A time-stamp mechanism may provide temporal information necessary for egocentric to allocentric spatial transformations

Finding their way around is an essential part of survival for many animals and helps them to locate food, mates and shelter. Animals have evolved the ability to form a 'map' or representation of their surroundings. For example, the electric fish Apteronotus leptorhynchus, is able to precisely learn the location of food and navigate there. It can do this in complete darkness by generating a weak electric field. As it swims, every object it encounters generates an ‘electric image’ that is detected on the skin and processed in the brain.

However, all the cues the fish comes across are from its own point of view – the information about its environment is processed with respect to its location. And yet, the map that it generates needs to be independent of the fish’s position – it has to work regardless of where the animal is. The way animals translate ‘self-centered’ experiences to form a general representation of their surroundings is not yet fully understood.

Now, Wallach et al. studied how internal brain maps are generated in A. leptorhynchus. Information about the fish's environment passes through a structure in the brain called the preglomerular complex. Measuring the activity of this region revealed that the preglomerular complex does not process much self-centered information. Instead, whenever the fish passed any object – regardless of where it was in relation to the fish – the event triggered a brief burst of preglomerular activity. The intensity of the activity depended on how recently the fish had encountered another object. This information, combined with the dynamics of the fish's movement, could be what allows the fish to convert a sequence of encounters into a general spatial map.

These findings could help to inform research on learning and navigation. Further research could also reveal whether other species, including humans, generate their mental maps in a similar way. This may be relevant for people suffering from diseases such as Alzheimer’s, in which a sense of orientation has become impaired.

Learning to navigate within the spatial organization of different habitats is essential for animals’ survival (Geva-Sagiv et al., 2015). Electric fish, for example, occupied a lucrative ecological niche by evolving the ability to navigate and localize food sources in complete darkness using short-range electrosensation (Jun et al., 2016). The spatial acuity that they exhibit, along with their reliance on learned landmark positions, strongly suggest that they memorize the relative arrangement of the landmarks and the environmental borders. The information animals use to generate such allocentric knowledge include sensory experiences collected during object encounters (Jun et al., 2016; Petreanu et al., 2012; Save et al., 1998) and motor actions (heading changes and distance traveled) executed between such encounters; utilization of these motor variables in spatial learning and navigation is termed path integration (Collett and Graham, 2004; Etienne and Jeffery, 2004). This acquired information, however, is always egocentric in nature. Fittingly, the primary brain regions dedicated to sensory and motor processing, such as the optic tectum (OT) of all vertebrates and many cortical regions in mammals are topographically organized along an egocentric coordinate system (Knudsen, 1982; Sparks and Nelson, 1987; Stein, 1992). Unravelling the neural operations underlying the transformation of egocentric sensory and motor information streams into an allocentric representation of the environment has been a central theme in studies of spatial learning and navigation. Recent studies in the mouse (Peyrache et al., 2017) have suggested that the key computations include vestibular input that defines the animal’s head direction (head direction cells, egocentric) and external sensory input that signals the presence of stable environmental features (i.e., landmarks). Linking the head directions that orient the animal to different environmental features are then hypothesized to generate an allocentric representation of those features. The neural circuits that have been hypothesized to implement these computations are, however, exceedingly complicated and include thalamic (head direction) and cortical (external sensory) input to the hippocampal formation. The proposed wiring diagrams are highly speculative and very far from providing a well-defined mechanistic model of how spatial maps are created.

Equivalent computations appear to be carried out in Drosophila (Seelig and Jayaraman, 2015). Visual orientation to landmarks and body direction via path integration are combined in the ellipsoid body with dynamics suggestive of a ring attractor. While these studies in the simpler nervous system of the fly are now closer to providing a mechanistic explanation of how egocentric and external (visual) inputs are combined, it is not clear if the fly has a full representation of the allocentric relations of different environmental features. It is also not at all clear that the dynamics of the ellipsoid body can be mapped onto the cortical and hippocampal circuitry of mammals.

Teleost fish offer an attractive model for studying this question, as their related brain circuitry is relatively tractable: lesion studies point to the dorsolateral pallium (DL) as the key telencephalic region required for allocentric spatial learning (Broglio et al., 2010; Durán et al., 2010; Rodríguez et al., 2002), similarly to the medial cortex in reptiles and the hippocampus in mammals (see Discussion). DL has strong excitatory recurrent connectivity (Elliott et al., 2017; Giassi et al., 2012b). Importantly, DL receives sensory and motor information related to electrosensory and visual object motion from OT (Bastian, 1982) via a single structure – the diencephalic preglomerular complex (PG, Giassi et al., 2012b, Figure 1A). The tectal recipient portion of PG projects solely to DL (Giassi et al., 2012a) in agreement with the lesion studies. Importantly, PG receives very little feedback from areas associated with DL (Giassi et al., 2012b) and therefore functions as an exclusive feed-forward bottleneck between OT and the pallium. DL in turn projects to the central pallium (DC, Giassi et al., 2012b); DL also has reciprocal connections with the dorsal pallium (DD) and DD itself has strong recurrent connectivity. DC is the only route by which DL can control motor activity and it does so solely via its projections to the OT (Giassi et al., 2012b). We hypothesize that egocentric object-related information (OT) conveyed by PG to DL, is converted to a learned allocentric spatial map by the recurrent circuitry of DL, DD and DC; DC, in turn, then controls the fish’s spatial behavior via its projections to OT.

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In what follows we describe the first electrophysiological recordings conducted in PG of any fish species. PG has been considered part of the fish thalamus, based on simple anatomical criteria (Giassi et al., 2012a; Ishikawa et al., 2007; Mueller, 2012). Our recordings provided an additional functional correspondence in that PG cells emit rapid spike bursts likely mediated by the T-type Ca²⁺ channels (Figure 1B,C and Figure 1—figure supplement 1) characteristic of the OT targets in thalamic regions of other vertebrates (Ramcharan et al., 2005; Reches and Gutfreund, 2009). In this contribution, we show a radical conversion of the topographic spatial representation in OT into a reliable non-topographic temporal representation of encounter sequences. We then use a computational model to demonstrate that this temporal information is readily accessible for decoding and that it is sufficiently accurate to account for spatial precision during naturalistic behavior (Jun et al., 2016).

We characterized the responses of 84 electrosensory PG cells of the weakly electric fish Apteronotus leptorhynchus to moving objects; several motion protocols were used and the sample size for each protocol is mentioned in context (Figure 1—figure supplement 2). Neuronal activity was recorded extracellularly (Figure 1—figure supplement 3) in immobilized fish while objects (brass or plastic spheres) were moved relative to the skin using a linear motor (Methods). Cells responding to this stimulation were predominantly found in the lateral nucleus of the PG complex, PGl (Figure 1—figure supplement 4).

Topographic spatial information is abolished in PG

We first examined the spatial representation in PG cells by measuring their receptive fields (RFs; measured in 27 cells). The OT electrosensory cells driving PG have spatially-restricted, topographically organized RFs (Bastian, 1982), and thus provide labeled-line information on the egocentric position of objects. In PG, by contrast, only 11% of the cells (3/27) were topographic with a spatially restricted RF (Figure 2A); the majority of PG cells (89%, 24/27) responded across most or all of the fish’s body (Figure 2B and Figure 2—figure supplement 1). Therefore, PG activity does not convey a topographic ‘labeled-line’ code of object position. We also checked whether object location is encoded by the firing-rate of PG neurons (i.e., a rate code). The firing-rate was significantly correlated with object position only in one non-topographic cell (4%, 1/24 neurons; p < 0.05, random-permutations test, Figure 2C). Similarly, mutual information between object position and firing-rate was significant only in two non-topographic cells (8%, 2/24 neurons; p < 0.05, random-permutations test, Figure 2D). Therefore, almost all PG cells have whole-body RFs and lack topographic spatial information– the hallmark of all electrosensory regions from the sensory periphery up to OT. We attempted to systematically sample throughout the full extent of PG. However, we cannot absolutely determine whether the subset of topographic cells represent a small distinct sub-nucleus or are sparsely distributed throughout the PG complex.

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PG cells respond to object encounters

Next, we checked what information PG neurons convey about object motion. OT cells, which drive PG, respond to an object moved parallel to the fish (longitudinal motion) while the object traverses their RFs (Bastian, 1982). Only a minority of recorded PG units (26%, 7 out of 27 tested with longitudinal motion) responded in this manner (Figure 3A). Rather, the majority of PG units (78%, 20/27) exhibited a strikingly different behavior, emitting a brief burst response confined to the onset (and sometimes to the offset) of object motion, but not during motion itself (Figure 3B). This is further demonstrated when motion in each direction was broken into four segments separated by wait periods (Figure 3C), evoking responses at the onset (yellow arrowheads) and offset (red arrows) of each segment across the entire body. Interestingly, we have encountered several lateral-line responsive PG units that, unlike most of their electrosensory counterparts, did respond persistently throughout (and even after) object motion (Figure 3—figure supplement 1).

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We next applied transverse motion, which mimics an object looming/receding (incoming/outgoing) into/from the electrosensory receptive field (tested in 40 cells). Three types of responses to such motion were identified: proximity detection, encounter detection, and motion-change detection; 50% (20/40) displayed more than one type of response. Proximity detectors (75%, 30/40) responded when an object was encountered very close to the skin (< 2 cm, Figure 3D); encounter detectors (32%, 13/40) responded when an object either entered to or departed from their electroreceptive range (~4 cm, Figure 3E); lastly, motion-change detectors (57.5%, 32/40) displayed a response similar to that observed in longitudinal motion, firing at the onset/offset of motion (i.e., when the object accelerated/decelerated, Figure 3F); remarkably, this type of response was relatively distance-invariant, yielding comparable responses both very close to (0.5 cm) and very far from (5.5 cm) the skin despite the drastic effects of distance on both the magnitude and spread of the object’s electrical image (Figure 2—figure supplement 1, see Chen et al., 2005). This discrete, nearly stereotypic response stands in contrast to the finely-tuned rate code of object distance previously reported in the primary electrosensory cells in ELL (Clarke et al., 2014; Clarke and Maler, 2017). Taken together, the variety of PG response-types mentioned above may constitute a distributed representation of object proximity. Unlike the loss of egocentric topographic mapping discussed in the previous section, this representation does provide DL with coarse-grained, non-directional egocentric information. The possible role(s) of this information was not further considered in our analyses.

We conclude that PG electrosensory cells predominantly respond to novelty: onset/offset of object motion within their receptive field or the introduction/removal of objects into/from this receptive field; we use the term object encounters to designate all such events. Most PG cells responded both to conductive and non-conductive objects (Figure 4) and would therefore not discriminate between different object types, for example, plants versus rocks. We can, therefore, infer that during active exploration of the environment, PG reports to the dorsal pallium whenever the fish encounters or leaves a prey or a landmark (e.g., root mass or rock) or alters its swimming trajectory near a landmark.

Figure 4

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PG cells display history-independent, spatially non-specific adaptation

While topographic egocentric information was scarce in PG, temporal information was prevalent. Many of the PG cells exhibited pronounced adaptation to repeated motion (45%, 15/33 neurons tested with repeated-motion protocol; Figure 5—figure supplement 1). We delivered a sequence of object encounters (motions in and out of the RF, Figure 5A); time-intervals between sequential encounters were drawn randomly and independently (in the range of 1–30 s). The response intensity (number of spikes within an individually determined time window) of these adapting cells to each encounter was strongly correlated with the time-interval immediately prior to that encounter (Figure 5B). By contrast, there was no significant correlation with intervals prior to the last one (inset of Figure 5B and Figure 5C). Thus, a large subset of PG cells encoded the duration of the time-interval preceding the last encounter – but did not convey information about the intervals prior to that. We term this history-independent adaptation. Interestingly, similar behavior was also found in visually-responsive cells (ventral PG, Figure 5—figure supplement 2). This result contrasts with many studies in the mammalian cortex, where adaptation is incremental and responses depend on multiple preceding intervals (Lampl and Katz, 2017; Ulanovsky et al., 2004). Moreover, a spatial ‘oddball’ experiment (Methods), which we conducted on 14 neurons (6 of which were adapting) revealed that this adaptation is also spatially non-specific – that is, encounters at one body location adapt the response to encounters at all other locations (Figure 3D–F). Therefore, this thalamic adaptation mechanism enables neurons to encode the time between the two most recent successive stimuli, without contamination by prior encounter history and irrespective of the objects’ egocentric position.

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PG cells convey readily accessible temporal information

Can the sequence of time intervals between encounters be accurately decoded from the activity of the adapting PG cells? To answer this question, we first constructed a simple model to describe the cells’ response dynamics. This model assumes each cell’s responsiveness is governed by a resource variable $x$ which is depleted following each encounter and recovers exponentially between encounters (Tsodyks and Markram, 1997). A parameter $\beta$ indicates the fraction of the resource remaining after depletion, while a time-constant $\tau$ sets the speed of recovery. The resource variable $x$ is converted into a firing rate variable $\lambda$ using static rectification with a gain parameter a and baseline activity parameter c. Finally, each encounter generates a spike count according to a Poisson distribution with the current value of the rate parameter $\lambda$ (Figure 6A). The parameter $\beta$ determines the extent to which past intervals in the sequence affect the current state (Figure 6B). For instance, $\beta$=0 signifies complete exhaustion of the resource at each and every encounter. For such a cell, therefore, the firing rate increases monotonically as a function of the last time interval (with the dependence taking the form of a saturating exponential function) regardless of past intervals. In other words, $\beta =0$ indicates a completely history-independent cell, as defined above. As $\beta$ approaches unity the memory of past intervals becomes more dominant, for example, a succession of short intervals will yield progressively weaker responses.

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All 15 adapting cells had statistically significant correlations between the responses and the fitted rate parameter ${\displaystyle \{T_n\}}$ (p < 0.05, random permutations, see Figure 6—figure supplement 1A, B). Consistent with the results in the previous section, most adapting cells had an extremely low value of $\beta$ (see parameter distributions in Figure 6—figure supplement 1); 33% of the cells (5/15) were best fitted with $\beta$ = 0 (see example in Figure 5B), the median $\beta$ was 0.12 and only 13% (2/15) had ${\displaystyle \beta >0.5}$. Hence, most cells were indeed predominantly affected only by the very last time interval. The fitted recovery time-scales were in the range 2.6-25.3s (see Figure 6—figure supplement 1C). Note, however, that this largely reflects the range explored with our stimulation protocol (1-30s intervals); it is quite probable that PG contains faster cells (i.e., with ${\displaystyle \tau <1s}$) that appear to be ‘non-adapting’ under this protocol, as well as slower cells (i.e., with ${\displaystyle \tau >30s}$) that quickly cease responding and were therefore not recorded from.

Using this model, we simulated the response of a population of adapting PG cells to random interval sequences. A Maximum-Likelihood Estimator (MLE, see Materials and methods) was used to decode the most recent interval from the population response to each encounter. To demonstrate this approach, we used a homogeneous population of identical memoryless neurons ($\beta =0)$. At intervals shorter than the cells’ adaptation time-constant $\tau$ the MLE was approximately unbiased (Figure 6C) and saturated the Cramér-Rao lower error bound (CRLB, Figure 6D). The error increased with the decoded time interval T and baseline spontaneous activity c and decreased with population size N and response gain a (Figure 6E-G). Finally, we checked the effect of non-zero adaptation memory (${\displaystyle \beta >0}$) while still using the same memoryless MLE decoder (constructed by fitting a memoryless model to the simulated responses). The estimation error and bias were nearly unchanged up to $\beta =0.2$ (Figure 6H). We conclude that the response of the majority of PG adapting cells to an encounter can be used to estimate the time interval elapsed prior to that encounter, using a simple, memoryless decoder.

It is important to note that the population model mentioned above assumes that the responses of individual cells are statistically independent given the interval sequence. This assumption may not hold in certain scenarios, such as the existence of a latent state variable (e.g. arousal) modulating the overall population responsiveness. Such correlations across the population, if not taken into account in the decoding algorithm, would degrade the estimation accuracy. One possible solution to this could be based on the population of non-adapting cells (55%, 18/33) which, by definition, are not significantly affected by the temporal pattern of stimulation but might be affected by such global modulations. Thus, this population may convey sufficient information to enable estimation of such confounding variables and correct the temporal estimation accordingly.

PG activity corresponds to observed path integration acuity

Can PG activity be used to explain features of spatial behavior in freely-swimming electric fish? To check this possibility, we must first measure the time-intervals being memorized by fish conducting a spatial learning task, as well as the error in the fish’s estimation of these intervals. To this end we used previously published data from spatial learning experiments conducted in our lab (Jun et al., 2016). In these experiments fish were trained to find food in a specific location in complete darkness. This was performed either with or without the aid of landmarks. Since only the short-range electrosense was available to the fish, they had to use path-integration from the encountered objects to the food location. In other words, the fish had to memorize the intervals/distances between these encounters in order to improve its behavioral performance and find the food more efficiently. Therefore, we measured the time-interval and the distance traveled by the trained fish from the last encounter with an object (tank wall or landmark) to the food in each trial, either with (Figure 7A) or without landmarks (Figure 7B). As one might expect, these intervals were longer in the absence of landmarks (Figure 7C).

Figure 7

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Next, in order to estimate the fish’s temporal accuracy, we randomly performed ‘probe’ trials in which no food was present in the arena. In these trials the fish vigorously searched for the missing food around its estimated position. We measured the distance between the center of the searched area and the designated food location to obtain the fish’s spatial error (Figure 7D, with landmarks; Figure 7E, without landmarks). This error increased in the absence of landmarks as well (Figure 7F). Dividing this error by the median velocity in each trial yielded the temporal error, that is the error in the fish’s estimation of the time elapsed between object encounters and the estimated food location (Figure 7F, inset). Thus, this behavioral analysis yielded the relation between the memorized time-intervals and the estimation error of this variable in two different scenarios.

PG is the only source of sensory information for the dorsolateral pallium (DL), the likely site of spatial memory (Rodriguez et al., 2002). Therefore, we hypothesized that the history-independent adapting PG cells provide DL with one necessary component for path integration: the temporal sequence of object encounters (the two other components are heading-direction and linear velocity). How many adapting PG cells are required to achieve the behavioral temporal acuity observed as described above? We constructed a heterogeneous population model using the empirically obtained parameters ($\beta$ was set to 0 for all neurons to simplify the simulations). This model was then stimulated at random time-intervals, which were then decoded from the population response using MLE. This estimation was approximately unbiased across the entire range tested (Figure 8A). We compared the simulated estimation error, as well as the analytically computed CRLB for the heterogeneous population, to the behavioral temporal results obtained with and without landmarks (Figure 8B). We also performed the comparison in spatial terms by using the fishes’ average velocity to convert the model’s results into units of distance (Figure 8C). The simulated PG population yielded temporal and spatial estimation errors comparable to those displayed in behavior (boxplots in Figure 8B, C), both with and without landmarks, using only ~500 adapting cells. The lateral subdivision of PG (PGl), in which most motion-responsive cells were found, contains about 60,000 cells (Trinh et al., 2016). Based on our data, we can estimate that over 9,000 of these are memoryless adapting cells (a conservative estimate using only strictly history-independent cells with $\beta =0$, 5/33 or 15%). Thus, we hypothesize that the number of PGl cells is sufficient to attain the observed behavioral precision, even when additional encoding errors (e.g. in heading and velocity estimation) are taken into account. Taken together, our simulations suggest that time-interval encoding in PG can consistently account for the observed behavioral precision of spatial learning. It should be noted that the validity of this computational analysis relies on our (admittedly simple) model correctly capturing the neuronal response dynamics. Finer details, such as the inter-dependency between the model’s various parameters, were not taken into account in this study. However, it seems reasonable to suggest that the plentitude of PGl cells provides a large margin of error to accommodate such extensions.

Our results suggest the following space-to-time transformation scheme: PG derives a sequence of discrete novelty events (encounters) from OT activity. The remarkable history-independent adaptation process provides an accessible, accurate and unbiased representation of the time intervals between encounters. We have found visually-responsive PG cells displaying similar adaptation features (Figure 5—figure supplement 2), suggesting that this mechanism is implemented across multiple sensory modalities. The elimination of egocentric topographic information in PG – both in the response itself and in its adaptation – ensures that the encoding of time is invariant to the specific body part encountering the object. This temporal information is then transmitted to DL, which can use it to integrate the fish’s swim velocity to obtain distance-traveled, a key allocentric variable. For fish, the necessary velocity information may be provided by the lateral-line system (Chagnaud et al., 2007; Oteiza et al., 2017); several lateral-line responsive PG units were encountered in our recordings (Figure 3—figure supplement 1). Finally, DL can combine the distance information with instantaneous heading-direction (vestibular system, Straka and Baker, 2013; Yoder and Taube, 2014) to yield the animal’s allocentric spatial position (Etienne and Jeffery, 2004). A recent study in zebrafish suggests that DL neurons can indeed process temporal information on the long time-scales discussed here (Cheng et al., 2014). Our computational analysis demonstrates that the PG temporal information is sufficient to account for the spatial acuity displayed in behavioral studies of gymnotiform fish utilizing electrosensory information alone (Figure 8).

Figure 8

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This space-to-time mechanism may shed light on the primitive basis of egocentric-to-allocentric transformations. Short-range sensing, used by ancestor species living in low-visibility environments, necessitated the perception of space through temporal sequences of object encounters. With the evolution of long-range sensory systems such as diurnal vision (MacIver et al., 2017), simultaneous apprehension of the spatial relations of environmental features became possible. The neural mechanisms implementing sequential (space-to-time) spatial inference and simultaneous spatial inference presumably both exist in mammals, for example, we can acquire a map of relative object locations by looking at a scene from afar, or by walking and sequentially encountering landmarks with our eyes closed. Whether the sequential or the simultaneous spatial-inference is more dominant may depend on the species (e.g., nocturnal or diurnal) and on context (e.g., open field or underground burrows). However, it is not clear whether sequentially versus simultaneously-acquired spatial knowledge is processed in a common circuit. Indeed, clinical case studies on the regaining of eyesight in blind humans indicate that sequential and simultaneous spatial perceptions are fundamentally different, and may therefore involve two distinct computations and neuronal pathways (Sacks, 1995). The population of thalamic neurons that we discovered may provide an essential component underlying one of these two major computations – the encoding of sequential temporal information – and we hypothesize that such neurons underlie sequential spatial learning in all vertebrates.

There is substantial evidence indicating that the pathway studied here indeed has parallels in other vertebrates, and specifically in mammals. PG’s homology to posterior thalamic nuclei is supported by previously published anatomical and developmental findings (Giassi et al., 2012a; Ishikawa et al., 2007; Mueller, 2012), as well as by physiological (Figure 1B,C) and molecular (Figure 1—figure supplement 1) results presented here. The thalamic pulvinar nucleus is particularly similar to PG in that it receives direct tectal input (Berman and Wurtz, 2011). Its involvement in visual attention and saliency in primates (Robinson and Petersen, 1992) corresponds to PG’s involvement in novelty detection (Figure 2). Moreover, pulvinar lesions are associated with saccadic abnormalities and deficits in the perception of complex visual scenes (Arend et al., 2008), suggesting a link to the sequential mode of spatial learning. Komura et al. (2001) demonstrated that posterior thalamic regions (including the rodent equivalent of the pulvinar) can implement interval timing computations over long time-scales (>>1 s); however, the mechanistic basis for these computations has not been identified (Simen et al., 2011) and potential contributions to path integration have not been explicated. A recent paper (Paton and Buonomano, 2018) reviewed models of temporal encoding based on recurrent neural networks. Further studies will be required to determine whether the novel adaptation encoding mechanism in PG engages the downstream recurrent networks of DD and DL to produce refined estimates of the time interval between salient sensory and/or motor events. Finally, a recent study in rodents demonstrated spatially non-specific adaptation in VPM (Jubran et al., 2016), a posterior thalamic nucleus responding to vibrissal object encounters (Yu et al., 2006). Taken together, we hypothesize that thalamic space-to-time mechanisms akin to those presented here play an important role in mammalian sequential spatial learning, especially in nocturnal animals relying on sparse sensory cues (Save et al., 1998).

The telencephalic target of PG, DL, resembles the mammalian hippocampus not only in function, as revealed in lesion studies (Rodríguez et al., 2002), but also in development, gross circuitry and gene expression (Elliott et al., 2017). The role of the hippocampus in spatial learning and navigation is well established, and hippocampal neural correlates of allocentric spatial variables have been exquisitely described (Barry and Burgess, 2014; Buzsáki and Moser, 2013). There is also evidence for the importance of time coding in the mammalian hippocampus: ‘Time cells’ responsive to elapsed time have been reported and, in some cases, these cells also respond at specific spatial loci (Eichenbaum, 2014). Furthermore, a recent study on the representation of goals in the hippocampus found cells encoding the length/duration of the traveled path (Sarel et al., 2017). The mechanism we have found may therefore contribute to creating temporal coding in the hippocampus, not just in the context of egocentric-to-allocentric transformations but rather whenever expectations associated with specific time intervals need to be generated. It should be noted, however, that unlike DL’s direct thalamic input via the PG bottleneck, the hippocampus receives sensory and motor information primarily via the cortex. Furthermore, multiple bi-directional pathways connect the mammalian sensory and motor cortical regions with the hippocampal network. Pinpointing the exact loci where egocentric-to-allocentric transformations may take place in the mammalian brain is therefore extremely challenging. We propose that this transformation is initiated in the mammalian thalamus where history-independent adaptation also encodes time between encounter events. Finally, we propose that this thalamic output contributes to the generation of an allocentric spatial representation in the mammalian hippocampus.

In this contribution, we propose a hypothesis about how gymnotiform fish, and perhaps vertebrates in general, generate their representation of position relative to the environment. Future experiments could test the predictions entailed by this hypothesis. Behaviorally, our model implies that the fish's sense of position is critically dependent on its last encounter with an object. Further behavioral studies of spatial learning could elucidate this relationship, for example, by manipulating the objects' arrangement relative to the navigation target. Combining these studies with chronic recordings of PG and its pallial targets in freely navigating fish will permit testing of our proposed space-to-time neural transformation scheme.

Datasets and analysis files have been deposited in Columbia University's Academic Commons repository (https://doi.org/10.7916/D86Q3F7S).

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Author details

1. Avner Wallach

   1. Department of Physics, University of Ottawa, Ottawa, Canada
   2. Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, Canada

   Present address

   The Zuckerman Institute, Columbia University, New York, United States

   Contribution

   Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing, Performed the electrophysiological experiments, data analysis and modeling

   For correspondence

   aw3057@columbia.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-2345-2942

2. Erik Harvey-Girard

   Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, Canada

   Contribution

   Investigation, Writing—review and editing, Performed PCR experiments

   Competing interests

   No competing interests declared

3. James Jaeyoon Jun

   Department of Physics, University of Ottawa, Ottawa, Canada

   Present address

   Center for Computational Mathematics, Flatiron Institute, New York, United States

   Contribution

   Data curation, Writing—review and editing, Performed behavioral experiments

   Competing interests

   No competing interests declared

4. André Longtin

   1. Department of Physics, University of Ottawa, Ottawa, Canada
   2. Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, Canada
   3. Center for Neural Dynamics, Mind and Brain Research Institute, University of Ottawa, Ottawa, Canada

   Contribution

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

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0678-9893

5. Len Maler

   1. Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, Canada
   2. Center for Neural Dynamics, Mind and Brain Research Institute, University of Ottawa, Ottawa, Canada

   Contribution

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

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-7666-2754

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