A continuous attractor network model without recurrent excitation: maintenance and integration in the head direction cell system

Bimodular continuous attractor neural networks with static and moving stimuli

We investigated the dynamical behaviors of bimodular continuous attractor neural networks, each processing a modality of sensory input and interacting with each other. We found that when bumps coexist in both modules, the position of each bump is shifted towards the other input when the intermodular couplings are excitatory and is shifted away when inhibitory. When one intermodular coupling is excitatory while another is moderately inhibitory, temporally modulated population spikes can be generated. On further increase of the inhibitory coupling, momentary spikes will emerge. In the regime of bump coexistence, bump heights are primarily strengthened by excitatory intermodular couplings, but there is a lesser weakening effect due to a bump being displaced from the direct input. When bimodular networks serve as decoders of multisensory integration, we extend the Bayesian framework to show that excitatory and inhibitory couplings encode attractive and repulsive priors, respectively. At low disparity, the bump positions decode the posterior means in the Bayesian framework, whereas at high disparity, multiple steady states exist. In the regime of multiple steady states, the less stable state can be accessed if the input causing the more stable state arrives after a sufficiently long delay. When one input is moving, the bump in the corresponding module is pinned when the moving stimulus is weak, unpinned at intermediate stimulus strength, and tracks the input at strong stimulus strength, and the stimulus strengths for these transitions increase with the velocity of the moving stimulus. These results are important to understanding multisensory integration of static and dynamic stimuli.

Oscillations and variability in neuronal systems: interplay of autonomous transient dynamics and fast deterministic fluctuations

Neuronal systems are subject to rapid fluctuations both intrinsically and externally. These fluctuations can be disruptive or constructive. We investigate the dynamic mechanisms underlying the interactions between rapidly fluctuating signals and the intrinsic properties of the target cells to produce variable and/or coherent responses. We use linearized and non-linear conductance-based models and piecewise constant (PWC) inputs with short duration pieces. The amplitude distributions of the constant pieces consist of arbitrary permutations of a baseline PWC function. In each trial within a given protocol we use one of these permutations and each protocol consists of a subset of all possible permutations, which is the only source of uncertainty in the protocol. We show that sustained oscillatory behavior can be generated in response to various forms of PWC inputs independently of whether the stable equilibria of the corresponding unperturbed systems are foci or nodes. The oscillatory voltage responses are amplified by the model nonlinearities and attenuated for conductance-based PWC inputs as compared to current-based PWC inputs, consistent with previous theoretical and experimental work. In addition, the voltage responses to PWC inputs exhibited variability across trials, which is reminiscent of the variability generated by stochastic noise (e.g., Gaussian white noise). Our analysis demonstrates that both oscillations and variability are the result of the interaction between the PWC input and the target cell's autonomous transient dynamics with little to no contribution from the dynamics in vicinities of the steady-state, and do not require input stochasticity.

A Spiking Neural Network Model of Rodent Head Direction Calibrated With Landmark Free Learning

Maintaining a stable estimate of head direction requires both self-motion (idiothetic) information and environmental (allothetic) anchoring. In unfamiliar or dark environments idiothetic drive can maintain a rough estimate of heading but is subject to inaccuracy, visual information is required to stabilize the head direction estimate. When learning to associate visual scenes with head angle, animals do not have access to the ‘ground truth' of their head direction, and must use egocentrically derived imprecise head direction estimates. We use both discriminative and generative methods of visual processing to learn these associations without extracting explicit landmarks from a natural visual scene, finding all are sufficiently capable at providing a corrective signal. Further, we present a spiking continuous attractor model of head direction (SNN), which when driven by idiothetic input is subject to drift. We show that head direction predictions made by the chosen model-free visual learning algorithms can correct for drift, even when trained on a small training set of estimated head angles self-generated by the SNN. We validate this model against experimental work by reproducing cue rotation experiments which demonstrate visual control of the head direction signal.

Online learning for orientation estimation during translation in an insect ring attractor network

Insect neural systems are a promising source of inspiration for new navigation algorithms, especially on low size, weight, and power platforms. There have been unprecedented recent neuroscience breakthroughs with Drosophila in behavioral and neural imaging experiments as well as the mapping of detailed connectivity of neural structures. General mechanisms for learning orientation in the central complex (CX) of Drosophila have been investigated previously; however, it is unclear how these underlying mechanisms extend to cases where there is translation through an environment (beyond only rotation), which is critical for navigation in robotic systems. Here, we develop a CX neural connectivity-constrained model that performs sensor fusion, as well as unsupervised learning of visual features for path integration; we demonstrate the viability of this circuit for use in robotic systems in simulated and physical environments. Furthermore, we propose a theoretical understanding of how distributed online unsupervised network weight modification can be leveraged for learning in a trajectory through an environment by minimizing orientation estimation error. Overall, our results may enable a new class of CX-derived low power robotic navigation algorithms and lead to testable predictions to inform future neuroscience experiments.

The Role of Idiothetic Signals, Landmarks, and Conjunctive Representations in the Development of Place and Head-Direction Cells: A Self-Organizing Neural Network Model

Place and head-direction (HD) cells are fundamental to maintaining accurate representations of location and heading in the mammalian brain across sensory conditions, and are thought to underlie path integration-the ability to maintain an accurate representation of location and heading during motion in the dark. Substantial evidence suggests that both populations of spatial cells function as attractor networks, but their developmental mechanisms are poorly understood. We present simulations of a fully self-organizing attractor network model of this process using well-established neural mechanisms. We show that the differential development of the two cell types can be explained by their different idiothetic inputs, even given identical visual signals: HD cells develop when the population receives angular head velocity input, whereas place cells develop when the idiothetic input encodes planar velocity. Our model explains the functional importance of conjunctive "state-action" cells, implying that signal propagation delays and a competitive learning mechanism are crucial for successful development. Consequently, we explain how insufficiently rich environments result in pathology: place cell development requires proximal landmarks; conversely, HD cells require distal landmarks. Finally, our results suggest that both networks are instantiations of general mechanisms, and we describe their implications for the neurobiology of spatial processing.

Microcircuits for spatial coding in the medial entorhinal cortex

The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism’s spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.

Sources of path integration error in young and aging humans

Path integration plays a vital role in navigation: it enables the continuous tracking of one's position in space by integrating self-motion cues. Path integration abilities vary widely across individuals, and tend to deteriorate in old age. The specific causes of path integration errors, however, remain poorly characterized. Here, we combine tests of path integration performance in participants of different ages with an analysis based on the Langevin equation for diffusive dynamics, which allows us to decompose errors into distinct causes that can corrupt path integration computations. We show that, across age groups, the dominant error source is unbiased noise that accumulates with travel distance not elapsed time, suggesting that the noise originates in the velocity input rather than within the integrator. Age-related declines are primarily traced to a growth in this noise. These findings shed light on the contributors to path integration error and the mechanisms underlying age-related navigational deficits.

Mechanisms Underlying the Neural Computation of Head Direction

Many animals use an internal sense of direction to guide their movements through the world. Neurons selective to head direction are thought to support this directional sense and have been found in a diverse range of species, from insects to primates, highlighting their evolutionary importance. Across species, most head-direction networks share four key properties: a unique representation of direction at all times, persistent activity in the absence of movement, integration of angular velocity to update the representation, and the use of directional cues to correct drift. The dynamics of theorized network structures called ring attractors elegantly account for these properties, but their relationship to brain circuits is unclear. Here, we review experiments in rodents and flies that offer insights into potential neural implementations of ring attractor networks. We suggest that a theory-guided search across model systems for biological mechanisms that enable such dynamics would uncover general principles underlying head-direction circuit function.

Why acute unilateral vestibular midbrain lesions rarely manifest with rotational vertigo: a clinical and modelling approach to head direction cell function

A retrospective clinical study focused on the frequency of rotational vertigo in 63 patients with acute unilateral midbrain strokes involving the vestibular and ocular motor systems. In contrast to unilateral pontomedullary brainstem lesions, rotational vertigo in midbrain lesions occurred with a low frequency (14%) and transient (< 1 day) course. Swaying vertigo or unspecific dizziness (22%) and postural imbalance (31%) were more frequent. Midbrain strokes with transient rotational vertigo manifested with lesions chiefly in the caudal midbrain tegmentum, while manifestations with swaying, unspecific, or no vertigo chiefly occurred in rostral mesencephalic or meso-diencephalic lesions. We hypothesize that these different manifestations can be explained by the distribution of two separate cell systems based on semicircular canal function: the angular head-velocity cells and the head direction cells, both of which code for head rotation. Animal experiments have shown that angular head-velocity cells are located mainly in the lower brainstem up to the midbrain, whereas the head direction cells are found from the midbrain and thalamic level up to cortical regions. Due to the differences in coding, unilateral dysfunction of the angular velocity cell system should result in the sensation of rotation, while unilateral dysfunction of the head direction cell system should result in dizziness and unsteadiness. We simulated the different manifestations of vestibular dysfunction using a mathematical neural network model of the head direction cell system. This model predicted and confirmed our clinical findings that unilateral caudal and rostral brainstem lesions have different effects on vestibular function.

A speed-accurate self-sustaining head direction cell path integration model without recurrent excitation

The head direction (HD) system signals HD in an allocentric frame of reference. The system is able to update firing based on internally derived information about self-motion, a process known as path integration. Of particular interest is how path integration might maintain concordance between true HD and internally represented HD. Here we present a self-sustaining two-layer model, capable of self-organizing, which produces extremely accurate path integration. The implications of this work for future investigations of HD system path integration are discussed.

Fundamental bound on the persistence and capacity of short-term memory stored as graded persistent activity

It is widely believed that persistent neural activity underlies short-term memory. Yet, as we show, the degradation of information stored directly in such networks behaves differently from human short-term memory performance. We build a more general framework where memory is viewed as a problem of passing information through noisy channels whose degradation characteristics resemble those of persistent activity networks. If the brain first encoded the information appropriately before passing the information into such networks, the information can be stored substantially more faithfully. Within this framework, we derive a fundamental lower-bound on recall precision, which declines with storage duration and number of stored items. We show that human performance, though inconsistent with models involving direct (uncoded) storage in persistent activity networks, can be well-fit by the theoretical bound. This finding is consistent with the view that if the brain stores information in patterns of persistent activity, it might use codes that minimize the effects of noise, motivating the search for such codes in the brain.

Coupled symmetric and asymmetric circuits underlying spatial orientation in fruit flies

Maintaining spatial orientation when carrying out goal-directed movements requires an animal to perform angular path integration. Such functionality has been recently demonstrated in the ellipsoid body (EB) of fruit flies, though the precise circuitry and underlying mechanisms remain unclear. We analyze recently published cellular-level connectomic data and identify the unique characteristics of the EB circuitry, which features coupled symmetric and asymmetric rings. By constructing a spiking neural circuit model based on the connectome, we reveal that the symmetric ring initiates a feedback circuit that sustains persistent neural activity to encode information regarding spatial orientation, while the asymmetric rings are capable of integrating the angular path when the body rotates in the dark. The present model reproduces several key features of EB activity and makes experimentally testable predictions, providing new insight into how spatial orientation is maintained and tracked at the cellular level.

Ellipsoid body (EB) neurons in the fruit fly represent the animal heading through a bump-like activity dynamics. Here the authors report a connectome-driven spiking neural circuit model of the EB and the protocerebral bridge (PB) that can maintain and update an activity bump related to the spatial orientation.

Activity dependent feedback inhibition may maintain head direction signals in mouse presubiculum

Orientation in space is represented in specialized brain circuits. Persistent head direction signals are transmitted from anterior thalamus to the presubiculum, but the identity of the presubicular target neurons, their connectivity and function in local microcircuits are unknown. Here, we examine how thalamic afferents recruit presubicular principal neurons and Martinotti interneurons, and the ensuing synaptic interactions between these cells. Pyramidal neuron activation of Martinotti cells in superficial layers is strongly facilitating such that high-frequency head directional stimulation efficiently unmutes synaptic excitation. Martinotti-cell feedback plays a dual role: precisely timed spikes may not inhibit the firing of in-tune head direction cells, while exerting lateral inhibition. Autonomous attractor dynamics emerge from a modelled network implementing wiring motifs and timing sensitive synaptic interactions in the pyramidal—Martinotti-cell feedback loop. This inhibitory microcircuit is therefore tuned to refine and maintain head direction information in the presubiculum.

Head direction is encoded by cells in the presubiculum, but the role of local circuitry in head direction encoding remains unknown. Here the authors demonstrate how a specific inhibitory neuron type, the Martinotti cell, together with excitatory pyramidal cells supports head direction signals.

Environmental Anchoring of Head Direction in a Computational Model of Retrosplenial Cortex

Allocentric (world-centered) spatial codes driven by path integration accumulate error unless reset by environmental sensory inputs that are necessarily egocentric (body-centered). Previous models of the head direction system avoided the necessary transformation between egocentric and allocentric reference frames by placing visual cues at infinity. Here we present a model of head direction coding that copes with exclusively proximal cues by making use of a conjunctive representation of head direction and location in retrosplenial cortex. Egocentric landmark bearing of proximal cues, which changes with location, is mapped onto this retrosplenial representation. The model avoids distortions due to parallax, which occur in simple models when a single proximal cue card is used, and can also accommodate multiple cues, suggesting how it can generalize to arbitrary sensory environments. It provides a functional account of the anatomical distribution of head direction cells along Papez' circuit, of place-by-direction coding in retrosplenial cortex, the anatomical connection from the anterior thalamic nuclei to retrosplenial cortex, and the involvement of retrosplenial cortex in navigation. In addition to parallax correction, the same mechanism allows for continuity of head direction coding between connected environments, and shows how a head direction representation can be stabilized by a single within arena cue. We also make predictions for drift during exploration of a new environment, the effects of hippocampal lesions on retrosplenial cells, and on head direction coding in differently shaped environments.

SIGNIFICANCE STATEMENT

The activity of head direction cells signals the direction of an animal's head relative to landmarks in the world. Although driven by internal estimates of head movements, head direction cells must be kept aligned to the external world by sensory inputs, which arrive in the reference frame of the sensory receptors. We present a computational model, which proposes that sensory inputs are correctly associated to head directions by virtue of a conjunctive representation of place and head directions in the retrosplenial cortex. The model allows for a stable head direction signal, even when the sensory input from nearby cues changes dramatically whenever the animal moves to a different location, and enables stable representations of head direction across connected environments.

Decision-making neural circuits mediating social behaviors : An attractor network model

We propose a mathematical model of a continuous attractor network that controls social behaviors. The model is examined with bifurcation analysis and computer simulations. The results show that the model exhibits stable steady states and thresholds for steady state transitions corresponding to some experimentally observed behaviors, such as aggression control. The performance of the model and the relation with experimental evidence are discussed.

Single Canonical Model of Reflexive Memory and Spatial Attention

Many neurons in the dorsal and ventral visual stream have the property that after a brief visual stimulus presentation in their receptive field, the spiking activity in these neurons persists above their baseline levels for several seconds. This maintained activity is not always correlated with the monkey’s task and its origin is unknown. We have previously proposed a simple neural network model, based on shape selective neurons in monkey lateral intraparietal cortex, which predicts the valence and time course of reflexive (bottom-up) spatial attention. In the same simple model, we demonstrate here that passive maintained activity or short-term memory of specific visual events can result without need for an external or top-down modulatory signal. Mutual inhibition and neuronal adaptation play distinct roles in reflexive attention and memory. This modest 4-cell model provides the first simple and unified physiologically plausible mechanism of reflexive spatial attention and passive short-term memory processes.

Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention and oscillations

A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model's parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC ('neural relativity'). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data.

Weighted cue integration in the rodent head direction system

How the brain combines information from different sensory modalities and of differing reliability is an important and still-unanswered question. Using the head direction (HD) system as a model, we explored the resolution of conflicts between landmarks and background cues. Sensory cue integration models predict averaging of the two cues, whereas attractor models predict capture of the signal by the dominant cue. We found that a visual landmark mostly captured the HD signal at low conflicts: however, there was an increasing propensity for the cells to integrate the cues thereafter. A large conflict presented to naive rats resulted in greater visual cue capture (less integration) than in experienced rats, revealing an effect of experience. We propose that weighted cue integration in HD cells arises from dynamic plasticity of the feed-forward inputs to the network, causing within-trial spatial redistribution of the visual inputs onto the ring. This suggests that an attractor network can implement decision processes about cue reliability using simple architecture and learning rules, thus providing a potential neural substrate for weighted cue integration.

Optic flow stimuli update anterodorsal thalamus head direction neuronal activity in rats

Head direction (HD) neurons fire selectively according to head orientation in the yaw plane relative to environmental landmark cues. Head movements provoke optic field flow signals that enter the vestibular nuclei, indicating head velocity, and hence angular displacements. To test whether optic field flow alone affects the directional firing of HD neurons, rats walked about on a circular platform as a spot array was projected onto the surrounding floor-to-ceiling cylindrical black curtain. Directional responses in the anterodorsal thalamus of four rats remained stable as they moved about with the point field but in the absence of landmark cues. Then, the spherical projector was rotated about its yaw axis at 4.5°/s for ∼90 s. In 27 sessions the mean drift speed of the preferred directions (PDs) was 1.48°/s (SD=0.78°/s; range: 0.15 to 2.88°/s). Thus, optic flow stimulation entrained PDs, albeit at drift speeds slower than the field rotation. This could be due to conflicts with vestibular, motor command, and efferent copy signals. After field rotation ended, 20/27 PDs drifted back to within 45° of the initial values over several minutes, generally following the shortest path to return to the initial value. Poststimulation drifts could change speed and/or direction, with mean speeds of 0.68±0.64°/s (range 0 to 1.36°/s). Since the HD cell pathway (containing anterodorsal thalamus) is the only known projection of head direction information to entorhinal grid cells and hippocampal place cells, yaw plane optic flow signals likely influence representations in this spatial reference coordinate system for orientation and navigation.

Recurrent inhibitory circuitry as a mechanism for grid formation

Grid cells in layer II of the medial entorhinal cortex form a principal component of the mammalian neural representation of space. The firing pattern of a single grid cell has been hypothesized to be generated through attractor dynamics in a network with a specific local connectivity including both excitatory and inhibitory connections. However, experimental evidence supporting the presence of such connectivity among grid cells in layer II is limited. Here we report recordings from more than 600 neuron pairs in rat entorhinal slices, demonstrating that stellate cells, the principal cell type in the layer II grid network, are mainly interconnected via inhibitory interneurons. Using a model attractor network, we demonstrate that stable grid firing can emerge from a simple recurrent inhibitory network. Our findings thus suggest that the observed inhibitory microcircuitry between stellate cells is sufficient to generate grid-cell firing patterns in layer II of the medial entorhinal cortex.

Fundamental limits on persistent activity in networks of noisy neurons

Neural noise limits the fidelity of representations in the brain. This limitation has been extensively analyzed for sensory coding. However, in short-term memory and integrator networks, where noise accumulates and can play an even more prominent role, much less is known about how neural noise interacts with neural and network parameters to determine the accuracy of the computation. Here we analytically derive how the stored memory in continuous attractor networks of probabilistically spiking neurons will degrade over time through diffusion. By combining statistical and dynamical approaches, we establish a fundamental limit on the network's ability to maintain a persistent state: The noise-induced drift of the memory state over time within the network is strictly lower-bounded by the accuracy of estimation of the network's instantaneous memory state by an ideal external observer. This result takes the form of an information-diffusion inequality. We derive some unexpected consequences: Despite the persistence time of short-term memory networks, it does not pay to accumulate spikes for longer than the cellular time-constant to read out their contents. For certain neural transfer functions, the conditions for optimal sensory coding coincide with those for optimal storage, implying that short-term memory may be co-localized with sensory representation.

How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rates in a self-organizing map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.

Spatial navigation is a critical competence of all higher mammals, and place cells in the hippocampus represent the large spaces in which they navigate. Recent modeling clarifies how this may occur via interactions between grid cells in the medial entorhinal cortex (MEC) and place cells. Grid cells exhibit hexagonal grid firing patterns across space and come in multiple spatial scales that increase along the dorsoventral axis of MEC. Signals from multiple scales of grid cells combine to activate place cells that represent much larger spaces than grid cells. This article shows how a gradient of cell response rates along the dorsoventral axis enables the learning of grid cells with the observed gradient of spatial scales as an animal navigates realistic trajectories. The observed gradient of grid cell membrane potential oscillation frequencies is shown to be a direct result of the gradient of response rates. This gradient mechanism for spatial learning is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections, thereby clarifying why both spatial and temporal representations are found in the entorhinal-hippocampal system.

Dynamics of feature categorization

In visual and auditory scenes, we are able to identify shared features among sensory objects and group them according to their similarity. This grouping is preattentive and fast and is thought of as an elementary form of categorization by which objects sharing similar features are clustered in some abstract perceptual space. It is unclear what neuronal mechanisms underlie this fast categorization. Here we propose a neuromechanistic model of fast feature categorization based on the framework of continuous attractor networks. The mechanism for category formation does not rely on learning and is based on biologically plausible assumptions, for example, the existence of populations of neurons tuned to feature values, feature-specific interactions, and subthreshold-evoked responses upon the presentation of single objects. When the network is presented with a sequence of stimuli characterized by some feature, the network sums the evoked responses and provides a running estimate of the distribution of features in the input stream. If the distribution of features is structured into different components or peaks (i.e., is multimodal), recurrent excitation amplifies the response of activated neurons, and categories are singled out as emerging localized patterns of elevated neuronal activity (bumps), centered at the centroid of each cluster. The emergence of bump states through sequential, subthreshold activation and the dependence on input statistics is a novel application of attractor networks. We show that the extraction and representation of multiple categories are facilitated by the rich attractor structure of the network, which can sustain multiple stable activity patterns for a robust range of connectivity parameters compatible with cortical physiology.

Learned integration of visual, vestibular, and motor cues in multiple brain regions computes head direction during visually guided navigation

Effective navigation depends upon reliable estimates of head direction (HD). Visual, vestibular, and outflow motor signals combine for this purpose in a brain system that includes dorsal tegmental nucleus, lateral mammillary nuclei, anterior dorsal thalamic nucleus, and the postsubiculum. Learning is needed to combine such different cues to provide reliable estimates of HD. A neural model is developed to explain how these three types of signals combine adaptively within the above brain regions to generate a consistent and reliable HD estimate, in both light and darkness, which explains the following experimental facts. Each HD cell is tuned to a preferred head direction. The cell's firing rate is maximal at the preferred direction and decreases as the head turns from the preferred direction. The HD estimate is controlled by the vestibular system when visual cues are not available. A well-established visual cue anchors the cell's preferred direction when the cue is in the animal's field of view. Distal visual cues are more effective than proximal cues for anchoring the preferred direction. The introduction of novel cues in either a novel or familiar environment can gain control over a cell's preferred direction within minutes. Turning out the lights or removing all familiar cues does not change the cell's firing activity, but it may accumulate a drift in the cell's preferred direction. The anticipated time interval (ATI) of the HD estimate is greater in early processing stages of the HD system than at later stages. The model contributes to an emerging unified neural model of how multiple processing stages in spatial navigation, including postsubiculum head direction cells, entorhinal grid cells, and hippocampal place cells, are calibrated through learning in response to multiple types of signals as an animal navigates in the world.

Attractor dynamics of spatially correlated neural activity in the limbic system

Attractor networks are a popular computational construct used to model different brain systems. These networks allow elegant computations that are thought to represent a number of aspects of brain function. Although there is good reason to believe that the brain displays attractor dynamics, it has proven difficult to test experimentally whether any particular attractor architecture resides in any particular brain circuit. We review models and experimental evidence for three systems in the rat brain that are presumed to be components of the rat's navigational and memory system. Head-direction cells have been modeled as a ring attractor, grid cells as a plane attractor, and place cells both as a plane attractor and as a point attractor. Whereas the models have proven to be extremely useful conceptual tools, the experimental evidence in their favor, although intriguing, is still mostly circumstantial.

Cholinergic modulation of the CAN current may adjust neural dynamics for active memory maintenance, spatial navigation and time-compressed replay

Suppression of cholinergic receptors and inactivation of the septum impair short-term memory, and disrupt place cell and grid cell activity in the medial temporal lobe (MTL). Location-dependent hippocampal place cell firing during active waking, when the acetylcholine level is high, switches to time-compressed replay activity during quiet waking and slow-wave-sleep (SWS), when the acetylcholine level is low. However, it remains largely unknown how acetylcholine supports short-term memory, spatial navigation, and the functional switch to replay mode in the MTL. In this paper, we focus on the role of the calcium-activated non-specific cationic (CAN) current which is activated by acetylcholine. The CAN current is known to underlie persistent firing, which could serve as a memory trace in many neurons in the MTL. Here, we review the CAN current and discuss possible roles of the CAN current in short-term memory and spatial navigation. We further propose a novel theoretical model where the CAN current switches the hippocampal place cell activity between real-time and time-compressed sequential activity during encoding and consolidation, respectively.

How do spatial learning and memory occur in the brain? Coordinated learning of entorhinal grid cells and hippocampal place cells

Spatial learning and memory are important for navigation and formation of episodic memories. The hippocampus and medial entorhinal cortex (MEC) are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of MEC provide inputs to place cells and exhibit remarkable regular hexagonal spatial firing patterns. They also exhibit a gradient of spatial scales along the dorsoventral axis of the MEC, with neighboring cells at a given dorsoventral location having different spatial phases. A neural model shows how a hierarchy of self-organizing maps, each obeying the same laws, responds to realistic rat trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with unimodal firing fields that fit neurophysiological data about their development in juvenile rats. The hippocampal place fields represent much larger spaces than the grid cells to support navigational behaviors. Both the entorhinal and hippocampal self-organizing maps amplify and learn to categorize the most energetic and frequent co-occurrences of their inputs. Top-down attentional mechanisms from hippocampus to MEC help to dynamically stabilize these spatial memories in both the model and neurophysiological data. Spatial learning through MEC to hippocampus occurs in parallel with temporal learning through lateral entorhinal cortex to hippocampus. These homologous spatial and temporal representations illustrate a kind of "neural relativity" that may provide a substrate for episodic learning and memory.

Using strategic movement to calibrate a neural compass: a spiking network for tracking head direction in rats and robots

The head direction (HD) system in mammals contains neurons that fire to represent the direction the animal is facing in its environment. The ability of these cells to reliably track head direction even after the removal of external sensory cues implies that the HD system is calibrated to function effectively using just internal (proprioceptive and vestibular) inputs. Rat pups and other infant mammals display stereotypical warm-up movements prior to locomotion in novel environments, and similar warm-up movements are seen in adult mammals with certain brain lesion-induced motor impairments. In this study we propose that synaptic learning mechanisms, in conjunction with appropriate movement strategies based on warm-up movements, can calibrate the HD system so that it functions effectively even in darkness. To examine the link between physical embodiment and neural control, and to determine that the system is robust to real-world phenomena, we implemented the synaptic mechanisms in a spiking neural network and tested it on a mobile robot platform. Results show that the combination of the synaptic learning mechanisms and warm-up movements are able to reliably calibrate the HD system so that it accurately tracks real-world head direction, and that calibration breaks down in systematic ways if certain movements are omitted. This work confirms that targeted, embodied behaviour can be used to calibrate neural systems, demonstrates that ‘grounding’ of modelled biological processes in the real world can reveal underlying functional principles (supporting the importance of robotics to biology), and proposes a functional role for stereotypical behaviours seen in infant mammals and those animals with certain motor deficits. We conjecture that these calibration principles may extend to the calibration of other neural systems involved in motion tracking and the representation of space, such as grid cells in entorhinal cortex.

Single-cell persistent activity in anterodorsal thalamus

The anterodorsal nucleus of the thalamus contains a high percentage of head-direction cells whose activities are correlated with an animal's directional heading in the horizontal plane. The firing of head-direction cells could involve self-sustaining reverberating activity in a recurrent network, but the thalamus by itself lacks strong excitatory recurrent synaptic connections to sustain tonic reverberating activity. Here we examined whether a single thalamic neuron could sustain its own activity without synaptic input by recording from individual neurons from anterodorsal thalamus in brain slices with synaptic blockers. We found that the rebound firing induced by hyperpolarizing pulses often decayed slowly so that a thalamic neuron could keep on firing for many minutes after stimulation. The hyperpolarization-induced persistent firing rate was graded under repeated current injections, and could be enhanced by serotonin. The effect of depolarizing pulses was much weaker and only slightly accelerated the decay of the hyperpolarization-induced persistent firing. Our finding provides the first direct evidence for single-cell persistent activity in the thalamus, supporting the notion that cellular mechanisms at the slow time scale of minutes might potentially contribute to the operations of the head-direction system.

Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex

Grid cells in the dorsal segment of the medial entorhinal cortex (dMEC) show remarkable hexagonal activity patterns, at multiple spatial scales, during spatial navigation. It has previously been shown how a self-organizing map can convert firing patterns across entorhinal grid cells into hippocampal place cells that are capable of representing much larger spatial scales. Can grid cell firing fields also arise during navigation through learning within a self-organizing map? This article describes a simple and general mathematical property of the trigonometry of spatial navigation which favors hexagonal patterns. The article also develops a neural model that can learn to exploit this trigonometric relationship. This GRIDSmap self-organizing map model converts path integration signals into hexagonal grid cell patterns of multiple scales. GRIDSmap creates only grid cell firing patterns with the observed hexagonal structure, predicts how these hexagonal patterns can be learned from experience, and can process biologically plausible neural input and output signals during navigation. These results support an emerging unified computational framework based on a hierarchy of self-organizing maps for explaining how entorhinal-hippocampal interactions support spatial navigation.

Interspike interval analyses reveal irregular firing patterns at short, but not long, intervals in rat head direction cells

Previous studies have shown that a subset of neurons in the rat anterodorsal thalamus discharge as a function of the animal's head direction (HD) in the horizontal plane, independent of the animal's location and behavior. These cells have consistent firing properties across a wide range of conditions and cell discharge appears highly regular when listened to through a loudspeaker. In contrast, interspike interval (ISI) analyses on cortical cells have found that cell firing is irregular, even under constant stimulus conditions. Here, we analyzed HD cells from the anterodorsal thalamus, while rats foraged for food pellets, to determine whether their firing was regular or irregular. ISIs were measured when the animal's HD was maintained within ± 6° of the cell's preferred firing direction. ISIs were highly variable with a mean coefficient of variation (CV) of 0.681. For each cell, the CV values at HDs ± 24° away from the cell's preferred direction were similar to the coefficient measured at the cell's preferred direction. A second recording session showed that cells had similar coefficients of variation as the first session, suggesting that the degree of variability in cell spiking was a characteristic property for each cell. There was little correlation between ISIs and angular head velocity or translational speed. ISIs measured in HD cells from the postsubiculum and lateral mammillary nuclei showed higher CV values. These results indicate that despite the appearance of regularity in their firing, HD cells, like cortical cells, have irregular ISIs. In contrast to the irregular firing observed for ISIs, analyses over longer time intervals indicated that HD cell firing was much more regular, more nearly resembling a rate code. These findings have implications for attractor networks that model the HD signal and for models proposed to explain the generation of grid cell signals in entorhinal cortex.

Persistent firing supported by an intrinsic cellular mechanism in a component of the head direction system

The rat postsubiculum has head direction cells that fire persistently when the rat's head is oriented in particular directions. This persistent firing is maintained even if the rat is motionless, when spatial cues are removed from the environment and in the dark, but the mechanism that supports persistent firing of the head direction cells is still unclear. Here, using in vitro whole-cell patch recording, we found that a short-triggering stimulus (as few as five induced spikes) can initiate persistent firing in cells of the postsubiculum. Pharmacological results indicated that this persistent firing is driven by a calcium-sensitive nonselective cation current. The distribution of cells with persistent firing in superficial and deep layers in the postsubiculum was similar to that of head direction cells. These results suggest that persistent firing of head direction cells in the postsubiculum could be supported by an intrinsic mechanism.

Anticipation in the Rodent Head Direction System Can Be Explained by an Interaction of Head Movements and Vestibular Firing Properties

The rodent head-direction (HD) system, which codes for the animal's head direction in the horizontal plane, is thought to be critically involved in spatial navigation. Electrophysiological recording studies have shown that HD cells can anticipate the animal's HD by up to 75–80 ms. The origin of this anticipation is poorly understood. In this modeling study, we provide a novel explanation for HD anticipation that relies on the firing properties of neurons afferent to the HD system. By incorporating spike rate adaptation and postinhibitory rebound as observed in medial vestibular nucleus neurons, our model produces realistic anticipation on a large corpus of rat movement data. In addition, HD anticipation varies between recording sessions of the same cell, between active and passive movement, and between different studies. Such differences do not appear to be correlated with behavioral variables and cannot be accounted for using earlier models. In the present model, anticipation depends on the power spectrum of the head movements. By direct comparison with recording data, we show that the model explains 60–80% of the observed anticipation variability. We conclude that HD afferent dynamics and the statistics of rat head movements are important in generating HD anticipation. This result contributes to understanding the functional circuitry of the HD system and has methodological implications for studies of HD anticipation.

Self-organizing path integration using a linked continuous attractor and competitive network: path integration of head direction

A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.

Neural network model of the primary visual cortex: from functional architecture to lateral connectivity and back

The role of intrinsic cortical dynamics is a debatable issue. A recent optical imaging study (Kenet et al., 2003) found that activity patterns similar to orientation maps (OMs), emerge in the primary visual cortex (V1) even in the absence of sensory input, suggesting an intrinsic mechanism of OM activation. To better understand these results and shed light on the intrinsic V1 processing, we suggest a neural network model in which OMs are encoded by the intrinsic lateral connections. The proposed connectivity pattern depends on the preferred orientation and, unlike previous models, on the degree of orientation selectivity of the interconnected neurons. We prove that the network has a ring attractor composed of an approximated version of the OMs. Consequently, OMs emerge spontaneously when the network is presented with an unstructured noisy input. Simulations show that the model can be applied to experimental data and generate realistic OMs. We study a variation of the model with spatially restricted connections, and show that it gives rise to states composed of several OMs. We hypothesize that these states can represent local properties of the visual scene.

Robust self-localisation and navigation based on hippocampal place cells

A computational model of the hippocampal function in spatial learning is presented. A spatial representation is incrementally acquired during exploration. Visual and self-motion information is fed into a network of rate-coded neurons. A consistent and stable place code emerges by unsupervised Hebbian learning between place- and head direction cells. Based on this representation, goal-oriented navigation is learnt by applying a reward-based learning mechanism between the hippocampus and nucleus accumbens. The model, validated on a real and simulated robot, successfully localises itself by recalibrating its path integrator using visual input. A navigation map is learnt after about 20 trials, comparable to rats in the water maze. In contrast to previous works, this system processes realistic visual input. No compass is needed for localisation and the reward-based learning mechanism extends discrete navigation models to continuous space. The model reproduces experimental findings and suggests several neurophysiological and behavioural predictions in the rat.