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.

From Whole-Brain Data to Functional Circuit Models: The Zebrafish Optomotor Response.

Detailed descriptions of brain-scale sensorimotor circuits underlying vertebrate behavior remain elusive. Recent advances in zebrafish neuroscience offer new opportunities to dissect such circuits via whole-brain imaging, behavioral analysis, functional perturbations, and network modeling. Here, we harness these tools to generate a brain-scale circuit model of the optomotor response, an orienting behavior evoked by visual motion. We show that such motion is processed by diverse neural response types distributed across multiple brain regions. To transform sensory input into action, these regions sequentially integrate eye- and direction-specific sensory streams, refine representations via interhemispheric inhibition, and demix locomotor instructions to independently drive turning and forward swimming. While experiments revealed many neural response types throughout the brain, modeling identified the dimensions of functional connectivity most critical for the behavior. We thus reveal how distributed neurons collaborate to generate behavior and illustrate a paradigm for distilling functional circuit models from whole-brain data.

Reward expectations direct learning and drive operant matching in Drosophila.

Foraging animals must use decision-making strategies that dynamically adapt to the changing availability of rewards in the environment. A wide diversity of animals do this by distributing their choices in proportion to the rewards received from each option, Herrnstein's operant matching law. Theoretical work suggests an elegant mechanistic explanation for this ubiquitous behavior, as operant matching follows automatically from simple synaptic plasticity rules acting within behaviorally relevant neural circuits. However, no past work has mapped operant matching onto plasticity mechanisms in the brain, leaving the biological relevance of the theory unclear. Here, we discovered operant matching in Drosophila and showed that it requires synaptic plasticity that acts in the mushroom body and incorporates the expectation of reward. We began by developing a dynamic foraging paradigm to measure choices from individual flies as they learn to associate odor cues with probabilistic rewards. We then built a model of the fly mushroom body to explain each fly's sequential choice behavior using a family of biologically realistic synaptic plasticity rules. As predicted by past theoretical work, we found that synaptic plasticity rules could explain fly matching behavior by incorporating stimulus expectations, reward expectations, or both. However, by optogenetically bypassing the representation of reward expectation, we abolished matching behavior and showed that the plasticity rule must specifically incorporate reward expectations. Altogether, these results reveal the first synapse-level mechanisms of operant matching and provide compelling evidence for the role of reward expectation signals in the fly brain.

Surface viscosities of lipid bilayers determined from equilibrium molecular dynamics simulations.

Lipid membrane viscosity is critical to biological function. Bacterial cells grown in different environments alter their lipid composition in order to maintain a specific viscosity, and membrane viscosity has been linked to the rate of cellular respiration. To understand the factors that determine the viscosity of a membrane, we ran equilibrium all-atom simulations of single component lipid bilayers and calculated their viscosities. The viscosity was calculated via a Green-Kubo relation, with the stress-tensor autocorrelation function modeled by a stretched exponential function. By simulating a series of lipids at different temperatures, we establish the dependence of viscosity on several aspects of lipid chemistry, including hydrocarbon chain length, unsaturation, and backbone structure. Sphingomyelin is found to have a remarkably high viscosity, roughly 20 times that of DPPC. Furthermore, we find that inclusion of the entire range of the dispersion interaction increases viscosity by up to 140%. The simulated viscosities are similar to experimental values obtained from the rotational dynamics of small chromophores and from the diffusion of integral membrane proteins but significantly lower than recent measurements based on the deformation of giant vesicles.

Exact learning dynamics of deep linear networks with prior knowledge.

Learning in deep neural networks is known to depend critically on the knowledge embedded in the initial network weights. However, few theoretical results have precisely linked prior knowledge to learning dynamics. Here we derive exact solutions to the dynamics of learning with rich prior knowledge in deep linear networks by generalising Fukumizu's matrix Riccati solution (Fukumizu 1998 Gen 1 1E-03). We obtain explicit expressions for the evolving network function, hidden representational similarity, and neural tangent kernel over training for a broad class of initialisations and tasks. The expressions reveal a class of task-independent initialisations that radically alter learning dynamics from slow non-linear dynamics to fast exponential trajectories while converging to a global optimum with identical representational similarity, dissociating learning trajectories from the structure of initial internal representations. We characterise how network weights dynamically align with task structure, rigorously justifying why previous solutions successfully described learning from small initial weights without incorporating their fine-scale structure. Finally, we discuss the implications of these findings for continual learning, reversal learning and learning of structured knowledge. Taken together, our results provide a mathematical toolkit for understanding the impact of prior knowledge on deep learning.

Impermanence of dendritic spines in live adult CA1 hippocampus.

The mammalian hippocampus is crucial for episodic memory formation and transiently retains information for about 3-4 weeks in adult mice and longer in humans. Although neuroscientists widely believe that neural synapses are elemental sites of information storage, there has been no direct evidence that hippocampal synapses persist for time intervals commensurate with the duration of hippocampal-dependent memory. Here we tested the prediction that the lifetimes of hippocampal synapses match the longevity of hippocampal memory. By using time-lapse two-photon microendoscopy in the CA1 hippocampal area of live mice, we monitored the turnover dynamics of the pyramidal neurons' basal dendritic spines, postsynaptic structures whose turnover dynamics are thought to reflect those of excitatory synaptic connections. Strikingly, CA1 spine turnover dynamics differed sharply from those seen previously in the neocortex. Mathematical modelling revealed that the data best matched kinetic models with a single population of spines with a mean lifetime of approximately 1-2 weeks. This implies ∼100% turnover in ∼2-3 times this interval, a near full erasure of the synaptic connectivity pattern. Although N-methyl-d-aspartate (NMDA) receptor blockade stabilizes spines in the neocortex, in CA1 it transiently increased the rate of spine loss and thus lowered spine density. These results reveal that adult neocortical and hippocampal pyramidal neurons have divergent patterns of spine regulation and quantitatively support the idea that the transience of hippocampal-dependent memory directly reflects the turnover dynamics of hippocampal synapses.

Whole-brain activity mapping onto a zebrafish brain atlas.

In order to localize the neural circuits involved in generating behaviors, it is necessary to assign activity onto anatomical maps of the nervous system. Using brain registration across hundreds of larval zebrafish, we have built an expandable open-source atlas containing molecular labels and definitions of anatomical regions, the Z-Brain. Using this platform and immunohistochemical detection of phosphorylated extracellular signal­regulated kinase (ERK) as a readout of neural activity, we have developed a system to create and contextualize whole-brain maps of stimulus- and behavior-dependent neural activity. This mitogen-activated protein kinase (MAP)-mapping assay is technically simple, and data analysis is completely automated. Because MAP-mapping is performed on freely swimming fish, it is applicable to studies of nearly any stimulus or behavior. Here we demonstrate our high-throughput approach using pharmacological, visual and noxious stimuli, as well as hunting and feeding. The resultant maps outline hundreds of areas associated with behaviors.

Symmetries in stimulus statistics shape the form of visual motion estimators.

The estimation of visual motion has long been studied as a paradigmatic neural computation, and multiple models have been advanced to explain behavioral and neural responses to motion signals. A broad class of models, originating with the Reichardt correlator model, proposes that animals estimate motion by computing a temporal cross-correlation of light intensities from two neighboring points in visual space. These models provide a good description of experimental data in specific contexts but cannot explain motion percepts in stimuli lacking pairwise correlations. Here, we develop a theoretical formalism that can accommodate diverse stimuli and behavioral goals. To achieve this, we treat motion estimation as a problem of Bayesian inference. Pairwise models emerge as one component of the generalized strategy for motion estimation. However, correlation functions beyond second order enable more accurate motion estimation. Prior expectations that are asymmetric with respect to bright and dark contrast use correlations of both even and odd orders, and we show that psychophysical experiments using visual stimuli with symmetric probability distributions for contrast cannot reveal whether the subject uses odd-order correlators for motion estimation. This result highlights a gap in previous experiments, which have largely relied on symmetric contrast distributions. Our theoretical treatment provides a natural interpretation of many visual motion percepts, indicates that motion estimation should be revisited using a broader class of stimuli, demonstrates how correlation-based motion estimation is related to stimulus statistics, and provides multiple experimentally testable predictions.

Optimization in Visual Motion Estimation.

Sighted animals use visual signals to discern directional motion in their environment. Motion is not directly detected by visual neurons, and it must instead be computed from light signals that vary over space and time. This makes visual motion estimation a near universal neural computation, and decades of research have revealed much about the algorithms and mechanisms that generate directional signals. The idea that sensory systems are optimized for performance in natural environments has deeply impacted this research. In this article, we review the many ways that optimization has been used to quantitatively model visual motion estimation and reveal its underlying principles. We emphasize that no single optimization theory has dominated the literature. Instead, researchers have adeptly incorporated different computational demands and biological constraints that are pertinent to the specific brain system and animal model under study. The successes and failures of the resulting optimization models have thereby provided insights into how computational demands and biological constraints together shape neural computation.

Photon shot noise limits on optical detection of neuronal spikes and estimation of spike timing.

Optical approaches for tracking neural dynamics are of widespread interest, but a theoretical framework quantifying the physical limits of these techniques has been lacking. We formulate such a framework by using signal detection and estimation theory to obtain physical bounds on the detection of neural spikes and the estimation of their occurrence times as set by photon counting statistics (shot noise). These bounds are succinctly expressed via a discriminability index that depends on the kinetics of the optical indicator and the relative fluxes of signal and background photons. This approach facilitates quantitative evaluations of different indicators, detector technologies, and data analyses. Our treatment also provides optimal filtering techniques for optical detection of spikes. We compare various types of Ca(2+) indicators and show that background photons are a chief impediment to voltage sensing. Thus, voltage indicators that change color in response to membrane depolarization may offer a key advantage over those that change intensity. We also examine fluorescence resonance energy transfer indicators and identify the regimes in which the widely used ratiometric analysis of signals is substantially suboptimal. Overall, by showing how different optical factors interact to affect signal quality, our treatment offers a valuable guide to experimental design and provides measures of confidence to assess optically extracted traces of neural activity.

Laparostomy management using the ABThera™ open abdomen negative pressure therapy system in a grade IV open abdomen secondary to acute pancreatitis.

Wound control in laparostomy for the treatment of intra-abdominal hypertension remains challenging and numerous techniques have been described. We report the first UK experience with a new commercially available device specifically designed to facilitate management of the open abdomen. A 44-year-old gentleman presented with a 3-day history of constant severe epigastric pain and associated vomiting. Amylase was markedly elevated and he was admitted for supportive management of pancreatitis, with subsequent transfer to intensive care due to severe systemic inflammatory syndrome. The patient decompensated, developing intra-abdominal hypertension with renal and respiratory failure. This was successfully managed by performing a laparostomy and using an ABThera™ Open Abdomen Negative Pressure Therapy System (KCI, San Antonio, TX). We describe its use to facilitate wound control, including enteroatmospheric fistula, allowing granulation and eventual restoration of gastrointestinal continuity 383-days after admission. We found the ABThera™ System proved to be a useful treatment adjunct, protecting intra-abdominal contents while removing large volumes of exudate and infected material from within the abdominal cavity. Complex cases such as this remain infrequent and this article provides a summary of our experience, including a review of indications for laparostomy and the underlying basic science in this difficult area.

Organizing memories for generalization in complementary learning systems.

Memorization and generalization are complementary cognitive processes that jointly promote adaptive behavior. For example, animals should memorize safe routes to specific water sources and generalize from these memories to discover environmental features that predict new ones. These functions depend on systems consolidation mechanisms that construct neocortical memory traces from hippocampal precursors, but why systems consolidation only applies to a subset of hippocampal memories is unclear. Here we introduce a new neural network formalization of systems consolidation that reveals an overlooked tension-unregulated neocortical memory transfer can cause overfitting and harm generalization in an unpredictable world. We resolve this tension by postulating that memories only consolidate when it aids generalization. This framework accounts for partial hippocampal-cortical memory transfer and provides a normative principle for reconceptualizing numerous observations in the field. Generalization-optimized systems consolidation thus provides new insight into how adaptive behavior benefits from complementary learning systems specialized for memorization and generalization.

Estimation theoretic measure of resolution for stochastic localization microscopy.

One approach to super-resolution fluorescence microscopy, termed stochastic localization microscopy, relies on the nanometer scale spatial localization of individual fluorescent emitters that stochastically label specific features of the specimen. The precision of emitter localization is an important determinant of the resulting image resolution but is insufficient to specify how well the derived images capture the structure of the specimen. We address this deficiency by considering the inference of specimen structure based on the estimated emitter locations. By using estimation theory, we develop a measure of spatial resolution that jointly depends on the density of the emitter labels, the precision of emitter localization, and prior information regarding the spatial frequency content of the labeled object. The Nyquist criterion does not set the scaling of this measure with emitter number. Given prior information and a fixed emitter labeling density, our resolution measure asymptotes to a finite value as the precision of emitter localization improves. By considering the present experimental capabilities, this asymptotic behavior implies that further resolution improvements require increases in labeling density above typical current values. Our treatment also yields algorithms to enhance reliable image features. Overall, our formalism facilitates the rigorous statistical interpretation of the data produced by stochastic localization imaging techniques.

Mimicking the folding pathway to improve homology-free protein structure prediction.

Since the demonstration that the sequence of a protein encodes its structure, the prediction of structure from sequence remains an outstanding problem that impacts numerous scientific disciplines, including many genome projects. By iteratively fixing secondary structure assignments of residues during Monte Carlo simulations of folding, our coarse-grained model without information concerning homology or explicit side chains can outperform current homology-based secondary structure prediction methods for many proteins. The computationally rapid algorithm using only single (phi,psi) dihedral angle moves also generates tertiary structures of accuracy comparable with existing all-atom methods for many small proteins, particularly those with low homology. Hence, given appropriate search strategies and scoring functions, reduced representations can be used for accurately predicting secondary structure and providing 3D structures, thereby increasing the size of proteins approachable by homology-free methods and the accuracy of template methods that depend on a high-quality input secondary structure.

Geometric framework to predict structure from function in neural networks.

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

Theoretical principles for illuminating sensorimotor processing with brain-wide neuronal recordings.

Modern recording techniques now permit brain-wide sensorimotor circuits to be observed at single neuron resolution in small animals. Extracting theoretical understanding from these recordings requires principles that organize findings and guide future experiments. Here we review theoretical principles that shed light onto brain-wide sensorimotor processing. We begin with an analogy that conceptualizes principles as streetlamps that illuminate the empirical terrain, and we illustrate the analogy by showing how two familiar principles apply in new ways to brain-wide phenomena. We then focus the bulk of the review on describing three more principles that have wide utility for mapping brain-wide neural activity, making testable predictions from highly parameterized mechanistic models, and investigating the computational determinants of neuronal response patterns across the brain.

Correcting for physical distortions in visual stimuli improves reproducibility in zebrafish neuroscience.

Optical refraction causes light to bend at interfaces between optical media. This phenomenon can significantly distort visual stimuli presented to aquatic animals in water, yet refraction has often been ignored in the design and interpretation of visual neuroscience experiments. Here we provide a computational tool that transforms between projected and received stimuli in order to detect and control these distortions. The tool considers the most commonly encountered interface geometry, and we show that this and other common configurations produce stereotyped distortions. By correcting these distortions, we reduced discrepancies in the literature concerning stimuli that evoke escape behavior, and we expect this tool will help reconcile other confusing aspects of the literature. This tool also aids experimental design, and we illustrate the dangers that uncorrected stimuli pose to receptive field mapping experiments.

A Neural Representation of Naturalistic Motion-Guided Behavior in the Zebrafish Brain.

All animals must transform ambiguous sensory data into successful behavior. This requires sensory representations that accurately reflect the statistics of natural stimuli and behavior. Multiple studies show that visual motion processing is tuned for accuracy under naturalistic conditions, but the sensorimotor circuits extracting these cues and implementing motion-guided behavior remain unclear. Here we show that the larval zebrafish retina extracts a diversity of naturalistic motion cues, and the retinorecipient pretectum organizes these cues around the elements of behavior. We find that higher-order motion stimuli, gliders, induce optomotor behavior matching expectations from natural scene analyses. We then image activity of retinal ganglion cell terminals and pretectal neurons. The retina exhibits direction-selective responses across glider stimuli, and anatomically clustered pretectal neurons respond with magnitudes matching behavior. Peripheral computations thus reflect natural input statistics, whereas central brain activity precisely codes information needed for behavior. This general principle could organize sensorimotor transformations across animal species.

Asymmetric ON-OFF processing of visual motion cancels variability induced by the structure of natural scenes.

Animals detect motion using a variety of visual cues that reflect regularities in the natural world. Experiments in animals across phyla have shown that motion percepts incorporate both pairwise and triplet spatiotemporal correlations that could theoretically benefit motion computation. However, it remains unclear how visual systems assemble these cues to build accurate motion estimates. Here, we used systematic behavioral measurements of fruit fly motion perception to show how flies combine local pairwise and triplet correlations to reduce variability in motion estimates across natural scenes. By generating synthetic images with statistics controlled by maximum entropy distributions, we show that the triplet correlations are useful only when images have light-dark asymmetries that mimic natural ones. This suggests that asymmetric ON-OFF processing is tuned to the particular statistics of natural scenes. Since all animals encounter the world's light-dark asymmetries, many visual systems are likely to use asymmetric ON-OFF processing to improve motion estimation.

Threshold-Based Ordering of Sequential Actions during Drosophila Courtship.

Goal-directed animal behaviors are typically composed of sequences of motor actions whose order and timing are critical for a successful outcome. Although numerous theoretical models for sequential action generation have been proposed, few have been supported by the identification of control neurons sufficient to elicit a sequence. Here, we identify a pair of descending neurons that coordinate a stereotyped sequence of engagement actions during Drosophila melanogaster male courtship behavior. These actions are initiated sequentially but persist cumulatively, a feature not explained by existing models of sequential behaviors. We find evidence consistent with a ramp-to-threshold mechanism, in which increasing neuronal activity elicits each action independently at successively higher activity thresholds.