The Neuroanatomical Ultrastructure and Function of a Biological Ring Attractor

Theoretical principles explain the structure of the insect head direction circuit

To navigate their environment, insects need to keep track of their orientation. Previous work has shown that insects encode their head direction as a sinusoidal activity pattern around a ring of neurons arranged in an eight-column structure. However, it is unclear whether this sinusoidal encoding of head direction is just an evolutionary coincidence or if it offers a particular functional advantage. To address this question, we establish the basic mathematical requirements for direction encoding and show that it can be performed by many circuits, all with different activity patterns. Among these activity patterns, we prove that the sinusoidal one is the most noise-resilient, but only when coupled with a sinusoidal connectivity pattern between the encoding neurons. We compare this predicted optimal connectivity pattern with anatomical data from the head direction circuits of the locust and the fruit fly, finding that our theory agrees with experimental evidence. Furthermore, we demonstrate that our predicted circuit can emerge using Hebbian plasticity, implying that the neural connectivity does not need to be explicitly encoded in the genetic program of the insect but rather can emerge during development. Finally, we illustrate that in our theory, the consistent presence of the eight-column organisation of head direction circuits across multiple insect species is not a chance artefact but instead can be explained by basic evolutionary principles.

A neural circuit architecture for rapid learning in goal-directed navigation

Anchoring goals to spatial representations enables flexible navigation but is challenging in novel environments when both representations must be acquired simultaneously. We propose a framework for how Drosophila uses internal representations of head direction (HD) to build goal representations upon selective thermal reinforcement. We show that flies use stochastically generated fixations and directed saccades to express heading preferences in an operant visual learning paradigm and that HD neurons are required to modify these preferences based on reinforcement. We used a symmetric visual setting to expose how flies' HD and goal representations co-evolve and how the reliability of these interacting representations impacts behavior. Finally, we describe how rapid learning of new goal headings may rest on a behavioral policy whose parameters are flexible but whose form is genetically encoded in circuit architecture. Such evolutionarily structured architectures, which enable rapidly adaptive behavior driven by internal representations, may be relevant across species.

Neurotransmitter classification from electron microscopy images at synaptic sites in Drosophila melanogaster

High-resolution electron microscopy of nervous systems has enabled the reconstruction of synaptic connectomes. However, we do not know the synaptic sign for each connection (i.e., whether a connection is excitatory or inhibitory), which is implied by the released transmitter. We demonstrate that artificial neural networks can predict transmitter types for presynapses from electron micrographs: a network trained to predict six transmitters (acetylcholine, glutamate, GABA, serotonin, dopamine, octopamine) achieves an accuracy of 87% for individual synapses, 94% for neurons, and 91% for known cell types across a D. melanogaster whole brain. We visualize the ultrastructural features used for prediction, discovering subtle but significant differences between transmitter phenotypes. We also analyze transmitter distributions across the brain and find that neurons that develop together largely express only one fast-acting transmitter (acetylcholine, glutamate, or GABA). We hope that our publicly available predictions act as an accelerant for neuroscientific hypothesis generation for the fly.

Continuous Bump Attractor Networks Require Explicit Error Coding for Gain Recalibration

Representations of continuous variables are crucial to create internal models of the external world. A prevailing model of how the brain maintains these representations is given by continuous bump attractor networks (CBANs) in a broad range of brain functions across different areas, such as spatial navigation in hippocampal/entorhinal circuits and working memory in prefrontal cortex. Through recurrent connections, a CBAN maintains a persistent activity bump, whose peak location can vary along a neural space, corresponding to different values of a continuous variable. To track the value of a continuous variable changing over time, a CBAN updates the location of its activity bump based on inputs that encode the changes in the continuous variable (e.g., movement velocity in the case of spatial navigation)-a process akin to mathematical integration. This integration process is not perfect and accumulates error over time. For error correction, CBANs can use additional inputs providing ground-truth information about the continuous variable's correct value (e.g., visual landmarks for spatial navigation). These inputs enable the network dynamics to automatically correct any representation error. Recent experimental work on hippocampal place cells has shown that, beyond correcting errors, ground-truth inputs also fine-tune the gain of the integration process, a crucial factor that links the change in the continuous variable to the updating of the activity bump's location. However, existing CBAN models lack this plasticity, offering no insights into the neural mechanisms and representations involved in the recalibration of the integration gain. In this paper, we explore this gap by using a ring attractor network, a specific type of CBAN, to model the experimental conditions that demonstrated gain recalibration in hippocampal place cells. Our analysis reveals the necessary conditions for neural mechanisms behind gain recalibration within a CBAN. Unlike error correction, which occurs through network dynamics based on ground-truth inputs, gain recalibration requires an additional neural signal that explicitly encodes the error in the network's representation via a rate code. Finally, we propose a modified ring attractor network as an example CBAN model that verifies our theoretical findings. Combining an error-rate code with Hebbian synaptic plasticity, this model achieves recalibration of integration gain in a CBAN, ensuring accurate representation for continuous variables.

The conserved RNA-binding protein Imp is required for the specification and function of olfactory navigation circuitry in Drosophila

Complex behaviors depend on the precise developmental specification of neuronal circuits, but the relationship between genetic programs for neural development, circuit structure, and behavioral output is often unclear. The central complex (CX) is a conserved sensory-motor integration center in insects, which governs many higher-order behaviors and largely derives from a small number of type II neural stem cells (NSCs). Here, we show that Imp, a conserved IGF-II mRNA-binding protein expressed in type II NSCs, plays a role in specifying essential components of CX olfactory navigation circuitry. We show the following: (1) that multiple components of olfactory navigation circuitry arise from type II NSCs. (2) Manipulating Imp expression in type II NSCs alters the number and morphology of many of these circuit elements, with the most potent effects on neurons targeting the ventral layers of the fan-shaped body (FB). (3) Imp regulates the specification of Tachykinin-expressing ventral FB input neurons. (4) Imp is required in type II NSCs for establishing proper morphology of the CX neuropil structures. (5) Loss of Imp in type II NSCs abolishes upwind orientation to attractive odor while leaving locomotion and odor-evoked regulation of movement intact. Taken together, our findings establish that a temporally expressed gene can regulate the expression of a complex behavior by developmentally regulating the specification of multiple circuit components and provides a first step toward a developmental dissection of the CX and its roles in behavior.

Distinct manifold encoding of navigational information in the subiculum and hippocampus

The subiculum (SUB) plays a crucial role in spatial navigation and encodes navigational information differently from the hippocampal CA1 area. However, the representation of subicular population activity remains unknown. Here, we investigated the neuronal population activity recorded extracellularly from the CA1 and SUB of rats performing T-maze and open-field tasks. The trajectory of population activity in both areas was confined to low-dimensional neural manifolds homoeomorphic to external space. The manifolds conveyed position, speed, and future path information with higher decoding accuracy in the SUB than in the CA1. The manifolds exhibited common geometry across rats and regions for the CA1 and SUB and between tasks in the SUB. During post-task ripples in slow-wave sleep, population activity represented reward locations/events more frequently in the SUB than in CA1. Thus, the CA1 and SUB encode information distinctly into the neural manifolds that underlie navigational information processing during wakefulness and sleep.

Transforming a head direction signal into a goal-oriented steering command

To navigate, we must continuously estimate the direction we are headed in, and we must correct deviations from our goal1. Direction estimation is accomplished by ring attractor networks in the head direction system2,3. However, we do not fully understand how the sense of direction is used to guide action. Drosophila connectome analyses4,5 reveal three cell populations (PFL3R, PFL3L and PFL2) that connect the head direction system to the locomotor system. Here we use imaging, electrophysiology and chemogenetic stimulation during navigation to show how these populations function. Each population receives a shifted copy of the head direction vector, such that their three reference frames are shifted approximately 120° relative to each other. Each cell type then compares its own head direction vector with a common goal vector; specifically, it evaluates the congruence of these vectors via a nonlinear transformation. The output of all three cell populations is then combined to generate locomotor commands. PFL3R cells are recruited when the fly is oriented to the left of its goal, and their activity drives rightward turning; the reverse is true for PFL3L. Meanwhile, PFL2 cells increase steering speed, and are recruited when the fly is oriented far from its goal. PFL2 cells adaptively increase the strength of steering as directional error increases, effectively managing the tradeoff between speed and accuracy. Together, our results show how a map of space in the brain can be combined with an internal goal to generate action commands, via a transformation from world-centric coordinates to body-centric coordinates.

Converting an allocentric goal into an egocentric steering signal

Neuronal signals that are relevant for spatial navigation have been described in many species1-10. However, a circuit-level understanding of how such signals interact to guide navigational behaviour is lacking. Here we characterize a neuronal circuit in the Drosophila central complex that compares internally generated estimates of the heading and goal angles of the fly-both of which are encoded in world-centred (allocentric) coordinates-to generate a body-centred (egocentric) steering signal. Past work has suggested that the activity of EPG neurons represents the fly's moment-to-moment angular orientation, or heading angle, during navigation2,11. An animal's moment-to-moment heading angle, however, is not always aligned with its goal angle-that is, the allocentric direction in which it wishes to progress forward. We describe FC2 cells12, a second set of neurons in the Drosophila brain with activity that correlates with the fly's goal angle. Focal optogenetic activation of FC2 neurons induces flies to orient along experimenter-defined directions as they walk forward. EPG and FC2 neurons connect monosynaptically to a third neuronal class, PFL3 cells12,13. We found that individual PFL3 cells show conjunctive, spike-rate tuning to both the heading angle and the goal angle during goal-directed navigation. Informed by the anatomy and physiology of these three cell classes, we develop a model that explains how this circuit compares allocentric heading and goal angles to build an egocentric steering signal in the PFL3 output terminals. Quantitative analyses and optogenetic manipulations of PFL3 activity support the model. Finally, using a new navigational memory task, we show that flies expressing disruptors of synaptic transmission in subsets of PFL3 cells have a reduced ability to orient along arbitrary goal directions, with an effect size in quantitative accordance with the prediction of our model. The biological circuit described here reveals how two population-level allocentric signals are compared in the brain to produce an egocentric output signal that is appropriate for motor control.

Seven-up acts in neuroblasts to specify adult central complex neuron identity and initiate neuroblast decommissioning

An unanswered question in neurobiology is how are diverse neuron cell types generated from a small number of neural stem cells? In the Drosophila larval central brain, there are eight bilateral Type 2 neuroblast (T2NB) lineages that express a suite of early temporal factors followed by a different set of late temporal factors and generate the majority of the central complex (CX) neurons. The early-to-late switch is triggered by the orphan nuclear hormone receptor Seven-up (Svp), yet little is known about how this Svp-dependent switch is involved in specifying CX neuron identities. Here, we: (1) birth date the CX neurons P-EN and P-FN (early and late, respectively); (2) show that Svp is transiently expressed in all early T2NBs; and (3) show that loss of Svp expands the population of early born P-EN neurons at the expense of late born P-FN neurons. Furthermore, in the absence of Svp, T2NBs fail decommissioning and abnormally extend their lineage into week-old adults. We conclude that Svp is required to specify CX neuron identity, as well as to initiate T2NB decommissioning.

Connectomic reconstruction predicts the functional organization of visual inputs to the navigation center of the Drosophila brain

Many animals, including humans, navigate their surroundings by visual input, yet we understand little about how visual information is transformed and integrated by the navigation system. In Drosophila melanogaster, compass neurons in the donut-shaped ellipsoid body of the central complex generate a sense of direction by integrating visual input from ring neurons, a part of the anterior visual pathway (AVP). Here, we densely reconstruct all neurons in the AVP using FlyWire, an AI-assisted tool for analyzing electron-microscopy data. The AVP comprises four neuropils, sequentially linked by three major classes of neurons: MeTu neurons, which connect the medulla in the optic lobe to the small unit of anterior optic tubercle (AOTUsu) in the central brain; TuBu neurons, which connect the anterior optic tubercle to the bulb neuropil; and ring neurons, which connect the bulb to the ellipsoid body. Based on neuronal morphologies, connectivity between different neural classes, and the locations of synapses, we identified non-overlapping channels originating from four types of MeTu neurons, which we further divided into ten subtypes based on the presynaptic connections in medulla and postsynaptic connections in AOTUsu. To gain an objective measure of the natural variation within the pathway, we quantified the differences between anterior visual pathways from both hemispheres and between two electron-microscopy datasets. Furthermore, we infer potential visual features and the visual area from which any given ring neuron receives input by combining the connectivity of the entire AVP, the MeTu neurons' dendritic fields, and presynaptic connectivity in the optic lobes. These results provide a strong foundation for understanding how distinct visual features are extracted and transformed across multiple processing stages to provide critical information for computing the fly's sense of direction.

Neuronal calcium spikes enable vector inversion in the Drosophila brain

A typical neuron signals to downstream cells when it is depolarized and firing sodium spikes. Some neurons, however, also fire calcium spikes when hyperpolarized. The function of such bidirectional signaling remains unclear in most circuits. Here we show how a neuron class that participates in vector computation in the fly central complex employs hyperpolarization-elicited calcium spikes to invert two-dimensional mathematical vectors. When cells switch from firing sodium to calcium spikes, this leads to a ~180° realignment between the vector encoded in the neuronal population and the fly's internal heading signal, thus inverting the vector. We show that the calcium spikes rely on the T-type calcium channel Ca-α1T, and argue, via analytical and experimental approaches, that these spikes enable vector computations in portions of angular space that would otherwise be inaccessible. These results reveal a seamless interaction between molecular, cellular and circuit properties for implementing vector math in the brain.

Neuropeptide Signaling is Required to Implement a Line Attractor Encoding a Persistent Internal Behavioral State

Internal states drive survival behaviors, but their neural implementation is not well understood. Recently we identified a line attractor in the ventromedial hypothalamus (VMH) that represents an internal state of aggressiveness. Line attractors can be implemented by recurrent connectivity and/or neuromodulatory signaling, but evidence for the latter is scant. Here we show that neuropeptidergic signaling is necessary for line attractor dynamics in this system, using a novel approach that integrates cell type-specific, anatomically restricted CRISPR/Cas9-based gene editing with microendoscopic calcium imaging. Co-disruption of receptors for oxytocin and vasopressin in adult VMH Esr1 + neurons that control aggression suppressed attack, reduced persistent neural activity and eliminated line attractor dynamics, while only modestly impacting neural activity and sex- or behavior-tuning. These data identify a requisite role for neuropeptidergic signaling in implementing a behaviorally relevant line attractor. Our approach should facilitate mechanistic studies in neuroscience that bridge different levels of biological function and abstraction.

Seven-up acts in neuroblasts to specify adult central complex neuron identity and initiate neuroblast decommissioning

An open question in neurobiology is how diverse neuron cell types are generated from a small number of neural stem cells. In the Drosophila larval central brain, there are eight bilateral Type 2 neuroblast (T2NB) lineages that express a suite of early temporal factors followed by a different set of late temporal factors and generate the majority of the central complex (CX) neurons. The early-to-late switch is triggered by the orphan nuclear hormone receptor Seven-up (Svp), yet little is known about this Svp-dependent switch in specifying CX neuron identities. Here, we (i) birthdate the CX neurons P-EN and P-FN (early and late, respectively); (ii) show that Svp is transiently expressed in all early T2NBs; and (iii) show that loss of Svp expands the population of early born P-EN neurons at the expense of late born P-FN neurons. Furthermore, in the absence of Svp, T2NBs fail decommissioning and abnormally extend their lineage into week-old adults. We conclude that Svp is required to specify CX neuron identity, as well as to initiate T2NB decommissioning.

Pynapple, a toolbox for data analysis in neuroscience

Datasets collected in neuroscientific studies are of ever-growing complexity, often combining high-dimensional time series data from multiple data acquisition modalities. Handling and manipulating these various data streams in an adequate programming environment is crucial to ensure reliable analysis, and to facilitate sharing of reproducible analysis pipelines. Here, we present Pynapple, the PYthon Neural Analysis Package, a lightweight python package designed to process a broad range of time-resolved data in systems neuroscience. The core feature of this package is a small number of versatile objects that support the manipulation of any data streams and task parameters. The package includes a set of methods to read common data formats and allows users to easily write their own. The resulting code is easy to read and write, avoids low-level data processing and other error-prone steps, and is open source. Libraries for higher-level analyses are developed within the Pynapple framework but are contained within a collaborative repository of specialized and continuously updated analysis routines. This provides flexibility while ensuring long-term stability of the core package. In conclusion, Pynapple provides a common framework for data analysis in neuroscience.

Stem cell-specific ecdysone signaling regulates the development and function of a Drosophila sleep homeostat

Complex behaviors arise from neural circuits that are assembled from diverse cell types. Sleep is a conserved and essential behavior, yet little is known regarding how the nervous system generates neuron types of the sleep-wake circuit. Here, we focus on the specification of Drosophila sleep-promoting neurons-long-field tangential input neurons that project to the dorsal layers of the fan-shaped body neuropil in the central complex (CX). We use lineage analysis and genetic birth dating to identify two bilateral Type II neural stem cells that generate these dorsal fan-shaped body (dFB) neurons. We show that adult dFB neurons express Ecdysone-induced protein E93, and loss of Ecdysone signaling or E93 in Type II NSCs results in the misspecification of the adult dFB neurons. Finally, we show that E93 knockdown in Type II NSCs affects adult sleep behavior. Our results provide insight into how extrinsic hormonal signaling acts on NSCs to generate neuronal diversity required for adult sleep behavior. These findings suggest that some adult sleep disorders might derive from defects in stem cell-specific temporal neurodevelopmental programs.

An insect-inspired model facilitating autonomous navigation by incorporating goal approaching and collision avoidance

Being one of the most fundamental and crucial capacity of robots and animals, autonomous navigation that consists of goal approaching and collision avoidance enables completion of various tasks while traversing different environments. In light of the impressive navigational abilities of insects despite their tiny brains compared to mammals, the idea of seeking solutions from insects for the two key problems of navigation, i.e., goal approaching and collision avoidance, has fascinated researchers and engineers for many years. However, previous bio-inspired studies have focused on merely one of these two problems at one time. Insect-inspired navigation algorithms that synthetically incorporate both goal approaching and collision avoidance, and studies that investigate the interactions of these two mechanisms in the context of sensory-motor closed-loop autonomous navigation are lacking. To fill this gap, we propose an insect-inspired autonomous navigation algorithm to integrate the goal approaching mechanism as the global working memory inspired by the sweat bee's path integration (PI) mechanism, and the collision avoidance model as the local immediate cue built upon the locust's lobula giant movement detector (LGMD) model. The presented algorithm is utilized to drive agents to complete navigation task in a sensory-motor closed-loop manner within a bounded static or dynamic environment. Simulation results demonstrate that the synthetic algorithm is capable of guiding the agent to complete challenging navigation tasks in a robust and efficient way. This study takes the first tentative step to integrate the insect-like navigation mechanisms with different functionalities (i.e., global goal and local interrupt) into a coordinated control system that future research avenues could build upon.

Neural Networks for Navigation: From Connections to Computations

Many animals can navigate toward a goal they cannot see based on an internal representation of that goal in the brain's spatial maps. These maps are organized around networks with stable fixed-point dynamics (attractors), anchored to landmarks, and reciprocally connected to motor control. This review summarizes recent progress in understanding these networks, focusing on studies in arthropods. One factor driving recent progress is the availability of the Drosophila connectome; however, it is increasingly clear that navigation depends on ongoing synaptic plasticity in these networks. Functional synapses appear to be continually reselected from the set of anatomical potential synapses based on the interaction of Hebbian learning rules, sensory feedback, attractor dynamics, and neuromodulation. This can explain how the brain's maps of space are rapidly updated; it may also explain how the brain can initialize goals as stable fixed points for navigation.

SAMPL is a high-throughput solution to study unconstrained vertical behavior in small animals

Balance and movement are impaired in many neurological disorders. Recent advances in behavioral monitoring provide unprecedented access to posture and locomotor kinematics but without the throughput and scalability necessary to screen candidate genes/potential therapeutics. Here, we present a scalable apparatus to measure posture and locomotion (SAMPL). SAMPL includes extensible hardware and open-source software with real-time processing and can acquire data from D. melanogaster, C. elegans, and D. rerio as they move vertically. Using SAMPL, we define how zebrafish balance as they navigate vertically and discover small but systematic variations among kinematic parameters between genetic backgrounds. We demonstrate SAMPL's ability to resolve differences in posture and navigation as a function of effect size and data gathered, providing key data for screens. SAMPL is therefore both a tool to model balance and locomotor disorders and an exemplar of how to scale apparatus to support screens.

Neuroscience: Fish and fly headed in the same direction

Using functional imaging and neural circuit reconstructions, a recent study reveals head direction neurons in the anterior hindbrain of zebrafish that resemble insect head-direction cells to a surprising degree.

Ring neurons in the Drosophila central complex act as a rheostat for sensory modulation of aging

Sensory perception modulates aging, yet we know little about how. An understanding of the neuronal mechanisms through which animals orchestrate biological responses to relevant sensory inputs would provide insight into the control systems that may be important for modulating lifespan. Here, we provide new awareness into how the perception of dead conspecifics, or death perception, which elicits behavioral and physiological effects in many different species, affects lifespan in the fruit fly, Drosophila melanogaster. Previous work demonstrated that cohousing Drosophila with dead conspecifics decreases fat stores, reduces starvation resistance, and accelerates aging in a manner that requires both sight and the serotonin receptor 5-HT2A. In this manuscript, we demonstrate that a discrete, 5-HT2A-expressing neural population in the ellipsoid body (EB) of the Drosophila central complex, identified as R2/R4 neurons, acts as a rheostat and plays an important role in transducing sensory information about the presence of dead individuals to modulate lifespan. Expression of the insulin-responsive transcription factor foxo in R2/R4 neurons and insulin-like peptides dilp3 and dilp5, but not dilp2, are required, with the latter likely altered in median neurosecretory cells (MNCs) after R2/R4 neuronal activation. These data generate new insights into the neural underpinnings of how perceptive events may impact aging and physiology across taxa.

A unifying perspective on neural manifolds and circuits for cognition

Two different perspectives have informed efforts to explain the link between the brain and behaviour. One approach seeks to identify neural circuit elements that carry out specific functions, emphasizing connectivity between neurons as a substrate for neural computations. Another approach centres on neural manifolds - low-dimensional representations of behavioural signals in neural population activity - and suggests that neural computations are realized by emergent dynamics. Although manifolds reveal an interpretable structure in heterogeneous neuronal activity, finding the corresponding structure in connectivity remains a challenge. We highlight examples in which establishing the correspondence between low-dimensional activity and connectivity has been possible, unifying the neural manifold and circuit perspectives. This relationship is conspicuous in systems in which the geometry of neural responses mirrors their spatial layout in the brain, such as the fly navigational system. Furthermore, we describe evidence that, in systems in which neural responses are heterogeneous, the circuit comprises interactions between activity patterns on the manifold via low-rank connectivity. We suggest that unifying the manifold and circuit approaches is important if we are to be able to causally test theories about the neural computations that underlie behaviour.

The RNA-binding protein, Imp specifies olfactory navigation circuitry and behavior in Drosophila

Complex behaviors depend on the precise developmental specification of neuronal circuits, but the relationship between genetic prograssms for neural development, circuit structure, and behavioral output is often unclear. The central complex (CX) is a conserved sensory-motor integration center in insects that governs many higher order behaviors and largely derives from a small number of Type II neural stem cells. Here, we show that Imp, a conserved IGF-II mRNA-binding protein expressed in Type II neural stem cells, specifies components of CX olfactory navigation circuitry. We show: (1) that multiple components of olfactory navigation circuitry arise from Type II neural stem cells and manipulating Imp expression in Type II neural stem cells alters the number and morphology of many of these circuit elements, with the most potent effects on neurons targeting the ventral layers of the fan-shaped body. (2) Imp regulates the specification of Tachykinin expressing ventral fan-shaped body input neurons. (3) Imp in Type II neural stem cells alters the morphology of the CX neuropil structures. (4) Loss of Imp in Type II neural stem cells abolishes upwind orientation to attractive odor while leaving locomotion and odor-evoked regulation of movement intact. Taken together, our work establishes that a single temporally expressed gene can regulate the expression of a complex behavior through the developmental specification of multiple circuit components and provides a first step towards a developmental dissection of the CX and its roles in behavior.

Visual processing in the fly, from photoreceptors to behavior

Originally a genetic model organism, the experimental use of Drosophila melanogaster has grown to include quantitative behavioral analyses, sophisticated perturbations of neuronal function, and detailed sensory physiology. A highlight of these developments can be seen in the context of vision, where pioneering studies have uncovered fundamental and generalizable principles of sensory processing. Here we begin with an overview of vision-guided behaviors and common methods for probing visual circuits. We then outline the anatomy and physiology of brain regions involved in visual processing, beginning at the sensory periphery and ending with descending motor control. Areas of focus include contrast and motion detection in the optic lobe, circuits for visual feature selectivity, computations in support of spatial navigation, and contextual associative learning. Finally, we look to the future of fly visual neuroscience and discuss promising topics for further study.

The influence of stimulus history on directional coding in the monarch butterfly brain

The central complex is a brain region in the insect brain that houses a neural network specialized to encode directional information. Directional coding has traditionally been investigated with compass cues that revolve in full rotations and at constant angular velocities around the insect's head. However, these stimulus conditions do not fully simulate an insect's sensory perception of compass cues during navigation. In nature, an insect flight is characterized by abrupt changes in moving direction as well as constant changes in velocity. The influence of such varying cue dynamics on compass coding remains unclear. We performed long-term tetrode recordings from the brain of monarch butterflies to study how central complex neurons respond to different stimulus velocities and directions. As these butterflies derive directional information from the sun during migration, we measured the neural response to a virtual sun. The virtual sun was either presented as a spot that appeared at random angular positions or was rotated around the butterfly at different angular velocities and directions. By specifically manipulating the stimulus velocity and trajectory, we dissociated the influence of angular velocity and direction on compass coding. While the angular velocity substantially affected the tuning directedness, the stimulus trajectory influenced the shape of the angular tuning curve. Taken together, our results suggest that the central complex flexibly adjusts its directional coding to the current stimulus dynamics ensuring a precise compass even under highly demanding conditions such as during rapid flight maneuvers.

Scalable Apparatus to Measure Posture and Locomotion (SAMPL): a high-throughput solution to study unconstrained vertical behavior in small animals

Balance and movement are impaired in a wide variety of neurological disorders. Recent advances in behavioral monitoring provide unprecedented access to posture and locomotor kinematics, but without the throughput and scalability necessary to screen candidate genes / potential therapeutics. We present a powerful solution: a Scalable Apparatus to Measure Posture and Locomotion (SAMPL). SAMPL includes extensible imaging hardware and low-cost open-source acquisition software with real-time processing. We first demonstrate that SAMPL's hardware and acquisition software can acquire data from from D. melanogaster, C. elegans, and D. rerio as they move vertically. Next, we leverage SAMPL's throughput to rapidly (two weeks) gather a new zebrafish dataset. We use SAMPL's analysis and visualization tools to replicate and extend our current understanding of how zebrafish balance as they navigate through a vertical environment. Next, we discover (1) that key kinematic parameters vary systematically with genetic background, and (2) that such background variation is small relative to the changes that accompany early development. Finally, we simulate SAMPL's ability to resolve differences in posture or vertical navigation as a function of affect size and data gathered -- key data for screens. Taken together, our apparatus, data, and analysis provide a powerful solution for labs using small animals to investigate balance and locomotor disorders at scale. More broadly, SAMPL is both an adaptable resource for labs looking process videographic measures of behavior in real-time, and an exemplar of how to scale hardware to enable the throughput necessary for screening.

Lineages to circuits: the developmental and evolutionary architecture of information channels into the central complex

The representation and integration of internal and external cues is crucial for any organism to execute appropriate behaviors. In insects, a highly conserved region of the brain, the central complex (CX), functions in the representation of spatial information and behavioral states, as well as the transformation of this information into desired navigational commands. How does this relatively invariant structure enable the incorporation of information from the diversity of anatomical, behavioral, and ecological niches occupied by insects? Here, we examine the input channels to the CX in the context of their development and evolution. Insect brains develop from ~ 100 neuroblasts per hemisphere that divide systematically to form "lineages" of sister neurons, that project to their target neuropils along anatomically characteristic tracts. Overlaying this developmental tract information onto the recently generated Drosophila "hemibrain" connectome and integrating this information with the anatomical and physiological recording of neurons in other species, we observe neuropil and lineage-specific innervation, connectivity, and activity profiles in CX input channels. We posit that the proliferative potential of neuroblasts and the lineage-based architecture of information channels enable the modification of neural networks across existing, novel, and deprecated modalities in a species-specific manner, thus forming the substrate for the evolution and diversification of insect navigational circuits.

Neuronal birthdate reveals topography in a vestibular brainstem circuit for gaze stabilization

Across the nervous system, neurons with similar attributes are topographically organized. This topography reflects developmental pressures. Oddly, vestibular (balance) nuclei are thought to be disorganized. By measuring activity in birthdated neurons, we revealed a functional map within the central vestibular projection nucleus that stabilizes gaze in the larval zebrafish. We first discovered that both somatic position and stimulus selectivity follow projection neuron birthdate. Next, with electron microscopy and loss-of-function assays, we found that patterns of peripheral innervation to projection neurons were similarly organized by birthdate. Finally, birthdate revealed spatial patterns of axonal arborization and synapse formation to projection neuron outputs. Collectively, we find that development reveals previously hidden organization to the input, processing, and output layers of a highly conserved vertebrate sensorimotor circuit. The spatial and temporal attributes we uncover constrain the developmental mechanisms that may specify the fate, function, and organization of vestibulo-ocular reflex neurons. More broadly, our data suggest that, like invertebrates, temporal mechanisms may assemble vertebrate sensorimotor architecture.

Bayesian inference in ring attractor networks

Working memories are thought to be held in attractor networks in the brain. These attractors should keep track of the uncertainty associated with each memory, so as to weigh it properly against conflicting new evidence. However, conventional attractors do not represent uncertainty. Here, we show how uncertainty could be incorporated into an attractor, specifically a ring attractor that encodes head direction. First, we introduce a rigorous normative framework (the circular Kalman filter) for benchmarking the performance of a ring attractor under conditions of uncertainty. Next, we show that the recurrent connections within a conventional ring attractor can be retuned to match this benchmark. This allows the amplitude of network activity to grow in response to confirmatory evidence, while shrinking in response to poor-quality or strongly conflicting evidence. This "Bayesian ring attractor" performs near-optimal angular path integration and evidence accumulation. Indeed, we show that a Bayesian ring attractor is consistently more accurate than a conventional ring attractor. Moreover, near-optimal performance can be achieved without exact tuning of the network connections. Finally, we use large-scale connectome data to show that the network can achieve near-optimal performance even after we incorporate biological constraints. Our work demonstrates how attractors can implement a dynamic Bayesian inference algorithm in a biologically plausible manner, and it makes testable predictions with direct relevance to the head direction system as well as any neural system that tracks direction, orientation, or periodic rhythms.

Navigating Like a Fly: Drosophila melanogaster as a Model to Explore the Contribution of Serotonergic Neurotransmission to Spatial Navigation

Serotonin is a monoamine that acts in vertebrates and invertebrates as a modulator promoting changes in the structure and activity of brain areas relevant to animal behavior, ranging from sensory perception to learning and memory. Whether serotonin contributes in Drosophila to human-like cognitive abilities, including spatial navigation, is an issue little studied. Like in vertebrates, the serotonergic system in Drosophila is heterogeneous, meaning that distinct serotonergic neurons/circuits innervate specific fly brain regions to modulate precise behaviors. Here we review the literature that supports that serotonergic pathways modify different aspects underlying the formation of navigational memories in Drosophila.

Global inhibition in head-direction neural circuits: a systematic comparison between connectome-based spiking neural circuit models

The recent discovery of the head-direction (HD) system in fruit flies has provided unprecedented insights into the neural mechanisms of spatial orientation. Despite the progress, the neural substance of global inhibition, an essential component of the HD circuits, remains controversial. Some studies suggested that the ring neurons provide global inhibition, while others suggested the Δ7 neurons. In the present study, we provide evaluations from the theoretical perspective by performing systematic analyses on the computational models based on the ring-neuron (R models) and Δ7-neurons (Delta models) hypotheses with modifications according to the latest connectomic data. We conducted four tests: robustness, persistency, speed, and dynamical characteristics. We discovered that the two models led to a comparable performance in general, but each excelled in different tests. The R Models were more robust, while the Delta models were better in the persistency test. We also tested a hybrid model that combines both inhibitory mechanisms. While the performances of the R and Delta models in each test are highly parameter-dependent, the Hybrid model performed well in all tests with the same set of parameters. Our results suggest the possibility of combined inhibitory mechanisms in the HD circuits of fruit flies.

Local shape descriptors for neuron segmentation

We present an auxiliary learning task for the problem of neuron segmentation in electron microscopy volumes. The auxiliary task consists of the prediction of local shape descriptors (LSDs), which we combine with conventional voxel-wise direct neighbor affinities for neuron boundary detection. The shape descriptors capture local statistics about the neuron to be segmented, such as diameter, elongation, and direction. On a study comparing several existing methods across various specimen, imaging techniques, and resolutions, auxiliary learning of LSDs consistently increases segmentation accuracy of affinity-based methods over a range of metrics. Furthermore, the addition of LSDs promotes affinity-based segmentation methods to be on par with the current state of the art for neuron segmentation (flood-filling networks), while being two orders of magnitudes more efficient-a critical requirement for the processing of future petabyte-sized datasets.

Integration of optic flow into the sky compass network in the brain of the desert locust

Flexible orientation through any environment requires a sense of current relative heading that is updated based on self-motion. Global external cues originating from the sky or the earth's magnetic field and local cues provide a reference frame for the sense of direction. Locally, optic flow may inform about turning maneuvers, travel speed and covered distance. The central complex in the insect brain is associated with orientation behavior and largely acts as a navigation center. Visual information from global celestial cues and local landmarks are integrated in the central complex to form an internal representation of current heading. However, it is less clear how optic flow is integrated into the central-complex network. We recorded intracellularly from neurons in the locust central complex while presenting lateral grating patterns that simulated translational and rotational motion to identify these sites of integration. Certain types of central-complex neurons were sensitive to optic-flow stimulation independent of the type and direction of simulated motion. Columnar neurons innervating the noduli, paired central-complex substructures, were tuned to the direction of simulated horizontal turns. Modeling the connectivity of these neurons with a system of proposed compass neurons can account for rotation-direction specific shifts in the activity profile in the central complex corresponding to turn direction. Our model is similar but not identical to the mechanisms proposed for angular velocity integration in the navigation compass of the fly Drosophila.

The sky compass network in the brain of the desert locust

Many arthropods and vertebrates use celestial signals such as the position of the sun during the day or stars at night as compass cues for spatial orientation. The neural network underlying sky compass coding in the brain has been studied in great detail in the desert locust Schistocerca gregaria. These insects perform long-range migrations in Northern Africa and the Middle East following seasonal changes in rainfall. Highly specialized photoreceptors in a dorsal rim area of their compound eyes are sensitive to the polarization of the sky, generated by scattered sunlight. These signals are combined with direct information on the sun position in the optic lobe and anterior optic tubercle and converge from both eyes in a midline crossing brain structure, the central complex. Here, head direction coding is achieved by a compass-like arrangement of columns signaling solar azimuth through a 360° range of space by combining direct brightness cues from the sun with polarization cues matching the polarization pattern of the sky. Other directional cues derived from wind direction and internal self-rotation input are likely integrated. Signals are transmitted as coherent steering commands to descending neurons for directional control of locomotion and flight.

Theory of the Multiregional Neocortex: Large-Scale Neural Dynamics and Distributed Cognition

The neocortex is a complex neurobiological system with many interacting regions. How these regions work together to subserve flexible behavior and cognition has become increasingly amenable to rigorous research. Here, I review recent experimental and theoretical work on the modus operandi of a multiregional cortex. These studies revealed several general principles for the neocortical interareal connectivity, low-dimensional macroscopic gradients of biological properties across cortical areas, and a hierarchy of timescales for information processing. Theoretical work suggests testable predictions regarding differential excitation and inhibition along feedforward and feedback pathways in the cortical hierarchy. Furthermore, modeling of distributed working memory and simple decision-making has given rise to a novel mathematical concept, dubbed bifurcation in space, that potentially explains how different cortical areas, with a canonical circuit organization but gradients of biological heterogeneities, are able to subserve their respective (e.g., sensory coding versus executive control) functions in a modularly organized brain.

A set of hub neurons and non-local connectivity features support global brain dynamics in C. elegans

The wiring architecture of neuronal networks is assumed to be a strong determinant of their dynamical computations. An ongoing effort in neuroscience is therefore to generate comprehensive synapse-resolution connectomes alongside brain-wide activity maps. However, the structure-function relationship, i.e., how the anatomical connectome and neuronal dynamics relate to each other on a global scale, remains unsolved. Systematically, comparing graph features in the C. elegans connectome with correlations in nervous system-wide neuronal dynamics, we found that few local connectivity motifs and mostly other non-local features such as triplet motifs and input similarities can predict functional relationships between neurons. Surprisingly, quantities such as connection strength and amount of common inputs do not improve these predictions, suggesting that the network's topology is sufficient. We demonstrate that hub neurons in the connectome are key to these relevant graph features. Consistently, inhibition of multiple hub neurons specifically disrupts brain-wide correlations. Thus, we propose that a set of hub neurons and non-local connectivity features provide an anatomical substrate for global brain dynamics.

Weighting of Celestial and Terrestrial Cues in the Monarch Butterfly Central Complex

Monarch butterflies rely on external cues for orientation during their annual long-distance migration from Northern US and Canada to Central Mexico. These external cues can be celestial cues, such as the sun or polarized light, which are processed in a brain region termed the central complex (CX). Previous research typically focused on how individual simulated celestial cues are encoded in the butterfly's CX. However, in nature, the butterflies perceive several celestial cues at the same time and need to integrate them to effectively use the compound of all cues for orientation. In addition, a recent behavioral study revealed that monarch butterflies can rely on terrestrial cues, such as the panoramic skyline, for orientation and use them in combination with the sun to maintain a directed flight course. How the CX encodes a combination of celestial and terrestrial cues and how they are weighted in the butterfly's CX is still unknown. Here, we examined how input neurons of the CX, termed TL neurons, combine celestial and terrestrial information. While recording intracellularly from the neurons, we presented a sun stimulus and polarized light to the butterflies as well as a simulated sun and a panoramic scene simultaneously. Our results show that celestial cues are integrated linearly in these cells, while the combination of the sun and a panoramic skyline did not always follow a linear integration of action potential rates. Interestingly, while the sun and polarized light were invariantly weighted between individual neurons, the sun stimulus and panoramic skyline were dynamically weighted when both stimuli were simultaneously presented. Taken together, this dynamic weighting between celestial and terrestrial cues may allow the butterflies to flexibly set their cue preference during navigation.

Learning accurate path integration in ring attractor models of the head direction system

Ring attractor models for angular path integration have received strong experimental support. To function as integrators, head direction circuits require precisely tuned connectivity, but it is currently unknown how such tuning could be achieved. Here, we propose a network model in which a local, biologically plausible learning rule adjusts synaptic efficacies during development, guided by supervisory allothetic cues. Applied to the Drosophila head direction system, the model learns to path-integrate accurately and develops a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading, and where the network remaps to integrate with different gains in rodents. Our model predicts that path integration requires self-supervised learning during a developmental phase, and proposes a general framework to learn to path-integrate with gain-1 even in architectures that lack the physical topography of a ring.

Myoinhibitory peptides in the central complex of the locust Schistocerca gregaria and colocalization with locustatachykinin-related peptides

The central complex in the brain of insects provides a neural network for sensorimotor processing that is essential for spatial navigation and locomotion and plays a role in sleep control. Studies on the neurochemical architecture of the central complex have been performed especially in the fruit fly Drosophila melangoaster and the desert locust, Schistocerca gregaria. In several insect species, myoinhibitory peptides (MIPs) are involved in circadian control and sleep-wake regulation. To identify neurons that might underlie these functions, we investigated the distribution of MIPs in the central complex of the locust. In silico transcript analysis suggests the presence of eight different MIPs in the desert locust. Through immunolabeling, we identified five systems of central-complex neurons that express MIP-like peptides. Two systems constitute columnar neurons of the protocerebral bridge and the lower division of the central body, while the other three systems are columnar neurons (two systems) and tangential neurons (one system) of the upper division of the central body. The innervation pattern and cell count of two systems of columnar neurons revealed the existence of 18 instead of 16 columns of the protocerebral bridge. Immunostaining of preparations containing intracellularly stained single cells allowed us to further specify subtypes of labeled columnar neurons. Double-label experiments showed that three systems of MIP-immunostained columnar neurons are also locustatachykinin-immunoreactive. No colocalization was found with serotonin immunostaining. The data provide novel insights into the architecture of the locust central complex and suggest that MIPs play a prominent role within the central-complex network.

Geometric framework to predict structure from function in neural networks

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of threshold-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate the solution space of all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. A generalization accounting for noise further reveals that the solution space geometry can undergo topological transitions as the allowed error increases, which could provide insight into both neuroscience and machine learning. We ultimately use this geometric characterization to derive certainty conditions guaranteeing a nonzero synapse between neurons. Our theoretical framework could thus be applied to neural activity data to make rigorous anatomical predictions that follow generally from the model architecture.

From Photons to Behaviors: Neural Implementations of Visual Behaviors in Drosophila

Neural implementations of visual behaviors in Drosophila have been dissected intensively in the past couple of decades. The availability of premiere genetic toolkits, behavioral assays in tethered or freely moving conditions, and advances in connectomics have permitted the understanding of the physiological and anatomical details of the nervous system underlying complex visual behaviors. In this review, we describe recent advances on how various features of a visual scene are detected by the Drosophila visual system and how the neural circuits process these signals and elicit an appropriate behavioral response. Special emphasis was laid on the neural circuits that detect visual features such as brightness, color, local motion, optic flow, and translating or approaching visual objects, which would be important for behaviors such as phototaxis, optomotor response, attraction (or aversion) to moving objects, navigation, and visual learning. This review offers an integrative framework for how the fly brain detects visual features and orchestrates an appropriate behavioral response.

Dopamine Modulation of Drosophila Ellipsoid Body Neurons, a Nod to the Mammalian Basal Ganglia

The central complex (CX) is a neural structure located on the midline of the insect brain that has been widely studied in the last few years. Its role in navigation and goal-oriented behaviors resembles those played by the basal ganglia in mammals. However, the neural mechanisms and the neurotransmitters involved in these processes remain unclear. Here, we exploited an in vivo bioluminescence Ca²⁺ imaging technique to record the activity in targeted neurons of the ellipsoid body (EB). We used different drugs to evoke excitatory Ca²⁺-responses, depending on the putative neurotransmitter released by their presynaptic inputs, while concomitant dopamine administration was employed to modulate those excitations. By using a genetic approach to knockdown the dopamine 1-like receptors, we showed that different dopamine modulatory effects are likely due to specific receptors expressed by the targeted population of neurons. Altogether, these results provide new data concerning how dopamine modulates and shapes the response of the ellipsoid body neurons. Moreover, they provide important insights regarding the similitude with mammals as far as the role played by dopamine in increasing and stabilizing the response of goal-related information.

Receptive field structures for two celestial compass cues at the input stage of the central complex in the locust brain

Successful navigation depends on an animal's ability to perceive its spatial orientation relative to visual surroundings. Heading direction in insects is represented in the central complex (CX), a navigation center in the brain, to generate steering commands. In insects that navigate relative to sky compass signals, CX neurons are tuned to celestial cues indicating the location of the sun. The desert locust CX contains a compass-like representation of two related celestial cues: the direction of unpolarized direct sunlight and the pattern of polarized light, which depends on the sun position. Whether congruent tuning to these two compass cues emerges within the CX network or is inherited from CX input neurons is unclear. To address this question, we intracellularly recorded from GABA-immunoreactive TL neurons, input elements to the locust CX (corresponding to R neurons in Drosophila), while applying visual stimuli simulating unpolarized sunlight and polarized light across the hemisphere above the animal. We show that TL neurons have large receptive fields for both types of stimuli. However, faithful integration of polarization angles across the dorsal hemisphere, or matched-filter ability to encode particular sun positions, was found in only two out of 22 recordings. Those two neurons also showed a good match in sun position coding through polarized and unpolarized light signaling, whereas 20 neurons showed substantial mismatch in signaling of the two compass cues. The data, therefore, suggest that considerable refinement of azimuth coding based on sky compass signals occurs at the synapses from TL neurons to postsynaptic CX compass neurons.

Dopamine promotes head direction plasticity during orienting movements

In neural networks that store information in their connection weights, there is a tradeoff between sensitivity and stability^1,2. Connections must be plastic to incorporate new information, but if they are too plastic, stored information can be corrupted. A potential solution is to allow plasticity only during epochs when task-specific information is rich, on the basis of a 'when-to-learn' signal³. We reasoned that dopamine provides a when-to-learn signal that allows the brain's spatial maps to update when new spatial information is available-that is, when an animal is moving. Here we show that the dopamine neurons innervating the Drosophila head direction network are specifically active when the fly turns to change its head direction. Moreover, their activity scales with moment-to-moment fluctuations in rotational speed. Pairing dopamine release with a visual cue persistently strengthens the cue's influence on head direction cells. Conversely, inhibiting these dopamine neurons decreases the influence of the cue. This mechanism should accelerate learning during moments when orienting movements are providing a rich stream of head direction information, allowing learning rates to be low at other times to protect stored information. Our results show how spatial learning in the brain can be compressed into discrete epochs in which high learning rates are matched to high rates of information intake.

Building an allocentric travelling direction signal via vector computation

Many behavioural tasks require the manipulation of mathematical vectors, but, outside of computational models1-7, it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation7-10, performs vector arithmetic. First, we describe a neural signal in the fan-shaped body that explicitly tracks the allocentric travelling angle of a fly, that is, the travelling angle in reference to external cues. Past work has identified neurons in Drosophila8,11-13 and mammals14 that track the heading angle of an animal referenced to external cues (for example, head direction cells), but this new signal illuminates how the sense of space is properly updated when travelling and heading angles differ (for example, when walking sideways). We then characterize a neuronal circuit that performs an egocentric-to-allocentric (that is, body-centred to world-centred) coordinate transformation and vector addition to compute the allocentric travelling direction. This circuit operates by mapping two-dimensional vectors onto sinusoidal patterns of activity across distinct neuronal populations, with the amplitude of the sinusoid representing the length of the vector and its phase representing the angle of the vector. The principles of this circuit may generalize to other brains and to domains beyond navigation where vector operations or reference-frame transformations are required.

Recent approaches to study the neural bases of complex insect behavior

Recent advances in biocompatible materials, miniaturized instrumentation, advanced computational algorithms, and genetic tools have enabled the development of novel methods and approaches to quantify the behavior of individuals or groups of animals. In conjunction with technologies that allow simultaneous monitoring of neural responses, quantitative studies of complex behaviors can reveal tighter links between the external sensory cues in the vicinity of the organism and neural responses they elicit, and how internal neural representations finally get mapped onto the behavior generated. In this review, we examine a few approaches that are beginning to be widely exploited for understanding neural-behavioral response transformations.

A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection

Flexible behaviors over long timescales are thought to engage recurrent neural networks in deep brain regions, which are experimentally challenging to study. In insects, recurrent circuit dynamics in a brain region called the central complex (CX) enable directed locomotion, sleep, and context- and experience-dependent spatial navigation. We describe the first complete electron-microscopy-based connectome of the Drosophila CX, including all its neurons and circuits at synaptic resolution. We identified new CX neuron types, novel sensory and motor pathways, and network motifs that likely enable the CX to extract the fly's head-direction, maintain it with attractor dynamics, and combine it with other sensorimotor information to perform vector-based navigational computations. We also identified numerous pathways that may facilitate the selection of CX-driven behavioral patterns by context and internal state. The CX connectome provides a comprehensive blueprint necessary for a detailed understanding of network dynamics underlying sleep, flexible navigation, and state-dependent action selection.

Plasticity between visual input pathways and the head direction system

Animals can maintain a stable sense of direction even when they navigate in novel environments, but how the animal's brain interprets and encodes unfamiliar sensory information in its navigation system to maintain a stable sense of direction is a mystery. Recent studies have suggested that distinct brain structures of mammals and insects have evolved to solve this common problem with strategies that share computational principles; specifically, a network structure called a ring attractor maintains the sense of direction. Initially, in a novel environment, the animal's sense of direction relies on self-motion cues. Over time, the mapping from visual inputs to head direction cells, responsible for the sense of direction, is established via experience-dependent plasticity. Yet the mechanisms that facilitate acquiring a world-centered sense of direction, how many environments can be stored in memory, and what visual features are selected, all remain unknown. Thanks to recent advances in large scale physiological recording, genetic tools, and theory, these mechanisms may soon be revealed.

Dynamical self-organization and efficient representation of space by grid cells

To plan trajectories and navigate, animals must maintain a mental representation of the environment and their own position within it. This "cognitive map" is thought to be supported in part by the entorhinal cortex, where grid cells are active when an animal occupies the vertices of a scaling hierarchy of periodic lattices of locations in an enclosure. Here, we review computational developments which suggest that the grid cell network is: (a) efficient, providing required spatial resolution with a minimum number of neurons, (b) self-organizing, dynamically coordinating the structure and scale of the responses, and (c) adaptive, re-organizing in response to changes in landmarks and the structure of the boundaries of spaces. We consider these ideas in light of recent discoveries of similar structures in the mental representation of abstract spaces of shapes and smells, and in other brain areas, and highlight promising directions for future research.