Coupled symmetric and asymmetric circuits underlying spatial orientation in fruit flies

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 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.

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.

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.

Sensory feedback expands dynamic complexity and aids in robustness against noise

It has been hypothesized that sensory feedback is a critical component in determining the functionality of a central pattern generator. To test this, Yu and Thomas's recent work Yu and Thomas (Biol Cybern 115(2):135-160, 2021) built a model of a half-center oscillator coupled to a simple muscular model with sensory feedback. They showed that sensory feedback increases robustness against external noise, while simultaneously expanding the potential repertoire of functions the half-center oscillator can perform. However, they show that this comes at the cost of robustness against internal noise.

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.

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.

Integration of sleep homeostasis and navigation in Drosophila

During sleep, the brain undergoes dynamic and structural changes. In Drosophila, such changes have been observed in the central complex, a brain area important for sleep control and navigation. The connectivity of the central complex raises the question about how navigation, and specifically the head direction system, can operate in the face of sleep related plasticity. To address this question, we develop a model that integrates sleep homeostasis and head direction. We show that by introducing plasticity, the head direction system can function in a stable way by balancing plasticity in connected circuits that encode sleep pressure. With increasing sleep pressure, the head direction system nevertheless becomes unstable and a sleep phase with a different plasticity mechanism is introduced to reset network connectivity. The proposed integration of sleep homeostasis and head direction circuits captures features of their neural dynamics observed in flies and mice.

Autonomous Flying With Neuromorphic Sensing

Autonomous flight for large aircraft appears to be within our reach. However, launching autonomous systems for everyday missions still requires an immense interdisciplinary research effort supported by pointed policies and funding. We believe that concerted endeavors in the fields of neuroscience, mathematics, sensor physics, robotics, and computer science are needed to address remaining crucial scientific challenges. In this paper, we argue for a bio-inspired approach to solve autonomous flying challenges, outline the frontier of sensing, data processing, and flight control within a neuromorphic paradigm, and chart directions of research needed to achieve operational capabilities comparable to those we observe in nature. One central problem of neuromorphic computing is learning. In biological systems, learning is achieved by adaptive and relativistic information acquisition characterized by near-continuous information retrieval with variable rates and sparsity. This results in both energy and computational resource savings being an inspiration for autonomous systems. We consider pertinent features of insect, bat and bird flight behavior as examples to address various vital aspects of autonomous flight. Insects exhibit sophisticated flight dynamics with comparatively reduced complexity of the brain. They represent excellent objects for the study of navigation and flight control. Bats and birds enable more complex models of attention and point to the importance of active sensing for conducting more complex missions. The implementation of neuromorphic paradigms for autonomous flight will require fundamental changes in both traditional hardware and software. We provide recommendations for sensor hardware and processing algorithm development to enable energy efficient and computationally effective flight control.

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.

Characterizing approach behavior of Drosophila melanogaster in Buridan's paradigm

The Buridan's paradigm is a behavioral task designed for testing visuomotor responses or phototaxis in fruit fly Drosophila melanogaster. In the task, a wing-shortened fruit fly freely moves on a round platform surrounded by a 360° white screen with two vertical black stripes placed at 0° and 180°. A normal fly will tend to approach the stripes one at a time and move back and forth between them. A variety of tasks developed based on the Buridan's paradigm were designed to test other cognitive functions such as visual spatial memory. Although the movement patterns and the behavioral preferences of the flies in the Buridan's or similar tasks have been extensively studies a few decades ago, the protocol and experimental settings are markedly different from what are used today. We revisited the Buridan's paradigm and systematically investigated the approach behavior of fruit flies under different stimulus settings. While early studies revealed an edge-fixation behavior for a wide stripe in the initial visuomotor responses, we did not discover such tendency in the Buridan's paradigm when observing a longer-term behavior up to minutes, a memory-task relevant time scale. Instead, we observed robust negative photoaxis in which the flies approached the central part of the dark stripes of all sizes. In addition, we found that stripes of 20°-30° width yielded the best performance of approach. We further varied the luminance of the stripes and the background screen, and discovered that the performance depended on the luminance ratio between the stripes and the screen. Our study provided useful information for designing and optimizing the Buridan's paradigm and other behavioral tasks that utilize the approach behavior.

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.

Identification of FoxP circuits involved in locomotion and object fixation in Drosophila

The FoxP family of transcription factors is necessary for operant self-learning, an evolutionary conserved form of motor learning. The expression pattern, molecular function and mechanisms of action of the Drosophila FoxP orthologue remain to be elucidated. By editing the genomic locus of FoxP with CRISPR/Cas9, we find that the three different FoxP isoforms are expressed in neurons, but not in glia and that not all neurons express all isoforms. Furthermore, we detect FoxP expression in, e.g. the protocerebral bridge, the fan-shaped body and in motor neurons, but not in the mushroom bodies. Finally, we discover that FoxP expression during development, but not adulthood, is required for normal locomotion and landmark fixation in walking flies. While FoxP expression in the protocerebral bridge and motor neurons is involved in locomotion and landmark fixation, the FoxP gene can be excised from dorsal cluster neurons and mushroom-body Kenyon cells without affecting these behaviours.

Comprehensive map of visual projection neurons for processing ultraviolet information in the Drosophila brain

The brain perceives visual information and controls behavior depending on its underlying neural circuits. How UV information is represented and processed in the brain remains poorly understood. In Drosophila melanogaster, UV light is detected by the R7 photoreceptor that projects exclusively into the medulla layer 6 (M₆ ). Herein, we imaged 28,768 single neurons and identified 238 visual projection neurons linking M₆ to the central brain. Based on morphology and connectivity, these visual projection neurons were systematically classified into 94 cell types belonging to 12 families. Three tracts connected M₆ in each optic lobe to the central brain: One dorsal tract linking to the ipsilateral lateral anterior optic tubercle (L-AOTU) and two medial tracts linking to the ipsilateral ventral medial protocerebrum (VMP) and the contralateral VMP. The M₆ information was primarily represented in the L-AOTU. Each L-AOTU consisted of four columns that each contained three glomeruli. Each L-AOTU glomerulus received inputs from M₆ subdomains and gave outputs to a glomerulus within the ellipsoid body dendritic region, suggesting specific processing of spatial information through the dorsal pathway. Furthermore, the middle columns of the L-AOTUs of both hemispheres were connected via the intertubercle tract, suggesting information integration between the two eyes. In contrast, an ascending neuron linked each VMP to all glomeruli in the bulb and the L-AOTU, bilaterally, suggesting general processing of information through the ventral pathway. Altogether, these diverse morphologies of the visual projection neurons suggested multi-dimensional processing of UV information through parallel and bilateral circuits in the Drosophila brain.

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.

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.

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 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.

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.

Diverse Community Structures in the Neuronal-Level Connectome of the Drosophila Brain

Drosophila melanogaster is one of the most important model animals in neurobiology owing to its manageable brain size, complex behaviour, and extensive genetic tools. However, without a comprehensive map of the brain-wide neural network, our ability to investigate brain functions at the systems level is seriously limited. In this study, we constructed a neuron-to-neuron network of the Drosophila brain based on the 28,573 fluorescence images of single neurons in the newly released FlyCircuit v1.2 (http://www.flycircuit.tw) database. By performing modularity and centrality analyses, we identified eight communities (right olfaction, left olfaction, olfactory core, auditory, motor, pre-motor, left vision, and right vision) in the brain-wide network. Further investigation on information exchange and structural stability revealed that the communities of different functions dominated different types of centralities, suggesting a correlation between functions and network structures. Except for the two olfaction and the motor communities, the network is characterized by overall small-worldness. A rich club (RC) structure was also found in this network, and most of the innermost RC members innervated the central complex, indicating its role in information integration. We further identified numerous loops with length smaller than seven neurons. The observation suggested unique characteristics in the information processing inside the fruit fly brain.

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.

A Single-Cell Level and Connectome-Derived Computational Model of the Drosophila Brain

Computer simulations play an important role in testing hypotheses, integrating knowledge, and providing predictions of neural circuit functions. While considerable effort has been dedicated into simulating primate or rodent brains, the fruit fly (Drosophila melanogaster) is becoming a promising model animal in computational neuroscience for its small brain size, complex cognitive behavior, and abundancy of data available from genes to circuits. Moreover, several Drosophila connectome projects have generated a large number of neuronal images that account for a significant portion of the brain, making a systematic investigation of the whole brain circuit possible. Supported by FlyCircuit (http://www.flycircuit.tw), one of the largest Drosophila neuron image databases, we began a long-term project with the goal to construct a whole-brain spiking network model of the Drosophila brain. In this paper, we report the outcome of the first phase of the project. We developed the Flysim platform, which (1) identifies the polarity of each neuron arbor, (2) predicts connections between neurons, (3) translates morphology data from the database into physiology parameters for computational modeling, (4) reconstructs a brain-wide network model, which consists of 20,089 neurons and 1,044,020 synapses, and (5) performs computer simulations of the resting state. We compared the reconstructed brain network with a randomized brain network by shuffling the connections of each neuron. We found that the reconstructed brain can be easily stabilized by implementing synaptic short-term depression, while the randomized one exhibited seizure-like firing activity under the same treatment. Furthermore, the reconstructed Drosophila brain was structurally and dynamically more diverse than the randomized one and exhibited both Poisson-like and patterned firing activities. Despite being at its early stage of development, this single-cell level brain model allows us to study some of the fundamental properties of neural networks including network balance, critical behavior, long-term stability, and plasticity.

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.