the leftmost neuron). This arrangement is for illustration purposes only; it is not known whether HD cells are topographically organized within any region of the rat brain. The pattern of activity in the layer forms a peak that looks very much like the tuning function of an individual HD cell, because the HD cell that represents the rat s current head direction is firing at a high rate, while cells representing nearby directions are less active, and cells representing directions that are far from the current direction do not fire at all. The activity peak can be centered over any HD cell within the layer, to represent whatever direction the rat s

14 176 The Neural Basis of Navigation head is currently facing. But the activity of HD cells should always form a single peak within the layer, and never assume other patterns that cannot be interpreted as a coherent representation of a single directional heading. When the rat turns its head, the activity of HD cells must be updated to reflect changes in the rat s head direction. For example, if the rat is facing north, and then turns CW by 90º to face east, the peak of HD cell activity must move to the right by 90º, so that HD cells representing east will be maximally active when the head turn is completed (Figure 8B). During the head turn, the peak of activity must shift through the layer of HD cells, and the dynamics of this shifting must be controlled precisely, so that the rate of shifting is exactly proportional to the velocity of head turning. Consequently, the activity peak always remains accurately centered over those HD cells that represent rat s current directional heading. A Recurrent Attractor Network Several theoretical models have proposed that the HD population vector is implemented in the brain by a neural architecture called a recurrent attractor network (Redish et al., 1996; Skaggs et al., 1995; Zhang, 1996a). A recurrent attractor network is a population of neurons that are interconnected in such a way that, over time, the network s activity will reliably converge to a stable pattern, called an attractor state (Hopfield, 1982). HD cell tuning properties indicate that the pattern of activity in the HD cell population vector constantly retains a peak-shaped profile, as in Figure 8. A likely explanation for this observation is that the HD cell activity peak is an attractor state of a recurrent network (Redish et al., 1996; Skaggs et al., 1995; Zhang, 1996a). If so, then this peak-shaped attractor state must be multi-stable, meaning that the peak is equally stable when it is centered over any HD cell within the layer. This allows the activity peak to represent whatever direction the rat s head is facing, without any bias towards representing certain directions over others. Theoretical studies have shown that a multi-stable, peak-shaped attractor state can emerge in a recurrent network with center-surround connectivity, in which neurons excite their nearby neighbors, and inhibit their more distant neighbors (Ben-Yishai, Lev Bar-Or, and Sompolinsky, 1995; Redish et al., 1996; Zhang, 1996a). Figure 8A illustrates how center-surround connectivity might be implemented in the HD network. For clarity, only the connections from a single HD cell are shown, but all cells in the network are assumed to be similarly connected to their neighbors. Excitatory connections are assumed to be direct connections among HD cells, whereas inhibitory connections are made through interneurons. For reasons to be explained below, we suggest that these inhibitory interneurons may reside in DTN. By modulating these interneurons with input from AV cells, the recurrent network can perform angular path integration.

15 H.T. Blair & P.E. Sharp 177 A B North North East LMN HD Cell CW AV Cell Excitation DTN Inhibitory Cell CCW AV Cell Inhibition Figure 8. A recurrent attractor model of the HD circuit. A: When the rat faces north, a stable peak of activity (gray bars) forms over the HD cell representing north, due to a center/surround pattern of excitation and inhibiton among HD cells. B: When the rat turns clockwise to face east, leftward inhibition among HD cells is enhanced by increased input from AV cells, causing the peak of activity to shift rightward until it is centered over the HD cell representing east. Angular Path Integration in a Recurrent Network As shown in Figure 8B, the peak of activity must shift through the layer of HD cells during head turns, to track changes in the rat s directional heading. This shifting behavior can occur in a recurrent attractor network if the pattern of lateral connections between HD cells is modified in an appropriate way (Skaggs et al., 1995; Redish et al., 1996; Zhang, 1996a). For example, during a CW head turn, the activity peak should shift rightward through the layer of HD cells, as in Figure 8B. Such a rightward shift will occur if HD cells excite their rightward neighbors more than leftward neighbors, or inhibit their leftward neighbors more than their rightward neighbors, or both. However, adjusting the strengths of lateral connections among HD cells is risky, because as discussed above, the stability of the peak-shaped attractor state depends upon the center-surround pattern of connections between HD cells. Changing this connection pattern can easily destroy the attractor state, causing the activity peak to become unstable and dissolve into a meaningless pattern. To preserve the shape of the activity peak as it shifts through the layer, the lateral connections among HD cells must be modified in a very precise way. Zhang (1996a) has shown that, in order for the activity peak to retain its shape when it shifts through the layer, the connection strengths between HD cells must be modified according to a derivative rule. Briefly, this rule states that the change in connection strength between any two HD cells must be proportional to the spatial derivative of the connection pattern within the entire layer. Details of this proof are beyond the scope of the present chapter,

16 178 The Neural Basis of Navigation but Zhang (1996b) has shown that the derivative rule can be implemented in a straightforward manner by a relatively simple recurrent network architecture. Anatomy of the Angular Path Integration Circuit In this section, we combine theoretical predictions of recurrent network models with physiological evidence reviewed in the previous section to suggest a specific anatomical organization of the HD attractor network within subcortical regions of the rat brain. LMN sends excitatory projections to DTN, and DTN sends inhibitory projections to LMN (see Figure 5). Hence, DTN is well positioned to provide lateral inhibition among HD cells in LMN. This suggests that a recurrent network for computing the HD signal might be implemented by connections between LMN and DTN. If so, then the primary layer of HD cells might reside in LMN, and lateral inhibition among these LMN HD cells could be routed through inhibitory cells in DTN. Furthermore, since DTN contains AV cells and receives vestibular information from NPH, DTN could be a site where angular velocity signals modulate the strength of lateral inhibition among HD cells, to implement angular path integration during head turns. When the rat s head is not turning, LMN HD cells should provide equal excitation and inhibition to their neighbors on either side, so that the peak of activity remains stationary within the HD cell layer (Figure 8A). However, when the rat turns its head in the clockwise direction, CW AV cells increase their firing rate, and CCW AV cells decrease their firing rate. These AV cells could modulate DTN cells that mediate lateral inhibition among LMN HD cells, so that during CW head turns, LMN HD cells inhibit their rightward neighbors less than their leftward neighbors (Figure 8B). This would cause the peak of activity to shift rightward (CW) through the layer of HD cells, in correspondence with the CW movement of the rat s head, thereby implementing a process of angular path integration. A similar, but reversed, process would occur during CCW turns, causing the activity peak to shift to the left. Physiological Evidence Our anatomical hypothesis might help to explain the firing properties of cells recorded in DTN and LMN. Recall that DTN contains both AV cells and HD cells (Sharp, Tinkelman and Cho, 2001), and the firing rate of many DTN HD cells is modulated by the angular velocity of the rat s head (see Figure 7). These are precisely the properties that would be expected of interneurons that provide angular-velocity modulated lateral connections among HD cells in a recurrent attractor-integrator network (Skaggs et al., 1995; Redish et al., 1996;

17 H.T. Blair & P.E. Sharp 179 Zhang, 1996b; Sharp, Tinkelman and Cho, 2001). However, the tuning width, but not the peak firing rate, of LMN HD cells is modulated by the angular velocity of the rat s head (see Figure 6). In theory, this modulation of LMN tuning widths should not occur in a recurrent network that implements Zhang s (1996a) derivative rule, because strict adherence to this rule would prevent the HD tuning peak from changing its shape as the peak shifts through the layer. The derivative rule predicts that the HD tuning peak should have the same tuning width at all times, regardless of how the rat s head is turning. This is true for HD cells in some brain structures, such as PoS and AD (Blair and Sharp, 1995; Taube and Muller, 1998), but it is not true for LMN HD cells. Are these findings consistent with a role for LMN in angular path integration? Zhang (1996b) has shown that, in order to obtain stable tuning widths in a recurrent attractor-integrator model of the HD circuit, lateral connections among HD cells must be modulated multiplicatively by the AV signal. If modulation of lateral connections by the AV signal is not perfectly multiplicative, then the tuning curve can become slightly skewed during head turns, causing them to change their tuning width in much the same way that LMN HD cells do during head turns. This suggests that the modulation of LMN HD cell tuning widths during head turns might be explained if DTN cells are modulated by angular head velocity in a manner that is not perfectly multiplicative. Further empirical and theoretical studies are needed to examine whether LMN cell firing properties can be fully explained by an attractor-integrator network model. SUMMARY AND CONCLUSIONS As a rat navigates through space, HD cells provide an ongoing signal of the animal s momentary directional heading, and they are thought to provide the neural basis for the rat s sense of direction. Considerable progress has been made in identifying how specific brain structures contribute to generating this directional signal. Available evidence suggests that HD cells rely on two interacting processes to compute the rat s directional heading: landmark orientation and angular path integration (McNaughton et al., 1991). In this chapter, we have argued that cortical regions containing HD cells, such as PoS and RsC, are primarily responsible for landmark orientation. By contrast, subcortical regions, such as DTN and LMN, may be mostly involved in angular path integration. One of the most exciting conclusions to emerge from HD cell research is that the rat HD circuit seems to provide a striking biological example of a recurrent multi-stable attractor network. Networks of this kind seem to be of fundamental importance in neurobiology, since they can perform many basic

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