Remembering the past and imagining the future

Neuronal representations

Data from electrophysiological recordings in behaving animals provides perhaps the most direct evidence of the nature of the representations at work in spatial cognition. We start with the apparently allocentric representations associated with the mammalian medial temporal lobe. View-invariant hippocampal “place cells” fire selectively for an animal’s location in space (e.g. O’Keefe, 1976), but show little dependence on the animal’s orientation during random, open field foraging. We refer to this representation as allocentric, representing location relative to the environment, even though the location represented is that of the animal itself. In a linear track place cells tend to be direction specific, however, when the track environment is enriched with place-unique cues the place cells are much less directionally selective (Battaglia, Sutherland & McNaughton, 2004). O’Keefe & Nadel (1978) argue that this collection of place-selective neurons forms the basis of a cognitive map and provides the rat’s internal allocentric representation of location within the environment. Evidence for the existence of place cells has also been found in the hippocampus in non-human primates (Matsumura et al., 1999; Ono, Nakamura, Nishijo & Eifuku, 1993) and in humans (Ekstrom et al., 2003). The representation of the complementary spatial information - orientation independent of location - has also been found; “head direction cells” (see e.g. Taube, 1998) are found along an anatomical circuit largely homologous to Papez’s circuit (Papez, 1937) leading from the mammillary bodies to the presubiculum via the anterior thalamus. A representation related to place cells has also been found in the parahippocampal and hippocampal region of both non-human (Rolls & O’Mara, 1995) and human primates (Ekstrom et al., 2003): “view-cells”, which fire when an animal is looking at a given location from a range of vantage points.

The location of a place cell’s response depends on large extended local landmarks rather than on discrete objects, while the orientation of the overall place and head direction representations depend on landmarks at or beyond the reachable environment (see Barry et al., 2006; Burgess & O’Keefe, 1996; Cressant, Muller & Poucet, 1997). Thus, the location and shape of the firing fields of hippocampal place cells can be explained if it is assumed that their firing is driven by the activity of a population of boundary vector cells (BVCs) (Hartley, Burgess, Lever, Cacucci & O’Keefe, 2000; O’Keefe & Burgess, 1996). These neurons, hypothesized to exist within parahippocampal cortex, show maximal firing when an animal is at a given distance and allocentric direction from an environmental landmark or boundary. The direct or indirect reciprocal connectivity of the hippocampal formation and parahippocampal regions with each other and with the perirhinal cortex (for a review, see Burgess et al., 1999), an area that is known to be important for object recognition (Davachi & Goldman-Rakic, 2001; Murray & Bussey, 1999; Norman & Eacott, 2004), probably allows for the positions and identities of landmarks visible at a particular location to be bound to that location.

In parallel to the above allocentric representations, egocentric representations, which are ubiquitous throughout the sensory, motor and parietal cortices, are clearly directly involved in all aspects of spatial cognition. Sensory representations will be egocentric, reflecting the reference frame of the receptor concerned (e.g. retinotopic in the case of visual input), while motor output will reflect the reference frame appropriate for the part of the body to be moved (see e.g. Georgopoulos, 1988). Coordinating these representations, the posterior parietal cortices are heavily involved in sensorimotor mappings. Posterior parietal cortex is known to contain neurons that respond to stimuli in multiple reference frames, especially areas near or within the intraparietal sulcus. In particular, Galletti, Bataglini & Fattori (1995) have found neurons in the anterior bank of the parieto-occipital sulcus (V6A) in ventromedial parietal cortex, that represent the positions of visual stimuli in a craniotopic reference frame. Also, area 7a contains neurons that exhibit egocentrically tuned responses which are modulated by variables such as eye position and body orientation (Andersen, Essick & Siegel, 1985; Snyder, Grieve, Brotchie & Andersen, 1998). Such coding can allow transformation of locations between reference frames (Pouget & Sejnowski, 1997; Zipser & Andersen, 1988). Furthermore, head direction selective neurons that exhibit responses tuned to various different reference frames have been found in the posterior cotices of the rat (Chen, Lin, Barnes & McNaughton, 1994). Such properties might allow for the establishment of the angular relationship between different representational frames.

A number of single unit recording studies have shown that areas of primate posterior parietal cortex, again in and around the intraparietal sulcus, contain neurons that exhibit firing patterns modulated by various combinations of head position, velocity, acceleration and visual stimuli (Andersen, Shenoy, Snyder, Bradley & Crowell, 1999; Bremmer, Klam, Duhamel, Hamed & Graf, 2002; Klam & Graf, 2003). The nature of these interactions appears to be complex, but Bremmer et al. suggest that this idiothetic modulation of parietal neuron firing might be related to object tracking during self-motion. This argument is indirectly supported by Duhamel, Colby & Goldberg, (1992) who have shown that eye movements that bring the location of a previously flashed stimulus into the receptive field of a parietal neuron elicit a response from that neuron even though the stimulus is no longer present (see also Colby, 1999). Area 7a is the part of parietal cortex most strongly connected with the medial temporal lobe, including efferent projections into the parahippocampus, presubiculum, and CA1 (Ding, Van Hoesen & Rockland, 2000; Rockland & Van Hoesen, 1999; Suzuki & Amaral, 1994) and afferent connections from entorhinal cortex and CA1 (Clower, West, Lynch & Strick, 2001). In addition, single unit recordings from monkey dorsolateral prefrontal and posterior parietal cortic es suggest that spatial working memory is, indeed, egocentric in nature (Chafee & Goldman-Rakic, 1998; Funahashi, Bruce & Goldman-Rakic, 1989).

Finally, some hints of the temporal dynamics of neural processing during navigation come from the observation that the theta rhythm (i.e. 4-12Hz) of the EEG invariably accompanies voluntary displacement motion of the rat (O’Keefe and Nadel, 1978). In addition, the phase of firing of place cells correlates strongly with the rat’s location within the firing field (O’Keefe and Recce, 1993), and independently of firing rate or running speed (Huxter, Burgess, O’Keefe, 2003). Recent results indicate a possible role for theta in human navigation (Caplan et al., 2003; Kahana, Sekuler, Caplan, Kirschen & Madsen, 1999), and several experiments indicate a role for theta phase (e.g., Pavlides, Greenstein, Grudman & Winsom, 1988) in modulating hippocampal synaptic plasticity, and theta power (Sederberg et al., 2003) or theta coherence between hippocampus and nearby neocortical areas (Fell et al., 2003) in modulating encoding into memory .

Lesions, neuropsychology and functional neuroimaging

The medial temporal lobes, and hippocampus in particular, have long been know to be crucial for long-term memory (Eichenbaum & Cohen, 1988; Scoville and Milner, 1957; Squire, 1986), together with other elements of Papez’s circuit (Aggelton and Brown, 1999). Within the spatial domain, neuropsychological studies have left little doubt that the medial temporal lobe, particularly in the right hemisphere, is critical for remembering the locations of several objects within a visual scene over a significant delay (Crane and Milner, 2005; Piggott & Milner, 1993; Smith & Milner, 1989). Within a broader memory deficit, hippocampal damage seems to specifically impair performance in tasks likely to require allocentric representations of location or representations that can be flexibly accessed from novel points of view, rather than being directly solved by use of egocentric representations. For example, where locations must be remembered from a different point of view to presentation, performance is impaired relative to location memory from the same view even over short timescales (Abrahams, Pickering, Polkey & Morris, 1997; Holdstock et al., 2000; King et al., 2002; Hartley et al., in press). More generally, accurate spatial navigation to an unmarked goal location is impaired by hippocampal damage in rats (e.g., Jarrard, 1993; Morris, Garrard, Rawlins & O’Keefe, 1982) and humans (Bohbot et al., 1998; Maguire, Burke, Phillips & Staunton, 1996; Spiers et al., 2001). Human neuroimaging studies also show involvement of the hippocampus in accurate navigation (Hartley, Maguire, Spiers & Burgess 2003; Iaria et al, 2003; Maguire et al., 1998). Additionally, neuroimaging of the perceptual processing of spatial scenes, including plain walled environments, implicates the parahippocampal cortex (Epstein & Kanwisher, 1998), a region associated with landmark recognition (Aguirre & D’Esposito, 1999) and navigation (Bohbot et al., 1998). See Burgess, Maguire & O’Keefe (2002) for a review.

Human neuropsychology has long recognized the parietal lobes as playing a major role in spatial cognition. Parietal damage leads to deficits in sensorimotor coordination such as optic ataxia, deficits in spatial manipulation such as mental rotation and deficits in spatial working memory (see e.g. Burgess, Jeffery & O’Keefe, 1999; Haarmeier, Thier, Repnow & Petersen, 1997; Karnath, Dick & Konczak, 1997). Visual processing in the temporal and parietal lobes has been generally characterized respectively in terms of the dorsal and ventral ‘what and where’ (Ungerleider and Mishkin, 1982) or ‘what and how’ (Goodale & Milner, 1992) processing streams. The parietal region in the dorsal stream is concerned with representing the locations of stimuli in the various egocentric reference frames appropriate to sensory perception and motor action, and translation between these frames to enable sensori-motor coordination. In contrast, the occipital and temporal visual regions in the ventral stream are concerned with visual perceptual processes related to object recognition, see Neuronal representations above.

Unilateral damage to parietal cortex (most often on the right) and surrounding areas commonly results in the syndrome of hemispatial neglect: a reduced awareness of stimuli and sensations on the contralateral side of space (‘perceptual neglect’). Of particular interest here is the phenomenon of ‘representational neglect’ - a lack of awareness of the contralateral side of internal representations derived from memory. In the classic demonstration (Bisiach and Luzzatti, 1978), patients were asked to imagine the Piazza del Duomo in Milan (with which they were very familiar) and to describe the scene from two opposite points of view. Buildings to the left of the given point of view (e.g. facing the Cathedral) were neglected, but those same buildings were described when given the opposite point of view (e.g. facing away from the Cathedral), indicating intact long-term memory of the entire Piazza, in spite of neglect of the left of each imagined scene. Perceptual and representational neglect depend, at least in part, on different neural systems, and can be dissociated, even within the same patient (Bechin, Basso & Della Sala, 2000). Interestingly representational, but not perceptual, neglect is associated with impaired navigation to an unmarked location (Guariglia, Piccardi, Iaria, Nico & Pizzamiglio, 2005). Consistent with these findings of parietal involvement in imagery, neuroimaging experiments have shown heightened activity within the precuneus (i.e. medial parietal cortex) during mental imagery (e.g., Fletcher, Shallice, Frith, Frackowiak & Dolan, 1996) and visuospatial working memory (e.g., Wallentin, Roepstorff, Glover, Burgess, 2006). Transcranial magnetic stimulation and fMRI studies also indicate that areas surrounding the right intraparietal sulcus, including areas 7a and 40, are essential in the generation and manipulation of egocentric mental imagery (Formisano et al., 2002; Knauff, Kassubek, Mulack & Greenlee, 2000; Sack et al., 2002).

Behavioral and single unit studies indicate that memory for locations in general, and the place cell representation of location in particular, is automatically updated by self-motion, a process more generally known as ‘path integration’ or ‘spatial updating’ (see below). This process may reflect an interaction between the parietal and hippocampal systems, as the parietal cortex appears to be centrally involved in this process (Alyan & McNaughton, 1999; Commins, Gemmel, Anderson, Gigg & O’Mara, 1999; Save, Guazzelli & Poucet, 2001; Save & Moghaddam, 1996). For example, Save, Paz-Villagran, Alexinsky & Poucet (2005) have shown that lesions to the associative parietal cortex of rats result in altered place cell firing, suggesting that egocentric sensory information must travel through parietal cortex in order to elicit appropriate place cell firing. This is consistent with a number of experiments that demonstrate that mental exploration/navigation depends on posterior parietal and extra-hippocampal medial temporal regions in primates, and on homologous regions in the rodent brain (Ghaem et al., 1997; Pinto-Hamuy, Montero & Torrealba, 2004). The interaction between parietal and medial temporal areas likely involves retrosplenial cortex, lesions of which selectively disrupt path integration (Cooper, Manka, Mizumori, 2001), and the parieto-occipital sulcus, which has been associated with topographical disorientation (Ino et al., 2002) and cells coding for locations in space (Galletti et al., 1995).

Prefrontal regions, as well as parietal ones, are implicated in spatial working memory, with parietal areas predominantly associated with storage and prefrontal areas with the application of control processes such as active maintenance or planning (Shallice, 1988; Levy and Goldman-Rakic 2000; Oliveri et al., 2001) using the posterior spatial representations. Thus, fMRI studies have shown activation in both of these areas when subjects were required to remember the locations of various objects for short periods of time (Galati et al., 2000; Sala, Rämä & Courtney, 2003). Manipulations of working memory may also involve making or planning eye movements in order to direct attention to spatial locations in imagery. In support of this notion, voluntary eye movements disrupt spatial working memory (Postle et al, 2006), while left hemispatial neglect patients show abnormal eye movements, which deviate about 30 degrees rightward during visual search (Behrmann et al, 1997) as well as while at rest (Fruhmann-Berger and Karnath, 2006). Moreover, adapting prisms that shift the neglected visual field toward the good side of space, which would compensate for a rightward bias in gaze direction, ameliorate both perceptual and representational neglect (Rode et al, 2001). Studies involving mental navigation and route planning consistently find elevated activation in frontal regions, especially on the left side (Ghaem et al., 1997; Ino et al., 2002; Maguire et al., 1998). For example, Maguire et al. (1998) found additional activation in left prefrontal cortex associated with the planning of detours when subjects were navigating in a familiar virtual town in which the most obvious route had suddenly been blocked. This suggests that left prefrontal areas contribute to route planning, perhaps guiding egocentric mental imagery within the temporoparietal systems activated by the basic navigation condition.

Cognitive psychology

Given the electrophysiological and lesion evidence for parallel egocentric and allocentric representations of location, we next consider converging evidence from cognitive psychology in which one or the other or both may contribute to behavior. Simons & Wang (1998; Wang & Simons, 1999) performed an elegant series of experiments in which subjects were required to remember an array of objects presented on a circular table. During the delay period preceding the memory test, the table would either remain stationary or rotate through a fixed angle. At the same time, the subject would either remain stationary or walk through the same angle around the table. Thus, the test stimuli could be aligned with the studied view, with a rotated view consistent with the subject’s motion, with both, or with neither. Subjects’ performance on a memory task (detecting which object had moved) provided evidence for the use of both: 1) a visual-snapshot representation of the presented array; and 2) an egocentric representation that is updated to accommodate self-motion; by showing an advantage whenever the test array was aligned with either representation. The latter “spatial updating” ability (Reiser, 1989) can be thought of as a generalization of path integration, allowing an organism to keep track of several locations, including its origin of motion, during real or imagined navigation in the absence of visual cues. The results suggest that both of types of representation exist in the brain. Interestingly, evidence suggests that allocentric representations of object locations (i.e., relative to visual landmarks external to the array) are also employed in this type of experiment, as shown by a subsequent study incorporating a rotatable landmark (Burgess, Spiers & Paleologou, 2004). Parallel influences of egocentric and allocentric representations are also indicated by human search patterns within deformable virtual reality environments (Hartley, Trinkler & Burgess, 2004). In these experiments, the locus of search can be predicted by a model based on the firing of hippocampal place cells, indicating allocentric processing of location. However, subjects also tended to adopt the same orientation at retrieval as at encoding, indicating egocentric processing of orientation.

Further evidence for the use of both egocentric and allocentric representations of space can be found in reaction time data from a number of experiments involving the recognition/recall of previously presented object configurations from novel viewpoints. Diwadkar & McNamara (1997) had subjects learn the locations of objects on a desktop from a number of viewpoints before taking part in a recognition test. When presented with a novel view of the same or a different object configuration, subjects’ reaction time was found to vary linearly with the angular distance between the observed view and the closest trained view. Related results were found when blindfolded subjects had to point to where a given object would be from a specific imagined viewpoint: accuracy and/or reaction time reflected the distance and angle between the studied viewpoint and the imagined viewpoint (Reiser 1989; Easton and Sholl, 1995; Shelton and McNamara 2001). These results are consistent with spatial updating of an egocentric representation. However, the additional use of allocentric representations in these tasks is indicated by improved performance for viewpoints aligned with the walls of the room or the sequence of learning (Mou & McNamara, 2002), or with external landmarks (McNamara, Rump & Werner, 2003), and with the absence of a relationship to distance or angle for objects configured into a regularly structured array (Reiser, 1989; Easton and Sholl, 1995). In possibly related findings, Wang & Spelke (2000) suggest that the high variance of the error in pointing to different objects after blindfolded disorientation indicates independent egocentric representations for the location of each object. In the same experiment, the lower variance in errors when pointing to features of the testing room indicated a single coherent (allocentric) representation for the layout of the room. Similarly, judgments of relative direction between objects from an imagined location at a third object do not increase in variance with disorientation, indicating use of a more coherent representation in this task than that used for egocentric pointing (Waller and Hodgson, 2006). See Burgess (2006) for further discussion.

Theoretical analyses

It has been proposed (e.g. Milner, Paulignan, Dijkerman, Michel & Jeannerod, 1999) that the relative contribution of egocentric and allocentric representations to spatial memory depends on the timescale of the task concerned. Short-term retention of perceptual information for the purpose of immediate action will be best served by egocentric representations appropriate to the corresponding sensory and motor systems. By contrast, long-term memory for locations will be best served by allocentric representations (i.e. relative to stable landmarks) because the location and configuration of the body at retrieval typically will be unrelated to that at encoding (see Burgess, Becker, King & O’Keefe, 2001 for further discussion). This observation is consistent with the evidence for the role of parietal and prefrontal areas in supporting egocentric representations and short-term memory, on the one hand, and the role of medial temporal lobe areas in supporting allocentric representations and long-term memory, reviewed above.

For intermediate timescales (e.g. tens of seconds), it may be possible to relate the configuration of the body at retrieval to that at encoding via the egocentric process of “path integration” or “spatial updating” referred to above. Pierrot-Deseilligny, Müri, Rivaud-Pechous, Gaymard & Ploner (2002) review evidence suggesting that spatial memory may have at least three important timescales. For the first approximately 20 seconds, they claim that a fronto-parietal spatial working memory system is the dominant mechanism, followed for approximately five minutes by a medium-term, parahippocampally dependent memory system, and finally by a hippocampally dependent long-term memory system which operates only after delays of several minutes. Spatial scale might also be a factor in determining which representations are used. For example, in mammals path integration becomes unreliable over long or convoluted paths (see e.g. Etienne, Maurer & Seguinot, 1996), while egocentric parietal and premotor representations may be preferentially recruited for representations of locations in “peri-personal” space that can be directly acted upon (e.g. Duhamel, Colby & Goldberg, 1998; Goodale & Milner, 1992; Graziano & Gross, 1993; Ladavas, di Pellegrino, Farne & Zeloni, 1998).

Along the above lines, Mou, McNamara, Valiquette and Rump (2004) propose a transient egocentric representation of object locations for immediate action and an allocentric representation of the environment, including the subject’s own location, for actions supported by information from long-term memory. On the basis of the experiments probing memory for object location as a function of differences between the studied, imagined and actual views, they argue that two types of spatial updating occur: spatial updating of egocentric representations of object locations, and spatial updating of the subject’s own location in the environmental representation. A related proposal suggests transient egocentric representations of single objects in parallel with a more coherent enduring representation (Waller and Hodgson, 2006). For a discussion of the neural mechanisms supporting the integration of self-motion and sensory information, see (Guazzelli, Bota & Arbib, 2001; Redish, 1999).

In summary, evidence from psychology and neuroscience indicates that spatial cognition involves multiple parallel frames of reference, with short-term/small-scale tasks more likely to recruit egocentric representations and long-term/large-scale tasks more likely to recruit additional allocentric representations. However, this proposed division of labour involving different reference frames is neither absolute nor uncontroversial. Thus, Wang & Brockmole (2003) have also argued that even long-term spatial memory is purely egocentric. They found the current view to influence the ability of students to point to an occluded but very familiar landmark on the campus. Conversely, even short-term memory can be shown to depend on the hippocampus when the viewpoint is changed between study and test (King et al., 2002; King et al., 2004; Hartley et al., in press), and on allocentric representations when landmarks are parametrically manipulated (Burgess, Spiers & Paleologou, 2004), see Burgess (2006) for further discussion.

The parietal window hypothesis

We hypothesize that a population of neurons maintains a head-centered, egocentric map of space that can be driven either by bottom-up sensory input or by top-down inputs from long-term memory. This map represents the locations of all landmarks/objects that are visible from an animal’s current location in space, or from a location that the animal recalls from previous experience. This neuronal population, assumed to exist within the posterior parietal cortex, and very likely within the precuneus, will henceforth be referred to as the parietal window. We claim that the contents of the parietal window are generated based upon some combination of information from the senses (dorsal visual stream, for example) and from allocentric long-term spatial memory, with the exact combination depending on the demands of the current task. Manipulation of spatial information for the purposes of planning or navigation, including spatial updating, occurs within the parietal window.

The network model also includes circuitry that can manipulate the contents of the parietal window so as to allow for spatial updating or mental exploration. In the case of spatial updating, this circuitry is activated by idiothetic information (proprioceptive cues signalling the observer’s change in direction and location), whereas in the case of mental exploration, it is activated by some mentally generated equivalent (e.g. imagined rotation and translation during path planning). The former ability allows the model to maintain an internal representation of its surroundings even with degraded or absent sensory input, while the latter provides a means of recalling the locations of occluded landmarks and generating navigational strategies for reaching them.

Allocentric representations in the medial temporal lobe

In contrast to the parietal window’s egocentric frame of reference, we postulate that an allocentric frame of reference is employed in the medial temporal lobe. The model’s egocentric reference frame has its origin bound to the observer’s location, with its y-axis fixed along the observer’s heading direction. The model’s “allocentric reference frame” has its origin bound to the observer’s location (in this sense, like place cell firing, it is not fully allocentric), but its orientation is fixed relative to the external environment. Therefore, both reference frames are similar in that they remain fixed with respect to the observer so long as the observer undergoes translational motion only. However, when the observer’s head rotates within the environment, while the egocentric frame rotates with it, the allocentric frame remains stationary with respect to the environment. An example of an object in the allocentric frame and its corresponding location in the egocentric frame is shown in figure 1.

Consider the situation depicted in figure 2 where an observer surrounded by six walls is located at the position marked “X”, with a heading direction indicated by the arrow. If the walls of this “two-room” environment are discretized uniformly into a set of “landmark segments” (to simplify later calculations), then the egocentric frame positions of the segments viewable from “X” can be inferred readily. These positions are depicted by open circles in the top panel of figure 3. Representation of this egocentric information by the parietal window neurons is accomplished by first forming a one-to-one correspondence between the set of neurons and a polar grid covering the egocentric reference frame. This grid is depicted by the closed circles in the top panel of figure 3. Each neuron in the grid is tuned to respond most strongly to an object or landmark at a particular direction and distance relative to the organism’s head, which is at the origin of the grid. The neuron’s response falls off exponentially for objects located further away from the neuron’s preferred distance and direction (see the appendix for details). When multiple segments are present within a neuron’s receptive field, they contribute additively to its firing rate, up to a maximum firing rate of 1. The parietal window representation of the information depicted in the top panel of figure 3 is shown in the bottom panel of the same figure, where the firing rate of each neuron is plotted at the location of its corresponding grid point.

We assume that the observer in figure 2 aligns its allocentric frame such that the y-axis is perpendicular to the wall labeled “1” and the x-axis is parallel to the same wall. The locations of the landmark segments in this frame, which will not depend on the observer’s heading direction, are depicted in the top panel of figure 4. By forming a one-to-one correspondence between a set of neurons and a polar grid centered at the origin of the allocentric reference frame, it becomes possible to represent the configuration of landmark segments by the firing rates of this neural population. In analogy with the egocentric parietal window neurons, each allocentric neuron in the grid is tuned to respond most strongly to an object or landmark at a particular distance from the organism’s head, which is fixed to the origin of the grid, and allocentric direction (relative to the fixed environment). Again, the neuron’s response falls off exponentially for objects located further away from the neuron’s preferred distance and direction. Note that these allocentrically tuned neurons are essentially the same as the BVCs described in the introduction, and will be referred to as such from this point on. The BVC representation of the information depicted in the top panel of figure 4 is shown in the bottom panel of the same figure, where the firing rate of each neuron is plotted at the location of its corresponding grid point. Although we assume these BVCs exist within parahippocampal cortex, we note that cells with BVC-like responses have been found in the subiculum (Barry et al., 2006; Sharp, 1999), an alternative location to the parahippocampal cortex, but less consistent with neuroimaging results in humans showing parahippocampal processing of spatial scenes including plain walled environments (Epstein & Kanwisher, 1998).

To form long-term memories for specific spatial locations, spatial input from BVCs and visual input from the perirhinal layer are combined into a place cell representation. Although in reality the hippocampal formation consists of multiple spatially selective regions (dentate gyrus, CA3, CA1), for simplicity, our model hippocampus contains a single layer of recurrently connected place cells. Their place preferences are arranged uniformly over a Cartesian grid that covers the relevant allocentric space for a given environment (see figure 2). In particular, a one-to-one correspondence is formed between each of the model place cells and the set of grid points so that a given place cell fires maximally when the model is located at that cell’s corresponding grid point. These model hippocampal neurons are reciprocally connected to the layer of BVCs and to a layer of perirhinal identity neurons, thus allowing environmental geometry and landmark identities to be bound simultaneously to a given “place”. In addition, the layer of BVCs is reciprocally connected to the layer of perirhinal neurons, thereby allowing the association of landmark identities with allocentric locations (see figure 6 for a schematic of the full model). The full reciprocal connectivity between the three medial temporal lobe components of the model allows for the recall of a landmark’s identity when attention is directed toward the parietal window representation of that landmark’s location. This process of recall is described in the next section.

Within our gross simplification of hippocampal circuitry, the model’s single layer of place cells is most consistent with area CA3, an area that is heavily recurrently connected, and that exhibits place selective firing. In our model, this recurrent connectivity allows for recall/pattern completion, as it is often argued to do in CA3 (Brun et al., 2002; Nakazawa et al., 2002). Another gross simplification in our model is the strictly spatial function of the hippocampus. Although the hippocampus is known to be important in spatial memory, its more general contribution to episodic memory is well established (for a review see Burgess, Maguire & O’Keefe 2002).

Transformation circuit

The assumption in our model of egocentric access to allocentrically stored spatial information has an important implication: there must be circuitry that transforms between these representations. In order to be able to recall the locations and identities of environmental boundaries relative to one’s own location and orientation, long-term allocentric internal representations of space must be transformed into egocentric representations. Conversely, in order for sensory input to cue such recall, or for it to enter long-term allocentric storage in the first place, the inverse transformation from egocentric to allocentric representation must be performed. That is, a visual stimulus at a retinocentrically encoded location must be transformed into an allocentrically encoded location in order to match against or store within spatial long-term memory. We assume that sensory information is first transformed into the head-centered egocentric parietal window reference frame and then to the allocentric BVC representation. The transformation from the parietal window representation to the BVC representation, and its inverse, can be accomplished very simply if absolute heading direction is known. Consider, for example, that you are facing West (90 degrees in allocentric angular coordinates, where North is zero degrees) and there is an object to your left (90 degrees in egocentric angular coordinates where straight ahead is zero degrees); the object’s allocentric direction can be calculated simply by adding the heading direction to the object’s egocentric direction to obtain 180 degrees; similarly if the object is known to be located to the South (an allocentric angle of 180 degrees) then its egocentric direction can be calculated by subtracting the heading direction from the object’s allocentric direction. Thus, in our model the egocentric-allocentric transformations are mediated by input from head direction cells which provide the necessary modulation of firing rates by head direction (Snyder et al., 1998), and the same neural circuitry can then perform the transformation in either direction. The computation is a bit more complicated than a simple subtraction or addition of angles because angular directions are encoded across populations of narrowly direction-tuned neurons; nonetheless, it can be accomplished in a single layer of neurons whose activities are non-linearly modulated by head direction (c.f. Pouget and Sejnowski, 1997). See figure 5 for a schematic of the full transformation circuit.

When an animal first enters a new environment, we assume that salient perceptual features reliably orient the head direction system. We model the head direction system as a set of neurons configured in a ring via lateral connections to behave as a one-dimensional continuous attractor, as in previous models (e.g. Skaggs, Knierim, Kudrimoti & McNaughton, 1995; Stringer, Trappenberg, Rolls & de Araujo, 2002; Zhang, 1996). The continuous attractor property implies that the network will stabilize on a single bump of activity corresponding to a single head direction, and this bump can move continuously through 360 degrees to reflect self-motion or perceptual inputs. Moreover, the reliability of the input mapping implies that if the animal returns to the same environment in the future, the head direction system will be oriented in exactly the same fashion, and will exhibit the same firing pattern as it did on the first exposure to the environment.

The egocentric-to-allocentric transformation is accomplished by a circuit that combines head direction information with egocentric spatial input from the parietal window. The transformation circuit, assumed to be in retrosplenial cortex / intra-parietal sulcus, is comprised of a set of N identical neural subpopulations, each tuned to a specific head direction. Each sub-population encodes a rotated egocentric map consistent with the direction of its preferred heading. Thus, connections between the parietal window and any one of the transformation subpopulations are weighted such that a rotated version of the egocentric spatial information contained in the parietal window is projected onto that transformation sub-layer. In our model there are twenty such sub-layers corresponding to evenly spaced allocentric directions. Each transformation sub-layer then projects an identical copy of its activation pattern onto the layer of BVCs. By setting connections from the layer of head direction cells to the transformation neurons such that only the sub-layer corresponding to the current head direction is active, the transformation from egocentric to allocentric coordinates is accomplished. See figures 5 and 6. In this way, when the animal’s head rotates within the environment, head direction cell activity and parietal window activity vary in time, but so long as the animal undergoes no translation, activity projected to BVC neurons remains constant. The gating function of the head direction cells is accomplished via a combination of direct excitation from the head direction cells to the appropriate transformation sub-layer, and indirect uniform inhibition of all transformation layers by a population of inhibitory interneurons driven by head direction cell activity. This circuitry allows a localized bump of activity in the head direction layer to select the set of transformation units corresponding to that head direction.

The egocentric-allocentric transformation results in a single viewpoint-independent representation of each location in an environment. The allocentric representation consists of a distributed pattern of activation across the boundary vector cell layer. To encode this pattern as a distinct place memory, and to permit subsequent cued recall, this pattern can be learned by an auto-associative memory system. A retrieval cue, such as incomplete egocentric sensory or mentally generated spatial information, can then feed forward through the transformation circuit and reactivate the correct allocentric representation of the model’s real or imagined surroundings. Conversely, the place memory can generate a viewpoint-specific mental image if we assume that the connections in the transformation circuit operate with equal weights in both directions. The recalled allocentric representation can thereby be converted back into egocentric mental imagery of the environment via the same neural circuitry.

Model dynamics

Neurons in our model are rate-coded (i.e. their activations represent average neural firing rates rather than individual spikes) and exhibit a continuous dynamics governed by “leaky-integrator” equations. The complete mathematical details of the model, along with these dynamical equations, can be found in the appendix. Here we present a more intuitive description of the model’s overall behaviour. For now, the issue of biologically realistic learning is ignored and it is assumed that the model has already learned about the spatial environments it encounters. The actual ad hoc training procedure used to set the model weights for this work will also be described briefly in a later section, with full details presented in the appendix. In a later section, we also discuss general principles that might underlie the learning of egocentric-allocentric transformations in biological systems.

At the highest level of dynamics, our model operates in alternating bottom-up and top-down stages, each lasting for 15 arbitrary “time units”. This periodic alternation in dynamics is based on modeling work by Hasselmo, Bodelón & Wyble (2002) who argue that the hippocampal theta rhythm regulates the communication of this structure with interconnected brain regions. In particular they argue that during troughs in the rhythm, the hippocampus primarily receives input from surrounding structures, but that during peaks, it primarily transmits information to these structures. We implement this alternating dynamics in our model both because of the evidence supporting its existence and because it allows the model to account for more experimental data than it otherwise could. In particular, without these distinct phases the model would have to engage in both bottom-up and top-down processing at the same time. We have found that a functional version of such a model exhibits states that strongly resist change in response to external inputs.

During the top-down phase, activity from the hippocampal layer feeds back to perirhinal cortex and also to the parietal window via the BVC and transformation layers. In addition, during this phase, the parietal window receives input from the senses, which we assume can be down-regulated if the model is performing mental exploration or recall of a familiar environment without actually changing its vantage point. See figures 5 and 6. During the bottom-up phase, the activity of the window is “frozen” to the last pattern present during the top-down phase. This activity pattern, which is the model’s current representation of the geometry of egocentric space, is hypothetically maintained by a fronto-parietal short-term memory system (which we do not model here), consistent with evidence presented earlier. The frozen information from the parietal window feeds forward during the bottom-up phase to the hippocampal layer along with information from perirhinal cortex, thus influencing the current hippocampal attractor state. In principle, rigid freezing of the parietal window representation during the bottom-up phase is not necessary, but such an approach eliminates the need for additional neural circuitry in the model.

An animal would need to recall the details of an environment stored in long term memory for two main reasons. First, there could be transient environmental conditions that impede sensory input and thus leave the animal with little direct access to spatial information. Second, the animal might need to remember what would be around it at an imagined location for the purposes of planning. For the former case, we assume that the model has enough sensory information to orient the head direction system. Although we only deal with visual information here, the model could be extended easily to include other cues such as vestibular input for this purpose as well. Once the head direction system is oriented, the available but incomplete sensory input to the parietal window and perirhinal cortex can flow to the hippocampus in a bottom-up phase and activate an attractor state for the complete corresponding allocentric representation. During the next top-down phase, this attractor state reconstructs the environmental geometric information in the parietal window. Once the model has reconstructed the geometry of the environment, it must be able to identify the boundaries/landmarks which surround it. This is assumed to occur via directed attention to a spatial location. We simulate this in our model as extra activation (calculated from equation A17, see Appendix) being directed to the area of interest in the parietal window. The boundary within the focus of attention in the parietal window will generate a corresponding focus of activation on its allocentric location within the BVC layer. The associative pathways within the medial temporal lobe can then retrieve the object’s identity in the perirhinal cortex.

As a concrete example of spatial attention, if the model is instructed (perhaps by some prefrontal brain region controlling planned eye movements, not modeled here) to identify a boundary to its egocentric left, then extra activation is directed to the parietal window neurons that represent space to the egocentric left. This activation then flows through the transformation circuit, to the BVC layer, and finally to the perirhinal layer. The extra activation from the parietal window increases the firing rate of all perirhinal neurons corresponding to boundary indentities that the model could encounter to its left when it has the current heading direction. The correct boundary identity, consistent with the subject’s current location, can then be disambiguated by allowing the top-down connections in the model to operate at a low level (5% of the normal top-down value) even during a bottom-up phase. In this way, the place cell activity can provide the requisite disambiguation. For consistency, we also allow bottom-up connections to operate at the same reduced level during top-down phases.

In cases where an animal needs to recall the details of its surroundings from a particular imagined point of view, we assume that the suggestion of (in the case of humans) or memory of a highly salient environmental feature located at some point in the animal’s egocentric space might be enough to orient the head direction system. The correct perirhinal units could also be activated by this process, and activity corresponding to the location of the feature could be sent to the parietal window. During the next bottom-up phase, the processes of pattern completion and directed attention would then follow as described above.

Spatial updating and mental exploration

The recall processes described in the previous section are useful only if an animal requires stationary “snapshots” of an environment. However, a moving animal, often faced with partially or fully occluded sensory information, requires an accurate, real-time representation of its surroundings. Similarly, if an animal wishes to plan a route through a familiar environment, the ability to perform mental exploration of the surrounding space would be useful.

A key part of our overall theory is that parietally generated egocentric mental imagery can be manipulated via real or mentally generated idiothetic information in order to accomplish spatial updating or mental exploration in familiar environments. A detailed neural mechanism for accomplishing such tasks in the case of pure short-term or working memory has been described elsewhere (Byrne & Becker, 2004). Here we are concerned primarily with the updating process applied to medial temporal lobe dependent long-term memory. For this case we assume that rotational and forward-translational egomotion signals act upon the egocentric parietal window representation of space via different mechanisms. In the case of rotation, the egomotion signal causes head direction cell activity to advance sequentially through the head direction map, thus rotating the image that is projected into the parietal window from the BVCs. This velocity-modulated updating of head direction is similar to the model described by Stringer, Trappenberg, Rolls & de Araujo (2002). The potential for such one dimensional continuous attractor networks to account for multiple aspects of the head direction cell assembly has been investigated in detail by Conklin & Eliasmith (2005), Goodridge & Touretzky (2000), Hahnloser (2003) and Redish, Elga & Touretzky (1996) among others. However, a detailed summary of such work is beyond the scope of this paper. For the case of forward translation, the egomotion signal gates the top-down connections from the parietal transformation layer to the parietal window such that the “normal” top-down weights connecting these regions are down-regulated, while a second, alternate set of top-down weights are up-regulated. With no forward velocity signal, the normal top-down connections perform reconstruction of a head-centered egocentric representation of the model’s current spatial surroundings in the parietal window using information originating from place cell activity. Once up-regulated by the velocity signal, the alternate set of top-down connections performs an almost identical function, except that the representation of space reconstructed in the parietal window is of the model’s current surroundings, but shifted backwards slightly in the model’s egocentric space. When the next bottom-up phase begins, the shifted spatial information, represented as parietal window activity, flows through the transformation and BVC layers to activate place cells that correspond to the location slightly ahead of the model’s current location. This process repeats itself during the next top-down/bottom-up cycle until the velocity signal dissipates, resulting in a continuous relocation of the model’s internal representation of its location in space. Further details of this updating procedure can be found in the appendix.

Learning in the model

The purpose of our model is to reproduce experimental data and generate novel predictions of spatial behavior in adult animals, rather than to account for learning in a biologically realistic manner. Hence, we use a simplistic Hebbian learning procedure that associates together pre-specified activation patterns in each layer of the model, in order to train all of the model connection strengths except for those involved with spatial updating/mental exploration. The latter connection strengths are calculated as described in the appendix. Briefly, learning for the remainder of the weights involves positioning the model at numerous random locations and heading directions within an environment while, at each of these locations, sequentially directing attention to each landmark segment viewable from the current location. For each attending event at each location, appropriate activation patterns are imposed upon the model layers and connection strengths between neurons are updated via a simple correlational rule. Once training is complete, weights are normalized. A detailed description of the training procedures is provided in the appendix.

It should be noted that the transformation circuitry in our model is only trained once, but the medial temporal component is retrained on each unique environment in the simulations reported here. Training on multiple environments with the relatively small-scale models used here can result in a degradation of information when it travels through the transformation circuitry, and activation of an incorrect hippocampal attractor state. This problem could be addressed by including a greater number of model neurons in the transformation layer. Additionally, a larger-scale version of the medial temporal lobe portion of the model should, in principle, be capable of storing multiple environments in distinct subsets of place cells (a possible role for the dentate gyrus and CA3 recurrent connections, McNaughton and Morris 1987; Samsonovich and McNaughton, 1997). There is no reason to expect that the simultaneous storage of attractor states corresponding to multiple environments would affect any of the results we obtain from the model in this paper.

Methods

In order to simulate representational neglect (see Introduction and Bisiach and Luzzatti, 1978), we first tested the ability of the intact model to recall environmental geometry and landmark identity. This was accomplished by first training the medial temporal component of the model on the simplified Cathedral Square depicted in the upper left panel of figure 7. During training, the allocentric reference frame was taken to be aligned with this depiction of the environment so that its y-axis would be perpendicular to the inward facing walls of buildings 1 and 3, but parallel to the inward facing walls of buildings 2 and 4. In reality, it is likely that the orientation of the allocentric reference frame within the environment would be set by the head direction system alignment when the animal first experiences the environment. Once training was complete, the model was cued to imagine itself facing the cathedral in the trained environment by injecting appropriate activation into the head direction, parietal window and perirhinal identity layers. Cueing activation for the parietal window was calculated by applying equation A5 (in the appendix) to a discretized linear boundary, representing the front of the cathedral, located directly in front of the model in the egocentric reference frame. Similarly, cueing activation for the perirhinal neurons was calculated from equation A3, with the cathedral (building identity 1) being the attended landmark. Finally, it was assumed that the cathedral is sufficiently salient that cueing its location relative to the subject is enough to orient the head direction system. Thus, activation for the head direction layer was calculated from equation A6, with the heading-direction, φ, set to zero, indicating perfect alignment between egocentric and allocentric reference frames. The cueing activations were applied to the model for two full bottom-up/top-down cycles, after which they were down-regulated, and the retrieved attractor states in the head direction system and hippocampal place cell layer maintained the model’s parietal window representation of the imagined geometry of the environment.

In order to “ask” the model to identify the boundaries that would be visible from the current viewpoint (see figure 7), we simulated the focus of attention along four different directions: left, right, forward and backward. In each direction the corresponding activation calculated from equation A17 was injected directly into the parietal window. During a subsequent bottom-up phase this activation flowed forward through the transformation and parahippocampal layers to activate the correct perirhinal identity neuron. For example, in the case of rightward attention, the correct response would be perirhinal activity corresponding to building 2, see Appendix for details.

Next, the model was cued to imagine itself in the square facing away from the cathedral. This was accomplished by focusing attention on a boundary directly behind the model in the parietal window, while simultaneously activating the perirhinal neurons representing the visual features of the cathedral, and the allocentric head direction 180 degrees away from the current egocentric frame

Once it was confirmed that the model could identify surrounding landmarks from different viewpoints, hemispatial neglect was simulated by performing a random knock-out of 50% of the parietal window neurons representing the left side of egocentric space, and then repeating exactly the same procedures as just described for testing the intact model.

Results and discussion

The ability of the intact model to recall environmental geometry and landmark identity, when cued that it was facing the cathedral, is shown in figure 7. The top four panels show the activity in the various network layers averaged over one full cycle after the removal of the cueing activity. Although the spatial resolution of the model’s representation of the environment is coarse, the geometry represented in the parietal window is roughly correct. The bottom panel of figure 7 shows the activity of perirhinal neurons at the end of a bottom-up phase. Perirhinal activity is plotted with open circles for leftward attention, asterisks for forward attention, crosses for rightward attention, and triangles for backward attention, indicating that the model can identify all landmarks correctly. Performance of the intact model when cued that it was facing away from the cathedral is shown in figure 8. The resultant activities of the various network layers averaged over a full cycle after down-regulation of cueing inputs are shown in the top four panels. Once again the model formed the correct egocentric representation of spatial information in the parietal window and directed attention resulted in the correct identification of the surrounding boundaries. For example, when attention was directed to the egocentric right, the identity of building 4 was activated in the perirhinal layer. Building 4 would be to the right of the model if it were facing away from the cathedral.

Results of the simulations with the lesioned model, simulating hemispatial neglect, are shown in figures 9 and 10, corresponding to figures 7 and 8 respectively. From these results it is clear that the model could identify landmarks to its right, but not to its left, regardless of its imagined heading direction. These simulation results are consistent with a central tenet of our model, namely, that allocentric representations of space are formed in long-term memory and are transformed into egocentric views as needed, in the service of memory recall and imagery. Moreover, our model provides a mechanistic explanation for patterns of deficits observed in perceptual and representational neglect patients, a previously perplexing phenomenon in neuropsychology. Both the long-term memory representation and the transformation mechanism are intact, whereas the egocentric representation projected from long-term memory, and/or the transformation mechanism itself, is faulty. This could arise in patients either from a lesion to the pathway from the transformation circuit to the parietal window (resulting in pure representational neglect) or a lesion to the parietal window itself (resulting in both perceptual and representational neglect). Pure perceptual neglect in the absence of representational neglect could arise from a lesion along the sensory or motor pathways projecting into and out of posterior parietal cortex. Testing of these predictions based on currently available data is difficult because of the extensive lesions suffered by most patients suffering from unilateral neglect. For the case of perceptual neglect, recent studies indicate that a disconnect between parietal cortex and prefrontal areas (Doricchi & Tomaiuolo, 2003; Thiebaut de Schotten et al., 2005), or between parietal cortex and medial temporal regions (Bird et al., 2006) is critical to a realization of the phenomenon. However, we are unaware of any data that so clearly indicate which regions of the brain must be damaged in order to induce pure representational neglect, the focus of the current set of simulations.

Methods

In order to simulate spatial updating or mental navigation, the medial temporal component of the model was trained on the “two-room” environment shown in the upper left panel of figure 11, with the allocentric reference frame taken to be aligned with the vertical axis of the environment as depicted. The training procedure and architecture for this component of the model were identical to those used in the previous set of simulations, except that in addition, within the parietal window, the velocity-gated translational weights given by equation A9, and the rotational head direction weights, trained as described in the appendix, now come into play.

After training was complete, the model was first cued to a location near to and directly facing wall 1. Such cueing would be equivalent to asking the model to imagine itself facing wall 1 in the two-room environment. This was accomplished as in the previous simulations by injecting appropriate activations into perirhinal, head direction, and parietal window neurons for two full cycles. Attention was then focused along four different directions, leftward, rightward, forward and backward, to demonstrate that the model could identify the surrounding landmarks from memory.

Next, we simulated spatial updating after several steps of imagined egomotion. The same situation could arise during real navigation if an animal spontaneously loses sensory information about its real surroundings (e.g. navigating in the dark). In either case, attractor states in the head direction system and in the hippocampal formation of our model are able to maintain an internal representation of its real/imagined surroundings. Mental exploration or spatial updating based on this self-sustaining internal representation was simulated in the model by a series of eight egomotion steps. This egomotion, if assumed to be generated by real idiothetic information, would correspond to spatial updating, or if generated by a mental equivalent, would correspond to mental exploration. In the first step, to simulate making a 180 degree turn, a counter-clockwise rotational velocity signal lasting for 150 time units gated the rotational head direction weights until the model’s egocentric representation of space rotated by a full 180 degrees. In the second step, to simulate forward egomotion, a translational velocity signal lasting 135 time units gated the transformation to parietal window translational weights causing the model’s egocentric representation of the locations of boundaries to translate backwards. Similarly, a further six egomotion steps were performed to complete the simulation.

As a control, we compared spatial updating in imagined versus sensory-driven navigation. Although the model’s ability to perform spatial updating/mental exploration on internally maintained representations of space is of primary interest, it must also function in a consistent way during real navigation through a familiar environment with intact sensory information. Thus, we simulated the same situation as above but in the presence of accurate sensory cues during the eight steps of egomotion. In this case, sensory information corresponding to visible boundaries calculated from equation A5 was simultaneously injected into the parietal window during egomotion.

Results and discussion

The ability of the model to retrieve the appropriate context in the two-room environment, when asked to imagine itself facing wall 1, is shown in figure 11. Network activity averaged over a full cycle after down-regulation of the cueing inputs can be seen in the top four panels of figure 11. The results of the four directed attention events are shown in the bottom panel of figure 11, indicating that the model could also identify the surrounding landmarks.

The performance of the model after several steps of imagined egomotion is shown in figures 12 and 13. Figure 12 shows activation in the various network layers averaged over one full cycle following the first two egomotion steps. The remaining six steps brought the model’s internal representation of space to that shown in figure 13, where it was nearby and facing wall 2. Three directed attention events show that the model could correctly identify surrounding boundaries from this new viewpoint (see bottom panel of figure 13).

In the case of sensory-driven navigation, the analogous results to figures 11-13 are shown in figures 14-16 respectively. Results of the sensory-driven simulations after 8 steps of egomotion are nearly indistinguishable from the corresponding results with imagined egomotion.

The fact that an egocentric translational velocity signal causes spatial updating/mental navigation to occur at a constant velocity will be discussed in more detail with respect to Simulation 4 and in the General Discussion. Here we simply note that it is consistent with the reasonably accurate (if scaled) correspondence between mental navigation times and actual navigation times (see e.g. Ghaem et al., 1997; Kosslyn, 1980).

Methods

A realistic simulation of the effects of lesions to the head direction cells in our model is not possible because of the use of a single inhibitory interneuron that causes each head direction cell to inhibit all transformation sub-layers equally. A more realistic circuit would employ a population of inhibitory interneurons that were connected randomly within the constraint that they would achieve the same gating function (in combination with excitatory head direction connections to the transformation layer). We did not employ such a population because, given the unnatural training methods used, it would have behaved like a single unit anyway. With a more natural configuration, partial lesions to the head direction system would result in reduced excitation to the selected transformation sub-layer and decreased inhibition to random regions of the overall transformation layer. To simulate the equivalent effect in our model, for each lesioned head direction, the excitatory head direction input to the corresponding transformation sub-layer was reduced, while the inhibitory input to a random selection of other transformation sub-layers was decreased. See Appendix for details.

Since the lesioning procedure does not involve the medial temporal structures, the latter region was trained once on the “box” environment shown in figure 17. The model was then localized at numerous positions within the environment by injecting appropriate egocentric sensory information from all of the environmental boundaries into the parietal window neurons. At each location the sensory input was maintained for one top-down/bottom-up cycle and the activity of a selected place cell was recorded and averaged over the bottom-up cycle. This procedure was performed for two simulated head directions, one of which corresponded to perfect alignment between egocentric and allocentric representations, and another that corresponded to perfect anti-alignment between the two representations.

Results and discussion

The average firing rates for a model place cell recorded when the lesioned model was localized at numerous locations within a rectangular sub-region of the “box” environment are depicted in figures 17 and 18. In figure 17 these rates correspond to the aligned heading direction, while in figure 18 the results correspond to the anti-aligned simulation condition. Clearly, the firing field of the model neuron varied with simulated head direction, and moreover, its peak-firing location for either head direction did not correspond to the location where the cell would have attained its maximal firing rate in the non-lesioned model (marked with an ‘X’ in both figures). In addition, for the aligned condition, the cell exhibited a firing maximum in one location, but with an additional area of elevated firing near ‘X’. These data are qualitatively similar to the data shown in figure 4B of Calton et al. (2003).

Our model makes two unique predictions regarding the outcome of experiments similar to those of Calton et al. (2003). First, a place cell that has a pre-lesion preference for a location about which there is a high degree of rotational symmetry (e.g. the center of a cylinder) should maintain its place preference post-lesion. Conversely, place cells that show pre-lesion preferences for locations of low rotational symmetry should tend to show shifts in their preferred locations after a lesion. An example of this latter effect is seen clearly in the simulation presented in figures 17 and 18. Second, the relative firing rates for place cells when measured at locations of high rotational symmetry should demonstrate little dependence on head direction after a lesion. For example, if cell A demonstrates a high post-lesion firing rate at the center of a cylinder for a given head direction, and if cell B demonstrates a low firing rate at that location and head direction, then for all other head directions, cells A and B should show similar relative firing rates at that location. Conversely, the relative firing rates for place cells when measured at locations with lower levels of rotational symmetry should exhibit higher levels of head direction dependence after a lesion.

In order to understand these predictions, one only needs to note that each transformation sub-layer contains a representation of the same egocentric space, but rotated about the origin. Therefore, if the egocentric parietal window representation shows a reasonable degree of rotational symmetry at a given location, then allowing extra regions of the overall transformation layer to project to the BVCs will not have a large effect on the resultant geometric information represented there, regardless of head direction. Hence, a place cell that fires maximally/minimally at such a location before a head direction system lesion would still receive high/low levels of stimulation there after a lesion; moreover, because of the rotational symmetry, it will do so for all head directions.

Methods

To simulate the key aspects of the linear track environment of Gothard et al. (1996), we trained our model on a symmetric environment consisting of two “boxes” that open towards each other, as in the lower left/middle panels of figure 21. Due to the absence of surrounding room cues, either box can be considered the movable box. In this way we were able to perform one set of simulations representing both outbound and inbound journeys. Medial temporal and parietal connections were set in the same manner as for the previous simulations. Before performing actual simulations of the Gothard et al. (1996) data, the forward translational velocity of the place cell representation under application of an egocentric velocity signal had to be calibrated. This was accomplished by applying the velocity signal after cuing the model to localize itself near box 1, facing box 2 (see figure 21) until place cell firing indicated localization near box 2. The model’s representation of its own location within the environment was calculated at any given instant by averaging the coordinates associated with maximally active place cells. By fitting a regression line to the roughly linear position-time data (see the rightmost panel of figure 21), a velocity of 0.044 space units per time unit was found. Such a simulation would correspond to the model mentally exploring this familiar environment, or performing spatial updating during actual locomotion in the absence of visual cues.

In the next step of the simulation the model was cued to a location two units away from box 1 along the direction towards box 2, while facing box 2. To simulate a shortened track, sensory input corresponding to box 2 was applied directly to the parietal window layer at either 0, 2, 4, 6, or 7 units closer to the egocentric origin than what would be consistent with the model’s learned representation for that location (see the top and bottom panels at the left of figure 22 for an example). For our initial set of simulations, sensory information corresponding to box 1 was not applied because we assumed that this landmark did not have the salience of the target landmark and a rat’s field of view is only approximately 300 degrees. Locomotion was simulated by turning on the forward velocity signal (corresponding to a velocity of 0.044 space units/time unit) and moving the sensory input corresponding to box 2 towards the origin of the parietal window coordinate system at the same speed. When this sensory input came within one unit of the origin, its movement was stopped, the velocity signal was turned off and the model was allowed to relax for 50 time steps before sensory input was down-regulated.

During locomotion, the rat’s head tends to bob up and down, so that it might well receive visual information from box 1. With this in mind we performed a second set of simulations identical to those just described, but with input representing box 1 also being applied to the parietal window component of the model. For these simulations, the additional input representing box 1 was initially configured so as to represent this landmark at 2 units behind the animal. During simulated locomotion, this “sensory” input was moved through the parietal window coordinate system at the same speed and in the same direction as the input representing box 2.

Finally, we performed simulations identical to those above, but with weakened overall connection strengths for the connections terminating on the BVC layer (see Table 1 for parameter values). The motivation for this was that a smaller proportion of space was filled with landmark segments in the linear-track environment than in the previous two environments. This was found to result in a very low resolution representation of space due to reduced lateral inhibition in the BVC, transformation and parietal window layers. However, results for both sets of simulations (with and without weakened parameters) are qualitatively similar, except for one difference as discussed below. Furthermore, a more realistic simulation in which the BVC and parietal window layers covered a more extensive region of space would have allowed for the inclusion of distal landmarks (room walls, etc.). Such inclusion would have generated increased lateral inhibition and a sharper representation of space without the need for altering any connection strengths.

Results and discussion

Results for the 6-unit-closer trial with no box 1 sensory information are shown in figure 22. Of particular interest is the fact that the maximum velocity of the place cell activity was 0.058 space units/time unit, or about 32% faster than when no inconsistent sensory input was present (see the rightmost panel of figure 22). Therefore, as with the data reported by Gothard et al. (1996), place cell activity was initially under the control of the nearest landmark, but during locomotion it “caught-up” to what it should have been had it been primarily under the influence of the target landmark (box 2).

In addition to recording the trajectory of place cell activity, the activity of eleven cells, representing equally-spaced locations within the environment, were recorded. If the simulation trials are considered as outward journeys, then we can plot the firing profiles in a way similar to that used by Gothard et al. (1996) to calculate displacement slopes. In figure 23 the firing profiles for four of the eleven recorded place cells in the condition with no box 1 sensory information are shown along with displacement slopes for all eleven in both conditions. The same information is plotted in figure 24 for the weak BVC input simulations. For the weak BVC input condition, place cell activity of the navigating model in the shortest track length trial hopped from one representation of location within the longest environment to another, resulting in a complete lack of firing from one of the four selected cells. Given the symmetry of our environment, displacement slope data can be determined for inward journeys by transforming the data for outward journeys as follows:

where DS(x) is the displacement slope for a neuron with peak firing position, x, in the box1 condition, and x is normalized to range between 0 (at the movable box) and 1 (at the fixed food cup). The transformed curves are shown in the lower right panel of 23 and 24. Notice that both sets of simulation-generated displacement slopes show patterns consistent with Gothard et al.’s results. In particular, the landmark that the animal is moving away from maintains considerable control over place cell firing until the target landmark is nearly reached. For the normal BVC input conditions this effect is similar whether or not we assume the animal has access to sensory information from both box 1 and 2. For the weak BVC input simulations we obtain a stronger effect if we assume the model has sensory input from both boxes.

In summary, our model performs in a manner consistent with the Gothard et al., (1996) data. In a subsequent experiment, the influence of the cue the rat is running from was seen to last for a constant time through the run rather than for a constant distance (Redish et al., 2000). This indicates either a time-limited usefulness for path integration (see e.g. Etienne, Maurer, & Seguinot,, 1996), or (as argued for in Redish et al., 2000) some temporal inertia in place cell firing possibly due to attractor dynamics (which can be seen under other experimental circumstances, e.g. Wills, Lever, Cacucci, Burgess & O’Keefe, 2005). Simulations comparing time and distance in this way were not performed (we used constant velocity), and remain for future work.

Finally, we compared our full model to a model lacking path integration. By considering only the part of the full model consisting of the BVCs, the place cells, and the feed-forward connections from the BVC to place cell layer, we were able to verify that the simple BVC explanation of Gothard et al.’s (1996) results does not produce the noted asymmetry. Specifically, we simulated navigation along each track length by providing direct input to the BVC neurons corresponding to the box 1 and box 2 landmarks, and then translated this input through the BVC coordinate system at 0.044 space units/time unit. In this way BVCs, and hence place cells, were driven directly by sensory input and the model’s current representation of space was not affected by previous representations of space or idiothetic information. Displacement slope curves for these simulations were calculated as above and plotted in the lower two panels of Figure 23 and 24. Notice that these curves are approximately symmetric about the mid-point of the full-length track. Thus the simple BVC model, in which distances to boundaries in allocentric directions are the only concern, is insufficient to produce the dependence on running direction noted in Gothard et al. (1996), O’Keefe & Burgess (1996), or Redish et al. (2000).

In the current model perceptual inputs and motion-related updating combine to influence the animal’s internal representation of location, and the operation of this mechanism seems to be consistent with the relevant existing data from place cell recording. The functional architecture of the current model was largely informed by thinking about imagery and planning in human spatial memory, however the simulations reported here indicate that it is also able to explain data at the single-unit level of description.

Temporo-parietal interactions, planning and imagery

Our specific model of the temporo-parietal interaction has some straightforward implications for functional anatomy. Thus, it explains why Papez’s (mammillo-anterior-thalamic-medial temporal) circuit is required for ‘episodic’ recollection into rich visuo-spatial imagery (Aggleton & Brown, 1999), and also provides the head direction signal in rats (Taube, 1998). It also suggests a functional role for retrosplenial cortex and intraparietal sulcus, which are well positioned to integrate or buffer the translation between egocentric and allocentric representations (Burgess, Becker et al., 2001), or correspondingly path integrative and mnemonic information (Cooper & Mizumori, 2001). Cooper & Mizumori (2001) and Maguire (2001) provide evidence that lesions to the retrosplenial cortex, an area interconnected with parietal and medial temporal regions (Kobayashi & Amaral, 2003; Wyss & Groen, 1992), do indeed impair the navigation of rats and humans under such circumstances. In humans, the intimate link between spatial imagery and navigation is made clear by the correlation of impairments in these two faculties following unilateral damage (Guariglia et al., 2005). Finally, our model proposes a role for the theta rhythm in coordinating the flow of information between medial temporal and parietal components of the model. Thus, “top-down” activation from medial temporal to parietal areas occurs at one phase of theta, while “bottom-up” activation from parietal to medial temporal areas occurs at the opposite phase of theta. A related proposal relates hippocampal encoding and retrieval to opposing phases of theta (e.g., Hasselmo et al., 2002), corresponding to our bottom-up and top-down phases respectively. In our model, spatial updating occurs over repeated top-down and bottom-up cycles as each (top-down) translation from allocentric to egocentric representations maps to locations adjusted for the subject’s velocity and then passes (bottom-up) back to update the allocentric representation.

In order to plan routes through complex environments, the brain must make use of long-term memories of the layout of those environments. Route planning also requires the ability to perform mental navigation: to imagine moving in a given direction, and the consequences of that action. Thus the task in our second set of simulations, involving mentally generating a velocity signal or “mock motor efference”, could be viewed as mental exploration of a familiar environment. This exploration would be useful for path planning and many other tasks. For example, this may be how people accomplish the task of Wang & Brockmole (2003) described in the introduction. Recall that in this task subjects were led along a path through a familiar environment and asked to point to occluded landmarks at various predetermined times. It was found that when subjects could not accurately point to a given landmark, they often could do so if allowed to walk to some point further along the path from which the landmark was still occluded. Within the framework of our model, subjects may have been mentally navigating from their current location to a location from which the occluded landmark was visible. By integrating the direction of the mentally generated velocity signal, a pointing direction could be generated. However, if the mental path was too long or complex, then the calculation would be swamped by cumulative error. In physically moving further along the path, subjects may have been simplifying the task by reducing the amount of mental navigation required.

Within the framework of route planning, a final prediction of the model presented here is that damage to connections between parietal and medial temporal cortices would impair the ability of an organism to navigate to occluded landmarks in familiar environments. This is because, without access to long-term spatial memory, the parietally supported egocentric window would only have access to short-term memory and direct sensory information, rendering the organism unable to mentally explore the familiar environment beyond regions very recently encountered. Equally, we might expect to see increased theta coherence between temporal and parietal regions as a function of this type of actual, or mental, navigation.

Differences between spatial updating and path integration in temporal and parietal cortices

Path integration can be defined as the ability of an organism to keep track of its current location relative to its starting point as it moves around, on the basis of idiothetic information alone, while spatial updating refers to the ability to also keep track of other locations within the environment, again using idiothetic information alone (for examples, see Etienne et al., 1998; Loomis et al., 1993; Mittelstaedt & Mittelstaedt, 2001; Morrongiello, Timney, Humphrey, Anderson & Skory, 1995). However, either process could operate either by individually updating the required egocentric location(s) relative to oneself, or by updating an allocentric representation of one’s own location relative to the environment. Both types of updating are probably available in parallel, with the former suitable for small numbers of locations and short movements and the latter for updating multiple locations and longer movements, when perceptual support from the environment is unavailable. Thus spatial updating over short timescales and small movements (e.g. less than 135 degree rotation) in unfamiliar environments appears to operate on transient egocentric parietal representations, showing independent accumulation of errors in the locations of different objects (Wang and Spelke, 2000; Waller and Hodgson, 2006). By contrast, spatial updating over longer durations or movements or in very familiar environments appears to operate on a coarser but enduring allocentric representation (Mou, McNamara, Rump & Xiao, in press; Waller & Hodgson, 2006). See Burgess (2006) for further discussion.

Corresponding to these two types of spatial updating, separate models have been proposed for the mechanisms within each (temporal or parietal) region. Byrne & Becker (2004) propose a purely parietal mechanism for motion-related updating of the egocentric locations in the parietal window, which would be consistent with single unit recording and effects of lesions within this region (see Introduction). On the other hand, strictly medial temporal mechanisms have been proposed for updating the location of the subject relative to the environment (see e.g. O’Keefe & Nadel, 1978; Redish, Rosenzweig, Bohanick, McNaughton & Barnes, 2000; Samsonovich & McNaughton, 1997; Howard, Fotedar, Datey, & Hasselmo, 2005). These latter models are supported by the recently discovered ‘grid cells’ in entorhinal cortex (Hafting et al., 2005), which appear well-suited to this task, with the hippocampus potentially required when path integration has to be tied to environmental locations (O’Keefe & Burgess, 2005; McNaughton et al., 2006). See Whishaw & Brooks (1999) and Save, Guazzelli, & Poucet (2001) for related discussion of the hippocampal contribution to path integration.

Our model primarily concerns the interaction of parietal and medial temporal representations, and assumes a single spatial updating mechanism derived as an extension of this interaction. Our second set of simulations provides a detailed mechanism by which the parietal cortex might make use of stored spatial representations in the medial temporal lobe to provide egocentric representations of an arbitrary number of locations within a familiar environment, and to update these locations following real or imagined self motion. Other tasks (such as pointing to a recently seen object, or imagery for objects or actions as opposed to environmental layout) will be purely parietal, and are not addressed by our model. Even within tasks that depend on both regions, such as those simulated, our model will not capture the finer distinctions between spatial updating driven more strongly by one region than the other. Similarly, we do not distinguish the processing of discrete objects, likely more strongly represented in parietal areas, from the processing of extended boundaries, likely key to driving the hippocampal representation. The BVC representation used provides the appropriate dependence of hippocampal representations on environmental geometry, but probably does not correspond so well to some aspects of egocentric parietal representations.

The provenance of the model

We have presented a working model of spatial cognition, without really addressing how the brain might have ‘learned’ such a solution. While a number of models of hippocampal learning have been presented (see e.g. Becker, 2005), principles underlying the learning of egocentric-allocentric transformations have not been firmly established. In recent work, we have attempted to elucidate more biologically realistic principles upon which such learning could be based (Byrne & Becker, submitted). Specifically, we have proposed two relatively simple learning principles that, when applied to a transformation circuit similar to the one presented here, reliably result in the generation of allocentric representations of space. The first principle is that of minimum reconstruction error. That is, for a given heading direction, the representation produced at the medial temporal lobe level should, through top-down connections, be able to reproduce the corresponding egocentric input. The second principle is the maximization of temporal inertia in medial temporal representations. This is motivated by empirical evidence that both hippocampal pyramidal cells (Redish, McNaughton & Barnes, 2000) and, under certain circumstances, superficial (Klink & Alonso, 1997) and deep layer (Egorov, Hamam, Fransén, Hasselmo & Alonso, 2002) entorhinal cells exhibit a resistance to rapid changes in firing rate. We speculate that spatial representations that vary as little as possible in time should maximize accuracy and precision in storage, as well as allowing more rapid spatial updating or mental exploration, because the medial temporal representations would have to vary less rapidly to keep up with the retrieval demands. We have tested the utility of these learning principles in two very different models, one trained by direct minimization of a cost function using steepest descent learning, and one consisting of a coupled network of restricted Boltzmann machines trained sequentially by contrastive Hebbian learning (Hinton, 2002; Hinton et al, 2006). Both models were able to learn allocentric representations of space at the medial temporal lobe output layer, and generate good reconstructions of the egocentric input layer.

Implications beyond spatial memory

Although we have concentrated on the role of the hippocampus in spatial memory, this structure is also known to be important in the maintenance of more general episodic memories (for recent reviews, see e.g. Burgess, Maguire & O’Keefe, 2002; Eichenbaum, 2001; for models see Howard et al., 2005; Marr, 1971; McClelland, McNaughton & O’Reilly, 1995; McNaughton & Morris, 1987; Treves & Rolls, 1992; Becker, 2005; among many others). In our model, hippocampal place cells bind the outputs of various BVCs and visual feature units together to form an allocentric map of an environment. The attractor dynamics of the medial temporal system then performs retrieval by allowing only those conjunctions of visual feature, distance and allocentric direction that are consistent with being in a single location (represented in the hippocampus). This information is then rotated, with the aid of Papez’s circuit, to form an egocentric parietal image corresponding to a specific direction of view, for conscious inspection. Our model is highly consistent with the pattern of fMRI activation in retrieving the spatial context of an event (Burgess, Maguire et al., 2001; King et al., 2005). Having defined this functional anatomy in the context of spatial memory, we suspect similar processing occurs much more generally during any detailed mental imagery for environmental layouts derived from long-term knowledge. This would be consistent with reports of deficits in detailed imagery for novel or future events in amnesic patients (Klein, Loftus & Khilstrom, 2002; Hassabis, Kumaran, Vann, Maguire, submitted; but see also Bayley, Gold, Hopkins, Squire, 2005), and similar patterns of activation for thinking about past and future events (Okuda et al., 2003; Addis, Wong & Schacter, submitted). This function might relate to characterizations of episodic or autobiographical memory in terms of retrieval of rich contextual information or feelings of “re-experiencing”, as distinct from the imagery for simple objects and actions which is preserved in amnesia (e.g., Rosenbaum, McKinnon, Levine, Moscovitch, 2004).

For simplicity, our simulations concerned a single familiar environment. However, retrieval from the best matching of several familiar environments could be mediated, as described by our model, by distinct subsets of place cells (McNaughton and Morris, 1987; Samsonovich and McNaughton, 1997) providing a distinct attractor representation of each environment (Wills et al., 2005). In this way, the hippocampus might be described as providing the spatial context appropriate to recollection (O’Keefe and Nadel, 1978), explaining its role, for example, in context-dependent fear conditioning, but not fear conditioning itself (Phillips and LeDoux, 1992; Kim and Fanselow, 1992). An interesting prediction here is that two situations can be identified in having different “contexts” requiring hippocampal disambiguation, if they illicit “remapped” (Muller, 1996) patterns of place cell firing, as occurs rapidly with dramatic multi-modal changes (Wills et al., 2005) or more slowly with unimodal changes (Lever et al., 2002).

Of course, hippocampal neurons are probably not limited to the spatial functions we have focused on here. For example, rat CA1 and CA3 pyramidal neurons can also respond to various non-spatial cues (see e.g. Huxter, Burgess & O’Keefe, 2003; Young, Fox & Eichenbaum, 1994). This ability to connect non-spatial and spatial information may allow the association of location within an environment to various other elements of experience, i.e. providing a spatio-temporal context to support context-dependent episodic memory more generally (see e.g. chapters 14 & 15 in O’Keefe & Nadel, 1978). We also note that the ability to perform spatial updating of the imagined viewpoint may both aid the process of search during episodic retrieval and the binding of places into remembered trajectories, or sequences, in memory for more extended dynamic episodes (see also Jensen & Lisman, 1996; Levy, 1996; Wallenstein, Eichenbaum & Hasselmo, 1998; Howard et al., 2005). Howard et al.’s temporal context model (TCM) of memory for lists of items provides an example of how such association across time might occur. The TCM works by associating items to a slowly varying context representation containing history-dependent information relating to the items themselves. Howard et al. note that this model is broadly compatible with a spatial function for the medial temporal lobe in providing a mechanism for path integration by representing the recent history of movements. In our model, the medial temporal lobe could be thought of as providing the spatial context of events by representing the actual surrounding spatial scene. Generation of more general representations of context, such a temporal contexts, would be one way in which our model might be extended to include the involvement of the medial temporal lobe in memories for trajectories through space, or in non-spatial memory.

Finally, while we have concentrated on spatial memory, the question of how long-term memory and short-term or working memory interact is equally pertinent to non-spatial memory. For example, although much has been learned about both long-term and working memory for verbal stimuli, the interaction of these two systems is a topic of much current interest (e.g. Baddeley, 2000; Burgess & Hitch, 2005). By staying within the spatial domain where there is much data at the single-unit level, we have provided a detailed model of one form of the interaction between long-term medial temporal and short-term parietal systems. However, our proposals for the functional roles and interactions of the regions in question should generalize to the generation of dynamic visuo-spatial imagery from stored verbal knowledge. Given the slight lateralization of visuo-spatial processing to the right hemisphere (e.g. Piggott & Milner, 1993; Smith & Milner, 1989; reviewed in Burgess et al., 2002), we would hope that some of the mechanisms considered here might generalize to the interaction of left medial temporal lobe long-term memory systems for narrative (e.g. Frisk & Milner, 1990) and parietal short-term memory systems for verbal working memory.