Ring Attractor Dynamics Emerge from a Spiking Model of the Entire Protocerebral Bridge

Synaptic ring attractor: A unified framework for attractor dynamics and multiple cues integration

Effective cue integration is essential for an animal's survival. The ring attractor network has emerged as a powerful framework for understanding how animals seamlessly integrate various cues. This network not only elucidates neural dynamics within the brain, especially in spatial encoding systems like the heading direction (HD) system, but also sheds light on cue integration within decision-making processes. Yet, many significant phenomena across different fields lack clear explanations. For instance, in physiology, the integration mechanism of Drosophila's compass neuron when confronted with conflicting self-motion cues and external sensory cues with varying gain control settings is not well elucidated. Similarly, in ethology, the decision-making system shows Bayesian integration (BI) under minimal cue conflicts, but shifts to a winner-take-all (WTA) mode as conflicts surpass a certain threshold. To address these gaps, we introduce a ring attractor network with asymmetrical neural connections and synaptic dynamics in this paper. A thorough series of simulations has been conducted to assess its ability to track external cues and integrate conflicting cues. The results from these simulations demonstrate that the proposed model replicates observed neural dynamics and offers a framework for modeling biologically plausible cue integration behaviors. Furthermore, our findings yield several testable predictions that could inform future neuroethological research, providing insights into the role of ring attractor dynamics in the animal brain.

Estimating orientation in natural scenes: A spiking neural network model of the insect central complex

The central complex of insects contains cells, organised as a ring attractor, that encode head direction. The 'bump' of activity in the ring can be updated by idiothetic cues and external sensory information. Plasticity at the synapses between these cells and the ring neurons, that are responsible for bringing sensory information into the central complex, has been proposed to form a mapping between visual cues and the heading estimate which allows for more accurate tracking of the current heading, than if only idiothetic information were used. In Drosophila, ring neurons have well characterised non-linear receptive fields. In this work we produce synthetic versions of these visual receptive fields using a combination of excitatory inputs and mutual inhibition between ring neurons. We use these receptive fields to bring visual information into a spiking neural network model of the insect central complex based on the recently published Drosophila connectome. Previous modelling work has focused on how this circuit functions as a ring attractor using the same type of simple visual cues commonly used experimentally. While we initially test the model on these simple stimuli, we then go on to apply the model to complex natural scenes containing multiple conflicting cues. We show that this simple visual filtering provided by the ring neurons is sufficient to form a mapping between heading and visual features and maintain the heading estimate in the absence of angular velocity input. The network is successful at tracking heading even when presented with videos of natural scenes containing conflicting information from environmental changes and translation of the camera.

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.

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.

Ring attractor bio-inspired neural network for social robot navigation

Introduction

We introduce a bio-inspired navigation system for a robot to guide a social agent to a target location while avoiding static and dynamic obstacles. Robot navigation can be accomplished through a model of ring attractor neural networks. This connectivity pattern between neurons enables the generation of stable activity patterns that can represent continuous variables such as heading direction or position. The integration of sensory representation, decision-making, and motor control through ring attractor networks offers a biologically-inspired approach to navigation in complex environments.

Methods

The navigation system is divided into perception, planning, and control stages. Our approach is compared to the widely-used Social Force Model and Rapidly Exploring Random Tree Star methods using the Social Individual Index and Relative Motion Index as metrics in simulated experiments. We created a virtual scenario of a pedestrian area with various obstacles and dynamic agents.

Results

The results obtained in our experiments demonstrate the effectiveness of this architecture in guiding a social agent while avoiding obstacles, and the metrics used for evaluating the system indicate that our proposal outperforms the widely used Social Force Model.

Discussion

Our approach points to improving safety and comfort specifically for human-robot interactions. By integrating the Social Individual Index and Relative Motion Index, this approach considers both social comfort and collision avoidance features, resulting in better human-robot interactions in a crowded environment.

In search of behavioral and brain processes involved in honey bee dance communication

Honey bees represent an iconic model animal for studying the underlying mechanisms affecting advanced sensory and cognitive abilities during communication among colony mates. After von Frisch discovered the functional value of the waggle dance, this complex motor pattern led ethologists and neuroscientists to study its neural mechanism, behavioral significance, and implications for a collective organization. Recent studies have revealed some of the mechanisms involved in this symbolic form of communication by using conventional behavioral and pharmacological assays, neurobiological studies, comprehensive molecular and connectome analyses, and computational models. This review summarizes several critical behavioral and brain processes and mechanisms involved in waggle dance communication. We focus on the role of neuromodulators in the dancer and the recruited follower, the interneurons and their related processing in the first mechano-processing, and the computational navigation centers of insect brains.

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.

A leaky integrate-and-fire computational model based on the connectome of the entire adult Drosophila brain reveals insights into sensorimotor processing

The forthcoming assembly of the adult Drosophila melanogaster central brain connectome, containing over 125,000 neurons and 50 million synaptic connections, provides a template for examining sensory processing throughout the brain. Here, we create a leaky integrate-and-fire computational model of the entire Drosophila brain, based on neural connectivity and neurotransmitter identity, to study circuit properties of feeding and grooming behaviors. We show that activation of sugar-sensing or water-sensing gustatory neurons in the computational model accurately predicts neurons that respond to tastes and are required for feeding initiation. Computational activation of neurons in the feeding region of the Drosophila brain predicts those that elicit motor neuron firing, a testable hypothesis that we validate by optogenetic activation and behavioral studies. Moreover, computational activation of different classes of gustatory neurons makes accurate predictions of how multiple taste modalities interact, providing circuit-level insight into aversive and appetitive taste processing. Our computational model predicts that the sugar and water pathways form a partially shared appetitive feeding initiation pathway, which our calcium imaging and behavioral experiments confirm. Additionally, we applied this model to mechanosensory circuits and found that computational activation of mechanosensory neurons predicts activation of a small set of neurons comprising the antennal grooming circuit that do not overlap with gustatory circuits, and accurately describes the circuit response upon activation of different mechanosensory subtypes. Our results demonstrate that modeling brain circuits purely from connectivity and predicted neurotransmitter identity generates experimentally testable hypotheses and can accurately describe complete sensorimotor transformations.

Sensory fusion in the hoverfly righting reflex

We study how falling hoverflies use sensory cues to trigger appropriate roll righting behavior. Before being released in a free fall, flies were placed upside-down with their legs contacting the substrate. The prior leg proprioceptive information about their initial orientation sufficed for the flies to right themselves properly. However, flies also use visual and antennal cues to recover faster and disambiguate sensory conflicts. Surprisingly, in one of the experimental conditions tested, hoverflies flew upside-down while still actively flapping their wings. In all the other conditions, flies were able to right themselves using two roll dynamics: fast ([Formula: see text]50ms) and slow ([Formula: see text]110ms) in the presence of consistent and conflicting cues, respectively. These findings suggest that a nonlinear sensory integration of the three types of sensory cues occurred. A ring attractor model was developed and discussed to account for this cue integration process.

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.

The neuronal building blocks of the navigational toolkit in the central complex of insects

The central complex in the brain of insects is a group of midline-spanning neuropils at the interface between sensory and premotor tasks of the brain. It is involved in sleep control, decision-making and most prominently in goal-directed locomotion behaviors. The recently published connectome of the central complex of Drosophila melanogaster is a milestone in understanding the intricacies of the central-complex circuits and will provide inspiration for testable hypotheses for the coming years. Here, I provide a basic neuroanatomical description of the central complex of Drosophila and other species and discuss some recent advancements, some of which, such as the discovery of coordinate transformation through vector math, have been predicted from connectomics data.

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.

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

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

The geometry of decision-making in individuals and collectives

Almost all animals must make decisions on the move. Here, employing an approach that integrates theory and high-throughput experiments (using state-of-the-art virtual reality), we reveal that there exist fundamental geometrical principles that result from the inherent interplay between movement and organisms’ internal representation of space. Specifically, we find that animals spontaneously reduce the world into a series of sequential binary decisions, a response that facilitates effective decision-making and is robust both to the number of options available and to context, such as whether options are static (e.g., refuges) or mobile (e.g., other animals). We present evidence that these same principles, hitherto overlooked, apply across scales of biological organization, from individual to collective decision-making.

Choosing among spatially distributed options is a central challenge for animals, from deciding among alternative potential food sources or refuges to choosing with whom to associate. Using an integrated theoretical and experimental approach (employing immersive virtual reality), we consider the interplay between movement and vectorial integration during decision-making regarding two, or more, options in space. In computational models of this process, we reveal the occurrence of spontaneous and abrupt “critical” transitions (associated with specific geometrical relationships) whereby organisms spontaneously switch from averaging vectorial information among, to suddenly excluding one among, the remaining options. This bifurcation process repeats until only one option—the one ultimately selected—remains. Thus, we predict that the brain repeatedly breaks multichoice decisions into a series of binary decisions in space–time. Experiments with fruit flies, desert locusts, and larval zebrafish reveal that they exhibit these same bifurcations, demonstrating that across taxa and ecological contexts, there exist fundamental geometric principles that are essential to explain how, and why, animals move the way they do.

Insect-Inspired Robots: Bridging Biological and Artificial Systems

This review article aims to address common research questions in hexapod robotics. How can we build intelligent autonomous hexapod robots that can exploit their biomechanics, morphology, and computational systems, to achieve autonomy, adaptability, and energy efficiency comparable to small living creatures, such as insects? Are insects good models for building such intelligent hexapod robots because they are the only animals with six legs? This review article is divided into three main sections to address these questions, as well as to assist roboticists in identifying relevant and future directions in the field of hexapod robotics over the next decade. After an introduction in section (1), the sections will respectively cover the following three key areas: (2) biomechanics focused on the design of smart legs; (3) locomotion control; and (4) high-level cognition control. These interconnected and interdependent areas are all crucial to improving the level of performance of hexapod robotics in terms of energy efficiency, terrain adaptability, autonomy, and operational range. We will also discuss how the next generation of bioroboticists will be able to transfer knowledge from biology to robotics and vice versa.

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.

The structure of behavioral variation within a genotype

Individual animals vary in their behaviors. This is true even when they share the same genotype and were reared in the same environment. Clusters of covarying behaviors constitute behavioral syndromes, and an individual’s position along such axes of covariation is a representation of their personality. Despite these conceptual frameworks, the structure of behavioral covariation within a genotype is essentially uncharacterized and its mechanistic origins unknown. Passing hundreds of inbred Drosophila individuals through an experimental pipeline that captured hundreds of behavioral measures, we found sparse but significant correlations among small sets of behaviors. Thus, the space of behavioral variation has many independent dimensions. Manipulating the physiology of the brain, and specific neural populations, altered specific correlations. We also observed that variation in gene expression can predict an individual’s position on some behavioral axes. This work represents the first steps in understanding the biological mechanisms determining the structure of behavioral variation within a genotype.

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.

A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.

A hierarchy of theoretical approaches to study a neuronal network depends on a tradeoff between biological fidelity and mathematical tractibility. Biophysically-detailed models consider cellular mechanisms and anatomically defined synaptic circuits, but are often too complex to reveal insights into fundamental principles. In contrast, increasingly abstract reduced models facilitate analytical insights. To better ground the latter to the underlying biology, we describe a systematic procedure to move across the model hierarchy that allows understanding how changes in biological parameters—physiological, pathophysiological, or because of new data—impact the behaviour of the network. We apply this approach to mammalian primary visual cortex, and examine how the different models in the hierarchy reproduce functional signatures of this area, in particular the tuning of neurons to the orientation of a visual stimulus. Our work provides a navigation of the complex parameter space of neural network models faithful to biology, as well as highlighting how simplifications made for mathematical convenience can fundamentally change their behaviour.

Accelerating with FlyBrainLab the discovery of the functional logic of the Drosophila brain in the connectomic and synaptomic era

In recent years, a wealth of Drosophila neuroscience data have become available including cell type and connectome/synaptome datasets for both the larva and adult fly. To facilitate integration across data modalities and to accelerate the understanding of the functional logic of the fruit fly brain, we have developed FlyBrainLab, a unique open-source computing platform that integrates 3D exploration and visualization of diverse datasets with interactive exploration of the functional logic of modeled executable brain circuits. FlyBrainLab's User Interface, Utilities Libraries and Circuit Libraries bring together neuroanatomical, neurogenetic and electrophysiological datasets with computational models of different researchers for validation and comparison within the same platform. Seeking to transcend the limitations of the connectome/synaptome, FlyBrainLab also provides libraries for molecular transduction arising in sensory coding in vision/olfaction. Together with sensory neuron activity data, these libraries serve as entry points for the exploration, analysis, comparison, and evaluation of circuit functions of the fruit fly brain.

Reverse Engineering and Robotics as Tools for Analyzing Neural Circuits

Understanding neuronal circuits that have evolved over millions of years to control adaptive behavior may provide us with alternative solutions to problems in robotics. Recently developed genetic tools allow us to study the connectivity and function of the insect nervous system at the single neuron level. However, neuronal circuits are complex, so the question remains, can we unravel the complex neuronal connectivity to understand the principles of the computations it embodies? Here, I illustrate the plausibility of incorporating reverse engineering to analyze part of the central complex, an insect brain structure essential for navigation behaviors such as maintaining a specific compass heading and path integration. I demonstrate that the combination of reverse engineering with simulations allows the study of both the structure and function of the underlying circuit, an approach that augments our understanding of both the computation performed by the neuronal circuit and the role of its components.

Towards a multi-level understanding in insect navigation

To understand the brain is to understand behaviour. However, understanding behaviour itself requires consideration of sensory information, body movements and the animal's ecology. Therefore, understanding the link between neurons and behaviour is a multi-level problem, which can be achieved when considering Marr's three levels of understanding: behaviour, computation, and neural implementation. Rather than establishing direct links between neurons and behaviour, the matter boils down to understanding two transitions: the link between neurons and brain computation on one hand, and the link between brain computations and behaviour on the other hand. The field of insect navigation illustrates well the power of such two-sided endeavour. We provide here examples revealing that each transition requires its own approach with its own intrinsic difficulties, and show how modelling can help us reach the desired multi-level understanding.

Oscillations in the central brain of Drosophila are phase locked to attended visual features

Object-based attention describes the brain's capacity to prioritize one set of stimuli while ignoring others. Human research suggests that the binding of diverse stimuli into one attended percept requires phase-locked oscillatory activity in the brain. Even insects display oscillatory brain activity during visual attention tasks, but it is unclear if neural oscillations in insects are selectively correlated to different features of attended objects. We addressed this question by recording local field potentials in the Drosophila central complex, a brain structure involved in visual navigation and decision making. We found that attention selectively increased the neural gain of visual features associated with attended objects and that attention could be redirected to unattended objects by activation of a reward circuit. Attention was associated with increased beta (20- to 30-Hz) oscillations that selectively locked onto temporal features of the attended visual objects. Our results suggest a conserved function for the beta frequency range in regulating selective attention to salient visual features.

The Neuroanatomical Ultrastructure and Function of a Biological Ring Attractor

Neural representations of head direction (HD) have been discovered in many species. Theoretical work has proposed that the dynamics associated with these representations are generated, maintained, and updated by recurrent network structures called ring attractors. We evaluated this theorized structure-function relationship by performing electron-microscopy-based circuit reconstruction and RNA profiling of identified cell types in the HD system of Drosophila melanogaster. We identified motifs that have been hypothesized to maintain the HD representation in darkness, update it when the animal turns, and tether it to visual cues. Functional studies provided support for the proposed roles of individual excitatory or inhibitory circuit elements in shaping activity. We also discovered recurrent connections between neuronal arbors with mixed pre- and postsynaptic specializations. Our results confirm that the Drosophila HD network contains the core components of a ring attractor while also revealing unpredicted structural features that might enhance the network's computational power.

Matched-filter coding of sky polarization results in an internal sun compass in the brain of the desert locust

Many animals use celestial cues for spatial orientation. These include the sun and, in insects, the polarization pattern of the sky, which depends on the position of the sun. The central complex in the insect brain plays a key role in spatial orientation. In desert locusts, the angle of polarized light in the zenith above the animal and the direction of a simulated sun are represented in a compass-like fashion in the central complex, but how both compasses fit together for a unified representation of external space remained unclear. To address this question, we analyzed the sensitivity of intracellularly recorded central-complex neurons to the angle of polarized light presented from up to 33 positions in the animal's dorsal visual field and injected Neurobiotin tracer for cell identification. Neurons were polarization sensitive in large parts of the virtual sky that in some cells extended to the horizon in all directions. Neurons, moreover, were tuned to spatial patterns of polarization angles that matched the sky polarization pattern of particular sun positions. The horizontal components of these calculated solar positions were topographically encoded in the protocerebral bridge of the central complex covering 360° of space. This whole-sky polarization compass does not support the earlier reported polarization compass based on stimulation from a small spot above the animal but coincides well with the previously demonstrated direct sun compass based on unpolarized light stimulation. Therefore, direct sunlight and whole-sky polarization complement each other for robust head direction coding in the locust central complex.

Idiosyncratic neural coding and neuromodulation of olfactory individuality in Drosophila

Innate behavioral biases and preferences can vary significantly among individuals of the same genotype. Though individuality is a fundamental property of behavior, it is not currently understood how individual differences in brain structure and physiology produce idiosyncratic behaviors. Here we present evidence for idiosyncrasy in olfactory behavior and neural responses in Drosophila We show that individual female Drosophila from a highly inbred laboratory strain exhibit idiosyncratic odor preferences that persist for days. We used in vivo calcium imaging of neural responses to compare projection neuron (second-order neurons that convey odor information from the sensory periphery to the central brain) responses to the same odors across animals. We found that, while odor responses appear grossly stereotyped, upon closer inspection, many individual differences are apparent across antennal lobe (AL) glomeruli (compact microcircuits corresponding to different odor channels). Moreover, we show that neuromodulation, environmental stress in the form of altered nutrition, and activity of certain AL local interneurons affect the magnitude of interfly behavioral variability. Taken together, this work demonstrates that individual Drosophila exhibit idiosyncratic olfactory preferences and idiosyncratic neural responses to odors, and that behavioral idiosyncrasies are subject to neuromodulation and regulation by neurons in the AL.

Precise spatial memory in local random networks

Self-sustained, elevated neuronal activity persisting on timescales of 10 s or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of the most well-known modeling frameworks for persistent activity, have been able to model crucial aspects of such spatial memory. These models tend to require highly structured or regular synaptic architectures. In contrast, we study numerical simulations of a geometrically embedded model with a local, but otherwise random, connectivity profile; imposing a global regulation of our system's mean firing rate produces localized, finely spaced discrete attractors that effectively span a two-dimensional manifold. We demonstrate how the set of attracting states can reliably encode a representation of the spatial locations at which the system receives external input, thereby accomplishing spatial memory via attractor dynamics without synaptic fine-tuning or regular structure. We then measure the network's storage capacity numerically and find that the statistics of retrievable positions are also equivalent to a full tiling of the plane, something hitherto achievable only with (approximately) translationally invariant synapses, and which may be of interest in modeling such biological phenomena as visuospatial working memory in two dimensions.

The head direction circuit of two insect species

Recent studies of the Central Complex in the brain of the fruit fly have identified neurons with activity that tracks the animal's heading direction. These neurons are part of a neuronal circuit with dynamics resembling those of a ring attractor. The homologous circuit in other insects has similar topographic structure but with significant structural and connectivity differences. We model the connectivity patterns of two insect species to investigate the effect of these differences on the dynamics of the circuit. We illustrate that the circuit found in locusts can also operate as a ring attractor but differences in the inhibition pattern enable the fruit fly circuit to respond faster to heading changes while additional recurrent connections render the locust circuit more tolerant to noise. Our findings demonstrate that subtle differences in neuronal projection patterns can have a significant effect on circuit performance and illustrate the need for a comparative approach in neuroscience.

A decentralised neural model explaining optimal integration of navigational strategies in insects

Insect navigation arises from the coordinated action of concurrent guidance systems but the neural mechanisms through which each functions, and are then coordinated, remains unknown. We propose that insects require distinct strategies to retrace familiar routes (route-following) and directly return from novel to familiar terrain (homing) using different aspects of frequency encoded views that are processed in different neural pathways. We also demonstrate how the Central Complex and Mushroom Bodies regions of the insect brain may work in tandem to coordinate the directional output of different guidance cues through a contextually switched ring-attractor inspired by neural recordings. The resultant unified model of insect navigation reproduces behavioural data from a series of cue conflict experiments in realistic animal environments and offers testable hypotheses of where and how insects process visual cues, utilise the different information that they provide and coordinate their outputs to achieve the adaptive behaviours observed in the wild.

Equilibrium States and Their Stability in the Head-Direction Ring Network

Head-direction cells have been found in several areas in the mammalian brains. The firing rate of an ideal head-direction cell reaches its peak value only when the animal's head points in a specific direction, and this preferred direction stays the same regardless of spatial location. In this paper we combine mathematical analytical techniques and numerical simulations to fully analyze the equilibrium states of a generic ring attractor network, which is a widely used modeling framework for the head-direction system. Under specific conditions, all solutions of the ring network are bounded, and there exists a Lyapunov function that guarantees the stability of the network for any given inputs, which may come from multiple sources in the biological system, including self-motion information for inertially based updating and landmark information for calibration. We focus on the first few terms of the Fourier series of the ring network to explicitly solve for all possible equilibrium states, followed by a stability analysis based on small perturbations. In particular, these equilibrium states include the standard single-peaked activity pattern as well as double-peaked activity pattern, whose existence is unknown but has testable experimental implications. To our surprise, we have also found an asymmetric equilibrium activity profile even when the network connectivity is strictly symmetric. Finally we examine how these different equilibrium solutions depend on the network parameters and obtain the phase diagrams in the parameter space of the ring network.

A Multi-regional Network Encoding Heading and Steering Maneuvers in Drosophila

An internal sense of heading direction is computed from various cues, including steering maneuvers of the animal. Although neurons encoding heading and steering have been found in multiple brain regions, it is unclear whether and how they are organized into neural circuits. Here we show that, in flying Drosophila, heading and turning behaviors are encoded by population dynamics of specific cell types connecting the subregions of the central complex (CX), a brain structure implicated in navigation. Columnar neurons in the fan-shaped body (FB) of the CX exhibit circular dynamics that multiplex information about turning behavior and heading. These dynamics are coordinated with those in the ellipsoid body, another CX subregion containing a heading representation, although only FB neurons flip turn preference depending on the visual environment. Thus, the navigational system spans multiple subregions of the CX, where specific cell types show coordinated but distinct context-dependent dynamics.

The head direction cell network: attractor dynamics, integration within the navigation system, and three-dimensional properties

Knowledge of head direction cell function has progressed remarkably in recent years. The predominant theory that they form an attractor has been confirmed by several experiments. Candidate pathways that may convey visual input have been identified. The pre-subicular circuitry that conveys head direction signals to the medial entorhinal cortex, potentially sustaining path integration by grid cells, has been resolved. Although the neuronal substrate of the attractor remains unknown in mammals, a simple head direction network, whose structure is astoundingly similar to neuronal models theorized decades earlier, has been identified in insects. Finally, recent experiments have revealed that these cells do not encode head direction in the horizontal plane only, but also in vertical planes, thus providing a 3D orientation signal.

A dynamical model exploring sensory integration in the insect central complex substructures

It is imperative that an animal has the ability to contextually integrate received sensory information to formulate appropriate behavioral responses. Determining a body heading based on a multitude of ego-motion cues and visual landmarks is an example of such a task that requires this context dependent integration. The work presented here simulates a sensory integrator in the insect brain called the central complex (CX). Based on the architecture of the CX, we assembled a dynamical neural simulation of two structures called the protocerebral bridge (PB) and the ellipsoid body (EB). Using non-spiking neuronal dynamics, our simulation was able to recreate in vivo neuronal behavior such as correlating body rotation direction and speed to activity bumps within the EB as well as updating the believed heading with quick secondary system updates. With this model, we performed sensitivity analysis of certain neuronal parameters as a possible means to control multi-system gains during sensory integration. We found that modulation of synapses in the memory network and EB inhibition are two possible mechanisms in which a sensory system could affect the memory stability and gain of another input, respectively. This model serves as an exploration in network design for integrating simultaneous idiothetic and allothetic cues in the task of body tracking and determining contextually dependent behavioral outputs.

The case for emulating insect brains using anatomical "wiring diagrams" equipped with biophysical models of neuronal activity

Developing whole-brain emulation (WBE) technology would provide immense benefits across neuroscience, biomedicine, artificial intelligence, and robotics. At this time, constructing a simulated human brain lacks feasibility due to limited experimental data and limited computational resources. However, I suggest that progress toward this goal might be accelerated by working toward an intermediate objective, namely insect brain emulation (IBE). More specifically, this would entail creating biologically realistic simulations of entire insect nervous systems along with more approximate simulations of non-neuronal insect physiology to make "virtual insects." I argue that this could be realistically achievable within the next 20 years. I propose that developing emulations of insect brains will galvanize the global community of scientists, businesspeople, and policymakers toward pursuing the loftier goal of emulating the human brain. By demonstrating that WBE is possible via IBE, simulating mammalian brains and eventually the human brain may no longer be viewed as too radically ambitious to deserve substantial funding and resources. Furthermore, IBE will facilitate dramatic advances in cognitive neuroscience, artificial intelligence, and robotics through studies performed using virtual insects.

Principles of Insect Path Integration

Continuously monitoring its position in space relative to a goal is one of the most essential tasks for an animal that moves through its environment. Species as diverse as rats, bees, and crabs achieve this by integrating all changes of direction with the distance covered during their foraging trips, a process called path integration. They generate an estimate of their current position relative to a starting point, enabling a straight-line return, following what is known as a home vector. While in theory path integration always leads the animal precisely back home, in the real world noise limits the usefulness of this strategy when operating in isolation. Noise results from stochastic processes in the nervous system and from unreliable sensory information, particularly when obtaining heading estimates. Path integration, during which angular self-motion provides the sole input for encoding heading (idiothetic path integration), results in accumulating errors that render this strategy useless over long distances. In contrast, when using an external compass this limitation is avoided (allothetic path integration). Many navigating insects indeed rely on external compass cues for estimating body orientation, whereas they obtain distance information by integration of steps or optic-flow-based speed signals. In the insect brain, a region called the central complex plays a key role for path integration. Not only does the central complex house a ring-attractor network that encodes head directions, neurons responding to optic flow also converge with this circuit. A neural substrate for integrating direction and distance into a memorized home vector has therefore been proposed in the central complex. We discuss how behavioral data and the theoretical framework of path integration can be aligned with these neural data.

From skylight input to behavioural output: A computational model of the insect polarised light compass

Many insects navigate by integrating the distances and directions travelled on an outward path, allowing direct return to the starting point. Fundamental to the reliability of this process is the use of a neural compass based on external celestial cues. Here we examine how such compass information could be reliably computed by the insect brain, given realistic constraints on the sky polarisation pattern and the insect eye sensor array. By processing the degree of polarisation in different directions for different parts of the sky, our model can directly estimate the solar azimuth and also infer the confidence of the estimate. We introduce a method to correct for tilting of the sensor array, as might be caused by travel over uneven terrain. We also show that the confidence can be used to approximate the change in sun position over time, allowing the compass to remain fixed with respect to 'true north' during long excursions. We demonstrate that the compass is robust to disturbances and can be effectively used as input to an existing neural model of insect path integration. We discuss the plausibility of our model to be mapped to known neural circuits, and to be implemented for robot navigation.

Automated real-time quantification of group locomotor activity in Drosophila melanogaster

Recent advances in neurogenetics have highlighted Drosophila melanogaster as an exciting model to study neural circuit dynamics and complex behavior. Automated tracking methods have facilitated the study of complex behaviors via high throughput behavioral screening. Here we describe a newly developed low-cost assay capable of real-time monitoring and quantifying Drosophila group activity. This platform offers reliable real-time quantification with open source software and a user-friendly interface for data acquisition and analysis. We demonstrate the utility of this platform by characterizing ethanol-induced locomotor activity in a dose-dependent manner as well as the effects of thermo and optogenetic manipulation of ellipsoid body neurons important for ethanol-induced locomotor activity. As expected, low doses of ethanol induced an initial startle and slow ramping of group activity, whereas high doses of ethanol induced sustained group activity followed by sedation. Advanced offline processing revealed discrete behavioral features characteristic of intoxication. Thermogenetic inactivation of ellipsoid body ring neurons reduced group activity whereas optogenetic activation increased activity. Together, these data establish the fly Group Activity Monitor (flyGrAM) platform as a robust means of obtaining an online read out of group activity in response to manipulations to the environment or neural activity, with an opportunity for more advanced post-processing offline.

Inverse Control of Turning Behavior by Dopamine D1 Receptor Signaling in Columnar and Ring Neurons of the Central Complex in Drosophila

Action selection is a prerequisite for decision-making and a fundamental aspect to any goal-directed locomotion; it requires integration of sensory signals and internal states to translate them into action sequences. Here, we introduce a novel behavioral analysis to study neural circuits and mechanisms underlying action selection and decision-making in freely moving Drosophila. We discovered preferred patterns of motor activity and turning behavior. These patterns are impaired in FoxP mutant flies, which present an altered temporal organization of motor actions and turning behavior, reminiscent of indecisiveness. Then, focusing on central complex (CX) circuits known to integrate different sensory modalities and controlling premotor regions, we show that action sequences and turning behavior are regulated by dopamine D1-like receptor (Dop1R1) signaling. Dop1R1 inputs onto CX columnar ellipsoid body-protocerebral bridge gall (E-PG) neuron and ellipsoid body (EB) R2/R4m ring neuron circuits both negatively gate motor activity but inversely control turning behavior. Although flies deficient of D1 receptor signaling present normal turning behavior despite decreased activity, restoring Dop1R1 level in R2/R4m-specific circuitry affects the temporal organization of motor actions and turning. We finally show EB R2/R4m neurons are in contact with E-PG neurons that are thought to encode body orientation and heading direction of the fly. These findings suggest that Dop1R1 signaling in E-PG and EB R2/4 m circuits are compared against each other, thereby modulating patterns of activity and turning behavior for goal-directed locomotion.

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Freely moving Drosophila present preferred patterns of activity and turning behavior

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FoxP mutations affect temporal distribution of motor actions and turning behavior

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Central complex columnar E-PG and R2/4 m ring neurons inversely regulate turning

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Dopamine D1-like receptor signaling in R2/R4m ring neurons modulates behavior

How the Internally Organized Direction Sense Is Used to Navigate

Head-direction cells preferentially discharge when the head points in a particular azimuthal direction, are hypothesized to collectively function as a single neural system for a unitary direction sense, and are believed to be essential for navigating extra-personal space by functioning like a compass. We tested these ideas by recording medial entorhinal cortex (MEC) head-direction cells while rats navigated on a familiar, continuously rotating disk that dissociates the environment into two spatial frames: one stationary and one rotating. Head-direction cells degraded directional tuning referenced to either of the externally referenced spatial frames, but firing rates, sub-second cell-pair action potential discharge relationships, and internally referenced directional tuning were preserved. MEC head-direction cell ensemble discharge collectively generates a subjective, internally referenced unitary representation of direction that, unlike a compass, is inconsistently registered to external landmarks during navigation. These findings indicate that MEC-based directional information is subjectively anchored, potentially providing for navigation without a stable externally anchored direction sense.

Neuroarchitecture of the Drosophila central complex: A catalog of nodulus and asymmetrical body neurons and a revision of the protocerebral bridge catalog

The central complex, a set of neuropils in the center of the insect brain, plays a crucial role in spatial aspects of sensory integration and motor control. Stereotyped neurons interconnect these neuropils with one another and with accessory structures. We screened over 5,000 Drosophila melanogaster GAL4 lines for expression in two neuropils, the noduli (NO) of the central complex and the asymmetrical body (AB), and used multicolor stochastic labeling to analyze the morphology, polarity, and organization of individual cells in a subset of the GAL4 lines that showed expression in these neuropils. We identified nine NO and three AB cell types and describe them here. The morphology of the NO neurons suggests that they receive input primarily in the lateral accessory lobe and send output to each of the six paired noduli. We demonstrate that the AB is a bilateral structure which exhibits asymmetry in size between the left and right bodies. We show that the AB neurons directly connect the AB to the central complex and accessory neuropils, that they target both the left and right ABs, and that one cell type preferentially innervates the right AB. We propose that the AB be considered a central complex neuropil in Drosophila. Finally, we present highly restricted GAL4 lines for most identified protocerebral bridge, NO, and AB cell types. These lines, generated using the split-GAL4 method, will facilitate anatomical studies, behavioral assays, and physiological experiments.

Building a functional connectome of the Drosophila central complex

The central complex is a highly conserved insect brain region composed of morphologically stereotyped neurons that arborize in distinctively shaped substructures. The region is implicated in a wide range of behaviors and several modeling studies have explored its circuit computations. Most studies have relied on assumptions about connectivity between neurons based on their overlap in light microscopy images. Here, we present an extensive functional connectome of Drosophila melanogaster's central complex at cell-type resolution. Using simultaneous optogenetic stimulation, calcium imaging and pharmacology, we tested the connectivity between 70 presynaptic-to-postsynaptic cell-type pairs. We identified numerous inputs to the central complex, but only a small number of output channels. Additionally, the connectivity of this highly recurrent circuit appears to be sparser than anticipated from light microscopy images. Finally, the connectivity matrix highlights the potentially critical role of a class of bottleneck interneurons. All data are provided for interactive exploration on a website.

Building a heading signal from anatomically defined neuron types in the Drosophila central complex

A network of a few hundred neurons in the Drosophila central complex carries an estimate of the fly's heading in the world, akin to the mammalian head-direction system. Here we describe how anatomically defined neuronal classes in this network are poised to implement specific sub-processes for building and updating this population-level heading signal. The computations we describe in the fly central complex strongly resemble those posited to exist in the mammalian brain, in computational models for building head-direction signals. By linking circuit anatomy to navigational physiology, the Drosophila central complex should provide a detailed example of how a heading signal is built.

Unraveling the neural basis of insect navigation

One of the defining features of animals is their ability to navigate their environment. Using behavioral experiments this topic has been under intense investigation for nearly a century. In insects, this work has largely focused on the remarkable homing abilities of ants and bees. More recently, the neural basis of navigation shifted into the focus of attention. Starting with revealing the neurons that process the sensory signals used for navigation, in particular polarized skylight, migratory locusts became the key species for delineating navigation-relevant regions of the insect brain. Over the last years, this work was used as a basis for research in the fruit fly Drosophila and extraordinary progress has been made in illuminating the neural underpinnings of navigational processes. With increasingly detailed understanding of navigation circuits, we can begin to ask whether there is a fundamentally shared concept underlying all navigation behavior across insects. This review highlights recent advances and puts them into the context of the behavioral work on ants and bees, as well as the circuits involved in polarized-light processing. A region of the insect brain called the central complex emerges as the common substrate for guiding navigation and its highly organized neuroarchitecture provides a framework for future investigations potentially suited to explain all insect navigation behavior at the level of identified neurons.

Neural Coding: Bumps on the Move

By meticulously deconstructing the Drosophila head-direction neural circuit, two recent studies have revealed the mechanism of how the fly's body rotations are translated into a continuously updated internal compass representation.

An Anatomically Constrained Model for Path Integration in the Bee Brain

Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task-a celestial-cue-based visual compass and an optic-flow-based visual odometer-but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light-based compass neurons and optic-flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy, we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically identified neurons suggested for each processing step. The resulting model circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e., a ground velocity that is not precisely aligned with body orientation) typical of bee flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings-suggesting a more basic function for central complex connectivity, from which path integration may have evolved.

In silico Interrogation of Insect Central Complex Suggests Computational Roles for the Ellipsoid Body in Spatial Navigation

The central complex in the insect brain is a composite of midline neuropils involved in processing sensory cues and mediating behavioral outputs to orchestrate spatial navigation. Despite recent advances, however, the neural mechanisms underlying sensory integration and motor action selections have remained largely elusive. In particular, it is not yet understood how the central complex exploits sensory inputs to realize motor functions associated with spatial navigation. Here we report an in silico interrogation of central complex-mediated spatial navigation with a special emphasis on the ellipsoid body. Based on known connectivity and function, we developed a computational model to test how the local connectome of the central complex can mediate sensorimotor integration to guide different forms of behavioral outputs. Our simulations show integration of multiple sensory sources can be effectively performed in the ellipsoid body. This processed information is used to trigger continuous sequences of action selections resulting in self-motion, obstacle avoidance and the navigation of simulated environments of varying complexity. The motor responses to perceived sensory stimuli can be stored in the neural structure of the central complex to simulate navigation relying on a collective of guidance cues, akin to sensory-driven innate or habitual behaviors. By comparing behaviors under different conditions of accessible sources of input information, we show the simulated insect computes visual inputs and body posture to estimate its position in space. Finally, we tested whether the local connectome of the central complex might also allow the flexibility required to recall an intentional behavioral sequence, among different courses of actions. Our simulations suggest that the central complex can encode combined representations of motor and spatial information to pursue a goal and thus successfully guide orientation behavior. Together, the observed computational features identify central complex circuitry, and especially the ellipsoid body, as a key neural correlate involved in spatial navigation.

Generating Executable Models of the Drosophila Central Complex

The central complex (CX) is a set of neuropils in the center of the fly brain that have been implicated as playing an important role in vision-mediated behavior and integration of spatial information with locomotor control. In contrast to currently available data regarding the neural circuitry of neuropils in the fly's vision and olfactory systems, comparable data for the CX neuropils is relatively incomplete; many categories of neurons remain only partly characterized, and the synaptic connectivity between CX neurons has yet to be fully determined. Successful modeling of the information processing functions of the CX neuropils therefore requires a means of easily constructing and testing a range of hypotheses regarding both the high-level structure of their neural circuitry and the properties of their constituent neurons and synapses. To this end, we have created a web application that enables simultaneous graphical querying and construction of executable models of the CX neural circuitry based upon currently available information regarding the geometry and polarity of the arborizations of identified local and projection neurons in the CX. The application's novel functionality is made possible by the Fruit Fly Brain Observatory, a platform for collaborative study and development of fruit fly brain models.

A neural circuit architecture for angular integration in Drosophila

Many animals keep track of their angular heading over time while navigating through their environment. However, a neural-circuit architecture for computing heading has not been experimentally defined in any species. Here we describe a set of clockwise- and anticlockwise-shifting neurons in the Drosophila central complex whose wiring and physiology provide a means to rotate an angular heading estimate based on the fly's angular velocity. We show that each class of shifting neurons exists in two subtypes, with spatiotemporal activity profiles that suggest different roles for each subtype at the start and end of tethered-walking turns. Shifting neurons are required for the heading system to properly track the fly's heading in the dark, and stimulation of these neurons induces predictable shifts in the heading signal. The central features of this biological circuit are analogous to those of computational models proposed for head-direction cells in rodents and may shed light on how neural systems, in general, perform integration.

Ring attractor dynamics in the Drosophila central brain

Ring attractors are a class of recurrent networks hypothesized to underlie the representation of heading direction. Such network structures, schematized as a ring of neurons whose connectivity depends on their heading preferences, can sustain a bump-like activity pattern whose location can be updated by continuous shifts along either turn direction. We recently reported that a population of fly neurons represents the animal's heading via bump-like activity dynamics. We combined two-photon calcium imaging in head-fixed flying flies with optogenetics to overwrite the existing population representation with an artificial one, which was then maintained by the circuit with naturalistic dynamics. A network with local excitation and global inhibition enforces this unique and persistent heading representation. Ring attractor networks have long been invoked in theoretical work; our study provides physiological evidence of their existence and functional architecture.