Robust path integration in the entorhinal grid cell system with hippocampal feed-back

The chicken and egg problem of grid cells and place cells

Place cells and grid cells are major building blocks of the hippocampal cognitive map. The prominent forward model postulates that grid-cell modules are generated by a continuous attractor network; that a velocity signal evoked during locomotion moves entorhinal activity bumps; and that place-cell activity constitutes summation of entorhinal grid-cell modules. Experimental data support the first postulate, but not the latter two. Several families of solutions that depart from these postulates have been put forward. We suggest a modified model (spatial modulation continuous attractor network; SCAN), whereby place cells are generated from spatially selective nongrid cells. Locomotion causes these cells to move the hippocampal activity bump, leading to movement of the entorhinal manifolds. Such inversion accords with the shift of hippocampal thought from navigation to more abstract functions.

The grid code for ordered experience

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

The Neuroscience of Spatial Navigation and the Relationship to Artificial Intelligence

Recent advances in artificial intelligence (AI) and neuroscience are impressive. In AI, this includes the development of computer programs that can beat a grandmaster at GO or outperform human radiologists at cancer detection. A great deal of these technological developments are directly related to progress in artificial neural networks-initially inspired by our knowledge about how the brain carries out computation. In parallel, neuroscience has also experienced significant advances in understanding the brain. For example, in the field of spatial navigation, knowledge about the mechanisms and brain regions involved in neural computations of cognitive maps-an internal representation of space-recently received the Nobel Prize in medicine. Much of the recent progress in neuroscience has partly been due to the development of technology used to record from very large populations of neurons in multiple regions of the brain with exquisite temporal and spatial resolution in behaving animals. With the advent of the vast quantities of data that these techniques allow us to collect there has been an increased interest in the intersection between AI and neuroscience, many of these intersections involve using AI as a novel tool to explore and analyze these large data sets. However, given the common initial motivation point-to understand the brain-these disciplines could be more strongly linked. Currently much of this potential synergy is not being realized. We propose that spatial navigation is an excellent area in which these two disciplines can converge to help advance what we know about the brain. In this review, we first summarize progress in the neuroscience of spatial navigation and reinforcement learning. We then turn our attention to discuss how spatial navigation has been modeled using descriptive, mechanistic, and normative approaches and the use of AI in such models. Next, we discuss how AI can advance neuroscience, how neuroscience can advance AI, and the limitations of these approaches. We finally conclude by highlighting promising lines of research in which spatial navigation can be the point of intersection between neuroscience and AI and how this can contribute to the advancement of the understanding of intelligent behavior.

An On-chip Spiking Neural Network for Estimation of the Head Pose of the iCub Robot

In this work, we present a neuromorphic architecture for head pose estimation and scene representation for the humanoid iCub robot. The spiking neuronal network is fully realized in Intel's neuromorphic research chip, Loihi, and precisely integrates the issued motor commands to estimate the iCub's head pose in a neuronal path-integration process. The neuromorphic vision system of the iCub is used to correct for drift in the pose estimation. Positions of objects in front of the robot are memorized using on-chip synaptic plasticity. We present real-time robotic experiments using 2 degrees of freedom (DoF) of the robot's head and show precise path integration, visual reset, and object position learning on-chip. We discuss the requirements for integrating the robotic system and neuromorphic hardware with current technologies.

Robust and efficient coding with grid cells

The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size. Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach to derive the grid parameters that maximise the coding range in the presence of noise. We derive an analytic upper bound on the coding range and provide examples for grid scales that achieve this bound and hence are optimal for encoding in unbounded environments. We show that in the absence of neuronal noise, the capacity of the system is extremely sensitive to the choice of the grid periods. However, when the accuracy of the representation is limited by neuronal noise, the capacity quickly becomes more robust against the choice of grid scales as the number of modules increases. Importantly, we found that the capacity of the system is near optimal even for random scale choices already for a realistic number of grid modules. Our study demonstrates that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies. Moreover, we suggest that having multiple grid modules in the entorhinal cortex is not only required for the exponentially large coding capacity, but is also a prerequisite for the robustness of the system.

Place and Grid Cells in a Loop: Implications for Memory Function and Spatial Coding

Place cells in the hippocampus and grid cells in the medial entorhinal cortex have different codes for space. However, how one code relates to the other is ill understood. Based on the anatomy of the entorhinal-hippocampal circuitry, we constructed a model of place and grid cells organized in a loop to investigate their mutual influence in the establishment of their codes for space. Using computer simulations, we first replicated experiments in rats that measured place and grid cell activity in different environments, and then assessed which features of the model account for different phenomena observed in neurophysiological data, such as pattern completion and pattern separation, global and rate remapping of place cells, and realignment of grid cells. We found that (1) the interaction between grid and place cells converges quickly; (2) the spatial code of place cells does not require, but is altered by, grid cell input; (3) plasticity in sensory inputs to place cells is key for pattern completion but not pattern separation; (4) grid realignment can be explained in terms of place cell remapping as opposed to the other way around; (5) the switch between global and rate remapping is self-organized; and (6) grid cell input to place cells helps stabilize their code under noisy and/or inconsistent sensory input. We conclude that the hippocampus-entorhinal circuit uses the mutual interaction of place and grid cells to encode the surrounding environment and propose a theory on how such interdependence underlies the formation and use of the cognitive map.SIGNIFICANCE STATEMENT The mammalian brain implements a positional system with two key pieces: place and grid cells. To gain insight into the dynamics of place and grid cell interaction, we built a computational model with the two cell types organized in a loop. The proposed model accounts for differences in how place and grid cells represent different environments and provides a new interpretation in which place and grid cells mutually interact to form a coupled code for space.

Environmental boundaries as a mechanism for correcting and anchoring spatial maps

Ubiquitous throughout the animal kingdom, path integration-based navigation allows an animal to take a circuitous route out from a home base and using only self-motion cues, calculate a direct vector back. Despite variation in an animal's running speed and direction, medial entorhinal grid cells fire in repeating place-specific locations, pointing to the medial entorhinal circuit as a potential neural substrate for path integration-based spatial navigation. Supporting this idea, grid cells appear to provide an environment-independent metric representation of the animal's location in space and preserve their periodic firing structure even in complete darkness. However, a series of recent experiments indicate that spatially responsive medial entorhinal neurons depend on environmental cues in a more complex manner than previously proposed. While multiple types of landmarks may influence entorhinal spatial codes, environmental boundaries have emerged as salient landmarks that both correct error in entorhinal grid cells and bind internal spatial representations to the geometry of the external spatial world. The influence of boundaries on error correction and grid symmetry points to medial entorhinal border cells, which fire at a high rate only near environmental boundaries, as a potential neural substrate for landmark-driven control of spatial codes. The influence of border cells on other entorhinal cell populations, such as grid cells, could depend on plasticity, raising the possibility that experience plays a critical role in determining how external cues influence internal spatial representations.

Environmental boundaries as an error correction mechanism for grid cells

Medial entorhinal grid cells fire in periodic, hexagonally patterned locations and are proposed to support path-integration-based navigation. The recursive nature of path integration results in accumulating error and, without a corrective mechanism, a breakdown in the calculation of location. The observed long-term stability of grid patterns necessitates that the system either performs highly precise internal path integration or implements an external landmark-based error correction mechanism. To distinguish these possibilities, we examined grid cells in behaving rodents as they made long trajectories across an open arena. We found that error accumulates relative to time and distance traveled since the animal last encountered a boundary. This error reflects coherent drift in the grid pattern. Further, interactions with boundaries yield direction-dependent error correction, suggesting that border cells serve as a neural substrate for error correction. These observations, combined with simulations of an attractor network grid cell model, demonstrate that landmarks are crucial to grid stability.

Bayesian integration of information in hippocampal place cells

Accurate spatial localization requires a mechanism that corrects for errors, which might arise from inaccurate sensory information or neuronal noise. In this paper, we propose that Hippocampal place cells might implement such an error correction mechanism by integrating different sources of information in an approximately Bayes-optimal fashion. We compare the predictions of our model with physiological data from rats. Our results suggest that useful predictions regarding the firing fields of place cells can be made based on a single underlying principle, Bayesian cue integration, and that such predictions are possible using a remarkably small number of model parameters.

Spatial coding and attractor dynamics of grid cells in the entorhinal cortex

Recent experiments support the theoretical hypothesis that recurrent connectivity plays a central role within the medial entorhinal cortex, by shaping activity of large neural populations, such that their joint activity lies within a continuous attractor. This conjecture involves dynamics within each population (module) of cells that share the same grid spacing. In addition, recent theoretical works raise a hypothesis that, taken together, grid cells from all modules maintain a sophisticated representation of position with uniquely large dynamical range, when compared with other known neural codes in the brain. To maintain such a code, activity in different modules must be coupled, within the entorhinal cortex or through the hippocampus.

Grid alignment in entorhinal cortex

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show mutually aligned grid patterns. Recent experimental findings have shown that grids can often be better described as elliptical rather than purely circular and that, beyond the mutual alignment of their grid axes, ellipses tend to also orient their long axis along preferred directions. Are grid alignment and ellipse orientation aspects of the same phenomenon? Does the grid alignment result from single-unit mechanisms or does it require network interactions? We address these issues by refining a single-unit adaptation model of grid formation, to describe specifically the spontaneous emergence of conjunctive grid-by-head-direction cells in layers III, V, and VI of mEC. We find that tight alignment can be produced by recurrent collateral interactions, but this requires head-direction (HD) modulation. Through a competitive learning process driven by spatial inputs, grid fields then form already aligned, and with randomly distributed spatial phases. In addition, we find that the self-organization process is influenced by any anisotropy in the behavior of the simulated rat. The common grid alignment often orients along preferred running directions (RDs), as induced in a square environment. When speed anisotropy is present in exploration behavior, the shape of individual grids is distorted toward an ellipsoid arrangement. Speed anisotropy orients the long ellipse axis along the fast direction. Speed anisotropy on its own also tends to align grids, even without collaterals, but the alignment is seen to be loose. Finally, the alignment of spatial grid fields in multiple environments shows that the network expresses the same set of grid fields across environments, modulo a coherent rotation and translation. Thus, an efficient metric encoding of space may emerge through spontaneous pattern formation at the single-unit level, but it is coherent, hence context-invariant, if aided by collateral interactions.

Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing

One of the two primary classes of models of grid cell spatial firing uses interference between oscillators at dynamically modulated frequencies. Generally, these models are presented in terms of idealized oscillators (modeled as sinusoids), which differ from biological oscillators in multiple important ways. Here we show that two more realistic, noisy neural models (Izhikevich's simple model and a biophysical model of an entorhinal cortex stellate cell) can be successfully used as oscillators in a model of this type. When additive noise is included in the models such that uncoupled or sparsely coupled cells show realistic interspike interval variance, both synaptic and gap-junction coupling can synchronize networks of cells to produce comparatively less variable network-level oscillations. We show that the frequency of these oscillatory networks can be controlled sufficiently well to produce stable grid cell spatial firing on the order of at least 2-5 min, despite the high noise level. Our results suggest that the basic principles of oscillatory interference models work with more realistic models of noisy neurons. Nevertheless, a number of simplifications were still made and future work should examine increasingly realistic models.

Physiological, behavioral, and ecological aspects of migration in reptiles

Seasonal movements between foraging, breeding, and overwintering sites occur in a wide variety of reptile species. Terrestrial snakes, lizards, and turtles migrate short distances (\20 km) between seasonal habitats, whereas fully aquatic marine turtles migrate hundreds to thousands of kilometers between foraging and breeding areas. The purpose of this article is to summarize aspects of migratory physiology and behavior in reptiles, particularly with regards to energetics and sensory mechanisms for navigation and orientation. We discuss the influence of aerobic scope, endurance, and cost of transport on migratory capacity, the effects of temperature and circulating hormones on activity and behavior, and mechanisms of detecting and transducing environmental cues to successfully navigate and orient toward a goal during migration. Topics worthy of further research are highlighted in the text, and we conclude with a discussion of how information on migration patterns of reptiles may be used to manage and conserve threatened populations.

Changing and shielded magnetic fields suppress c-Fos expression in the navigation circuit: input from the magnetosensory system contributes to the internal representation of space in a subterranean rodent

The neural substrate subserving magnetoreception and magnetic orientation in mammals is largely unknown. Previous experiments have demonstrated that the processing of magnetic sensory information takes place in the superior colliculus. Here, the effects of magnetic field conditions on neuronal activity in the rodent navigation circuit were assessed by quantifying c-Fos expression. Ansell's mole-rats (Fukomys anselli), a mammalian model to study the mechanisms of magnetic compass orientation, were subjected to natural, periodically changing, and shielded magnetic fields while exploring an unfamiliar circular arena. In the undisturbed local geomagnetic field, the exploration of the novel environment and/or nesting behaviour induced c-Fos expression throughout the head direction system and the entorhinal-hippocampal spatial representation system. This induction was significantly suppressed by exposure to periodically changing and/or shielded magnetic fields; discrete decreases in c-Fos were seen in the dorsal tegmental nucleus, the anterodorsal and the laterodorsal thalamic nuclei, the postsubiculum, the retrosplenial and entorhinal cortices, and the hippocampus. Moreover, in inactive animals, magnetic field intensity manipulation suppressed c-Fos expression in the CA1 and CA3 fields of the hippocampus and the dorsal subiculum, but induced expression in the polymorph layer of the dentate gyrus. These findings suggest that key constituents of the rodent navigation circuit contain populations of neurons responsive to magnetic stimuli. Thus, magnetic information may be integrated with multimodal sensory and motor information into a common spatial representation of allocentric space within this circuit.