Functional dissection of circuitry in a neural integrator

Neural flip-flops I: Short-term memory

The networks proposed here show how neurons can be connected to form flip-flops, the basic building blocks in sequential logic systems. The novel neural flip-flops (NFFs) are explicit, dynamic, and can generate known phenomena of short-term memory. For each network design, all neurons, connections, and types of synapses are shown explicitly. The neurons' operation depends only on explicitly stated, minimal properties of excitement and inhibition. This operation is dynamic in the sense that the level of neuron activity is the only cellular change, making the NFFs' operation consistent with the speed of most brain functions. Memory tests have shown that certain neurons fire continuously at a high frequency while information is held in short-term memory. These neurons exhibit seven characteristics associated with memory formation, retention, retrieval, termination, and errors. One of the neurons in each of the NFFs produces all of the characteristics. This neuron and a second neighboring neuron together predict eight unknown phenomena. These predictions can be tested by the same methods that led to the discovery of the first seven phenomena. NFFs, together with a decoder from a previous paper, suggest a resolution to the longstanding controversy of whether short-term memory depends on neurons firing persistently or in brief, coordinated bursts. Two novel NFFs are composed of two and four neurons. Their designs follow directly from a standard electronic flip-flop design by moving each negation symbol from one end of the connection to the other. This does not affect the logic of the network, but it changes the logic of each component to a logic function that can be implemented by a single neuron. This transformation is reversible and is apparently new to engineering as well as neuroscience.

Interactions between circuit architecture and plasticity in a closed-loop cerebellar system

Determining the sites and directions of plasticity underlying changes in neural activity and behavior is critical for understanding mechanisms of learning. Identifying such plasticity from neural recording data can be challenging due to feedback pathways that impede reasoning about cause and effect. We studied interactions between feedback, neural activity, and plasticity in the context of a closed-loop motor learning task for which there is disagreement about the loci and directions of plasticity: vestibulo-ocular reflex learning. We constructed a set of circuit models that differed in the strength of their recurrent feedback, from no feedback to very strong feedback. Despite these differences, each model successfully fit a large set of neural and behavioral data. However, the patterns of plasticity predicted by the models fundamentally differed, with the direction of plasticity at a key site changing from depression to potentiation as feedback strength increased. Guided by our analysis, we suggest how such models can be experimentally disambiguated. Our results address a long-standing debate regarding cerebellum-dependent motor learning, suggesting a reconciliation in which learning-related changes in the strength of synaptic inputs to Purkinje cells are compatible with seemingly oppositely directed changes in Purkinje cell spiking activity. More broadly, these results demonstrate how changes in neural activity over learning can appear to contradict the sign of the underlying plasticity when either internal feedback or feedback through the environment is present.

Neural circuit models for evidence accumulation through choice-selective sequences

Decision making is traditionally thought to be mediated by populations of neurons whose firing rates persistently accumulate evidence across time. However, recent decision-making experiments in rodents have observed neurons across the brain that fire sequentially as a function of spatial position or time, rather than persistently, with the subset of neurons in the sequence depending on the animal's choice. We develop two new candidate circuit models, in which evidence is encoded either in the relative firing rates of two competing chains of neurons or in the network location of a stereotyped pattern ("bump") of neural activity. Encoded evidence is then faithfully transferred between neuronal populations representing different positions or times. Neural recordings from four different brain regions during a decision-making task showed that, during the evidence accumulation period, different brain regions displayed tuning curves consistent with different candidate models for evidence accumulation. This work provides mechanistic models and potential neural substrates for how graded-value information may be precisely accumulated within and transferred between neural populations, a set of computations fundamental to many cognitive operations.

A telencephalon cell type atlas for goldfish reveals diversity in the evolution of spatial structure and cell types

Teleost fish form the largest group of vertebrates and show a tremendous variety of adaptive behaviors, making them critically important for the study of brain evolution and cognition. The neural basis mediating these behaviors remains elusive. We performed a systematic comparative survey of the goldfish telencephalon. We mapped cell types using single-cell RNA sequencing and spatial transcriptomics, resulting in de novo molecular neuroanatomy parcellation. Glial cells were highly conserved across 450 million years of evolution separating mouse and goldfish, while neurons showed diversity and modularity in gene expression. Specifically, somatostatin interneurons, famously interspersed in the mammalian isocortex for local inhibitory input, were curiously aggregated in a single goldfish telencephalon nucleus but molecularly conserved. Cerebral nuclei including the striatum, a hub for motivated behavior in amniotes, had molecularly conserved goldfish homologs. We suggest elements of a hippocampal formation across the goldfish pallium. Last, aiding study of the teleostan everted telencephalon, we describe substantial molecular similarities between goldfish and zebrafish neuronal taxonomies.

A brainstem integrator for self-location memory and positional homeostasis in zebrafish

To track and control self-location, animals integrate their movements through space. Representations of self-location are observed in the mammalian hippocampal formation, but it is unknown if positional representations exist in more ancient brain regions, how they arise from integrated self-motion, and by what pathways they control locomotion. Here, in a head-fixed, fictive-swimming, virtual-reality preparation, we exposed larval zebrafish to a variety of involuntary displacements. They tracked these displacements and, many seconds later, moved toward their earlier location through corrective swimming ("positional homeostasis"). Whole-brain functional imaging revealed a network in the medulla that stores a memory of location and induces an error signal in the inferior olive to drive future corrective swimming. Optogenetically manipulating medullary integrator cells evoked displacement-memory behavior. Ablating them, or downstream olivary neurons, abolished displacement corrections. These results reveal a multiregional hindbrain circuit in vertebrates that integrates self-motion and stores self-location to control locomotor behavior.

Flexibility of neural circuits regulating mating behaviors in mice and flies

Mating is essential for the reproduction of animal species. As mating behaviors are high-risk and energy-consuming processes, it is critical for animals to make adaptive mating decisions. This includes not only finding a suitable mate, but also adapting mating behaviors to the animal's needs and environmental conditions. Internal needs include physical states (e.g., hunger) and emotional states (e.g., fear), while external conditions include both social cues (e.g., the existence of predators or rivals) and non-social factors (e.g., food availability). With recent advances in behavioral neuroscience, we are now beginning to understand the neural basis of mating behaviors, particularly in genetic model organisms such as mice and flies. However, how internal and external factors are integrated by the nervous system to enable adaptive mating-related decision-making in a state- and context-dependent manner is less well understood. In this article, we review recent knowledge regarding the neural basis of flexible mating behaviors from studies of flies and mice. By contrasting the knowledge derived from these two evolutionarily distant model organisms, we discuss potential conserved and divergent neural mechanisms involved in the control of flexible mating behaviors in invertebrate and vertebrate brains.

The emergence and influence of internal states

Animal behavior is shaped by a variety of "internal states"-partially hidden variables that profoundly shape perception, cognition, and action. The neural basis of internal states, such as fear, arousal, hunger, motivation, aggression, and many others, is a prominent focus of research efforts across animal phyla. Internal states can be inferred from changes in behavior, physiology, and neural dynamics and are characterized by properties such as pleiotropy, persistence, scalability, generalizability, and valence. To date, it remains unclear how internal states and their properties are generated by nervous systems. Here, we review recent progress, which has been driven by advances in behavioral quantification, cellular manipulations, and neural population recordings. We synthesize research implicating defined subsets of state-inducing cell types, widespread changes in neural activity, and neuromodulation in the formation and updating of internal states. In addition to highlighting the significance of these findings, our review advocates for new approaches to clarify the underpinnings of internal brain states across the animal kingdom.

Neural Algorithms and Circuits for Motor Planning

The brain plans and executes volitional movements. The underlying patterns of neural population activity have been explored in the context of movements of the eyes, limbs, tongue, and head in nonhuman primates and rodents. How do networks of neurons produce the slow neural dynamics that prepare specific movements and the fast dynamics that ultimately initiate these movements? Recent work exploits rapid and calibrated perturbations of neural activity to test specific dynamical systems models that are capable of producing the observed neural activity. These joint experimental and computational studies show that cortical dynamics during motor planning reflect fixed points of neural activity (attractors). Subcortical control signals reshape and move attractors over multiple timescales, causing commitment to specific actions and rapid transitions to movement execution. Experiments in rodents are beginning to reveal how these algorithms are implemented at the level of brain-wide neural circuits.

Robustness and Flexibility of Neural Function through Dynamical Criticality

In theoretical biology, robustness refers to the ability of a biological system to function properly even under perturbation of basic parameters (e.g., temperature or pH), which in mathematical models is reflected in not needing to fine-tune basic parameter constants; flexibility refers to the ability of a system to switch functions or behaviors easily and effortlessly. While there are extensive explorations of the concept of robustness and what it requires mathematically, understanding flexibility has proven more elusive, as well as also elucidating the apparent opposition between what is required mathematically for models to implement either. In this paper we address a number of arguments in theoretical neuroscience showing that both robustness and flexibility can be attained by systems that poise themselves at the onset of a large number of dynamical bifurcations, or dynamical criticality, and how such poising can have a profound influence on integration of information processing and function. Finally, we examine critical map lattices, which are coupled map lattices where the coupling is dynamically critical in the sense of having purely imaginary eigenvalues. We show that these map lattices provide an explicit connection between dynamical criticality in the sense we have used and “edge of chaos” criticality.

Fixational drift is driven by diffusive dynamics in central neural circuitry

During fixation and between saccades, our eyes undergo diffusive random motion called fixational drift. The role of fixational drift in visual coding and inference has been debated in the past few decades, but the mechanisms that underlie this motion remained unknown. In particular, it has been unclear whether fixational drift arises from peripheral sources, or from central sources within the brain. Here we show that fixational drift is correlated with neural activity, and identify its origin in central neural circuitry within the oculomotor system, upstream to the ocular motoneurons (OMNs). We analyzed a large data set of OMN recordings in the rhesus monkey, alongside precise measurements of eye position, and found that most of the variance of fixational eye drifts must arise upstream of the OMNs. The diffusive statistics of the motion points to the oculomotor integrator, a memory circuit responsible for holding the eyes still between saccades, as a likely source of the motion. Theoretical modeling, constrained by the parameters of the primate oculomotor system, supports this hypothesis by accounting for the amplitude as well as the statistics of the motion. Thus, we propose that fixational ocular drift provides a direct observation of diffusive dynamics in a neural circuit responsible for storage of continuous parameter memory in persistent neural activity. The identification of a mechanistic origin for fixational drift is likely to advance the understanding of its role in visual processing and inference.

Toroidal topology of population activity in grid cells

The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment¹. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations², and are organized in modules³ that collectively form a population code for the animal’s allocentric position¹. The invariance of the correlation structure of this population code across environments^4,5 and behavioural states^6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern^1,8–11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models¹². This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

Simultaneous recordings from hundreds of grid cells in rats, combined with topological data analysis, show that network activity in grid cells resides on a toroidal manifold that is invariant across environments and brain states.

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.

Robust rhythmogenesis via spike-timing-dependent plasticity

Rhythmic activity has been observed in numerous animal species ranging from insects to humans, and in relation to a wide range of cognitive tasks. Various experimental and theoretical studies have investigated rhythmic activity. The theoretical efforts have mainly been focused on the neuronal dynamics, under the assumption that network connectivity satisfies certain fine-tuning conditions required to generate oscillations. However, it remains unclear how this fine-tuning is achieved. Here we investigated the hypothesis that spike-timing-dependent plasticity (STDP) can provide the underlying mechanism for tuning synaptic connectivity to generate rhythmic activity. We addressed this question in a modeling study. We examined STDP dynamics in the framework of a network of excitatory and inhibitory neuronal populations that has been suggested to underlie the generation of oscillations in the gamma range. Mean-field Fokker-Planck equations for the synaptic weight dynamics are derived in the limit of slow learning. We drew on this approximation to determine which types of STDP rules drive the system to exhibit rhythmic activity, and we demonstrate how the parameters that characterize the plasticity rule govern the rhythmic activity. Finally, we propose a mechanism that can ensure the robustness of self-developing processes in general, and for rhythmogenesis in particular.

Corollary discharge promotes a sustained motor state in a neural circuit for navigation

Animals exhibit behavioral and neural responses that persist on longer timescales than transient or fluctuating stimulus inputs. Here, we report that Caenorhabditis elegans uses feedback from the motor circuit to a sensory processing interneuron to sustain its motor state during thermotactic navigation. By imaging circuit activity in behaving animals, we show that a principal postsynaptic partner of the AFD thermosensory neuron, the AIY interneuron, encodes both temperature and motor state information. By optogenetic and genetic manipulation of this circuit, we demonstrate that the motor state representation in AIY is a corollary discharge signal. RIM, an interneuron that is connected with premotor interneurons, is required for this corollary discharge. Ablation of RIM eliminates the motor representation in AIY, allows thermosensory representations to reach downstream premotor interneurons, and reduces the animal's ability to sustain forward movements during thermotaxis. We propose that feedback from the motor circuit to the sensory processing circuit underlies a positive feedback mechanism to generate persistent neural activity and sustained behavioral patterns in a sensorimotor transformation.

Low-Dimensional Manifolds Support Multiplexed Integrations in Recurrent Neural Networks

We study the learning dynamics and the representations emerging in recurrent neural networks (RNNs) trained to integrate one or multiple temporal signals. Combining analytical and numerical investigations, we characterize the conditions under which an RNN with n neurons learns to integrate D(≪n) scalar signals of arbitrary duration. We show, for linear, ReLU, and sigmoidal neurons, that the internal state lives close to a D-dimensional manifold, whose shape is related to the activation function. Each neuron therefore carries, to various degrees, information about the value of all integrals. We discuss the deep analogy between our results and the concept of mixed selectivity forged by computational neuroscientists to interpret cortical recordings.

Dense Circuit Reconstruction to Understand Neuronal Computation: Focus on Zebrafish

The dense reconstruction of neuronal wiring diagrams from volumetric electron microscopy data has the potential to generate fundamentally new insights into mechanisms of information processing and storage in neuronal circuits. Zebrafish provide unique opportunities for dynamical connectomics approaches that combine reconstructions of wiring diagrams with measurements of neuronal population activity and behavior. Such approaches have the power to reveal higher-order structure in wiring diagrams that cannot be detected by sparse sampling of connectivity and that is essential for neuronal computations. In the brain stem, recurrently connected neuronal modules were identified that can account for slow, low-dimensional dynamics in an integrator circuit. In the spinal cord, connectivity specifies functional differences between premotor interneurons. In the olfactory bulb, tuning-dependent connectivity implements a whitening transformation that is based on the selective suppression of responses to overrepresented stimulus features. These findings illustrate the potential of dynamical connectomics in zebrafish to analyze the circuit mechanisms underlying higher-order neuronal computations.

The neural basis for a persistent internal state in Drosophila females

Sustained changes in mood or action require persistent changes in neural activity, but it has been difficult to identify the neural circuit mechanisms that underlie persistent activity and contribute to long-lasting changes in behavior. Here, we show that a subset of Doublesex+ pC1 neurons in the Drosophila female brain, called pC1d/e, can drive minutes-long changes in female behavior in the presence of males. Using automated reconstruction of a volume electron microscopic (EM) image of the female brain, we map all inputs and outputs to both pC1d and pC1e. This reveals strong recurrent connectivity between, in particular, pC1d/e neurons and a specific subset of Fruitless+ neurons called aIPg. We additionally find that pC1d/e activation drives long-lasting persistent neural activity in brain areas and cells overlapping with the pC1d/e neural network, including both Doublesex+ and Fruitless+ neurons. Our work thus links minutes-long persistent changes in behavior with persistent neural activity and recurrent circuit architecture in the female brain.

Cerebellar Roles in Frequency Competitive Motor Learning of the Vestibulo-ocular Reflex

Biological motions commonly contain multiple frequency components in which each fundamental has to be adjusted by motor learning to acquire a new motor skill or maintain acquired skills. At times during this motor performance one frequency component needs to be enhanced (gain-up) while another is suppressed (gain-down). This pattern of simultaneous gain-up and -down adjustments at different frequencies is called frequency competitive motor learning. Currently we investigated cerebellar roles in this behavior utilizing the goldfish vestibulo-ocular reflex (VOR). Previously, VOR motor learning was shown in primates to be frequency selective and exhibit frequency competitive motor learning. Here we demonstrate that the goldfish VOR performs frequency competitive motor learning when high and low frequency components are trained to gain-up and gain-down, respectively. However, when the two frequency components were trained in the opposite directions only gain-up component was observed. We also found that cerebellectomy precluded any frequency competitive VOR motor learning. Complementary single unit recordings from vestibulo-cerebellar Purkinje cells revealed changes in firing modulation along with gain-down learning, but not with gain-up learning irrespective of frequency. These results demonstrate that the cerebellum is required for all frequency competitive VOR motor learning and Purkinje cell activity therein is well correlated with all gain-down behaviors independent of frequency. However, frequency competitive gain-up learning requires intact, recursive brainstem/cerebellar pathways. Collectively these findings support the idea that VOR gain-up and gain-down learning utilize separate brainstem/cerebellar circuitry that, in turn, clearly underlies the unique ability of the oculomotor system to deal with multiple frequency components.

Randomly connected networks generate emergent selectivity and predict decoding properties of large populations of neurons

Modern recording methods enable sampling of thousands of neurons during the performance of behavioral tasks, raising the question of how recorded activity relates to theoretical models. In the context of decision making, functional connectivity between choice-selective cortical neurons was recently reported. The straightforward interpretation of these data suggests the existence of selective pools of inhibitory and excitatory neurons. Computationally investigating an alternative mechanism for these experimental observations, we find that a randomly connected network of excitatory and inhibitory neurons generates single-cell selectivity, patterns of pairwise correlations, and the same ability of excitatory and inhibitory populations to predict choice, as in experimental observations. Further, we predict that, for this task, there are no anatomically defined subpopulations of neurons representing choice, and that choice preference of a particular neuron changes with the details of the task. We suggest that distributed stimulus selectivity and functional organization in population codes could be emergent properties of randomly connected networks.

Different Activation Mechanisms of Excitatory Networks in the Rat Oculomotor Integrators for Vertical and Horizontal Gaze Holding

Gaze holding in the horizontal and vertical directions is separately controlled via the oculomotor neural integrators, the prepositus hypoglossi nucleus (PHN) and the interstitial nucleus of Cajal (INC), respectively. Our previous in vitro studies demonstrated that transient, high-frequency local stimulation of the PHN and the INC increased the frequency of spontaneous EPSCs that lasted for several seconds. The sustained EPSC response of PHN neurons was attributed to the activation of local excitatory networks primarily mediated via Ca²⁺-permeable AMPA (CP-AMPA) receptors and Ca²⁺-activated nonselective cation (CAN) channels. However, the contribution of CP-AMPA receptors to the activation of INC excitatory networks appeared to be small. In this study, we clarified the mechanisms of excitatory network activation in the PHN and INC using whole-cell recordings in rat brainstem slices. Although physiological and histological analyses showed that neurons that expressed CP-AMPA receptors existed not only in the PHN but also in the INC, the effect of a CP-AMPA receptor antagonist on the sustained EPSC response was significantly weaker in INC neurons than in PHN neurons. Meanwhile, the effect of an NMDA receptor antagonist on the sustained EPSC response was significantly stronger in INC neurons than in PHN neurons. Furthermore, the current and the charge transfer mediated via NMDA receptors were significantly larger in INC neurons than in PHN neurons. These results strongly suggest that these excitatory networks are activated via different synaptic mechanisms: a CP-AMPA receptor and CAN channel-dependent mechanism and an NMDA receptor-dependent mechanism in horizontal and vertical integrators, respectively.

Functional architecture underlying binocular coordination of eye position and velocity in the larval zebrafish hindbrain

BACKGROUND

The oculomotor integrator (OI) in the vertebrate hindbrain transforms eye velocity input into persistent position coding output, which plays a crucial role in retinal image stability. For a mechanistic understanding of the integrator function and eye position control, knowledge about the tuning of the OI and other oculomotor nuclei is needed. Zebrafish are increasingly used to study integrator function and sensorimotor circuits, yet the precise neuronal tuning to motor variables remains uncharacterized.

RESULTS

Here, we recorded cellular calcium signals while evoking monocular and binocular optokinetic eye movements at different slow-phase eye velocities. Our analysis reveals the anatomical distributions of motoneurons and internuclear neurons in the nucleus abducens as well as those of oculomotor neurons in caudally adjacent hindbrain volumes. Each neuron is tuned to eye position and/or velocity to variable extents and is only activated after surpassing particular eye position and velocity thresholds. While the abducens (rhombomeres 5/6) mainly codes for eye position, in rhombomeres 7/8, a velocity-to-position coding gradient exists along the rostro-caudal axis, which likely corresponds to the oculomotor structures storing velocity and position, and is in agreement with a feedforward mechanism of persistent activity generation. Position encoding neurons are recruited at eye position thresholds distributed across the behaviourally relevant dynamic range, while velocity-encoding neurons have more centred firing thresholds for velocity. In the abducens, neurons coding exclusively for one eye intermingle with neurons coding for both eyes. Many of these binocular neurons are preferentially active during conjugate eye movements and less active during monocular eye movements. This differential recruitment during monocular versus conjugate tasks represents a functional diversification in the final common motor pathway.

CONCLUSIONS

We localized and functionally characterized the repertoire of oculomotor neurons in the zebrafish hindbrain. Our findings provide evidence for a mixed but task-specific binocular code and suggest that generation of persistent activity is organized along the rostro-caudal axis in the hindbrain.

A simple decision to move in response to touch reveals basic sensory memory and mechanisms for variable response times

KEY POINTS

Short-term working memory and decision-making are usually studied in the cerebral cortex; in many models of simple decision making, sensory signals build slowly and noisily to threshold to initiate a motor response after long, variable delays. When touched, hatchling frog tadpoles decide whether to swim; we define the long and variable delays to swimming and use whole-cell recordings to uncover the neurons and processes responsible. Firing in sensory and sensory pathway neurons is short latency, and too brief and invariant to explain these delays, while recordings from hindbrain reticulospinal neurons controlling swimming reveal a prolonged and variable build-up of synaptic excitation which can reach firing threshold and initiate swimming. We propose this excitation provides a sensory memory of the stimulus and may be generated by small reverberatory hindbrain networks. Our results uncover fundamental network mechanisms that allow animals to remember brief sensory stimuli and delay simple motor decisions.

ABSTRACT

Many motor responses to sensory input, like locomotion or eye movements, are much slower than reflexes. Can simpler animals provide fundamental answers about the cellular mechanisms for motor decisions? Can we observe the 'accumulation' of excitation to threshold proposed to underlie decision making elsewhere? We explore how somatosensory touch stimulation leads to the decision to swim in hatchling Xenopus tadpoles. Delays measured to swimming in behaving and immobilised tadpoles are long and variable. Activity in their extensively studied sensory and sensory pathway neurons is too short-lived to explain these response delays. Instead, whole-cell recordings from the hindbrain reticulospinal neurons that drive swimming show that these receive prolonged, variable synaptic excitation lasting for nearly a second following a brief stimulus. They fire and initiate swimming when this excitation reaches threshold. Analysis of the summation of excitation requires us to propose extended firing in currently undefined presynaptic hindbrain neurons. Simple models show that a small excitatory recurrent-network inserted in the sensory pathway can mimic this process. We suggest that such a network may generate slow, variable summation of excitation to threshold. This excitation provides a simple memory of the sensory stimulus. It allows temporal and spatial integration of sensory inputs and explains the long, variable delays to swimming. The process resembles the 'accumulation' of excitation proposed for cortical circuits in mammals. We conclude that fundamental elements of sensory memory and decision making are present in the brainstem at a surprisingly early stage in development.

Neuronal, mathematical, and molecular bases of perceptual decision-making in C. elegans

Animals process sensory information from the environment to make behavioral decisions. Although environmental information may be ambiguous or gradually changing, animals can still choose one behavioral option among several through perceptual decision-making. Perceptual decision-making has been intensively studied in primates and rodents, and neural activity that accumulates sensory information has been shown to be crucial. However, it remains unclear how the accumulating neural activity is generated, and whether such activity is a conserved decision-making strategy across the animal kingdom. Here, we review the previous perceptual decision-making studies in vertebrates and invertebrates and our recent achievement in an invertebrate model animal, the nematode Caenorhabditis elegans. In the study, we analyzed temporal dynamics of neuronal activity during perceptual decision-making in navigational behavior of C. elegans. We identified neural activity that accumulates sensory information and elucidated the molecular mechanism for the accumulating activity, which may be relevant to decision-making across the animal kingdom.

Purinergic modulation of neuronal activity in the rat prepositus hypoglossi nucleus

In the nervous system, adenosine 5'-trisphosphate (ATP) functions as a neurotransmitter and binds to ionotropic P2X receptors and metabotropic P2Y receptors. Although ATP receptors are expressed in the prepositus hypoglossi nucleus (PHN), which is a brainstem structure involved in controlling horizontal gaze, it is unclear whether ATP indeed affects the activity of PHN neurons. In this study, we investigated the effects of ATP on spontaneous firing of PHN neurons using whole-cell recordings in rat brainstem slices. Bath application of ATP increased or decreased the spontaneous firing rate of the neurons in a dose-dependent manner, indicating that ATP indeed affects PHN neuronal activity. To clarify the mechanisms of the ATP effects, we investigated the current responses of PHN neurons to a local application of ATP. The ATP application induced a fast inward (FI) current, a slow inward (SI) current, and/or a slow outward (SO) current in the neurons. The agonists of P2X and P2Y receptors induced FI and SI currents, respectively. The SO currents were not induced by the ATP agonists but were induced by adenosine, which may be extracellularly converted from ATP by ectonucleotidases. An antagonist of adenosine P1 (A₁ ) receptors abolished the adenosine-induced SO currents and bath application of adenosine decreased the spontaneous firing rate of all PHN neurons tested. These results indicate that PHN neurons express functional purinoceptors and show that the FI, SI, and SO currents were mediated via P2X, P2Y, and A₁ receptors, respectively.

Rats adopt the optimal timescale for evidence integration in a dynamic environment

Decision making in dynamic environments requires discounting old evidence that may no longer inform the current state of the world. Previous work found that humans discount old evidence in a dynamic environment, but do not discount at the optimal rate. Here we investigated whether rats can optimally discount evidence in a dynamic environment by adapting the timescale over which they accumulate evidence. Using discrete evidence pulses, we exactly compute the optimal inference process. We show that the optimal timescale for evidence discounting depends on both the stimulus statistics and noise in sensory processing. When both of these components are taken into account, rats accumulate and discount evidence with the optimal timescale. Finally, by changing the volatility of the environment, we demonstrate experimental control over the rats' accumulation timescale. The mechanisms supporting integration are a subject of extensive study, and experimental control over these timescales may open new avenues of investigation.

Rhythmogenesis evolves as a consequence of long-term plasticity of inhibitory synapses

Brain rhythms are widely believed to reflect numerous cognitive processes. Changes in rhythmicity have been associated with pathological states. However, the mechanism underlying these rhythms remains unknown. Here, we present a theoretical analysis of the evolvement of rhythm generating capabilities in neuronal circuits. We tested the hypothesis that brain rhythms can be acquired via an intrinsic unsupervised learning process of activity dependent plasticity. Specifically, we focused on spike timing dependent plasticity (STDP) of inhibitory synapses. We detail how rhythmicity can develop via STDP under certain conditions that serve as a natural prediction of the hypothesis. We show how global features of the STDP rule govern and stabilize the resultant rhythmic activity. Finally, we demonstrate how rhythmicity is retained even in the face of synaptic variability. This study suggests a role for inhibitory plasticity that is beyond homeostatic processes.

Mutual Information and Information Gating in Synfire Chains

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains—SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Cortical computations via transient attractors

The ability of sensory networks to transiently store information on the scale of seconds can confer many advantages in processing time-varying stimuli. How a network could store information on such intermediate time scales, between typical neurophysiological time scales and those of long-term memory, is typically attributed to persistent neural activity. An alternative mechanism which might allow for such information storage is through temporary modifications to the neural connectivity which decay on the same second-long time scale as the underlying memories. Earlier work that has explored this method has done so by emphasizing one attractor from a limited, pre-defined set. Here, we describe an alternative, a Transient Attractor network, which can learn any pattern presented to it, store several simultaneously, and robustly recall them on demand using targeted probes in a manner reminiscent of Hopfield networks. We hypothesize that such functionality could be usefully embedded within sensory cortex, and allow for a flexibly-gated short-term memory, as well as conferring the ability of the network to perform automatic de-noising, and separation of input signals into distinct perceptual objects. We demonstrate that the stored information can be refreshed to extend storage time, is not sensitive to noise in the system, and can be turned on or off by simple neuromodulation. The diverse capabilities of transient attractors, as well as their resemblance to many features observed in sensory cortex, suggest the possibility that their actions might underlie neural processing in many sensory areas.

Population-scale organization of cerebellar granule neuron signaling during a visuomotor behavior

Granule cells at the input layer of the cerebellum comprise over half the neurons in the human brain and are thought to be critical for learning. However, little is known about granule neuron signaling at the population scale during behavior. We used calcium imaging in awake zebrafish during optokinetic behavior to record transgenically identified granule neurons throughout a cerebellar population. A significant fraction of the population was responsive at any given time. In contrast to core precerebellar populations, granule neuron responses were relatively heterogeneous, with variation in the degree of rectification and the balance of positive versus negative changes in activity. Functional correlations were strongest for nearby cells, with weak spatial gradients in the degree of rectification and the average sign of response. These data open a new window upon cerebellar function and suggest granule layer signals represent elementary building blocks under-represented in core sensorimotor pathways, thereby enabling the construction of novel patterns of activity for learning.

Comparisons of Neuronal and Excitatory Network Properties between the Rat Brainstem Nuclei that Participate in Vertical and Horizontal Gaze Holding

Gaze holding is primarily controlled by neural structures including the prepositus hypoglossi nucleus (PHN) for horizontal gaze and the interstitial nucleus of Cajal (INC) for vertical and torsional gaze. In contrast to the accumulating findings of the PHN, there is no report regarding the membrane properties of INC neurons or the local networks in the INC. In this study, to verify whether the neural structure of the INC is similar to that of the PHN, we investigated the neuronal and network properties of the INC using whole-cell recordings in rat brainstem slices. Three types of afterhyperpolarization (AHP) profiles and five firing patterns observed in PHN neurons were also observed in INC neurons. However, the overall distributions based on the AHP profile and the firing patterns of INC neurons were different from those of PHN neurons. The application of burst stimulation to a nearby site of a recorded INC neuron induced an increase in the frequency of spontaneous EPSCs. The duration of the increased EPSC frequency of INC neurons was not significantly different from that of PHN neurons. The percent of duration reduction induced by a Ca²⁺-permeable AMPA (CP-AMPA) receptor antagonist was significantly smaller in the INC than in the PHN. These findings suggest that local excitatory networks that activate sustained EPSC responses also exist in the INC, but their activation mechanisms including the contribution of CP-AMPA receptors differ between the INC and the PHN.

Electron Microscopic Reconstruction of Functionally Identified Cells in a Neural Integrator

Neural integrators are involved in a variety of sensorimotor and cognitive behaviors. The oculomotor system contains a simple example, a hindbrain neural circuit that takes velocity signals as inputs and temporally integrates them to control eye position. Here we investigated the structural underpinnings of temporal integration in the larval zebrafish by first identifying integrator neurons using two-photon calcium imaging and then reconstructing the same neurons through serial electron microscopic analysis. Integrator neurons were identified as those neurons with activities highly correlated with eye position during spontaneous eye movements. Three morphological classes of neurons were observed: ipsilaterally projecting neurons located medially, contralaterally projecting neurons located more laterally, and a population at the extreme lateral edge of the hindbrain for which we were not able to identify axons. Based on their somatic locations, we inferred that neurons with only ipsilaterally projecting axons are glutamatergic, whereas neurons with only contralaterally projecting axons are largely GABAergic. Dendritic and synaptic organization of the ipsilaterally projecting neurons suggests a broad sampling from inputs on the ipsilateral side. We also observed the first conclusive evidence of synapses between integrator neurons, which have long been hypothesized by recurrent network models of integration via positive feedback.

Calcium dynamics regulating the timing of decision-making in C. elegans

Brains regulate behavioral responses with distinct timings. Here we investigate the cellular and molecular mechanisms underlying the timing of decision-making during olfactory navigation in Caenorhabditis elegans. We find that, based on subtle changes in odor concentrations, the animals appear to choose the appropriate migratory direction from multiple trials as a form of behavioral decision-making. Through optophysiological, mathematical and genetic analyses of neural activity under virtual odor gradients, we further find that odor concentration information is temporally integrated for a decision by a gradual increase in intracellular calcium concentration ([Ca2+]i), which occurs via L-type voltage-gated calcium channels in a pair of olfactory neurons. In contrast, for a reflex-like behavioral response, [Ca2+]i rapidly increases via multiple types of calcium channels in a pair of nociceptive neurons. Thus, the timing of neuronal responses is determined by cell type-dependent involvement of calcium channels, which may serve as a cellular basis for decision-making.

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.

Functional Connectomics: How Maggots Make Up Their Minds

How Drosophila larvae select one behavior or a sequence of behaviors, and then persist in the final one, has been addressed by a powerful combination of electron-microscopy reconstruction of neuronal connections, genetic manipulations, electrophysiology, and neuronal modeling. Surprisingly, reciprocal inhibitory synaptic connections are major players in choosing, sequencing and maintaining behaviors.

Optimal compensation for neuron loss

The brain has an impressive ability to withstand neural damage. Diseases that kill neurons can go unnoticed for years, and incomplete brain lesions or silencing of neurons often fail to produce any behavioral effect. How does the brain compensate for such damage, and what are the limits of this compensation? We propose that neural circuits instantly compensate for neuron loss, thereby preserving their function as much as possible. We show that this compensation can explain changes in tuning curves induced by neuron silencing across a variety of systems, including the primary visual cortex. We find that compensatory mechanisms can be implemented through the dynamics of networks with a tight balance of excitation and inhibition, without requiring synaptic plasticity. The limits of this compensatory mechanism are reached when excitation and inhibition become unbalanced, thereby demarcating a recovery boundary, where signal representation fails and where diseases may become symptomatic.

Computational principles of memory

The ability to store and later use information is essential for a variety of adaptive behaviors, including integration, learning, generalization, prediction and inference. In this Review, we survey theoretical principles that can allow the brain to construct persistent states for memory. We identify requirements that a memory system must satisfy and analyze existing models and hypothesized biological substrates in light of these requirements. We also highlight open questions, theoretical puzzles and problems shared with computer science and information theory.

Cervical dystonia: a neural integrator disorder

Ocular motor neural integrators ensure that eyes are held steady in straight-ahead and eccentric positions of gaze. Abnormal function of the ocular motor neural integrator leads to centripetal drifts of the eyes with consequent gaze-evoked nystagmus. In 2002 a neural integrator, analogous to that in the ocular motor system, was proposed for the control of head movements. Recently, a counterpart of gaze-evoked eye nystagmus was identified for head movements; in which the head could not be held steady in eccentric positions on the trunk. These findings lead to a novel pathophysiological explanation in cervical dystonia, which proposed that the abnormalities of head movements stem from a malfunctioning head neural integrator, either intrinsically or as a result of impaired cerebellar, basal ganglia, or peripheral feedback. Here we briefly recapitulate the history of the neural integrator for eye movements, then further develop the idea of a neural integrator for head movements, and finally discuss its putative role in cervical dystonia. We hypothesize that changing the activity in an impaired head neural integrator, by modulating feedback, could treat dystonia.

Robust neuronal dynamics in premotor cortex during motor planning

Neural activity maintains representations that bridge past and future events, often over many seconds. Network models can produce persistent and ramping activity, but the positive feedback that is critical for these slow dynamics can cause sensitivity to perturbations. Here we use electrophysiology and optogenetic perturbations in the mouse premotor cortex to probe the robustness of persistent neural representations during motor planning. We show that preparatory activity is remarkably robust to large-scale unilateral silencing: detailed neural dynamics that drive specific future movements were quickly and selectively restored by the network. Selectivity did not recover after bilateral silencing of the premotor cortex. Perturbations to one hemisphere are thus corrected by information from the other hemisphere. Corpus callosum bisections demonstrated that premotor cortex hemispheres can maintain preparatory activity independently. Redundancy across selectively coupled modules, as we observed in the premotor cortex, is a hallmark of robust control systems. Network models incorporating these principles show robustness that is consistent with data.

Modelling Feedback Excitation, Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.

Development of functional hindbrain oculomotor circuitry independent of both vascularization and neuronal activity in larval zebrafish

We investigated the contribution of blood vessel formation and neuronal excitability to the development of functional neural circuitry in larval zebrafish by analyzing oculomotor performance in response to visual and vestibular stimuli. To address the dependence of neuronal function on the presence of blood vessels, we compared wild type embryos to reck and cloche mutants that lacked intracerebral blood vessels. To test how neuronal excitability impacts neuronal development and intracerebral vascularization, we blocked neural activity using Tetraodotoxin (TTX) and Tricaine. In reck mutants, we found both slow phase horizontal tracking and fast phase resets with only a slightly reduced amplitude and bandwidth. Spontaneous saccades, eye position holding and vestibular gravitoinertial induced eye rotation were also present. All of these behaviors except for visual tracking were observed in cloche mutants that lacked any head vasculature. Thus, numerous oculomotor neuronal circuits spanning the forebrain, midbrain and hindbrain compartments, ending in motor innervations of the eye muscles, were correctly formed and generated appropriate oculomotor behaviors without blood vessels. However, our observations indicate that beginning at approximately six days, circulation was required for sustained behavioral performance. We further found that blocking neuronal excitability with either TTX or Tricaine up to 4-5 days post fertilization did not noticeably interfere with intracerebral blood vessel formation in wild type larvae. After removal of drug treatments, the oculomotor behaviors returned within hours. Thus, development of neuronal circuits that drive oculomotor performance does not require neuronal spiking or activity. Together these findings demonstrate that neither vascularization nor neuronal excitability are essential for the formation of numerous oculomotor nuclei with intricately designed connectivity and signal processing. We conclude that a genetic blueprint specifies early larval structural and physiological features, and this developmental strategy may be viewed as a unique adaptation required for early survival.

Sources of noise during accumulation of evidence in unrestrained and voluntarily head-restrained rats

Decision-making behavior is often characterized by substantial variability, but its source remains unclear. We developed a visual accumulation of evidence task designed to quantify sources of noise and to be performed during voluntary head restraint, enabling cellular resolution imaging in future studies. Rats accumulated discrete numbers of flashes presented to the left and right visual hemifields and indicated the side that had the greater number of flashes. Using a signal-detection theory-based model, we found that the standard deviation in their internal estimate of flash number scaled linearly with the number of flashes. This indicates a major source of noise that, surprisingly, is not consistent with the widely used 'drift-diffusion modeling' (DDM) approach but is instead closely related to proposed models of numerical cognition and counting. We speculate that this form of noise could be important in accumulation of evidence tasks generally.

DOI:http://dx.doi.org/10.7554/eLife.11308.001

Perceptual decision-making, i.e. making choices based on observed evidence, is rarely perfect. Humans and other animals tend to respond correctly on some trials and incorrectly on others. For over a century, this variability has been used to study the basis of decision-making. Most behavioral models assume that random fluctuations or 'noise' in the decision-making process is the primary source of variability and errors. However, the nature of this noise is unclear and the subject of intense scrutiny.

To investigate the sources of the behavioral variability during decision-making, Scott, Constantinople et al. trained rats to perform a visual 'accumulation of evidence' task. The animals counted flashes of light that appeared on either their left or their right. Up to 15 flashes occurred on each side, in a random order, and the rats then received a reward if they selected the side that the greatest number of flashes had occurred on. The rats chose correctly on many occasions but not on every single one.

Using a computer-controlled rat training facility or 'rat academy', Scott, Constantinople et al. collected hundreds of thousands of behavioral trials from over a dozen rats. This large dataset provided the statistical power necessary to test the assumptions of leading models of behavioral variability during decision-making, and revealed that noise grew more rapidly with the number of flashes than previously predicted. This finding explained patterns of behavior that previous models struggled with, most notably the fact that individuals make errors even on the easiest trials. The analysis also revealed that animals maintain two separate running totals – one of stimuli on the left and another of stimuli on the right – rather than a single tally of the difference between the two.

Scott, Constantinople et al. further demonstrated that rats could be trained to perform this task using a new system that enables functional brain imaging. The next step is to repeat these experiments while simultaneously recording brain activity to study the neural circuits that underlie decision-making and its variability.

DOI:http://dx.doi.org/10.7554/eLife.11308.002

The diagnostic value of saccades in movement disorder patients: a practical guide and review

Saccades are rapid eye movements designed to shift the fovea to objects of visual interest. Abnormalities of saccades offer important clues in the diagnosis of a number of movement disorders. In this review, we explore the anatomy of horizontal and vertical saccades, discuss practical aspects of their examination, and review how saccadic abnormalities in hyperkinetic and hypokinetic movement disorders aid in diagnosis, with video demonstration of classic examples. Documentation of the ease of saccade initiation, range of motion and conjugacy of saccades, speed and accuracy of saccades, dynamic saccadic trajectory, and the presence or absence of saccadic intrusions and oscillations are important components of this exam. We also provide a practical algorithm to demonstrate the value of saccades in the differential diagnosis of the movement disorders patient.

A structural and genotypic scaffold underlying temporal integration

The accumulation and storage of information over time, temporal integration, is key to numerous behaviors. Many oculomotor tasks depend on integration of eye-velocity signals to eye-position commands, a transformation achieved by a hindbrain cell group termed the velocity-to-position neural integrator (VPNI). Although the VPNI's coding properties have been well characterized, its mechanism of function remains poorly understood because few links exist between neuronal activity, structure, and genotypic identity. To fill this gap, we used calcium imaging and single-cell electroporation during oculomotor behaviors to map VPNI neural activity in zebrafish onto a hindbrain scaffold consisting of alternating excitatory and inhibitory parasagittal stripes. Three distinct classes of VPNI cells were identified. One glutamatergic class was medially located along a stripe associated with the alx transcription factor; these cells had ipsilateral projections terminating near abducens motoneurons and collateralized extensively within the ipsilateral VPNI in a manner consistent with integration through recurrent excitation. A second glutamatergic class was more laterally located along a stripe associated with transcription factor dbx1b; these glutamatergic cells had contralateral projections collateralizing near abducens motoneurons, consistent with a role in disconjugate eye movements. A third class, immunohistochemically suggested to be GABAergic, was located primarily in the dbx1b stripe and also had contralateral projections terminating near abducens motoneurons; these cells collateralized extensively in the dendritic field of contralateral VPNI neurons, consistent with a role in coordinating activity between functionally opposing populations. This mapping between VPNI activity, structure, and genotype may provide a blueprint for understanding the mechanisms governing temporal integration.

Neural dynamics for landmark orientation and angular path integration

Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed flies walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body — a toroidal structure in the center of the fly brain. The population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity — a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors — network structures proposed to support the function of navigational brain circuits.

Local population synchrony and the encoding of eye position in the primate neural integrator

Encoding horizontal eye position in the oculomotor system occurs through temporal integration of eye velocity inputs to produce tonic outputs. The nucleus prepositus is commonly believed to be the "neural integrator" that accomplishes this function through the activity of its ensemble of predominantly burst-tonic neurons. Single-unit characterizations and labeling studies of these neurons have suggested that their collective output is achieved through local feedback loops produced by direct connections between them. If this is the case, then the ensemble of burst-tonic neurons should exhibit correlated activity. To obtain electrophysiological evidence of local interactions between neurons, we simultaneously recorded pairs (n = 29) of burst-tonic neurons in the nucleus prepositus of rhesus macaque monkeys using eight-channel linear microelectrode arrays. We computed the magnitude of synchrony between their spike trains as a function of eye position during ocular fixations and as a function of distance between neurons. Importantly, we found that neurons exhibit unexpected levels of positive synchrony, which is maximal during contralateral fixations and weakest when neurons are located far apart from one another (>300 μm). Together, our results support a role for shared inputs to ipsilateral pairs of burst-tonic neurons in the encoding of eye position in the primate nucleus prepositus.