The ability to reconstruct perceptual experiences into imagery constitutes one of the hallmarks of human cognition, from the ability to imagine past episodes (Tulving 1985) to planning future scenarios (Schacter et al., 2007). Intriguingly, this ability (also known as ‘scene construction’ and ‘episodic future thinking’) appears to depend on the hippocampal system (Schacter et al., 2007; Hassabis et al., 2007; Buckner, 2010), in which direct (spatial) correlates of the activities of single neurons have long been identified in rodents (O'Keefe and Nadel, 1978; Taube et al., 1990a; Hafting et al., 2005) and more recently in humans (Ekstrom et al., 2003; Jacobs et al., 2010). The rich catalog of behavioral, neuropsychological and functional imaging findings on one side, and the vast literature of electrophysiological research on the other (see e.g. Burgess et al., 2002), promises to allow an explanation of higher cognitive functions such as spatial memory and imagery directly in terms of the interactions of neural populations in specific brain areas. However, while attaining this type of understanding is a major aim of cognitive neuroscience, it cannot usually be captured by a few simple equations because of the number and complexity of the systems involved. Here, we show how neural activity could give rise to spatial cognition, using simulations of multiple brain areas whose predictions can be directly compared to experimental data at neuronal, systems and behavioral levels.

Extending the Byrne, Becker and Burgess model of spatial memory and imagery of empty environments (Burgess et al., 2001a; Byrne et al., 2007), we propose a large-scale systems-level model of the interaction between Papez’ circuit, parietal, retrosplenial, and medial temporal areas. The model relates the neural response properties of well-known cells types in multiple brain regions to cognitive phenomena such as memory for the spatial context of encountered objects and mental navigation within familiar environments. In brief, egocentric (i.e. body-centered) representations of the local sensory environment, corresponding to a specific point of view, are transformed into viewpoint-independent (allocentric or world-centered) representations for long-term storage in the medial temporal lobes (MTL). The reverse process allows reconstruction of viewpoint-dependent egocentric representations from stored allocentric representations, supporting imagery and recollection.

Neural populations in the medial temporal lobe (MTL) are modeled after cell types reported in rodent electrophysiology studies. These include place cells (PCs), which fire when an animal traverses a specific location within the environment (O'Keefe and Dostrovsky, 1971); head direction cells (HDCs), which fire according to the animal’s head direction relative to the external environment, irrespective of location (Taube and Ranck, 1990; Taube et al., 1990a; Taube et al., 1990b); boundary vector cells (Lever et al., 2009); henceforth BVCs), which fire in response to the presence of a boundary at a specific combination of distance and allocentric direction (i.e. North, East, West, South, irrespective of an agent’s orientation); and grid cells (GCs), which exhibit multiple, regularly spaced firing fields (Hafting et al., 2005). Evidence for the presence of these cell types in human and non-human primates is mounting steadily (Robertson et al., 1999; Ekstrom et al., 2003; Jacobs et al., 2010; Doeller et al., 2010; Bellmund et al., 2016; Horner et al., 2016; Nadasdy et al., 2017).

The egocentric representation supporting imagery has been suggested to reside in medial parietal cortex (e.g. the precuneus; Fletcher et al., 1996; Knauff et al., 2000; Formisano et al., 2002; Sack et al., 2002; Wallentin et al. (2006); Hebscher et al., 2018). In the model, it is referred to as the ‘parietal window’ (PW). Its neurons code for the presence of scene elements (boundaries, landmarks, objects) in peri-personal space (ahead, left, right) and correspond to a representation along the dorsal visual stream (the ‘where’ pathway; Ungerleider, 1982; Mishkin et al., 1983). The parietal window boundary coding (PWb) cells are egocentric analogues of BVCs (Barry et al., 2006; Lever et al., 2009), consistent with evidence that parietal areas support egocentric spatial processing (Bisiach and Luzzatti, 1978; Nitz, 2009; Save and Poucet, 2009; Wilber et al., 2014).

The transformation between egocentric (parietal) and allocentric (MTL) reference frames is performed by a gain-field circuit in retrosplenial cortex (Burgess et al., 2001a; Byrne et al., 2007; Wilber et al., 2014; Alexander and Nitz, 2015; Bicanski and Burgess, 2016), analogous to gain-field neurons found in posterior parietal cortex (Snyder et al., 1998; Salinas and Abbott, 1995; Pouget and Sejnowski, 1997; Pouget et al., 2002) or parieto-occipital areas (Galletti et al., 1995). Head-direction provides the gain-modulation in the transformation circuit, producing directionally modulated boundary vector cells which connect egocentric and allocentric boundary coding neurons. That this transformation between egocentric directions (left, right, ahead) and environmentally-referenced directions (nominally North, South, East, West) requires input from the head-direction cells found along Papez’s circuit (Taube et al., 1990a; Taube et al., 1990b) is consistent with its involvement in episodic memory (e.g. Aggleton and Brown, 1999; Delay and Brion, 1969).

During perception the egocentric parietal window representation is based on (highly processed) sensory inputs. That is, it is driven in a bottom-up manner, and the transformation circuit maps the egocentric PWb representation to allocentric BVCs. When the transformation circuit acts in reverse (top-down mode), it reconstructs the parietal representation from BVCs which are co-active with other medial temporal cell populations, forming the substrate of viewpoint-independent (i.e. allocentric) memory. This yields an orientation-specific (egocentric) parietal representation (a specific point of view) and constitutes the model’s account of (spatial) imagery and explicit recall of spatial configurations of known spaces (Burgess et al., 2001a; Byrne et al., 2007). Figure 1 depicts a simplified schematic of the model.

Figure 1

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To account for the presence of objects within the environment, we propose allocentric object vector cells (OVCs) analogous to BVCs, and show how object-locations can be embedded into spatial memory, supported by visuo-spatial attention. Importantly, the proposed object-coding populations in the MTL map onto recently discovered neuronal populations (Deshmukh and Knierim, 2013; Hoydal et al., 2017). We also predict a population of egocentric object-coding cells in the parietal window (PWo cells: egocentric analogues to OVCs), as well as directionally modulated boundary and object coding neurons (in the transformation circuit). Finally, we include a grid cell population to account for mental navigation and planning, which drives sequential place cell firing reminiscent of hippocampal ‘replay’ (Wilson and McNaughton, 1994; Foster and Wilson, 2006; Diba and Buzsáki, 2007; Karlsson and Frank, 2009; Carr et al., 2011) and preplay (Dragoi and Tonegawa, 2011; Ólafsdóttir et al., 2015). We refer to this model as the BB-model.

Here, we describe the neural populations of the BB-model and how they interact in detail. Technical details of the implementation, equations, and parameter values can be found in the Appendix.

Receptive field topology and visualization of data

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We visualize the firing properties of individual spatially selective neurons as firing rate maps that reflect the activity of a neuron averaged over time spent in each location. We also show population activity by arranging all neurons belonging to one population according to the relative locations of their receptive fields (see Figure 2A–C), plotting a snapshot of their momentary firing rates. In the case of boundary-selective neurons such a population snapshot will yield an outline of the current sensory environment (Figure 2C). Naturally, these neurons may not be physically organized in the same way, and these plots should not be confused with the firing rate maps of individual neurons (Figure 2D). Hence, population snapshots (heat maps) and firing rate maps (Matlab ‘jet’ colormap) are shown in distinct color-codes (Figure 2).

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Video 1

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The parietal window

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Perceived and imagined egocentric sensory experience is represented in the ‘parietal window’ (PW), which consists of two neural populations - one coding for extended boundaries (‘PWb neurons’), and one for discrete objects (‘PWo neurons’). The receptive fields of both populations lie in peri-personal space, that is are tuned to distances and directions ahead, left or right of the agent, tile the ground around the agent, and rotate together with the agent (Figure 2A2, Figure 3). Reciprocal connections to and from the retrosplenial transformation circuit (RSC/TR, see below) allow the parietal window representations to be transformed into allocentric (orientation-independent) representations (i.e. boundary and object vector cells) in the MTL and vice versa. Intriguingly, cells that encode an egocentric representation of boundary locations (akin to parietal window neurons in the present model) have recently been described (Hinman et al., 2017).

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Model summary

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An agent employing a simple model of attention alongside dedicated object-related neural populations in perirhinal, parietal and parahippocampal (BVCs and OVCs) cortices allow the encoding of scene representations (i.e. objects in a spatial context) into memory. Transforming egocentric representations via the retrosplenial transformation circuit yields viewpoint-independent (allocentric) representations in the medial temporal lobe, while reconstructing the parietal window representation (which is driven by sensory inputs during perception) from memory is the model’s account of recall as an act of visuo-spatial imagery. Grid cells allow for mental navigation. Figure 4 shows the complete schematic of the BB-model, see Figure 2—figure supplement 1 for details of the RSC transformation circuit.

Figure 4

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In this section, we explore the capabilities of the BB-model in simulations and derive predictions for future research. Each simulation is accompanied by a Figure, a supplementary video visualizing the time course of activity patterns of neural populations, and a brief discussion. In Section Discussion, we offer a more general discussion of the model.

Encoding of objects in spatial memory and recall (Simulation 1.0)

We let the agent model explore the square environment depicted in Figure 3A. However, the spatial context now contains an isolated object (Figure 5). During exploration, parietal window (PWb) neurons activate BVCs via the retrosplenial transformation circuit (RSC/TR), which in turn drive place cell activity. Similarly, when the object is present PWo neurons are activated, which drive OVCs via the transformation circuit. At the same time, object/boundary identity is signalled by perirhinal neurons (PRb/o). When the agent comes within a certain distance (here 55 cm) of an object, the following connection weights are changed to form Hebbian associations: PRo neurons are associated with PCs, HDCs, and OVCs; OVCs are associated with PCs and PRo neurons (also see Figure 3D); PCs are already connected to BVCs (in a familiar context). The weight change is calculated as the outer product of population vectors of the corresponding neuronal populations (yielding the Hebbian update), normalized, and added to the given weight matrix.

Figure 5

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After the agent has finished its assigned trajectory, we test object-location memory via object-cued recall. That is, modeling some external trigger to remember a given object (e.g. ‘Where did I leave my keys?'), current is injected into the PRo neuron coding for the identity of the object to-be recalled. By virtue of learned connections, the PRo neuron drives the PCs which were active at encoding. Pattern completion in the MTL recovers the complete spatial context by driving activity in BVCs and PRb neurons. The connections from PRo neurons to head direction cells (Figure 3D) ensure a modulation of the transformation circuit such that allocentric BVC and OVC activity will be transformed to yield the parietal representation (i.e. a point of view) similar to the one at the time of encoding. That is, object-cued recall corresponds to a full reconstruction of the scene when the object was encoded. Figure 5 depicts the encoding (Figure 5A) and recall phases (Figure 5B) of simulation 1.0. Video 2 shows the entire trial. To facilitate matching simulation numbers and figures to videos, Table 1 lists all simulations and relates them to their corresponding figures and videos.

Table 1

Simulation no.	Content	Related figures	Video no.
0	Activity in the transformation circuit	Figure 2—figure supplement 1	1
1.0	Object-cued recall	Figures 5 and 6,8A	2
1.0n1	Object-cued recall with neuron loss	Figure 8B	3
1.0n2	Object-cued recall with firing rate noise	Figure 8C	4
1.1	Papez’ circuit Lesion (anterograde amnesia)	Figure 7A	5
1.2	Papez’ circuit Lesion (retrograde amnesia)	Figure 7B	6
1.3	Object novelty (intact hippocampus)	Figure 9A	7
1.4	Object novelty (lesioned hippocampus)	Figure 9B	8
2.1	Boundary trace responses	Figure 10A,B,C	9
2.2	Object trace responses	Figure 10D	10
3.0	Inspection of scene elements in imagery	Figure 11	11
4.0	Mental Navigation	Figure 12	12
5.0	Planning and short-cutting	Figure 13	13

Video 2

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Recollection in the BB-model results in visuo-spatial imagery of a coherent scene from a single viewpoint and direction, that is it implements a process of scene construction (Burgess et al., 2001a; Byrne et al., 2007; Schacter et al., 2007; Hassabis et al., 2007; Buckner, 2010) at the neuronal level. A mental image is re-constructed in the parietal window reminiscent of the perceptual activity present at encoding. Note that during imagery BVCs (and hence PWb neurons, Figure 5B) all around the agent are reactivated by place cells, because the environment is familiar (the agent having experienced multiple points of view at each location during the training phase). We do not simulate selective attention for boundaries (i.e. PWb neurons), although see Byrne et al., 2007.

Similar tasks in humans appear to engage the full network, including Papez’ circuit, where head direction cells are found (for review see Taube, 2007); retrosplenial cortex (where we hypothesize the transformation circuit to be located) (Burgess et al., 2001a; Lambrey et al., 2012; Auger and Maguire, 2013; Epstein and Vass, 2014; Marchette et al., 2014; Shine et al., 2016); medial parietal areas (Fletcher et al., 1996; Hebscher et al., 2018); parahippocampus and hippocampus (Hassabis et al., 2007; Addis et al., 2007; Schacter et al., 2007; Bird et al., 2010); and possibly the entorhinal cortex (Atance and O'Neill, 2001; Bellmund et al., 2016; Horner et al. 2016; also see Simulation 4.0).

At the neuronal level, a key component of the BB-model are the object vector cells (OVCs) which code for the location of objects in peri-personal space. In Figure 5 the cells are organized according to the topology of their receptive fields in space, with the agent at the center (also compare to Figure 2A2). However, in rodent experiments individual spatially selective cells (like PCs or GCs) are normally visualized as time-integrated firing rate maps. We ran a separate simulation with three objects in the environment to examine firing rate maps of individual cells. OVCs show firing fields at a fixed allocentric distance and angle from objects (Figure 6). The BB-model predicts that OVC-like responses should be found as close as one synapse away from the hippocampus and were introduced as a parsimonious object code, analogous to BVCs and exploiting the existing transformation circuit. However, these rate maps show a striking resemblance to similar data from cells recently reported in the hippocampus of rodents (Figure 6C, compare to Deshmukh and Knierim, 2013). While Deshmukh and Knierim (2013) found these cells in the hippocampus, the object selectivity of these hippocampal neurons may have been inherited from other areas, such as lateral entorhinal cortex (Tsao et al., 2013), parahippocampal cortex (due to their similarities to BVCs) or medial entorhinal cortex (Solstad et al., 2008; Hoydal et al., 2017).

Figure 6

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Anatomical connections between the potential loci of BVCs/OVCs and retrosplenial cortex (the suggested location of the egocentric-allocentric transformation circuit) exist. BVCs have been found in the subicular complex (Lever et al., 2009), and the related border cells and OVCs in medial entorhinal cortex (Solstad et al., 2008; Hoydal et al., 2017). Both areas receive projections from retrosplenial cortex (Jones and Witter, 2007), and project back to it (Wyss and Van Groen, 1992).

Papez’ circuit lesions induce amnesia (Simulations 1.1, 1.2)

Figure 5 depicts the model performing encoding and object-cued recall. However, the model also allows simulation of some of the classic pathologies of long-term memory. Lesions along Papez’ circuit have long been known to induce amnesia (Delay and Brion, 1969; Squire and Slater, 1978; 1989; Parker and Gaffan, 1997; Aggleton et al., 2016). Thus, lesions to the fornix and mammilary bodies severely impact recollection, although recognition can be less affected (Tsivilis et al., 2008). In the context of spatial representations, Papez’ circuit is notable for containing head direction cells (as well as many other cell types not in the model). That is, the mammillary bodies (more specifically the lateral mammillary nucleus, LMN), anterior dorsal thalamus, retrosplenial cortex, parts of the subicular complex and medial entorhinal cortex all contain head direction cells (Taube, 2007; Sargolini et al., 2006). Thus, lesioning Papez’ circuit removes (at least) the head direction signal from our model, and is modeled by setting the input from head direction cells to the retrosplenial transformation circuit (RSC/TR) to zero.

In the bottom-up mode of operation (perception), the lesion removes drive to the transformation circuit and consequently to the boundary vector cells and object vector cells. That is, the perceived location of an object (present in the egocentric parietal representation) cannot elicit activity in the MTL and thus cannot be encoded into memory (Figure 7). Some residual MTL activity reflects input from perirhinal neurons representing the identity of perceived familiar boundaries (i.e. recognition mediated by perirhinal cells is spared). In the top-down mode of operation (recall) there are two effects: (i) Since no new elements can be encoded into memory, post-lesion events cannot be recalled (anterograde amnesia; Simulation 1.1, Figure 7A, Video 5); and (ii) For pre-existing memories (e.g. of an object encountered prior to the lesion), place cells (and thus the remaining MTL populations) can be driven via learned connections from perirhinal neurons (e.g. when cued with the object identity; Simulation 1.2, Figure 7B, Video 6), but no meaningful egocentric representation can be instantiated in parietal areas, preventing episodic recollection/imagery. Equating the absence of parietal activity with the inability to recollect is strongly suggested by the fact that visuo-spatial imagery in humans relies on access to an egocentric representation (as in hemispatial representational neglect; Bisiach and Luzzatti, 1978). Simulations 1.1 and 1.2 show that the egocentric neural correlates of objects and boundaries present in the visual field persist in the parietal window only while the agent perceives them (they could also be held in working memory, which is not modelled here). Note that perirhinal cells and upstream ventral visual stream inputs are spared, so that an agent could still report the identity of the object.

Figure 7

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Quantification, robustness to noise and neuron loss

Figure 8A shows correlations between population vectors of neural patterns during imagery/recall and those during encoding for Simulation 1.0 (Object-cued recall; Figure 5). OVCs and PCs exhibit correlation values close to one, indicating faithful reproduction of patterns. BVC correlations are somewhat diminished because recall reactivates all boundaries fully, compared to a field of view of 180 degrees during perception with limited reactivation of cells representing boundaries outside the field of view. PW neurons show correlations below one because at recall reinstatement in parietal areas requires the egocentric-allocentric transformation (i.e. OVC signals passed through retrosplenial cells), which blurs the pattern compared to perceptual instatement in the parietal window (i.e. imagined representations are not as precise as those generated by perception).

Figure 8

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To test the model’s robustness with regard to firing rate noise and neuron loss, we perform two sets of simulations (modifications of Simulation 1.0, object-cued recall). In the first set we randomly chose cells in equal proportions in all model areas (except HDCs) to be permanently deactivated and assess recall into visuo-spatial imagery. Up to 20% of the place cells, grid cells, OVCs, BVCs, parietal and retrosplenial neurons were deactivated. Head direction cells were excluded because of the very low number simulated (see below). Although we do not attempt to model any specific neurological condition, this type of simulation could serve as a starting point for models of diffuse damage, as might occur in anoxia, Alzheimer’s disease or aging. The average correlations between the population vectors at encoding versus recall are shown in Figure 8B.

The ability to maintain a stable attractor state among place cells and head direction cells is critical to the functioning of the model, while damage in the remaining (feed-forward) model components manifests in gradual degradation in the ability to represent the locations of objects and boundaries (see accompanying Video 3). For example, if certain parts of the parietal window suffer from neuron loss, the reconstruction in imagery is impaired only at the locations in peri-personal space encoded by the missing neurons (indeed, this can model representational neglect; Byrne et al., 2007), see also Pouget and Sejnowski, 1997). The place cell population was more robust to silencing than the head-direction population (containing only 100 neurons), simply because greater numbers of neurons were simulated, giving greater redundancy. As long as a stable attractor state is present, the model can still encode and recall meaningful representations, giving highly correlated perceived and recalled patterns (Figure 8B).

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The model is also robust to adding firing rate noise (up to 20% of peak firing rate) to all cells. Correlations between patterns at encoding and recall remain similar to the noise-free case, see Figure 8C. Videos 3 and 4 show an instance from the neuron-loss and firing rate noise simulations respectively.

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Video 5

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Novelty detection (Simulations 1.3, 1.4)

In the model, hippocampal place cells bind all scene elements together. The locations of these scene elements relative to the agent are encoded in the firing of boundary vector cells (BVCs) and object vector cells (OVCs). Rats show a spontaneous preference for exploring novel/altered stimuli compared to familiar/unchanged ones. We simulate one of these experiments (Mumby et al., 2002), in which rats preferentially explore one of two objects that has been shifted to a new location within a given environment, a behavior impaired by hippocampal lesions. In Simulations 1.3 and 1.4, the agent experiences an environment containing two objects, one of which is later moved. We define a mismatch signal as the difference in firing of object vector cells during encoding versus recall (modelled as imagery, at the encoding location), and assume that the relative amounts of exploration would be proportional to the mismatch signal.

With an intact hippocampus (Figure 9; Video 7), the moved object generates a significant novelty signal, due to the mismatch between recalled (top-down) OVC firing and perceptual (bottom-up) OVC firing at the encoding location. That detection of a change in position requires the hippocampus is consistent with place cells binding the relative location of an object (via object vector cells) to perirhinal neurons signalling the identity of an object.

Figure 9

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Video 7

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Hippocampal lesions are implemented by setting the firing rates of hippocampal neurons to zero. A hippocampal lesion (Figure 9; Video 8) precludes the generation of a meaningful novelty signal because the agent is incapable of generating a coherent point of view for recollection, and the appropriate BVC configuration cannot be activated by the now missing hippocampal input. Connections between object vector cells and perirhinal neurons (see Figure 3D) can still form during encoding in the lesioned agent. Thus some OVC activity is present during recall due to these connections. However, this activity is not location specific. Without the reference frame of place cells and thence BVC activity this residual OVC activity during recall can be generated anywhere (see Figure 9F–H). It only tells the agent that it has seen this object at a given distance and direction, but not where in the environment it was seen. Hence, the mismatch signal is equal for both objects, and exploration time would be split roughly evenly between them. However, if the agent happens to be at the same distance and direction from the objects as at encoding, then perceptual OVC activity will match the recalled OVC activity (Figure 9G,H), which might correspond to the ability of focal hippocampal amnesics to detect the familiarity of an arrangement of objects if tested from the same viewpoint as encoding (King et al., 2002; but see also Shrager et al., 2007).

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Rats also show preferential exploration of a familiar object that was previously experienced in a different environment, compared with one previously experienced in the same environment, and this preference is also abolished by hippocampal lesions (Mumby et al., 2002; Eacott and Norman, 2004; Langston and Wood, 2010). We have not simulated different environments (using separate place cell ensembles), but note that ‘remapping’ of PCs between distinct environments (i.e. much reduced overlap of PC population activity; e.g. Bostock et al., 1991; Anderson and Jeffery, 2003; Wills et al., 2005) suggests a mismatch signal for the changed-context object would be present in PC population vectors. Initiating recall of object A, belonging to context 1, in context 2, would re-activate the PC ensemble belonging to context 1, creating an imagined scene from context one which would mismatch the activity of PCs representing context two during perception. A hippocampal lesion precludes such a mismatch signal by removing PCs.

Finally, it has been argued that object recognition (irrespective of context) is spared after hippocampal but not perirhinal lesions (Aggleton and Brown, 1999; Winters et al., 2004; Norman and Eacott, 2004) which would be compatible with the model given that its perirhinal neuronal population signals an object’s identity irrespective of location.

‘Top-down’ activity and trace responses (Simulations 2.1, 2.2)

Simulations 1.3 and 1.4 dealt with a moved object. Similarly, if a scene element (a boundary or an object) has been removed after encoding, probing the memorized MTL representation can reveal trace activity reflecting the previously encoded and now absent boundary or object.

Section (Bottom-up vs top-down modes of operation) summarizes how top-down and bottom-up phases are implemented by a modulation of connection strengths (see Figures 1 and 4, Materials and methods section Embedding Object-representations into a Spatial Context: Attention and Encoding, and Appendix). During perception, the ‘top-down’ connections from the MTL to the transformation circuit and thence to the parietal window are reduced to 5% of their maximum strength, to ensure that learned connections do not interfere with on-going, perceptually driven activity. During imagery, the ‘bottom-up’ connections from the parietal window to the transformation circuit and thence to the MTL are reduced to 5 percent of their maximum strength.

In rodents, it has been proposed that encoding and retrieval are gated by the theta rhythm (Hasselmo et al., 2002): a constantly present modulation of the local field potential during exploration. In humans, theta is restricted to shorter bursts, but is associated with encoding and retrieval (Düzel et al., 2010). If rodent theta determines the flow of information (encoding vs retrieval) then it may be viewed as a periodic comparison between memorized and perceived representations, without deliberate recall of a specific item in its context (that is, without changing the point of view). In Simulations 2.1 and 2.2, we implement this scenario. There is no cue to recall anything specific, regular sensory inputs are continuously engaged, and we periodically switch between bottom-up and top-down modes (at roughly theta frequency) to allow for an on-going comparison between perception and recall. Activity due to the modulation of top-down connectivity during perception propagates to the parietal window representations (PWb/o), allowing for a detection of mismatch between sensorily driven and imagery representations.

In Simulation 2.1, the agent has a set of MTL weights which encode the contextual representation of a square room with an inserted barrier (i.e. a barrier was present in the training phase). However, when the agent explores the environment, the barrier is absent (Figure 10A). Due to the modulation of top-down connectivity, the memory of the barrier (in form of BVC activity) periodically bleeds into the parietal representation during perception (Figures 10B1, 2 and 3 and Video 9). The resultant dynamics carry useful information. First, letting the memory representation bleed into the perceptual one allows an agent, in principle, to localize and attend to a region of space in the egocentric frame of reference (as indicated by parietal window activity) where a change has occurred. A mismatch between the perceived (low bottom-up gain) and partially reconstructed (high bottom-up gain) representations, can signal novelty (compare to Simulations 1.3, 1.4), and could underlie the production of memory-guided attention (e.g. Moores et al., 2003; Summerfield et al., 2006). Moreover, the theta-like periodic modulation of top-down connectivity causes the appearance of ‘trace’ responses in BVC firing rate maps, indicating the location of previously encoded, now absent, boundary elements (Figures 10C1 and 2)

Figure 10

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Video 9

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Simulation 2.2 (Figures 10D1,D2 and Video 10) shows similar’ trace’ responses for OVCs. The agent has a set of MTL weights which encode the scene from Simulation 1.0 (Figure 5) where it encountered and encoded an object. The object is now absent (small red circle in Figure 10D1), but the periodic modulation of top-down connectivity reactivates corresponding OVCs, yielding trace fields in firing rate maps. This activity can bleed into the parietal representation during perception (e.g. at simulation time 9:40-10:00 in Video 6), albeit only when the location of encoding is crossed by the agent, and with weaker intensity than missing boundary activity (the smaller extent of the OVC representation leads to more attenuation of the pattern as it is processed by the transformation circuit).

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Interestingly, perirhinal identity neurons, which normally fire irrespective of location, can appear as spatially selective trace cells due to the periodic modulation of top-down connectivity at the location of encoding. Figure 10D3 shows the firing rate map of a perirhinal identity neuron. Every time the memorized representation is probed (high top-down gain), if the agent is near the location of encoding, the learned connection from PCs to perirhinal cells (PRo) lead to perirhinal firing for the absent object, yielding a spatial trace firing field for this nominally non-spatial cell.

The presence of some memory-related activity during nominally bottom-up (perceptual) processing can have benefits beyond the assessment of change discussed above. For instance, additional activity in the contextual representations (BVCs, PC, PRb neurons) due to pattern completion in the MTL can enhance the firing of BVCs coding for scene elements outside the current field of view. This activity can propagate to the PW, as is readily apparent during full recall/imagery (Figure 5) but is also present in weaker form during perception. Such activity may support awareness of our spatial surrounding outside of the immediate field of view, or may enhance perceptually driven representations when sensory inputs are weak or noisy.

Sampling multiple objects in imagery (Simulation 3.0)

Humans can focus attention on different elements in an imagined scene, sampling one after another, without necessarily adopting a new imagined viewpoint. This implies that the set of active PCs need not change while different objects are inspected in imagery. Moreover, humans can localize an object in imagined scenes and retrieve its identity (e.g. ‘What was next to the fireplace in the restaurant we ate at?”).

In Simulation 1.0 (encoding and object-cued recall, Figure 5), in addition to connection weights from perirhinal (PRo) neurons to PCs and OVCs, the reciprocal weights from OVCs to PRo neurons were also learned. These connections allow the model to sample and inspect different objects in an imagined scene. To illustrate this we place two objects in a scene and allow the agent to encode both visible objects from the same point of view. Encoding still proceeds sequentially. That is, our attention model first samples one object (boosting its activity in the PW) and then the other.

We propose that encoded objects that are not currently the focus of attention in imagery can attract attention by virtue of their residual activity in the parietal window (weak secondary peak in the PWo population in Figure 11B). Thus, any of these targets can be focused on by scanning the parietal window and shifting attention to the corresponding location (e.g. ‘the next object on a table’). Boosting the drive to such a cluster of PWo cells in the parietal window leads to corresponding activity in the OVC population (via the retrosplenial transformation circuit). The learned connection from OVCs to perirhinal PRo neurons will then drive PRo activity corresponding to the object which, at the time of encoding, was at the location in peripersonal space which is now the new focus of attention. Mutual inhibition between PRo neurons suppresses the previously active PRo neuron. The result is a top-down drive of perirhinal neurons (as opposed to bottom-up object recognition), which allows inferring the identity of a given object. That is, by shifting its focus of attention in peripersonal space (i.e. in the parietal window) during imagery the agent can infer the identity of scene elements which it did not initially recall.

Figure 11

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Figure 11 and Video 11 show sequential (attention-based) encoding, subsequent recall and attentional sampling of scene elements. The agent sequentially encodes two objects from one location (Figure 11A), moves on until both objects are out of view, and engages imagery to recall object one in its spatial context (Figure 11B). The agent can then sample object two by allocating attention to the secondary peak in the parietal window (boosting the residual activity by injecting current in the PWo cells corresponding to the location of object 2). This activity spreads back to the MTL network, via OVCs, driving the corresponding PRo neuron (Figure 11C). Thus, the agent infers the identity of object 2, by inspecting it in imagery. Attention ensures disambiguation of objects at encoding, while reciprocity of connections in the MTL is necessary to form a stored attractor in spatial memory.

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Grid cells and mental navigation (Simulation 4.0)

The parietal window neurons encode the perceived spatial layout of an environment, in an egocentric frame of reference, as an agent explores it (i.e. a representation of the current point of view). In imagery, this viewpoint onto a scene is reconstructed from memory (top-down mode as opposed to bottom-up mode). We refer to mental navigation as internally driven translation and rotation of the viewpoint in the absence of perceptual input. In Simulation 4.0, we let the agent encode a set of objects into memory and then perform mental navigation with the help of grid and head direction cells.

Grid cell (GC) firing is thought to update the location represented by place cell firing, driven by signals relating to self-motion (O'Keefe and Burgess, 2005; McNaughton et al., 2006; Fuhs and Touretzky, 2006; Solstad et al., 2006). During imagination, we suppose that GC firing is driven by mock motor-efference signals (i.e. imagined movement without actual motor output) and used to translate the activity bump on the sheet of place cells. Pattern completion in the MTL network would then update the BVC population activity accordingly, which will spread through the transformation circuit and update parietal window activity. That is, mock motor efference could smoothly translate the viewpoint in imagery (i.e. scene elements represented in the parietal window flow past the point of view of the agent). Similarly, mock rotational signals to the head direction attractor could rotate the viewpoint in imagery. Both together are sufficient to implement mental navigation.

GCs are implemented heuristically, approximating the output of more sophisticated models (e.g., Burgess et al., 2007; Burak and Fiete, 2009; Bush and Burgess, 2014). Firing rate maps for 7 modules of 100 cells each are pre-calculated (see Appendix), providing the firing rates of GCs as a function of location. GC to PC weights are pre-calculated as Hebbian associations (to simulate a familiar environment), where the connection strength is maximal if the center of a PC’s receptive field coincides with (one of) the GC’s firing peaks. During (bottom-up) perception and navigation, GC input provides a small contribution to PC activity, which is mainly determined by BVC inputs (O'Keefe and Burgess, 1996; Hartley et al., 2000; Lever et al., 2009), to highlight the ability of the model to self-localize based on sensory inputs. Stronger grid cell input simply makes the location estimate more stable without detriment to the model. In the absence of reliable sensory information strong GC inputs are required to make PCs fire reliably (Bush et al., 2014; Poucet et al., 2014; Evans et al., 2016). Imagery is an extreme case of this situation, where no sensory input is provided to PCs. Consequently, GC input is up-regulated during imagery (similar to other connections in the switch from bottom-up to top-down modes), constituting a major input to PCs. This GC input can then translate the agent’s viewpoint in imagery (via their effect on PCs) without directly affecting the transformation circuit.

Figure 12 and Video 12 show an example of mental navigation. The agent approaches three objects in sequence, encodes them into memory and then initiates recall cued by object 1. From that (imagined) location, it initiates mental navigation in a straight line. GCs shift the PC activity bump along the trajectory. The allocentric boundary representation (BVCs) follows the shifting PCs (due to pattern completion) and the retrosplenial transformation circuit (RSC/TR) translates the shifting BVC representation into a shifting (i.e. ‘flowing past the agent’) egocentric representation of boundary distance (imagery of motion in an imagined scene, not shown in Figure 12, however, see Video 12). Importantly, the imagined trajectory takes the agent through the area of space at which object three was encoded, however this time coming from a novel direction. The transformation circuit nevertheless instantiates the correct activity in the parietal window for object 3, making it appear to the agent’s right, instead of to it’s left (as during its original encoding, coming from object 2). Not only does the object populate the imagined scene as the agent mentally navigates past it, the event also generates an imagined representation which has never been experienced by the agent.

Translating an established BVC pattern due to updated perceptual input (in response to real motion) also translates the PC activity bump. In fact, this is how perceptual information updates the estimate of position (self-localization) in a familiar environment (PWb→RSC→BVC→PC) in the model. Similarly, shifting the activity pattern across PCs via GCs in mental navigation can update the parietal window (PWb) during mental navigation (GC→PC→BVC→RSC→PWb). With this account of mental exploration of different routes (including potentially novel imagined experiences; see next section), the model provides a neural implementation of important aspects of ‘scene construction’ (Hassabis et al., 2007) and ‘episodic future thinking’ (Schacter et al., 2007), although these concepts also extend beyond the capabilities of the model (see Discussion). The inclusion of GCs allows for a parsimonious account of mental navigation in humans, consistent with observation of grid-like activity during imagined movement through familiar environments (Bellmund et al., 2016; Horner et al. 2016).

Figure 12

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Shortcutting and ‘preplay-like’ activity (Simulation 5.0)

It is a small step from imagined movement to planned navigation. GCs have been suggested to compute the vector to a goal location from the current location (see Kubie and Fenton, 2012; Erdem and Hasselmo, 2012; Bush et al., 2015; Stemmler et al., 2015), a capability necessary to explain the ability to take a shortcut across previously unexplored territory (Tolman, 1948). We propose that this ability is based on mental (vector-based) navigation supported by GCs. In Simulation 5, we let the agent explore a novel part of the environment, extending a pre-existing representation of a spatial context. Simulation 5.0 consists of three distinct phases: planning movement across a previously unvisited area to a reward location (phase 1); actual navigation of this shortcut (phase 2); and finally mental navigation across the now familiar area (phase 3).

In phase 1, the agent generates a trajectory along the shortest path to the goal using GCs (i.e. a straight line where the barriers happened to be in the way, Figure 13B). However, unlike in Simulation 4.0 (Figure 12), this process differs from mental navigation since the unexplored part of the environment is devoid of any meaningful PC-BVC connections and so a scene cannot be generated in the parietal window (PWb). Extending the medial temporal lobe (MTL) representations requires incorporating additional place cells into the MTL attractor. These (future) place cells are referred to as ‘reservoir cells’ and have no relationship to physical space yet, so visualizing their firing rates in a topographic manner is not possible. However, as the agent generates a trajectory towards its goal using GCs, sparse random GC-to-PC connections cause a subset of the reservoir cells to fire (Figure 13B and Video 13). The activity of reservoir cells does not form an attractor bump, as PC-PC connections have not been learned, but their firing is normalised to a level of activity similar to when an attractor bump is present (implemented by an adaptive feedback current, see Appendix). In Figure 13B (rightmost panel) reservoir cells are ordered according to their time of maximum firing along the imagined trajectory.

Figure 13

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Video 12

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Video 13

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In phase 2, the barriers are removed and the agent performs the previously imagined trajectory in real space, using the novel shortcut. The same GCs are active along the trajectory and hence the same reservoir cells which fired before exploring the area, now fire in a spatial sequence along the actual trajectory. Since the agent is now actively perceiving its environment BVCs are driven in a bottom-up manner and Hebbian-like plasticity can strengthen connections between BVCs and reservoir cells as they fire along the trajectory (an analogous mechanism should also associate perirhinal neurons, which is omitted here). Hence, the reservoir cells have now effectively become place cells, with firing fields tied to the agent’s location in space (Figure 13C and Video 13). Figure 13C (rightmost panel) shows place cell activity along the trajectory during phase 2. Crucially, these cells are plotted in the order of activity shown during the previous imagined navigation (Figure 13B), indicating ‘pre-play-like’ behavior, in that the sequence of PC firing seen prior to first exploration is subsequently recapitulated during actual navigation (Figure 13C; Dragoi and Tonegawa, 2011; Ólafsdóttir et al., 2015).

Finally, in phase 3, the agent initiates imagery and performs mental navigation along the shortcut (i.e. recalls the episode of traversal), demonstrating that the MTL representation has been extended, and that a scene can be generated (Figure 13D and Video 13). The newly learned connections from reservoir PCs to BVCs complete the MTL representation of the spatial context and the transformation circuit reinstates the corresponding parietal window (PWb) representation (imagery, Figure 10D, panel 2).

The ability to plan a route by driving a sweep of PC activity with a sweep of GC activity via established GC-PC connections (Figures 12–13) could relate to the observation of ‘forward sweeps’ of PC activity during navigation (Johnson and Redish, 2007; Pfeiffer and Foster, 2015) and ‘replay’ during rest (Wilson and McNaughton, 1994; Foster and Wilson, 2006; Diba and Buzsáki, 2007; Karlsson and Frank, 2009; Carr et al., 2011). However, both of these phenomena, and the ‘pre-play-like’ activity discussed above, occur at compressed timescales in experimental animals. Thus, modeling forward sweeps, replay or pre-play would require a spiking neuron model able to capture the faster time scale of the sharp-wave ripple events associated with replay and pre-play, and the theta sequences associated with forward sweeps (Burgess et al., 1994; Skaggs et al., 1995; Gupta et al., 2012).

We propose a model of how sensory experiences, which are ultimately egocentric in nature, are transformed into viewpoint-invariant representations for long-term spatial memory in the medial temporal lobe (MTL) via processing in parietal and retrosplenial cortices. According to the model, imagery and recollection of scenes correspond to the re-construction of egocentric representations in parietal areas (the parietal window, PWb/o) from MTL representations. The MTL is the repository of viewpoint-invariant knowledge which is used to generate spatially coherent scenes by retrieving information consistent with perception from a single location and orientation. Pattern completion (via attractor dynamics) implements retrieval of a neural representation across the MTL, while head-direction cells enable the translation into egocentric coordinates via a retrosplenial transformation circuit, making use of gain-field neurons (Snyder et al., 1998; Galletti et al., 1995; Pouget and Sejnowski, 1997). Thus, for example, unilateral lesions in parietal regions could cause perceptual hemispatial neglect, and unilateral lesions to parietal or retrosplenial cortex could cause representational hemispatial neglect (in imagery) for a scene for which the MTL representation is complete (Bisiach and Luzzatti, 1978; see also Pouget and Sejnowski, 1997; Burgess et al., 2001a; Byrne et al., 2007).

The model can be used to account for human spatial cognition at the level of single neurons far from the sensory periphery: Place cells, head direction cells, gain-field neurons, boundary- and object-vector cells (BVCs and OVCs), and grid cells. Future work should try to integrate the present account of spatial cognition with recent progress concerning spatial coding in parietal areas (Nitz, 2006; Nitz, 2009; Nitz, 2012; Harvey et al., 2012; Whitlock et al., 2012; Raposo et al., 2014; Vedder et al., 2017), and a broader view of retrosplenial function (e.g., Alexander and Nitz, 2015; Alexander and Nitz, 2017). Notably, BVCs were predicted by an early predecessor of the present model (Hartley et al., 2000; Burgess et al., 2001a). Here, we have introduced OVCs to show how items introduced into a familiar environment may be coded for and incorporated into long-term memory. Intriguingly, OVC-like responses have been reported recently (Deshmukh and Knierim, 2013; Hoydal et al., 2017). We also explored how long-term memory might be probed to assess novelty. Finally, we incorporated grid cells and investigated their role in exploratory behavior and mental navigation. We can thus begin to frame abstract notions such as episodic future thinking and scene construction in terms of neural mechanisms, although we note that these concepts extend beyond our model to include completely fictional scenes/scenarios (Burgess et al., 2001a; Hassabis et al., 2007; Schacter et al., 2007).

Matlab code to build all model components and run all simulations will be made available on GitHub in the following repository: https://github.com/bicanski/HBPcollab/tree/master/SpatialEpisodicMemoryModel; copy archived at https://github.com/elifesciences-publications/HBPcollab/tree/master/SpatialEpisodicMemoryModel.

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Author details

1. Andrej Bicanski

   Institute of Cognitive Neuroscience, University College London, London, United Kingdom

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   a.bicanski@ucl.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3356-1034

2. Neil Burgess

   Institute of Cognitive Neuroscience, University College London, London, United Kingdom

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Project administration, Writing—review and editing

   For correspondence

   n.burgess@ucl.ac.uk

   Competing interests

   Reviewing Editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0003-0646-6584

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