Path Integration
path integration
Brain circuits for spatial navigation
In this webinar on spatial navigation circuits, three researchers—Ann Hermundstad, Ila Fiete, and Barbara Webb—discussed how diverse species solve navigation problems using specialized yet evolutionarily conserved brain structures. Hermundstad illustrated the fruit fly’s central complex, focusing on how hardwired circuit motifs (e.g., sinusoidal steering curves) enable rapid, flexible learning of goal-directed navigation. This framework combines internal heading representations with modifiable goal signals, leveraging activity-dependent plasticity to adapt to new environments. Fiete explored the mammalian head-direction system, demonstrating how population recordings reveal a one-dimensional ring attractor underlying continuous integration of angular velocity. She showed that key theoretical predictions—low-dimensional manifold structure, isometry, uniform stability—are experimentally validated, underscoring parallels to insect circuits. Finally, Webb described honeybee navigation, featuring path integration, vector memories, route optimization, and the famous waggle dance. She proposed that allocentric velocity signals and vector manipulation within the central complex can encode and transmit distances and directions, enabling both sophisticated foraging and inter-bee communication via dance-based cues.
Navigating semantic spaces: recycling the brain GPS for higher-level cognition
Humans share with other animals a complex neuronal machinery that evolved to support navigation in the physical space and that supports wayfinding and path integration. In my talk I will present a series of recent neuroimaging studies in humans performed in my Lab aimed at investigating the idea that this same neural navigation system (the “brain GPS”) is also used to organize and navigate concepts and memories, and that abstract and spatial representations rely on a common neural fabric. I will argue that this might represent a novel example of “cortical recycling”, where the neuronal machinery that primarily evolved, in lower level animals, to represent relationships between spatial locations and navigate space, in humans are reused to encode relationships between concepts in an internal abstract representational space of meaning.
Central place foraging: how insects anchor spatial information
Many insect species maintain a nest around which their foraging behaviour is centered, and can use path integration to maintain an accurate estimate of their distance and direction (a vector) to their nest. Some species, such as bees and ants, can also store the vector information for multiple salient locations in the world, such as food sources, in a common coordinate system. They can also use remembered views of the terrain around salient locations or along travelled routes to guide return. Recent modelling of these abilities shows convergence on a small set of algorithms and assumptions that appear sufficient to account for a wide range of behavioural data, and which can be mapped to specific insect brain circuits. Notably, this does not include any significant topological knowledge: the insect does not need to recover the information (implicit in their vector memory) about the relationships between salient places; nor to maintain any connectedness or ordering information between view memories; nor to form any associations between views and vectors. However, there remains some experimental evidence not fully explained by these algorithms that may point towards the existence of a more complex or integrated mental map in insects.
A specialized role for entorhinal attractor dynamics in combining path integration and landmarks during navigation
During navigation, animals estimate their position using path integration and landmarks. In a series of two studies, we used virtual reality and electrophysiology to dissect how these inputs combine to generate the brain’s spatial representations. In the first study (Campbell et al., 2018), we focused on the medial entorhinal cortex (MEC) and its set of navigationally-relevant cell types, including grid cells, border cells, and speed cells. We discovered that attractor dynamics could explain an array of initially puzzling MEC responses to virtual reality manipulations. This theoretical framework successfully predicted both MEC grid cell responses to additional virtual reality manipulations, as well as mouse behavior in a virtual path integration task. In the second study (Campbell*, Attinger* et al., 2021), we asked whether these principles generalize to other navigationally-relevant brain regions. We used Neuropixels probes to record thousands of neurons from MEC, primary visual cortex (V1), and retrosplenial cortex (RSC). In contrast to the prevailing view that “everything is everywhere all at once,” we identified a unique population of MEC neurons, overlapping with grid cells, that became active with striking spatial periodicity while head-fixed mice ran on a treadmill in darkness. These neurons exhibited unique cue-integration properties compared to other MEC, V1, or RSC neurons: they remapped more readily in response to conflicts between path integration and landmarks; they coded position prospectively as opposed to retrospectively; they upweighted path integration relative to landmarks in conditions of low visual contrast; and as a population, they exhibited a lower-dimensional activity structure. Based on these results, our current view is that MEC attractor dynamics play a privileged role in resolving conflicts between path integration and landmarks during navigation. Future work should include carefully designed causal manipulations to rigorously test this idea, and expand the theoretical framework to incorporate notions of uncertainty and optimality.
Neural circuits for vector processing in the insect brain
Several species of insects have been observed to perform accurate path integration, constantly updating a vector memory of their location relative to a starting position, which they can use to take a direct return path. Foraging insects such as bees and ants are also able to store and recall the vectors to return to food locations, and to take novel shortcuts between these locations. Other insects, such as dung beetles, are observed to integrate multimodal directional cues in a manner well described by vector addition. All these processes appear to be functions of the Central Complex, a highly conserved and strongly structured circuit in the insect brain. Modelling this circuit, at the single neuron level, suggests it has general capabilities for vector encoding, vector memory, vector addition and vector rotation that can support a wide range of directed and navigational behaviours.
Distance-tuned neurons drive specialized path integration calculations in medial entorhinal cortex
During navigation, animals estimate their position using path integration and landmarks, engaging many brain areas. Whether these areas follow specialized or universal cue integration principles remains incompletely understood. We combine electrophysiology with virtual reality to quantify cue integration across thousands of neurons in three navigation-relevant areas: primary visual cortex (V1), retrosplenial cortex (RSC), and medial entorhinal cortex (MEC). Compared with V1 and RSC, path integration influences position estimates more in MEC, and conflicts between path integration and landmarks trigger remapping more readily. Whereas MEC codes position prospectively, V1 codes position retrospectively, and RSC is intermediate between the two. Lowered visual contrast increases the influence of path integration on position estimates only in MEC. These properties are most pronounced in a population of MEC neurons, overlapping with grid cells, tuned to distance run in darkness. These results demonstrate the specialized role that path integration plays in MEC compared with other navigation-relevant cortical areas.
Adaptive bottleneck to pallium for sequence memory, path integration and mixed selectivity representation
Spike-driven adaptation involves intracellular mechanisms that are initiated by neural firing and lead to the subsequent reduction of spiking rate followed by a recovery back to baseline. We report on long (>0.5 second) recovery times from adaptation in a thalamic-like structure in weakly electric fish. This adaptation process is shown via modeling and experiment to encode in a spatially invariant manner the time intervals between event encounters, e.g. with landmarks as the animal learns the location of food. These cells also come in two varieties, ones that care only about the time since the last encounter, and others that care about the history of encounters. We discuss how the two populations can share in the task of representing sequences of events, supporting path integration and converting from ego-to-allocentric representations. The heterogeneity of the population parameters enables the representation and Bayesian decoding of time sequences of events which may be put to good use in path integration and hilus neuron function in hippocampus. Finally we discuss how all the cells of this gateway to the pallium exhibit mixed selectivity of social features of their environment. The data and computational modeling further reveal that, in contrast to a long-held belief, these gymnotiform fish are endowed with a corollary discharge, albeit only for social signalling.
Adaptation-driven sensory detection and sequence memory
Spike-driven adaptation involves intracellular mechanisms that are initiated by spiking and lead to the subsequent reduction of spiking rate. One of its consequences is the temporal patterning of spike trains, as it imparts serial correlations between interspike intervals in baseline activity. Surprisingly the hidden adaptation states that lead to these correlations themselves exhibit quasi-independence. This talk will first discuss recent findings about the role of such adaptation in suppressing noise and extending sensory detection to weak stimuli that leave the firing rate unchanged. Further, a matching of the post-synaptic responses to the pre-synaptic adaptation time scale enables a recovery of the quasi-independence property, and can explain observations of correlations between post-synaptic EPSPs and behavioural detection thresholds. We then consider the involvement of spike-driven adaptation in the representation of intervals between sensory events. We discuss the possible link of this time-stamping mechanism to the conversion of egocentric to allocentric coordinates. The heterogeneity of the population parameters enables the representation and Bayesian decoding of time sequences of events which may be put to good use in path integration and hilus neuron function in hippocampus.
“Wasn’t there food around here?”: An Agent-based Model for Local Search in Drosophila
The ability to keep track of one’s location in space is a critical behavior for animals navigating to and from a salient location, and its computational basis is now beginning to be unraveled. Here, we tracked flies in a ring-shaped channel as they executed bouts of search triggered by optogenetic activation of sugar receptors. Unlike experiments in open field arenas, which produce highly tortuous search trajectories, our geometrically constrained paradigm enabled us to monitor flies’ decisions to move toward or away from the fictive food. Our results suggest that flies use path integration to remember the location of a food site even after it has disappeared, and flies can remember the location of a former food site even after walking around the arena one or more times. To determine the behavioral algorithms underlying Drosophila search, we developed multiple state transition models and found that flies likely accomplish path integration by combining odometry and compass navigation to keep track of their position relative to the fictive food. Our results indicate that whereas flies re-zero their path integrator at food when only one feeding site is present, they adjust their path integrator to a central location between sites when experiencing food at two or more locations. Together, this work provides a simple experimental paradigm and theoretical framework to advance investigations of the neural basis of path integration.
Learning Neurobiology with electric fish
Electric Gymnotiform fish live in muddy, shallow waters near the shore – hiding in the dense filamentous roots of floating plants such as Eichornia crassipes (“camalote”). They explore their surroundings by using a series of electric pulses that serve as self emitted carrier of electrosensory signals. This propagates at the speed of light through this spongiform habitat and is barely sensed by the lateral line of predators and prey. The emitted field polarizes the surroundings according to the difference in impedance with water which in turn modifies the profile of transcutaneous currents considered as an electrosensory image. Using this system, pulse Gymnotiformes create an electrosensory bubble where an object’s location, impedance, size and other characteristics are discriminated and probably recognized. Although consciousness is still not well-proven, cognitive functions as volition, attention, and path integration have been shown. Here I will summarize different aspects of the electromotor electrosensory loop of pulse Gymnotiforms. First, I will address how objects are polarized with a stereotyped but temporospatially complex electric field, consisting of brief pulses emitted at regular intervals. This relies on complex electric organs quasi periodically activated through an electromotor coordination system by a pacemaker in the medulla. Second, I will deal with the imaging mechanisms of pulse gymnotiform fish and the presence of two regions in the electrosensory field, a rostral region where the field time course is coherent and field vector direction is constant all along the electric organ discharge and a lateral region where the field time course is site specific and field vector direction describes a stereotyped 3D trajectory. Third, I will describe the electrosensory mosaic and their characteristics. Receptor and primary afferents correspond one to one showing subtypes optimally responding to the time course of the self generated pulse with a characteristic train of spikes. While polarized objects at the rostral region project their electric images on the perioral region where electrosensory receptor density, subtypes and central projection are maximal, the image of objects on the side recruit a single type of scattered receptors. Therefore, the rostral mosaic has been likened to an electrosensory fovea and its receptive field referred to as foveal field. The rest of the mosaic and field are referred to as peripheral. Finally, I will describe ongoing work on early processing structures. I will try to generate an integrated view, including anatomical and functional data obtained in vitro, acute experiments, and unitary recordings in freely moving fish. We have recently shown have shown that these fish tract allo-generated fields and the virtual fields generated by nearby objects in the presence of self-generated fields to explore the nearby environment. These data together with the presence of a multimodal receptor mosaic at the cutaneous surface particularly surrounding the mouth and an important role of proprioception in early sensory processing suggests the hypothesis that the active electrosensory system is part of a multimodal haptic sense.
Who can turn faster? Comparison of the head direction circuit of two species
Ants, bees and other insects have the ability to return to their nest or hive using a navigation strategy known as path integration. Similarly, fruit flies employ path integration to return to a previously visited food source. An important component of path integration is the ability of the insect to keep track of its heading relative to salient visual cues. A highly conserved brain region known as the central complex has been identified as being of key importance for the computations required for an insect to keep track of its heading. However, the similarities or differences of the underlying heading tracking circuit between species are not well understood. We sought to address this shortcoming by using reverse engineering techniques to derive the effective underlying neural circuits of two evolutionary distant species, the fruit fly and the locust. Our analysis revealed that regardless of the anatomical differences between the two species the essential circuit structure has not changed. Both effective neural circuits have the structural topology of a ring attractor with an eight-fold radial symmetry (Fig. 1). However, despite the strong similarities between the two ring attractors, there remain differences. Using computational modelling we found that two apparently small anatomical differences have significant functional effect on the ability of the two circuits to track fast rotational movements and to maintain a stable heading signal. In particular, the fruit fly circuit responds faster to abrupt heading changes of the animal while the locust circuit maintains a heading signal that is more robust to inhomogeneities in cell membrane properties and synaptic weights. We suggest that the effects of these differences are consistent with the behavioural ecology of the two species. On the one hand, the faster response of the ring attractor circuit in the fruit fly accommodates the fast body saccades that fruit flies are known to perform. On the other hand, the locust is a migratory species, so its behaviour demands maintenance of a defined heading for a long period of time. Our results highlight that even seemingly small differences in the distribution of dendritic fibres can have a significant effect on the dynamics of the effective ring attractor circuit with consequences for the behavioural capabilities of each species. These differences, emerging from morphologically distinct single neurons highlight the importance of a comparative approach to neuroscience.
Learning accurate path integration in ring attractor models of the head direction system
COSYNE 2022
Learning accurate path integration in ring attractor models of the head direction system
COSYNE 2022
Path integration in insects as an optimized circuit
COSYNE 2023
A rate code for position error in a ring attractor model of path integration
COSYNE 2023
Self-supervised predictive learning across saccades enables visual path integration
COSYNE 2025
Grid field anchoring enhances path integration-dependent but not cue-based navigation
FENS Forum 2024
Home vector degrades over short timescales during path integration in the fiddler crab, Leptuca pugilator
FENS Forum 2024