Ring attractor dynamics in the Drosophila central brain

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.

From synapse to network: models of information storage and retrieval in neural circuits

The mechanisms of information storage and retrieval in brain circuits are still the subject of debate. It is widely believed that information is stored at least in part through changes in synaptic connectivity in networks that encode this information and that these changes lead in turn to modifications of network dynamics, such that the stored information can be retrieved at a later time. Here, we review recent progress in deriving synaptic plasticity rules from experimental data and in understanding how plasticity rules affect the dynamics of recurrent networks. We show that the dynamics generated by such networks exhibit a large degree of diversity, depending on parameters, similar to experimental observations in vivo during delayed response tasks.

Spherical arena reveals optokinetic response tuning to stimulus location, size, and frequency across entire visual field of larval zebrafish

Many animals have large visual fields, and sensory circuits may sample those regions of visual space most relevant to behaviours such as gaze stabilisation and hunting. Despite this, relatively small displays are often used in vision neuroscience. To sample stimulus locations across most of the visual field, we built a spherical stimulus arena with 14,848 independently controllable LEDs. We measured the optokinetic response gain of immobilised zebrafish larvae to stimuli of different steradian size and visual field locations. We find that the two eyes are less yoked than previously thought and that spatial frequency tuning is similar across visual field positions. However, zebrafish react most strongly to lateral, nearly equatorial stimuli, consistent with previously reported spatial densities of red, green, and blue photoreceptors. Upside-down experiments suggest further extra-retinal processing. Our results demonstrate that motion vision circuits in zebrafish are anisotropic, and preferentially monitor areas with putative behavioural relevance.

Balancing Flexibility and Interference in Working Memory

Working memory is central to cognition, flexibly holding the variety of thoughts needed for complex behavior. Yet, despite its importance, working memory has a severely limited capacity, holding only three to four items at once. In this article, I review experimental and computational evidence that the flexibility and limited capacity of working memory reflect the same underlying neural mechanism. I argue that working memory relies on interactions between high-dimensional, integrative representations in the prefrontal cortex and structured representations in the sensory cortex. Together, these interactions allow working memory to flexibly maintain arbitrary representations. However, the distributed nature of working memory comes at the cost of causing interference between items in memory, resulting in a limited capacity. Finally, I discuss several mechanisms used by the brain to reduce interference and maximize the effective capacity of working memory. Expected final online publication date for the Annual Review of Vision Science, Volume 7 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Spatially structured inhibition defined by polarized parvalbumin interneuron axons promotes head direction tuning

In cortical microcircuits, it is generally assumed that fast-spiking parvalbumin interneurons mediate dense and nonselective inhibition. Some reports indicate sparse and structured inhibitory connectivity, but the computational relevance and the underlying spatial organization remain unresolved. In the rat superficial presubiculum, we find that inhibition by fast-spiking interneurons is organized in the form of a dominant super-reciprocal microcircuit motif where multiple pyramidal cells recurrently inhibit each other via a single interneuron. Multineuron recordings and subsequent 3D reconstructions and analysis further show that this nonrandom connectivity arises from an asymmetric, polarized morphology of fast-spiking interneuron axons, which individually cover different directions in the same volume. Network simulations assuming topographically organized input demonstrate that such polarized inhibition can improve head direction tuning of pyramidal cells in comparison to a "blanket of inhibition." We propose that structured inhibition based on asymmetrical axons is an overarching spatial connectivity principle for tailored computation across brain regions.

Inferring the function performed by a recurrent neural network

A central goal in systems neuroscience is to understand the functions performed by neural circuits. Previous top-down models addressed this question by comparing the behaviour of an ideal model circuit, optimised to perform a given function, with neural recordings. However, this requires guessing in advance what function is being performed, which may not be possible for many neural systems. To address this, we propose an inverse reinforcement learning (RL) framework for inferring the function performed by a neural network from data. We assume that the responses of each neuron in a network are optimised so as to drive the network towards 'rewarded' states, that are desirable for performing a given function. We then show how one can use inverse RL to infer the reward function optimised by the network from observing its responses. This inferred reward function can be used to predict how the neural network should adapt its dynamics to perform the same function when the external environment or network structure changes. This could lead to theoretical predictions about how neural network dynamics adapt to deal with cell death and/or varying sensory stimulus statistics.

A visual pathway for skylight polarization processing in Drosophila

Many insects use patterns of polarized light in the sky to orient and navigate. Here, we functionally characterize neural circuitry in the fruit fly, Drosophila melanogaster, that conveys polarized light signals from the eye to the central complex, a brain region essential for the fly's sense of direction. Neurons tuned to the angle of polarization of ultraviolet light are found throughout the anterior visual pathway, connecting the optic lobes with the central complex via the anterior optic tubercle and bulb, in a homologous organization to the 'sky compass' pathways described in other insects. We detail how a consistent, map-like organization of neural tunings in the peripheral visual system is transformed into a reduced representation suited to flexible processing in the central brain. This study identifies computational motifs of the transformation, enabling mechanistic comparisons of multisensory integration and central processing for navigation in the brains of insects.

Biomimetic FPGA-based spatial navigation model with grid cells and place cells

The mammalian spatial navigation system is characterized by an initial divergence of internal representations, with disparate classes of neurons responding to distinct features including location, speed, borders and head direction; an ensuing convergence finally enables navigation and path integration. Here, we report the algorithmic and hardware implementation of biomimetic neural structures encompassing a feed-forward trimodular, multi-layer architecture representing grid-cell, place-cell and decoding modules for navigation. The grid-cell module comprised of neurons that fired in a grid-like pattern, and was built of distinct layers that constituted the dorsoventral span of the medial entorhinal cortex. Each layer was built as an independent continuous attractor network with distinct grid-field spatial scales. The place-cell module comprised of neurons that fired at one or few spatial locations, organized into different clusters based on convergent modular inputs from different grid-cell layers, replicating the gradient in place-field size along the hippocampal dorso-ventral axis. The decoding module, a two-layer neural network that constitutes the convergence of the divergent representations in preceding modules, received inputs from the place-cell module and provided specific coordinates of the navigating object. After vital design optimizations involving all modules, we implemented the tri-modular structure on Zynq Ultrascale+ field-programmable gate array silicon chip, and demonstrated its capacity in precisely estimating the navigational trajectory with minimal overall resource consumption involving a mere 2.92% Look Up Table utilization. Our implementation of a biomimetic, digital spatial navigation system is stable, reliable, reconfigurable, real-time with execution time of about 32 s for 100k input samples (in contrast to 40 minutes on Intel Core i7-7700 CPU with 8 cores clocking at 3.60 GHz) and thus can be deployed for autonomous-robotic navigation without requiring additional sensors.

Daily rewiring of a neural circuit generates a predictive model of environmental light

Behavioral responsiveness to external stimulation is shaped by context. We studied how sensory information can be contextualized, by examining light-evoked locomotor responsiveness of Drosophila relative to time of day. We found that light elicits an acute increase in locomotion (startle) that is modulated in a time-of-day-dependent manner: Startle is potentiated during the nighttime, when light is unexpected, but is suppressed during the daytime. The internal daytime-nighttime context is generated by two interconnected and functionally opposing populations of circadian neurons-LNvs generating the daytime state and DN1as generating the nighttime state. Switching between the two states requires daily remodeling of LNv and DN1a axons such that the maximum presynaptic area in one population coincides with the minimum in the other. We propose that a dynamic model of environmental light resides in the shifting connectivities of the LNv-DN1a circuit, which helps animals evaluate ongoing conditions and choose a behavioral response.

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.

Temporally coherent perturbation of neural dynamics during retention alters human multi-item working memory

Temporarily storing a list of items in working memory (WM), a fundamental ability in cognition, has been posited to rely on the temporal dynamics of multi-item neural representations during retention. However, the causal evidence, particularly in human subjects, is still lacking, let alone WM manipulation. Here, we develop a novel "dynamic perturbation" approach to manipulate the relative memory strength of WM items held in human brain, by presenting temporally correlated luminance sequences during retention to interfere with the multi-item neural dynamics. Six experiments on more than 150 subjects confirm the effectiveness of this WM manipulation approach. A computational model combining continuous attractor neural network (CANN) and short-term synaptic plasticity (STP) principles further reproduces all the empirical findings. The model reveals that the "dynamic perturbation" modifies the synaptic efficacies of WM items through STP principles, eventually leading to changes in their relative memory strengths. Our results support the causal role of temporal dynamics of neural network in mediating multi-item WM, and offer a promising, purely bottom-up approach to manipulate WM.

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.

Two-Photon Optogenetic Stimulation of Drosophila Neurons

Optogenetics enables experimental control over neural activity using light. Channelrhodopsin and its variants are typically activated using visible light excitation but can also be activated using infrared two-photon excitation. Two-photon excitation can improve the spatial precision of stimulation in scattering tissue but has several practical limitations that need to be considered before use. Here we describe the methodology and best practices for using two-photon optogenetic stimulation of neurons within the brain of the fruit fly, Drosophila melanogaster, with an emphasis on projection neurons of the antennal lobe.

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.

Two Brain Pathways Initiate Distinct Forward Walking Programs in Drosophila

An animal at rest or engaged in stationary behaviors can instantaneously initiate goal-directed walking. How descending brain inputs trigger rapid transitions from a non-walking state to an appropriate walking state is unclear. Here, we identify two neuronal types, P9 and BPN, in the Drosophila brain that, upon activation, initiate and maintain two distinct coordinated walking patterns. P9 drives forward walking with ipsilateral turning, receives inputs from central courtship-promoting neurons and visual projection neurons, and is necessary for a male to pursue a female during courtship. In contrast, BPN drives straight, forward walking and is not required during courtship. BPN is instead recruited during and required for fast, straight, forward walking bouts. Thus, this study reveals separate brain pathways for object-directed walking and fast, straight, forward walking, providing insight into how the brain initiates context-appropriate walking programs.

Inhibitory stabilization and cortical computation

Neuronal networks with strong recurrent connectivity provide the brain with a powerful means to perform complex computational tasks. However, high-gain excitatory networks are susceptible to instability, which can lead to runaway activity, as manifested in pathological regimes such as epilepsy. Inhibitory stabilization offers a dynamic, fast and flexible compensatory mechanism to balance otherwise unstable networks, thus enabling the brain to operate in its most efficient regimes. Here we review recent experimental evidence for the presence of such inhibition-stabilized dynamics in the brain and discuss their consequences for cortical computation. We show how the study of inhibition-stabilized networks in the brain has been facilitated by recent advances in the technological toolbox and perturbative techniques, as well as a concomitant development of biologically realistic computational models. By outlining future avenues, we suggest that inhibitory stabilization can offer an exemplary case of how experimental neuroscience can progress in tandem with technology and theory to advance our understanding of the brain.

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.

Parallel Visual Pathways with Topographic versus Nontopographic Organization Connect the Drosophila Eyes to the Central Brain

One hallmark of the visual system is a strict retinotopic organization from the periphery toward the central brain, where functional imaging in Drosophila revealed a spatially accurate representation of visual cues in the central complex. This raised the question how, on a circuit level, the topographic features are implemented, as the majority of visual neurons enter the central brain converge in optic glomeruli. We discovered a spatial segregation of topographic versus nontopographic projections of distinct classes of medullo-tubercular (MeTu) neurons into a specific visual glomerulus, the anterior optic tubercle (AOTU). These parallel channels synapse onto different tubercular-bulbar (TuBu) neurons, which in turn relay visual information onto specific central complex ring neurons in the bulb neuropil. Hence, our results provide the circuit basis for spatially accurate representation of visual information and highlight the AOTU's role as a prominent relay station for spatial information from the retina to the central brain.

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A Drosophila visual circuit conveys input from the periphery to the central brain

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Several synaptic pathways form parallel channels using the anterior optic tubercle

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Some pathways maintain topographic relationships across several synaptic steps

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Different target neurons in the central brain are identified

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.

A Neural Network for Wind-Guided Compass Navigation

Spatial maps in the brain are most accurate when they are linked to external sensory cues. Here, we show that the compass in the Drosophila brain is linked to the direction of the wind. Shifting the wind rightward rotates the compass as if the fly were turning leftward, and vice versa. We describe the mechanisms of several computations that integrate wind information into the compass. First, an intensity-invariant representation of wind direction is computed by comparing left-right mechanosensory signals. Then, signals are reformatted to reduce the coding biases inherent in peripheral mechanics, and wind cues are brought into the same circular coordinate system that represents visual cues and self-motion signals. Because the compass incorporates both mechanosensory and visual cues, it should enable navigation under conditions where no single cue is consistently reliable. These results show how local sensory signals can be transformed into a global, multimodal, abstract representation of space.

Hot coffee: associative memory with bump attractor cell assemblies of spiking neurons

Networks of spiking neurons can have persistently firing stable bump attractors to represent continuous spaces (like temperature). This can be done with a topology with local excitatory synapses and local surround inhibitory synapses. Activating large ranges in the attractor can lead to multiple bumps, that show repeller and attractor dynamics; however, these bumps can be merged by overcoming the repeller dynamics. A simple associative memory can include these bump attractors, allowing the use of continuous variables in these memories, and these associations can be learned by Hebbian rules. These simulations are related to biological networks, showing that this is a step toward a more complete neural cognitive associative memory.

Experience- and Context-Dependent Modulation of the Invertebrate Compass System

How are head direction signals computed and maintained in neural circuits? In this issue of Neuron, Shiozaki et al. (2020) expand our understanding of the fly "compass" network, revealing context- and experience-dependent changes in the multiplexed encoding of head direction and steering maneuvers.

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.

Nonequilibrium Statistical Mechanics of Continuous Attractors

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent nonequilibrium memory capacity in neural networks.

Anti-instinctive Learning Behavior Revealed by Locomotion-Triggered Mild Heat Stress in Drosophila

Anti-instinctive learning, an ability to modify an animal's innate behaviors in ways that go against one's innate tendency, can confer great evolutionary advantages to animals and enable them to better adapt to the changing environment. Yet, our understanding of anti-instinctive learning and its underlying mechanisms is still limited. In this work, we describe a new anti-instinctive learning behavior of fruit flies. This learning paradigm requires the fruit fly to respond to a recurring, aversive, mild heat stress by modifying its innate locomotion behavior. We found that experiencing movement-triggered mild heat stress repeatedly significantly reduced walking activity in wild type fruit flies, indicating that fruit flies are capable of anti-instinctive learning. We also report that such learning ability is reduced in dopamine 1-like receptor 1 (Dop1R1) null mutant and dopamine 2-like receptor (Dop2R) null mutant flies, suggesting that these two dopamine receptors are involved in mediating anti-instinctive learning in flies.

A virtual reality system to analyze neural activity and behavior in adult zebrafish

Virtual realities are powerful tools to analyze and manipulate interactions between animals and their environment and to enable measurements of neuronal activity during behavior. In many species, however, optical access to the brain and/or the behavioral repertoire are limited. We developed a high-resolution virtual reality for head-restrained adult zebrafish, which exhibit cognitive behaviors not shown by larvae. We noninvasively measured activity throughout the dorsal telencephalon by multiphoton calcium imaging. Fish in the virtual reality showed regular swimming patterns and were attracted to animations of conspecifics. Manipulations of visuo-motor feedback revealed neurons that responded selectively to the mismatch between the expected and the actual visual consequences of motor output. Such error signals were prominent in multiple telencephalic areas, consistent with models of predictive processing. A virtual reality system for adult zebrafish therefore provides opportunities to analyze neuronal processing mechanisms underlying higher brain functions including decision making, associative learning, and social interactions.

Bumps and oscillons in networks of spiking neurons

We study localized patterns in an exact mean-field description of a spatially extended network of quadratic integrate-and-fire neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps, and give an analytic estimate for the parameter range, where these solutions exist in parameter space, when one or more microscopic network parameters are varied. We develop Galerkin methods for the model equations, which enable numerical bifurcation analysis of stationary and time-periodic spatially extended solutions. We study the emergence of patterns composed of multiple bumps, which are arranged in a snake-and-ladder bifurcation structure if a homogeneous or heterogeneous synaptic kernel is suitably chosen. Furthermore, we examine time-periodic, spatially localized solutions (oscillons) in the presence of external forcing, and in autonomous, recurrently coupled excitatory and inhibitory networks. In both cases, we observe period-doubling cascades leading to chaotic oscillations.

Adaptive Tuning Curve Widths Improve Sample Efficient Learning

Natural brains perform miraculously well in learning new tasks from a small number of samples, whereas sample efficient learning is still a major open problem in the field of machine learning. Here, we raise the question, how the neural coding scheme affects sample efficiency, and make first progress on this question by proposing and analyzing a learning algorithm that uses a simple reinforce-type plasticity mechanism and does not require any gradients to learn low dimensional mappings. It harnesses three bio-plausible mechanisms, namely, population codes with bell shaped tuning curves, continous attractor mechanisms and probabilistic synapses, to achieve sample efficient learning. We show both theoretically and by simulations that population codes with broadly tuned neurons lead to high sample efficiency, whereas codes with sharply tuned neurons account for high final precision. Moreover, a dynamic adaptation of the tuning width during learning gives rise to both, high sample efficiency and high final precision. We prove a sample efficiency guarantee for our algorithm that lies within a logarithmic factor from the information theoretical optimum. Our simulations show that for low dimensional mappings, our learning algorithm achieves comparable sample efficiency to multi-layer perceptrons trained by gradient descent, although it does not use any gradients. Furthermore, it achieves competitive sample efficiency in low dimensional reinforcement learning tasks. From a machine learning perspective, these findings may inspire novel approaches to improve sample efficiency. From a neuroscience perspective, these findings suggest sample efficiency as a yet unstudied functional role of adaptive tuning curve width.

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.

Capacity-Resolution Trade-Off in the Optimal Learning of Multiple Low-Dimensional Manifolds by Attractor Neural Networks

Recurrent neural networks (RNN) are powerful tools to explain how attractors may emerge from noisy, high-dimensional dynamics. We study here how to learn the ∼N^{2} pairwise interactions in a RNN with N neurons to embed L manifolds of dimension D≪N. We show that the capacity, i.e., the maximal ratio L/N, decreases as |logε|^{-D}, where ε is the error on the position encoded by the neural activity along each manifold. Hence, RNN are flexible memory devices capable of storing a large number of manifolds at high spatial resolution. Our results rely on a combination of analytical tools from statistical mechanics and random matrix theory, extending Gardner's classical theory of learning to the case of patterns with strong spatial correlations.

Unsupervised Learning of Persistent and Sequential Activity

Two strikingly distinct types of activity have been observed in various brain structures during delay periods of delayed response tasks: Persistent activity (PA), in which a sub-population of neurons maintains an elevated firing rate throughout an entire delay period; and Sequential activity (SA), in which sub-populations of neurons are activated sequentially in time. It has been hypothesized that both types of dynamics can be “learned” by the relevant networks from the statistics of their inputs, thanks to mechanisms of synaptic plasticity. However, the necessary conditions for a synaptic plasticity rule and input statistics to learn these two types of dynamics in a stable fashion are still unclear. In particular, it is unclear whether a single learning rule is able to learn both types of activity patterns, depending on the statistics of the inputs driving the network. Here, we first characterize the complete bifurcation diagram of a firing rate model of multiple excitatory populations with an inhibitory mechanism, as a function of the parameters characterizing its connectivity. We then investigate how an unsupervised temporally asymmetric Hebbian plasticity rule shapes the dynamics of the network. Consistent with previous studies, we find that for stable learning of PA and SA, an additional stabilization mechanism is necessary. We show that a generalized version of the standard multiplicative homeostatic plasticity (Renart et al., 2003; Toyoizumi et al., 2014) stabilizes learning by effectively masking excitatory connections during stimulation and unmasking those connections during retrieval. Using the bifurcation diagram derived for fixed connectivity, we study analytically the temporal evolution and the steady state of the learned recurrent architecture as a function of parameters characterizing the external inputs. Slow changing stimuli lead to PA, while fast changing stimuli lead to SA. Our network model shows how a network with plastic synapses can stably and flexibly learn PA and SA in an unsupervised manner.

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.

Studying complex brain dynamics using Drosophila

The field has successfully used Drosophila genetic tools to identify neurons and sub-circuits important for specific functions. However, for an organism with complex and changing internal states to succeed in a complex and changing natural environment, many neurons and circuits need to interact dynamically. Drosophila's many advantages, combined with new imaging tools, offer unique opportunities to study how the brain functions as a complex dynamical system. We give an overview of complex activity patterns and how they can be observed, as well as modeling strategies, adding proof of principle in some cases.

Eigenvalue repulsion and eigenvector localization in sparse non-Hermitian random matrices

Complex networks with directed, local interactions are ubiquitous in nature and often occur with probabilistic connections due to both intrinsic stochasticity and disordered environments. Sparse non-Hermitian random matrices arise naturally in this context and are key to describing statistical properties of the nonequilibrium dynamics that emerges from interactions within the network structure. Here we study one-dimensional (1D) spatial structures and focus on sparse non-Hermitian random matrices in the spirit of tight-binding models in solid state physics. We first investigate two-point eigenvalue correlations in the complex plane for sparse non-Hermitian random matrices using methods developed for the statistical mechanics of inhomogeneous two-dimensional interacting particles. We find that eigenvalue repulsion in the complex plane directly correlates with eigenvector delocalization. In addition, for 1D chains and rings with both disordered nearest-neighbor connections and self-interactions, the self-interaction disorder tends to decorrelate eigenvalues and localize eigenvectors more than simple hopping disorder. However, remarkable resistance to eigenvector localization by disorder is provided by large cycles, such as those embodied in 1D periodic boundary conditions under strong directional bias. The directional bias also spatially separates the left and right eigenvectors, leading to interesting dynamics in excitation and response. These phenomena have important implications for asymmetric random networks and highlight a need for mathematical tools to describe and understand them analytically.

Mechanisms Underlying the Neural Computation of Head Direction

Many animals use an internal sense of direction to guide their movements through the world. Neurons selective to head direction are thought to support this directional sense and have been found in a diverse range of species, from insects to primates, highlighting their evolutionary importance. Across species, most head-direction networks share four key properties: a unique representation of direction at all times, persistent activity in the absence of movement, integration of angular velocity to update the representation, and the use of directional cues to correct drift. The dynamics of theorized network structures called ring attractors elegantly account for these properties, but their relationship to brain circuits is unclear. Here, we review experiments in rodents and flies that offer insights into potential neural implementations of ring attractor networks. We suggest that a theory-guided search across model systems for biological mechanisms that enable such dynamics would uncover general principles underlying head-direction circuit function.

Sensorimotor experience remaps visual input to a heading-direction network

In the Drosophila brain, 'compass' neurons track the orientation of the body and head (the fly's heading) during navigation 1,2. In the absence of visual cues, the compass neuron network estimates heading by integrating self-movement signals over time3,4. When a visual cue is present, the estimate of the network is more accurate1,3. Visual inputs to compass neurons are thought to originate from inhibitory neurons called R neurons (also known as ring neurons); the receptive fields of R neurons tile visual space5. The axon of each R neuron overlaps with the dendrites of every compass neuron6, raising the question of how visual cues are integrated into the compass. Here, using in vivo whole-cell recordings, we show that a visual cue can evoke synaptic inhibition in compass neurons and that R neurons mediate this inhibition. Each compass neuron is inhibited only by specific visual cue positions, indicating that many potential connections from R neurons onto compass neurons are actually weak or silent. We also show that the pattern of visually evoked inhibition can reorganize over minutes as the fly explores an altered virtual-reality environment. Using ensemble calcium imaging, we demonstrate that this reorganization causes persistent changes in the compass coordinate frame. Taken together, our data suggest a model in which correlated pre- and postsynaptic activity triggers associative long-term synaptic depression of visually evoked inhibition in compass neurons. Our findings provide evidence for the theoretical proposal that associative plasticity of sensory inputs, when combined with attractor dynamics, can reconcile self-movement information with changing external cues to generate a coherent sense of direction7-12.

Generation of stable heading representations in diverse visual scenes

Many animals rely on an internal heading representation when navigating in varied environments1-10. How this representation is linked to the sensory cues that define different surroundings is unclear. In the fly brain, heading is represented by 'compass' neurons that innervate a ring-shaped structure known as the ellipsoid body3,11,12. Each compass neuron receives inputs from 'ring' neurons that are selective for particular visual features13-16; this combination provides an ideal substrate for the extraction of directional information from a visual scene. Here we combine two-photon calcium imaging and optogenetics in tethered flying flies with circuit modelling, and show how the correlated activity of compass and visual neurons drives plasticity17-22, which flexibly transforms two-dimensional visual cues into a stable heading representation. We also describe how this plasticity enables the fly to convert a partial heading representation, established from orienting within part of a novel setting, into a complete heading representation. Our results provide mechanistic insight into the memory-related computations that are essential for flexible navigation in varied surroundings.

Two-photon imaging with silicon photomultipliers

We compared performance of recently developed silicon photomultipliers (SiPMs) to GaAsP photomultiplier tubes (PMTs) for two-photon imaging of neural activity. Despite higher dark counts, SiPMs match or exceed the signal-to-noise ratio of PMTs at photon rates encountered in typical calcium imaging experiments due to their low pulse height variability. At higher photon rates encountered during high-speed voltage imaging, SiPMs substantially outperform PMTs.

Heading choices of flying Drosophila under changing angles of polarized light

Many navigating insects include the celestial polarization pattern as an additional visual cue to orient their travels. Spontaneous orientation responses of both walking and flying fruit flies (Drosophila melanogaster) to linearly polarized light have previously been demonstrated. Using newly designed modular flight arenas consisting entirely of off-the-shelf parts and 3D-printed components we present individual flying flies with a slow and continuous rotational change in the incident angle of linear polarization. Under such open-loop conditions, single flies choose arbitrary headings with respect to the angle of polarized light and show a clear tendency to maintain those chosen headings for several minutes, thereby adjusting their course to the slow rotation of the incident stimulus. Importantly, flies show the tendency to maintain a chosen heading even when two individual test periods under a linearly polarized stimulus are interrupted by an epoch of unpolarized light lasting several minutes. Finally, we show that these behavioral responses are wavelength-specific, existing under polarized UV stimulus while being absent under polarized green light. Taken together, these findings provide further evidence supporting Drosophila’s abilities to use celestial cues for visually guided navigation and course correction.

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.

Semaphorin 2b Regulates Sleep-Circuit Formation in the Drosophila Central Brain

The fan-shaped body (FB) neuropil in the Drosophila brain central complex (CX) controls a variety of adult behaviors, including navigation and sleep. How neuronal processes are organized into precise layers and columns in the FB and how alterations in FB neural-circuit wiring affect animal behaviors are unknown. We report here that secreted semaphorin 2b (Sema-2b) acts through its transmembrane receptor Plexin B (PlexB) to locally attract neural processes to specific FB laminae. Aberrant Sema-2b/PlexB signaling leads to select disruptions in neural lamination, and these disruptions result in the formation of ectopic inhibitory connections between subsets of FB neurons. These structural alternations and connectivity defects are associated with changes in fly sleep and arousal, emphasizing the importance of lamination-mediated neural wiring in a central brain region critical for normal sleep behavior.

Velocity coupling of grid cell modules enables stable embedding of a low dimensional variable in a high dimensional neural attractor

Grid cells in the medial entorhinal cortex (MEC) encode position using a distributed representation across multiple neural populations (modules), each possessing a distinct spatial scale. The modular structure of the representation confers the grid cell neural code with large capacity. Yet, the modularity poses significant challenges for the neural circuitry that maintains the representation, and updates it based on self motion. Small incompatible drifts in different modules, driven by noise, can rapidly lead to large, abrupt shifts in the represented position, resulting in catastrophic readout errors. Here, we propose a theoretical model of coupled modules. The coupling suppresses incompatible drifts, allowing for a stable embedding of a two-dimensional variable (position) in a higher dimensional neural attractor, while preserving the large capacity. We propose that coupling of this type may be implemented by recurrent synaptic connectivity within the MEC with a relatively simple and biologically plausible structure.

Non-Hermitian quasilocalization and ring attractor neural networks

Eigenmodes of a broad class of "sparse" random matrices, with interactions concentrated near the diagonal, exponentially localize in space, as initially discovered in 1957 by Anderson for quantum systems. Anderson localization plays ubiquitous roles in varieties of problems from electrons in solids to mechanical and optical systems. However, its implications in neuroscience (where the connections can be strongly asymmetric) have been largely unexplored, mainly because synaptic connectivity matrices of neural systems are often "dense," which makes the eigenmodes spatially extended. Here we explore roles that Anderson localization could be playing in neural networks by focusing on "spatially structured" disorder in synaptic connectivity matrices. Recently neuroscientists have experimentally confirmed that the local excitation and global inhibition (LEGI) ring attractor model can functionally represent head direction cells in Drosophila melanogaster central brain. We first study a non-Hermitian (i.e., asymmetric) tight-binding model with disorder and then establish a connection to the LEGI ring attractor model. We discover that (1) principal eigenvectors of the LEGI ring attractor networks with structured nearest-neighbor disorder are "quasilocalized," even with fully dense inhibitory connections; and (2) the quasilocalized eigenvectors play dominant roles in the early time neural dynamics, and the location of the principal quasilocalized eigenvectors predicts an initial location of the "bump of activity" representing, for example, a head direction of an insect. Our investigations open up venues for explorations at the intersection between the theory of Anderson localization and neural networks with spatially structured disorder.