Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

 A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot. Received: 02 July 1999 / Accepted in revised form: 20 March 2000     

The ant’s path integration system: a neural architecture

 A model is developed by which path integration as observed in many animal species could be implemented neurobiologically. The proposed architecture is able to describe the navigation behaviour of Cataglyphis ants, and that of other social insects, at the level of interacting neurons. The basic idea of this architecture is the concept of activity patterns travelling along neural chains. Although experimental evidence has yet to be provided, this concept seems biologically plausible and not limited to the navigation problem. Neural chains are able to represent variables by activity patterns with high accuracy and temporal stability. Moreover, they are able to integrate incremental signals with high precision. Cyclical chains of neurons show superior performance as soon as cyclical variables are to be represented and integrated. Finally, representation of cyclical variables by travelling activity peaks allows simple approximations of goniometric functions as they are used in path integration systems. Received: 15 November 1994/Accepted in revised form: 30 May 1995     

How do insects use path integration for their navigation?

 We combine experimental findings on ants and bees, and build on earlier models, to give an account of how these insects navigate using path integration, and how path integration interacts with other modes of navigation. At the core of path integration is an accumulator. This is set to an initial state at the nest and is updated as the insect moves so that it always reports the insect's current position relative to the nest. Navigation that uses path integration requires, in addition, a way of storing states of the accumulator at significant places for subsequent recall as goals, and a means of computing the direction to such goals. We discuss three models of how path integration might be used for this process, which we call vector navigation. Vector navigation is the principal means of navigating over unfamiliar terrain, or when landmarks are unavailable. Under other conditions, insects often navigate by landmarks, and ignore the output of the vector navigation system. Landmark navigation does not interfere with the updating of the accumulator. There is an interesting symmetry in the use of landmarks and path integration. In the short term, vector navigation can be independent of landmarks, and landmark navigation needs no assistance from path integration. In the longer term, visual landmarks help keep path vector navigation calibrated, and the learning of visual landmarks is guided by path integration. Received: 6 June 1999 / Accepted in revised form: 20 March 2000     

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.     

Finding the way with a noisy brain

Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the oldest and most ubiquitous navigation strategies in the animal kingdom. Despite a plethora of computational models, from equational to neural network form, there is currently no consensus, even in principle, of how this important phenomenon occurs neurally. Recently, all path integration models were examined according to a novel, unifying classification system. Here we combine this theoretical framework with recent insights from directed walk theory, and develop an intuitive yet mathematically rigorous proof that only one class of neural representation of space can tolerate noise during path integration. This result suggests many existing models of path integration are not biologically plausible due to their intolerance to noise. This surprising result imposes significant computational limitations on the neurobiological spatial representation of all successfully navigating animals, irrespective of species. Indeed, noise-tolerance may be an important functional constraint on the evolution of neuroarchitectural plans in the animal kingdom.     

A computational model of the hippocampus that represents environmental structure and goal location,and guides movement

Hippocampal place cells (PCs) are believed to represent environmental structure. However, it is unclear how and which brain regions represent goals and guide movements. Recently, another type of cells that fire around a goal was found in rat hippocampus (we designate these cells as goal place cells, GPCs). This suggests that the hippocampus is also involved in goal representation. Assuming that the activities of GPCs depend on the distance to a goal, we propose an adaptive navigation model. By monitoring the population activity of GPCs, the model navigates to shorten the distance to the goal. To achieve the distance-dependent activities of GPCs, plastic connections are assumed between PCs and GPCs, which are modified depending on two reward-triggered activities: activity propagation through PC–PC network representing the topological environmental structure, and the activity of GPCs with different durations. The former activity propagation is regarded as a computational interpretation of “reverse replay” phenomenon found in rat hippocampus. Simulation results confirm that after reaching a goal only once, the model can navigate to the goal along almost the shortest path from arbitrary places in the environment. This indicates that the hippocampus might play a primary role in the representation of not only the environmental structure but also the goal, in addition to guiding the movement. This navigation strategy using the population activity of GPCs is equivalent to the taxis strategy, the simplest and most basic for biological systems. Our model is unique because this simple strategy allows the model to follow the shortest path in the topological map of the environment.     

Homing in fiddler crabs (Uca lactea annulipes and Uca vomeris : Ocypodidae)

Fiddler crabs emerge from burrows on intertidal sand- and mudflats to feed during low tide. In the species studied here (Uca lactea annulipes, Uca vomeris) a crab normally wanders no more than about 1 m away from its burrow and, when frightened, dashes back along a straight line to take cover. Feeding crabs tend to move sideways, without changing orientation, along paths radiating from the burrow. When they move along circumferential paths they adjust their orientation so that one side continues to point towards the burrow. The crabs do not need to see the burrow in order to stay aligned with the home vector, and they are not misled by a dummy hole close to their own burrow unless they have come to within about 10 cm of it. The home runs of crabs end within a few centimeters of a burrow that is covered with a sheet of sandpaper and then give way to search runs, centred upon a position slightly short of the burrow location. Feeding crabs can be displaced on sandpapers and their subsequent home runs end at a position where the burrow would be, had there been no displacement. Landmarks close to the burrow do not influence the home runs of displaced crabs. Crabs that are rotated on a sheet of sandpaper, counter-turn to keep their original orientation constant. Fiddler crabs thus employ path integration with external compass information and close range visual guidance for homing. Accepted: 11 May 1998     

Path Integration of Head Direction: Updating a Packet of Neural Activity at the Correct Speed Using Axonal Conduction Delays

The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a “look-up” table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.     

Chronic Homework in Emerging Borderlands of Healthcare

The task of caring for those with chronic illnesses has gained a new centrality in health care at a global level. We introduce the concept of “chronic homework” to offer a critical reflection on the treatment of chronic illnesses in three quite different national and local contexts: Uganda, Denmark, and the United States. A major challenge for clinicians, patients, and family caregivers is how to navigate the task of moving health care from clinic to home. By “chronic homework,” we refer to the work patients and families are expected to carry out in their home contexts as part of the treatment of chronic conditions. Families and patients spend time receiving training by clinical experts in the various tasks they are to do at home. While this “colonization” of the popular domain could easily be understood from a Foucauldian perspective as yet another emerging mode of governmentality, this a conceptualization can oversimplify the way specific practices of homework are re-imagined and redirected by patients and significant others in their home surroundings. In light of this re-invention of homework in local home contexts, we foreground another conceptual trope, describing chronic homework as a borderland practice.     

Vector calibration in Australian desert ants,Melophorus bagoti: Effects of a delay after the acquisition of vector information

Desert ants navigate by using two chief strategies: path integration, keeping track of the straight‐line distance and direction to the starting point as they travel, and landmark guidance, orientation based on the visual panorama. Both Cataglyphis ants in North Africa and Melophorus bagoti in Central Australia are known to adjust their vectors derived from path integration to compensate for mismatches between their outbound direction of travel and (the reverse of) the inbound direction of travel that takes them home, a process known as vector calibration. We created mismatches of 90° between the outbound vector and the homebound direction by displacing ants from a feeder before their homebound run. We examined temporal factors in vector calibration by varying the delay (0, 1 or 3 hr) between the outbound run to the feeder and the homebound run from the displacement site. According to the temporal weighting rule, such a delay should decrease the weight given to the vector information obtained from the outbound run. This in turn should favour reliance on the visual panorama and thus speed up calibration. Results did not support this prediction. At the displacement site, a delay had little effect on the extent of calibration or the speed of calibration (the number of trials to reach maximum calibration). Just before being displaced, ants were also tested in a test ring surrounded by high walls that obliterated the visual scenery. In the test ring, a delay made the ants less likely to rely on their vector: ants were often not oriented as a group. Otherwise, the ants in the test ring also did not calibrate any more or any faster.     

Animat navigation using a cognitive graph

 This article describes a computational model of the hippocampus that makes it possible for a simulated rat to navigate in a continuous environment containing obstacles. This model views the hippocampus as a “cognitive graph”, that is, a hetero-associative network that learns temporal sequences of visited places and stores a topological representation of the environment. Calling upon place cells, head direction cells, and “goal cells”, it suggests a biologically plausible way of exploiting such a spatial representation for navigation that does not require complicated graph-search algorithms. Moreover, it permits “latent learning” during exploration, that is, the building of a spatial representation without the need of any reinforcement. When the rat occasionally discovers some rewarding place it may wish to rejoin subsequently, it simply records within its cognitive graph, through a series of goal and sub-goal cells, the direction in which to move from any given start place. Accordingly, the model implements a simple “place-recognition-triggered response” navigation strategy. Two implementations of place cell management are studied in parallel. The first one associates place cells with place fields that are given a priori and that are uniformly distributed in the environment. The second one dynamically recruits place cells as exploration proceeds and adjusts the density of such cells to the local complexity of the environment. Both implementations lead to identical results. The article ends with a few predictions about results to be expected in experiments involving simultaneous recordings of multiple cells in the rat hippocampus. Received: 25 June 1999 / Accepted in revised form: 20 March 2000     

Path integration of head direction: updating a packet of neural activity at the correct speed using neuronal time constants

A key question in understanding the neural basis of path integration is how individual, spatially responsive, neurons may self-organize into networks that can, through learning, integrate velocity signals to update a continuous representation of location within an environment. It is of vital importance that this internal representation of position is updated at the correct speed, and in real time, to accurately reflect the motion of the animal. In this article, we present a biologically plausible model of velocity path integration of head direction that can solve this problem using neuronal time constants to effect natural time delays, over which associations can be learned through associative Hebbian learning rules. The model comprises a linked continuous attractor network and competitive network. In simulation, we show that the same model is able to learn two different speeds of rotation when implemented with two different values for the time constant, and without the need to alter any other model parameters. The proposed model could be extended to path integration of place in the environment, and path integration of spatial view.     

Neuronal representation of optic flow experienced by unilaterally blinded flies on their mean walking trajectories

Asymmetries in the optic flow on both eyes may indicate an unintended turn of an animal and evoke compensatory optomotor responses. On a straight path in an evenly structured environment, the optic flow on both eyes is balanced corresponding to a state of optomotor equilibrium. When one eye is occluded an optomotor equilibrium is expected to be reached on a curved path provided that the translatory optic flow component is cancelled by a superimposed rotation. This hypothesis is tested by analysing how the HSE cell, a constituent element of the fly's optomotor system, represents optic flow in behavioural situations. The optic flow as seen on the average trajectory of freely walking monocular flies is reconstructed. This optic flow is used as stimulus of the HSE cell in electrophysiological experiments and as input of a model of the fly's optomotor system. The responses of the HSE cell and of the model fluctuate around the resting potential. On average, they are much smaller than the responses evoked by optic flow experienced on a straight path. These results corroborate the hypothesis that the mean trajectory of monocular flies corresponds to a path of optomotor equilibrium. Accepted: 29 February 2000     

Animal navigation: the difficulty of moving in a straight line

In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and continually reorienting with reference to it, while the other is to infer body rotations from internal sensory information only. We show here that, while the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, the second strategy will not do so, even after an infinite number of steps. Thus, an external directional reference—some form of compass—is indispensable for ensuring progress away from home. This limitation must place significant constraints on the evolution of biological navigation systems. Some specific examples are discussed. An important corollary arising from the analysis of compassless navigation is that the maximum expected displacement represents a robust measure of the straightness of a path.     

Panpsychic Organicism: Sewall Wright’s Philosophy for Understanding Complex Genetic Systems

Sewall Wright first encountered the complex systems characteristic of gene combinations while a graduate student at Harvard’s Bussey Institute from 1912 to 1915. In Mendelian breeding experiments, Wright observed a hierarchical dependence of the organism’s phenotype on dynamic networks of genetic interaction and organization. An animal’s physical traits, and thus its autonomy from surrounding environmental constraints, depended greatly on how genes behaved in certain combinations. Wright recognized that while genes are the material determinants of the animal phenotype, operating with great regularity, the special nature of genetic systems contributes to the animal phenotype a degree of spontaneity and novelty, creating unpredictable trait variations by virtue of gene interactions. As a result of his experimentation, as well as his keen interest in the philosophical literature of his day, Wright was inspired to see genetic systems as conscious, living organisms in their own right. Moreover, he decided that since genetic systems maintain ordered stability and cause unpredictable novelty in their organic wholes (the animal phenotype), it would be necessary for biologists to integrate techniques for studying causally ordered phenomena (experimental method) and chance phenomena (correlation method). From 1914 to 1921 Wright developed his “method of path coefficient” (or “path analysis”), a new procedure drawing from both laboratory experimentation and statistical correlation in order to analyze the relative influence of specific genetic interactions on phenotype variation. In this paper I aim to show how Wright’s philosophy for understanding complex genetic systems (panpsychic organicism) logically motivated his 1914–1921 design of path analysis.     

Independence of the unimodal tuning of firing rate from theta phase precession in hippocampal place cells

There are two prominent features for place cells in rat hippocampus. The firing rate remarkably increases when rat enters the cell’s place field and reaches a maximum around the center of place field, and it decreases when the animal approaches the end of the place field. Simultaneously the spikes gradually and monotonically advance to earlier phase relative to hippocampal theta rhythm as the rat traverses along the cell’s place field, known as temporal coding. In this paper, we investigate whether two main characteristics of place cell firing are independent or not by mainly focusing on the generation mechanism of the unimodal tuning of firing rate by using a reduced CA1 two-compartment neuron model. Based on recent evidences, we hypothesize that the coupling of dendritic with the somatic compartment is not constant but dynamically regulated as the animal moves further along the place field, in contrast to previous two-compartment modeling. Simulations show that the regulable coupling is critically responsible for the generation of unimodal firing rate profile in place cells, independent of phase precession. Predictions of our model accord well with recent observations like occurrence of phase precession with very low as well as high firing rate (Huxter et al. Nature 425:828–832, 2003) and persistency of phase precession after transient silence of hippocampus activity (Zugaro et al. Nat Neurosci 8:67–71, 2005.     

Which coordinate system for modelling path integration?

Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate, called the home vector, of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature, and has been studied for over a century. In that time, canonical and neural network models have flourished, based on a wide range of assumptions, justifications and supporting data. Despite the importance of the phenomenon, consensus and unifying principles appear lacking. A fundamental issue is the neural representation of space needed for biological path integration. This paper presents a scheme to classify path integration systems on the basis of the way the home vector records and updates the spatial relationship between the animal and its home location. Four extended classes of coordinate systems are used to unify and review both canonical and neural network models of path integration, from the arthropod and mammalian literature. This scheme demonstrates analytical equivalence between models which may otherwise appear unrelated, and distinguishes between models which may superficially appear similar. A thorough analysis is carried out of the equational forms of important facets of path integration including updating, steering, searching and systematic errors, using each of the four coordinate systems. The type of available directional cue, namely allothetic or idiothetic, is also considered. It is shown that on balance, the class of home vectors which includes the geocentric Cartesian coordinate system, appears to be the most robust for biological systems. A key conclusion is that deducing computational structure from behavioural data alone will be difficult or impossible, at least in the absence of an analysis of random errors. Consequently it is likely that further theoretical insights into path integration will require an in-depth study of the effect of noise on the four classes of home vectors.     

Sensory feedback in a bump attractor model of path integration

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal’s current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal’s knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541–4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.