Adaptive, locally linear models of complex dynamics

Discovery of a novel piperazine derivative, cmp2: a selective TRPC6 activator suitable for treatment of synaptic deficiency in Alzheimer's disease hippocampal neurons

Alzheimer disease (AD) is characterized by progressive loss of memory. Synaptic loss is now the best correlate of cognitive dysfunction in patients with Alzheimer's disease. Thus, restoration or limitation of synapse loss is a promising strategy for pharmacotherapy of AD. N-N substituted piperazines are widely used chemical compounds for drug interventions to treat different illnesses including CNS diseases such as drug abuse, mental and anxiety disorders. Piperazine derivatives are small molecules that are usually well tolerated and cross blood brain barrier (BBB). Thus, disubstituted piperazines are good tools for searching and developing novel disease-modifying drugs. Previously, we have determined the piperazine derivative, 51164, as an activator of TRPC6 in dendritic spines. We have demonstrated synaptoprotective properties of 51164 in AD mouse models. However, 51164 was not able to cross BBB. Within the current study, we identified a novel piperazine derivative, cmp2, that is structurally similar to 51164 but is able to cross BBB. Cmp2 binds central part of monomeric TRPC6 in similar way as hypeforin does. Cmp2 selectively activates TRPC6 but not structurally related TRPC3 and TRPC7. Novel piperazine derivative exhibits synaptoprotective properties in culture and slices and penetrates the BBB. In vivo study indicated cmp2 (10 mg/kg I.P.) reversed deficits in synaptic plasticity in the 5xFAD mice. Thus, we suggest that cmp2 is a novel lead compound for drug development. The mechanism of cmp2 action is based on selective TRPC6 stimulation and it is expected to treat synaptic deficiency in hippocampal neurons.

A Markovian dynamics for Caenorhabditis elegans behavior across scales

How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm Caenorhabditis elegans, we show that a single dynamics connects posture-scale fluctuations with trajectory diffusion and longer-lived behavioral states. We take short posture sequences as an instantaneous behavioral measure, fixing the sequence length for maximal prediction. Within the space of posture sequences, we construct a fine-scale, maximum entropy partition so that transitions among microstates define a high-fidelity Markov model, which we also use as a means of principled coarse-graining. We translate these dynamics into movement using resistive force theory, capturing the statistical properties of foraging trajectories. Predictive across scales, we leverage the longest-lived eigenvectors of the inferred Markov chain to perform a top-down subdivision of the worm's foraging behavior, revealing both "runs-and-pirouettes" as well as previously uncharacterized finer-scale behaviors. We use our model to investigate the relevance of these fine-scale behaviors for foraging success, recovering a trade-off between local and global search strategies.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Light evokes stereotyped global brain dynamics in Caenorhabditis elegans

Stereotyped oscillations in population neural activity recordings from immobilized Caenorhabditis elegans have garnered interest for their striking low dimensionality and their evocative state-space trajectories or manifolds. Previously these oscillations have been interpreted as intrinsically driven global motor commands. Here we test whether these oscillations are intrinsic. We show that similar oscillations are evoked by high-intensity blue light commonly used for calcium imaging. Oscillations are reduced or absent and have a lower frequency when a longer imaging wavelength is used. Under the original blue light illumination, oscillations are reduced or have a lower frequency in animals that lack GUR-3, an endogenous light- and hydrogen-peroxide-sensitive gustatory receptor. Additional experiments with hydrogen peroxide are consistent with GUR-3's involvement. We therefore propose that blue light evokes global oscillations in part through the creation of reactive oxygen species that activate the hydrogen-peroxide-sensing receptor GUR-3.

Fluctuating landscapes and heavy tails in animal behavior

Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales. This immense variability hampers quantitative reasoning and renders the identification of universal principles elusive. Through data analysis and theory, we here show that slow non-ergodic drives generally give rise to heavy-tailed statistics in behaving animals. We leverage high-resolution recordings of C. elegans locomotion to extract a self-consistent reduced order model for an inferred reaction coordinate, bridging from sub-second chaotic dynamics to long-lived stochastic transitions among metastable states. The slow mode dynamics exhibits heavy-tailed first passage time distributions and correlation functions, and we show that such heavy tails can be explained by dynamics on a time-dependent potential landscape. Inspired by these results, we introduce a generic model in which we separate faster mixing modes that evolve on a quasi-stationary potential, from slower non-ergodic modes that drive the potential landscape, and reflect slowly varying internal states. We show that, even for simple potential landscapes, heavy tails emerge when barrier heights fluctuate slowly and strongly enough. In particular, the distribution of first passage times and the correlation function can asymptote to a power law, with related exponents that depend on the strength and nature of the fluctuations. We support our theoretical findings through direct numerical simulations.

Rapid automated 3-D pose estimation of larval zebrafish using a physical model-trained neural network

Quantitative ethology requires an accurate estimation of an organism's postural dynamics in three dimensions plus time. Technological progress over the last decade has made animal pose estimation in challenging scenarios possible with unprecedented detail. Here, we present (i) a fast automated method to record and track the pose of individual larval zebrafish in a 3-D environment, applicable when accurate human labeling is not possible; (ii) a rich annotated dataset of 3-D larval poses for ethologists and the general zebrafish and machine learning community; and (iii) a technique to generate realistic, annotated larval images in different behavioral contexts. Using a three-camera system calibrated with refraction correction, we record diverse larval swims under free swimming conditions and in response to acoustic and optical stimuli. We then employ a convolutional neural network to estimate 3-D larval poses from video images. The network is trained against a set of synthetic larval images rendered using a 3-D physical model of larvae. This 3-D model samples from a distribution of realistic larval poses that we estimate a priori using a template-based pose estimation of a small number of swim bouts. Our network model, trained without any human annotation, performs larval pose estimation three orders of magnitude faster and with accuracy comparable to the template-based approach, capturing detailed kinematics of 3-D larval swims. It also applies accurately to other datasets collected under different imaging conditions and containing behavioral contexts not included in our training.

Non-Stationary Dynamic Mode Decomposition

Many physical processes display complex high-dimensional time-varying behavior, from global weather patterns to brain activity. An outstanding challenge is to express high dimensional data in terms of a dynamical model that reveals their spatiotemporal structure. Dynamic Mode Decomposition is a means to achieve this goal, allowing the identification of key spatiotemporal modes through the diagonalization of a finite dimensional approximation of the Koopman operator. However, DMD methods apply best to time-translationally invariant or stationary data, while in many typical cases, dynamics vary across time and conditions. To capture this temporal evolution, we developed a method, Non-Stationary Dynamic Mode Decomposition (NS-DMD), that generalizes DMD by fitting global modulations of drifting spatiotemporal modes. This method accurately predicts the temporal evolution of modes in simulations and recovers previously known results from simpler methods. To demonstrate its properties, the method is applied to multi-channel recordings from an awake behaving non-human primate performing a cognitive task.

Schrödinger Dynamics and Berry Phase of Undulatory Locomotion

Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.

Open-source tools for behavioral video analysis: Setup, methods, and best practices

Recently developed methods for video analysis, especially models for pose estimation and behavior classification, are transforming behavioral quantification to be more precise, scalable, and reproducible in fields such as neuroscience and ethology. These tools overcome long-standing limitations of manual scoring of video frames and traditional 'center of mass' tracking algorithms to enable video analysis at scale. The expansion of open-source tools for video acquisition and analysis has led to new experimental approaches to understand behavior. Here, we review currently available open-source tools for video analysis and discuss how to set up these methods for labs new to video recording. We also discuss best practices for developing and using video analysis methods, including community-wide standards and critical needs for the open sharing of datasets and code, more widespread comparisons of video analysis methods, and better documentation for these methods especially for new users. We encourage broader adoption and continued development of these tools, which have tremendous potential for accelerating scientific progress in understanding the brain and behavior.

Social behavioral profiling by unsupervised deep learning reveals a stimulative effect of dopamine D3 agonists on zebrafish sociality

It has been a major challenge to systematically evaluate and compare how pharmacological perturbations influence social behavioral outcomes. Although some pharmacological agents are known to alter social behavior, precise description and quantification of such effects have proven difficult. We developed a scalable social behavioral assay for zebrafish named ZeChat based on unsupervised deep learning to characterize sociality at high resolution. High-dimensional and dynamic social behavioral phenotypes are automatically classified using this method. By screening a neuroactive compound library, we found that different classes of chemicals evoke distinct patterns of social behavioral fingerprints. By examining these patterns, we discovered that dopamine D3 agonists possess a social stimulative effect on zebrafish. The D3 agonists pramipexole, piribedil, and 7-hydroxy-DPAT-HBr rescued social deficits in a valproic-acid-induced zebrafish autism model. The ZeChat platform provides a promising approach for dissecting the pharmacology of social behavior and discovering novel social-modulatory compounds.

A deep learning framework for inference of single-trial neural population dynamics from calcium imaging with subframe temporal resolution

In many areas of the brain, neural populations act as a coordinated network whose state is tied to behavior on a millisecond timescale. Two-photon (2p) calcium imaging is a powerful tool to probe such network-scale phenomena. However, estimating the network state and dynamics from 2p measurements has proven challenging because of noise, inherent nonlinearities and limitations on temporal resolution. Here we describe Recurrent Autoencoder for Discovering Imaged Calcium Latents (RADICaL), a deep learning method to overcome these limitations at the population level. RADICaL extends methods that exploit dynamics in spiking activity for application to deconvolved calcium signals, whose statistics and temporal dynamics are quite distinct from electrophysiologically recorded spikes. It incorporates a new network training strategy that capitalizes on the timing of 2p sampling to recover network dynamics with high temporal precision. In synthetic tests, RADICaL infers the network state more accurately than previous methods, particularly for high-frequency components. In 2p recordings from sensorimotor areas in mice performing a forelimb reach task, RADICaL infers network state with close correspondence to single-trial variations in behavior and maintains high-quality inference even when neuronal populations are substantially reduced.

Neural mechanisms underlying the temporal organization of naturalistic animal behavior

Naturalistic animal behavior exhibits a strikingly complex organization in the temporal domain, with variability arising from at least three sources: hierarchical, contextual, and stochastic. What neural mechanisms and computational principles underlie such intricate temporal features? In this review, we provide a critical assessment of the existing behavioral and neurophysiological evidence for these sources of temporal variability in naturalistic behavior. Recent research converges on an emergent mechanistic theory of temporal variability based on attractor neural networks and metastable dynamics, arising via coordinated interactions between mesoscopic neural circuits. We highlight the crucial role played by structural heterogeneities as well as noise from mesoscopic feedback loops in regulating flexible behavior. We assess the shortcomings and missing links in the current theoretical and experimental literature and propose new directions of investigation to fill these gaps.

Inferring couplings in networks across order-disorder phase transitions

Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods, and the structure in the data. To this end, we characterize the efficacy of direct coupling analysis (DCA) - a highly successful method for analyzing amino acid sequence data-in inferring pairwise interactions from samples of ferromagnetic Ising models on random graphs. Our approach allows for physically motivated exploration of qualitatively distinct data regimes separated by phase transitions. We show that inference quality depends strongly on the nature of data-generating distributions: optimal accuracy occurs at an intermediate temperature where the detrimental effects from macroscopic order and thermal noise are minimal. Importantly our results indicate that DCA does not always outperform its local-statistics-based predecessors; while DCA excels at low temperatures, it becomes inferior to simple correlation thresholding at virtually all temperatures when data are limited. Our findings offer insights into the regime in which DCA operates so successfully, and more broadly, how inference interacts with the structure in the data.

Discovering sparse control strategies in neural activity

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations—ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms—to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, “pivotal” neurons that account for most of the system’s sensitivity, suggesting a sparse mechanism of collective control.

Fixed Point Attractor Theory Bridges Structure and Function in C. elegans Neuronal Network

Understanding the structure–function relationship in a neuronal network is one of the major challenges in neuroscience research. Despite increasing researches at circuit connectivity and neural network structure, their structure-based biological interpretability remains unclear. Based on the attractor theory, here we develop an analytical framework that links neural circuit structures and their functions together through fixed point attractor in Caenorhabditis elegans. In this framework, we successfully established the structural condition for the emergence of multiple fixed points in C. elegans connectome. Then we construct a finite state machine to explain how functions related to bistable phenomena at the neural activity and behavioral levels are encoded. By applying the proposed framework to the command circuit in C. elegans, we provide a circuit level interpretation for the forward-reverse switching behaviors. Interestingly, network properties of the command circuit and first layer amphid interneuron circuit can also be inferred from their functions in this framework. Our research indicates the reliability of the fixed point attractor bridging circuit structure and functions, suggesting its potential applicability to more complex neuronal circuits in other species.

Large-scale neural recordings call for new insights to link brain and behavior

Neuroscientists today can measure activity from more neurons than ever before, and are facing the challenge of connecting these brain-wide neural recordings to computation and behavior. In the present review, we first describe emerging tools and technologies being used to probe large-scale brain activity and new approaches to characterize behavior in the context of such measurements. We next highlight insights obtained from large-scale neural recordings in diverse model systems, and argue that some of these pose a challenge to traditional theoretical frameworks. Finally, we elaborate on existing modeling frameworks to interpret these data, and argue that the interpretation of brain-wide neural recordings calls for new theoretical approaches that may depend on the desired level of understanding. These advances in both neural recordings and theory development will pave the way for critical advances in our understanding of the brain.

A lexical approach for identifying behavioural action sequences

Animals display characteristic behavioural patterns when performing a task, such as the spiraling of a soaring bird or the surge-and-cast of a male moth searching for a female. Identifying such recurring sequences occurring rarely in noisy behavioural data is key to understanding the behavioural response to a distributed stimulus in unrestrained animals. Existing models seek to describe the dynamics of behaviour or segment individual locomotor episodes rather than to identify the rare and transient sequences of locomotor episodes that make up the behavioural response. To fill this gap, we develop a lexical, hierarchical model of behaviour. We designed an unsupervised algorithm called "BASS" to efficiently identify and segment recurring behavioural action sequences transiently occurring in long behavioural recordings. When applied to navigating larval zebrafish, BASS extracts a dictionary of remarkably long, non-Markovian sequences consisting of repeats and mixtures of slow forward and turn bouts. Applied to a novel chemotaxis assay, BASS uncovers chemotactic strategies deployed by zebrafish to avoid aversive cues consisting of sequences of fast large-angle turns and burst swims. In a simulated dataset of soaring gliders climbing thermals, BASS finds the spiraling patterns characteristic of soaring behaviour. In both cases, BASS succeeds in identifying rare action sequences in the behaviour deployed by freely moving animals. BASS can be easily incorporated into the pipelines of existing behavioural analyses across diverse species, and even more broadly used as a generic algorithm for pattern recognition in low-dimensional sequential data.

Insect locomotion: Flies show you how to stay on course

Walking animals are faced with making a trade-off between maintaining a stable posture and gait and pursuing other goals such as keeping a straight path. A new study on exploratory walking in flies provides a sophisticated quantitative account of this behavioural problem, with some intriguing discoveries.

Fast tuning of posture control by visual feedback underlies gaze stabilization in walking Drosophila

Locomotion requires a balance between mechanical stability and movement flexibility to achieve behavioral goals despite noisy neuromuscular systems, but rarely is it considered how this balance is orchestrated. We combined virtual reality tools with quantitative analysis of behavior to examine how Drosophila uses self-generated visual information (reafferent visual feedback) to control gaze during exploratory walking. We found that flies execute distinct motor programs coordinated across the body to maximize gaze stability. However, the presence of inherent variability in leg placement relative to the body jeopardizes fine control of gaze due to posture-stabilizing adjustments that lead to unintended changes in course direction. Surprisingly, whereas visual feedback is dispensable for head-body coordination, we found that self-generated visual signals tune postural reflexes to rapidly prevent turns rather than to promote compensatory rotations, a long-standing idea for visually guided course control. Together, these findings support a model in which visual feedback orchestrates the interplay between posture and gaze stability in a manner that is both goal dependent and motor-context specific.

Unsupervised quantification of naturalistic animal behaviors for gaining insight into the brain

Neural computation has evolved to optimize the behaviors that enable our survival. Although much previous work in neuroscience has focused on constrained task behaviors, recent advances in computer vision are fueling a trend toward the study of naturalistic behaviors. Automated tracking of fine-scale behaviors is generating rich datasets for animal models including rodents, fruit flies, zebrafish, and worms. However, extracting meaning from these large and complex data often requires sophisticated computational techniques. Here we review the latest methods and modeling approaches providing new insights into the brain from behavior. We focus on unsupervised methods for identifying stereotyped behaviors and for resolving details of the structure and dynamics of behavioral sequences.

Decoding locomotion from population neural activity in moving C. elegans

We investigated the neural representation of locomotion in the nematode C. elegans by recording population calcium activity during movement. We report that population activity more accurately decodes locomotion than any single neuron. Relevant signals are distributed across neurons with diverse tunings to locomotion. Two largely distinct subpopulations are informative for decoding velocity and curvature, and different neurons’ activities contribute features relevant for different aspects of a behavior or different instances of a behavioral motif. To validate our measurements, we labeled neurons AVAL and AVAR and found that their activity exhibited expected transients during backward locomotion. Finally, we compared population activity during movement and immobilization. Immobilization alters the correlation structure of neural activity and its dynamics. Some neurons positively correlated with AVA during movement become negatively correlated during immobilization and vice versa. This work provides needed experimental measurements that inform and constrain ongoing efforts to understand population dynamics underlying locomotion in C. elegans.

Tracking changes in behavioural dynamics using prediction error

Automated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterise behavioural dynamics. For the model roundworm Caenorhabditis elegans, body pose can be accurately quantified from video as coordinates in a single low-dimensional space. We focus on this well-established case as an illustrative example and propose a method to reveal subtle variations in behaviour at high time resolution. Our data-driven method, based on empirical dynamic modeling, quantifies behavioural change as prediction error with respect to a time-delay-embedded ‘attractor’ of behavioural dynamics. Because this attractor is constructed from a user-specified reference data set, the approach can be tailored to specific behaviours of interest at the individual or group level. We validate the approach by detecting small changes in the movement dynamics of C. elegans at the initiation and completion of delta turns. We then examine an escape response initiated by an aversive stimulus and find that the method can track return to baseline behaviour in individual worms and reveal variations in the escape response between worms. We suggest that this general approach—defining dynamic behaviours using reference attractors and quantifying dynamic changes using prediction error—may be of broad interest and relevance to behavioural researchers working with video-derived time series.

Nonequilibrium Green's Functions for Functional Connectivity in the Brain

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a continuous-variable network of neurons. We show how the connectivity is related to the measurable response functions, and provide two illustrative examples via numerical calculations, inspired from Caenorhabditis elegans.

Artificial Intelligence Segmented Dynamic Video Images for Continuity Analysis in the Detection of Severe Cardiovascular Disease

In this paper, an artificial intelligence segmented dynamic video image based on the process of intensive cardiovascular and cerebrovascular disease monitoring is deeply investigated, and a sparse automatic coding deep neural network with a four layers stack structure is designed to automatically extract the deep features of the segmented dynamic video image shot, and six categories of normal, atrial premature, ventricular premature, right bundle branch block, left bundle branch block, and pacing are achieved through hierarchical training and optimization. Accurate recognition of heartbeats with an average accuracy of 99.5%. It provides technical assistance for the intelligent prediction of high-risk cardiovascular diseases like ventricular fibrillation. An intelligent prediction algorithm for sudden cardiac death based on the echolocation network was proposed. By designing an echolocation network with a multilayer serial structure, an intelligent distinction between sudden cardiac death signal and non-sudden death signal was realized, and the signal was predicted 5 min before sudden death occurred, with an average prediction accuracy of 94.32%. Using the self-learning capability of stack sparse auto-coding network, a large amount of label-free data is designed to train the stack sparse auto-coding deep neural network to automatically extract deep representations of plaque features. A small amount of labeled data then introduced to micro-train the entire network. Through the automatic analysis of the fiber cap thickness in the plaques, the automatic identification of thin fiber cap-like vulnerable plaques was achieved, and the average overlap of vulnerable regions reached 87%. The overall time for the automatic plaque and vulnerable plaque recognition algorithm was 0.54 s. It provides theoretical support for accurate diagnosis and endogenous analysis of high-risk cardiovascular diseases.

Nonlinear Control in the Nematode C. elegans

Recent whole-brain calcium imaging recordings of the nematode C. elegans have demonstrated that the neural activity associated with behavior is dominated by dynamics on a low-dimensional manifold that can be clustered according to behavioral states. Previous models of C. elegans dynamics have either been linear models, which cannot support the existence of multiple fixed points in the system, or Markov-switching models, which do not describe how control signals in C. elegans neural dynamics can produce switches between stable states. It remains unclear how a network of neurons can produce fast and slow timescale dynamics that control transitions between stable states in a single model. We propose a global, nonlinear control model which is minimally parameterized and captures the state transitions described by Markov-switching models with a single dynamical system. The model is fit by reproducing the timeseries of the dominant PCA mode in the calcium imaging data. Long and short time-scale changes in transition statistics can be characterized via changes in a single parameter in the control model. Some of these macro-scale transitions have experimental correlates to single neuro-modulators that seem to act as biological controls, allowing this model to generate testable hypotheses about the effect of these neuro-modulators on the global dynamics. The theory provides an elegant characterization of control in the neuron population dynamics in C. elegans. Moreover, the mathematical structure of the nonlinear control framework provides a paradigm that can be generalized to more complex systems with an arbitrary number of behavioral states.

Measuring and modeling whole-brain neural dynamics in Caenorhabditis elegans

The compact nervous system of the nematode Caenorhabditis elegans makes it a powerful playground to study how neural dynamics constrained by neuroanatomy generate neural function and behavior. The ability to record neural activity from the whole brain simultaneously in this worm has opened several research avenues and is providing insights into brain-wide neural coding of locomotion, sleep, and other behaviors. We review these findings and the development of new methods, including new microscopes, new genetic tools, and new modeling approaches. We conclude with a discussion of the role of theory in interpreting or driving new experiments in C. elegans and potential paths forward.

Unsupervised learning of control signals and their encodings in Caenorhabditis elegans whole-brain recordings

A major goal of computational neuroscience is to understand the relationship between synapse-level structure and network-level functionality. Caenorhabditis elegans is a model organism to probe this relationship due to the historic availability of the synaptic structure (connectome) and recent advances in whole brain calcium imaging techniques. Recent work has applied the concept of network controllability to neuronal networks, discovering some neurons that are able to drive the network to a certain state. However, previous work uses a linear model of the network dynamics, and it is unclear if the real neuronal network conforms to this assumption. Here, we propose a method to build a global, low-dimensional model of the dynamics, whereby an underlying global linear dynamical system is actuated by temporally sparse control signals. A key novelty of this method is discovering candidate control signals that the network uses to control itself. We analyse these control signals in two ways, showing they are interpretable and biologically plausible. First, these control signals are associated with transitions between behaviours, which were previously annotated via expert-generated features. Second, these signals can be predicted both from neurons previously implicated in behavioural transitions but also additional neurons previously unassociated with these behaviours. The proposed mathematical framework is generic and can be generalized to other neurosensory systems, potentially revealing transitions and their encodings in a completely unsupervised way.

Quantifying behavior to understand the brain

Over the past years, numerous methods have emerged to automate the quantification of animal behavior at a resolution not previously imaginable. This has opened up a new field of computational ethology and will, in the near future, make it possible to quantify in near completeness what an animal is doing as it navigates its environment. The importance of improving the techniques with which we characterize behavior is reflected in the emerging recognition that understanding behavior is an essential (or even prerequisite) step to pursuing neuroscience questions. The use of these methods, however, is not limited to studying behavior in the wild or in strictly ethological settings. Modern tools for behavioral quantification can be applied to the full gamut of approaches that have historically been used to link brain to behavior, from psychophysics to cognitive tasks, augmenting those measurements with rich descriptions of how animals navigate those tasks. Here we review recent technical advances in quantifying behavior, particularly in methods for tracking animal motion and characterizing the structure of those dynamics. We discuss open challenges that remain for behavioral quantification and highlight promising future directions, with a strong emphasis on emerging approaches in deep learning, the core technology that has enabled the markedly rapid pace of progress of this field. We then discuss how quantitative descriptions of behavior can be leveraged to connect brain activity with animal movements, with the ultimate goal of resolving the relationship between neural circuits, cognitive processes and behavior.

DeepPoseKit, a software toolkit for fast and robust animal pose estimation using deep learning

Quantitative behavioral measurements are important for answering questions across scientific disciplines-from neuroscience to ecology. State-of-the-art deep-learning methods offer major advances in data quality and detail by allowing researchers to automatically estimate locations of an animal's body parts directly from images or videos. However, currently available animal pose estimation methods have limitations in speed and robustness. Here, we introduce a new easy-to-use software toolkit, DeepPoseKit, that addresses these problems using an efficient multi-scale deep-learning model, called Stacked DenseNet, and a fast GPU-based peak-detection algorithm for estimating keypoint locations with subpixel precision. These advances improve processing speed >2x with no loss in accuracy compared to currently available methods. We demonstrate the versatility of our methods with multiple challenging animal pose estimation tasks in laboratory and field settings-including groups of interacting individuals. Our work reduces barriers to using advanced tools for measuring behavior and has broad applicability across the behavioral sciences.

DeepPoseKit, a software toolkit for fast and robust animal pose estimation using deep learning

Quantitative behavioral measurements are important for answering questions across scientific disciplines-from neuroscience to ecology. State-of-the-art deep-learning methods offer major advances in data quality and detail by allowing researchers to automatically estimate locations of an animal's body parts directly from images or videos. However, currently available animal pose estimation methods have limitations in speed and robustness. Here, we introduce a new easy-to-use software toolkit, DeepPoseKit, that addresses these problems using an efficient multi-scale deep-learning model, called Stacked DenseNet, and a fast GPU-based peak-detection algorithm for estimating keypoint locations with subpixel precision. These advances improve processing speed >2x with no loss in accuracy compared to currently available methods. We demonstrate the versatility of our methods with multiple challenging animal pose estimation tasks in laboratory and field settings-including groups of interacting individuals. Our work reduces barriers to using advanced tools for measuring behavior and has broad applicability across the behavioral sciences.

DeepPoseKit, a software toolkit for fast and robust animal pose estimation using deep learning

Quantitative behavioral measurements are important for answering questions across scientific disciplines-from neuroscience to ecology. State-of-the-art deep-learning methods offer major advances in data quality and detail by allowing researchers to automatically estimate locations of an animal's body parts directly from images or videos. However, currently available animal pose estimation methods have limitations in speed and robustness. Here, we introduce a new easy-to-use software toolkit, DeepPoseKit, that addresses these problems using an efficient multi-scale deep-learning model, called Stacked DenseNet, and a fast GPU-based peak-detection algorithm for estimating keypoint locations with subpixel precision. These advances improve processing speed >2x with no loss in accuracy compared to currently available methods. We demonstrate the versatility of our methods with multiple challenging animal pose estimation tasks in laboratory and field settings-including groups of interacting individuals. Our work reduces barriers to using advanced tools for measuring behavior and has broad applicability across the behavioral sciences.