Maximally predictive states: From partial observations to long timescales.

Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally predictive states by concatenating measurements in time, partitioning the resulting sequences using maximum entropy, and choosing the sequence length to maximize short-time predictive information. Transitions between these states yield a simple approximation of the transfer operator, which we use to reveal timescale separation and long-lived collective modes through the operator spectrum. Applicable to both deterministic and stochastic processes, we illustrate our approach through partial observations of the Lorenz system and the stochastic dynamics of a particle in a double-well potential. We use our transfer operator approach to provide a new estimator of the Kolmogorov-Sinai entropy, which we demonstrate in discrete and continuous-time systems, as well as the movement behavior of the nematode worm C. elegans.

Social Relationship as a Factor for the Development of Stress Incubation in Adult Mice.

While stress reactions can emerge long after the triggering event, it remains elusive how they emerge after a protracted, seemingly stress-free period during which stress incubates. Here, we study the behavioral development in mice isolated after observing an aggressive encounter inflicted upon their pair-housed partners. We developed a spatially resolved fine-scale behavioral analysis and applied it to standard behavioral tests. It reveals that the seemingly sudden behavioral changes developed gradually. These behavioral changes were not observed if the aggressive encounter happened to a stranger mouse, suggesting that social bonding is a prerequisite for stress incubation in this paradigm. This finding was corroborated by hemisphere-specific morphological changes in cortex regions centering at the anterior cingulate cortex, a cognitive and emotional center. Our non-invasive analytical methods to capture informative behavioral details may have applications beyond laboratory animals.

WormPose: Image synthesis and convolutional networks for pose estimation in C. elegans.

An important model system for understanding genes, neurons and behavior, the nematode worm C. elegans naturally moves through a variety of complex postures, for which estimation from video data is challenging. We introduce an open-source Python package, WormPose, for 2D pose estimation in C. elegans, including self-occluded, coiled shapes. We leverage advances in machine vision afforded from convolutional neural networks and introduce a synthetic yet realistic generative model for images of worm posture, thus avoiding the need for human-labeled training. WormPose is effective and adaptable for imaging conditions across worm tracking efforts. We quantify pose estimation using synthetic data as well as N2 and mutant worms in on-food conditions. We further demonstrate WormPose by analyzing long (∼ 8 hour), fast-sampled (∼ 30 Hz) recordings of on-food N2 worms to provide a posture-scale analysis of roaming/dwelling behaviors.

Flow-mediated olfactory communication in honeybee swarms.

Honeybee swarms are a landmark example of collective behavior. To become a coherent swarm, bees locate their queen by tracking her pheromones. But how can distant individuals exploit these chemical signals, which decay rapidly in space and time? Here, we combine a behavioral assay with the machine vision detection of organism location and scenting (pheromone propagation via wing fanning) behavior to track the search and aggregation dynamics of the honeybee Apis mellifera L. We find that bees collectively create a scenting-mediated communication network by arranging in a specific spatial distribution where there is a characteristic distance between individuals and directional signaling away from the queen. To better understand such a flow-mediated directional communication strategy, we developed an agent-based model where bee agents obeying simple, local behavioral rules exist in a flow environment in which the chemical signals diffuse and decay. Our model serves as a guide to exploring how physical parameters affect the collective scenting behavior and shows that increased directional bias in scenting leads to a more efficient aggregation process that avoids local equilibrium configurations of isotropic (nondirectional and axisymmetric) communication, such as small bee clusters that persist throughout the simulation. Our results highlight an example of extended classical stigmergy: Rather than depositing static information in the environment, individual bees locally sense and globally manipulate the physical fields of chemical concentration and airflow.

Markerless tracking of an entire honey bee colony.

From cells in tissue, to bird flocks, to human crowds, living systems display a stunning variety of collective behaviors. Yet quantifying such phenomena first requires tracking a significant fraction of the group members in natural conditions, a substantial and ongoing challenge. We present a comprehensive, computational method for tracking an entire colony of the honey bee Apis mellifera using high-resolution video on a natural honeycomb background. We adapt a convolutional neural network (CNN) segmentation architecture to automatically identify bee and brood cell positions, body orientations and within-cell states. We achieve high accuracy (~10% body width error in position, ~10° error in orientation, and true positive rate > 90%) and demonstrate months-long monitoring of sociometric colony fluctuations. These fluctuations include ~24 h cycles in the counted detections, negative correlation between bee and brood, and nightly enhancement of bees inside comb cells. We combine detected positions with visual features of organism-centered images to track individuals over time and through challenging occluding events, recovering ~79% of bee trajectories from five observation hives over 5 min timespans. The trajectories reveal important individual behaviors, including waggle dances and crawling inside comb cells. Our results provide opportunities for the quantitative study of collective bee behavior and for advancing tracking techniques of crowded systems.

OrganoidTracker: Efficient cell tracking using machine learning and manual error correction.

Time-lapse microscopy is routinely used to follow cells within organoids, allowing direct study of division and differentiation patterns. There is an increasing interest in cell tracking in organoids, which makes it possible to study their growth and homeostasis at the single-cell level. As tracking these cells by hand is prohibitively time consuming, automation using a computer program is required. Unfortunately, organoids have a high cell density and fast cell movement, which makes automated cell tracking difficult. In this work, a semi-automated cell tracker has been developed. To detect the nuclei, we use a machine learning approach based on a convolutional neural network. To form cell trajectories, we link detections at different time points together using a min-cost flow solver. The tracker raises warnings for situations with likely errors. Rapid changes in nucleus volume and position are reported for manual review, as well as cases where nuclei divide, appear and disappear. When the warning system is adjusted such that virtually error-free lineage trees can be obtained, still less than 2% of all detected nuclei positions are marked for manual analysis. This provides an enormous speed boost over manual cell tracking, while still providing tracking data of the same quality as manual tracking.

Energy consumption and cooperation for optimal sensing.

The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing.

Modelling the ballistic-to-diffusive transition in nematode motility reveals variation in exploratory behaviour across species.

A quantitative understanding of organism-level behaviour requires predictive models that can capture the richness of behavioural phenotypes, yet are simple enough to connect with underlying mechanistic processes. Here, we investigate the motile behaviour of nematodes at the level of their translational motion on surfaces driven by undulatory propulsion. We broadly sample the nematode behavioural repertoire by measuring motile trajectories of the canonical laboratory strain Caenorhabditis elegans N2 as well as wild strains and distant species. We focus on trajectory dynamics over time scales spanning the transition from ballistic (straight) to diffusive (random) movement and find that salient features of the motility statistics are captured by a random walk model with independent dynamics in the speed, bearing and reversal events. We show that the model parameters vary among species in a correlated, low-dimensional manner suggestive of a common mode of behavioural control and a trade-off between exploration and exploitation. The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these nematode lineages employ contrasting 'bet-hedging' strategies for foraging.

Adaptive, locally linear models of complex dynamics.

The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode Caenorhabditis elegans, our approach identifies fine-grained behavioral states and model dynamics which fluctuate about an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. We analyze whole-brain imaging in C. elegans and show that global brain dynamics is damped away from the instability boundary by a decrease in oxygen concentration. We provide additional evidence for such near-critical dynamics from the analysis of electrocorticography in monkey and the imaging of a neural population from mouse visual cortex at single-cell resolution.

Exploiting ecology in drug pulse sequences in favour of population reduction.

A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment.

Bias, belief, and consensus: Collective opinion formation on fluctuating networks.

With the advent of online networks, societies have become substantially more interconnected with individual members able to easily both maintain and modify their own social links. Here, we show that active network maintenance exposes agents to confirmation bias, the tendency to confirm one's beliefs, and we explore how this bias affects collective opinion formation. We introduce a model of binary opinion dynamics on a complex, fluctuating network with stochastic rewiring and we analyze these dynamics in the mean-field limit of large networks and fast link rewiring. We show that confirmation bias induces a segregation of individuals with different opinions and stabilizes the consensus state. We further show that bias can have an unusual, nonmonotonic effect on the time to consensus and this suggests a novel avenue for large-scale opinion manipulation.

Resolving coiled shapes reveals new reorientation behaviors in C. elegans.

We exploit the reduced space of C. elegans postures to develop a novel tracking algorithm which captures both simple shapes and also self-occluding coils, an important, yet unexplored, component of 2D worm behavior. We apply our algorithm to show that visually complex, coiled sequences are a superposition of two simpler patterns: the body wave dynamics and a head-curvature pulse. We demonstrate the precise Ω-turn dynamics of an escape response and uncover a surprising new dichotomy in spontaneous, large-amplitude coils; deep reorientations occur not only through classical Ω-shaped postures but also through larger postural excitations which we label here as δ-turns. We find that omega and delta turns occur independently, suggesting a distinct triggering mechanism, and are the serpentine analog of a random left-right step. Finally, we show that omega and delta turns occur with approximately equal rates and adapt to food-free conditions on a similar timescale, a simple strategy to avoid navigational bias.

Hierarchical compression of Caenorhabditis elegans locomotion reveals phenotypic differences in the organization of behaviour.

Regularities in animal behaviour offer insights into the underlying organizational and functional principles of nervous systems and automated tracking provides the opportunity to extract features of behaviour directly from large-scale video data. Yet how to effectively analyse such behavioural data remains an open question. Here, we explore whether a minimum description length principle can be exploited to identify meaningful behaviours and phenotypes. We apply a dictionary compression algorithm to behavioural sequences from the nematode worm Caenorhabditis elegans freely crawling on an agar plate both with and without food and during chemotaxis. We find that the motifs identified by the compression algorithm are rare but relevant for comparisons between worms in different environments, suggesting that hierarchical compression can be a useful step in behaviour analysis. We also use compressibility as a new quantitative phenotype and find that the behaviour of wild-isolated strains of C. elegans is more compressible than that of the laboratory strain N2 as well as the majority of mutant strains examined. Importantly, in distinction to more conventional phenotypes such as overall motor activity or aggregation behaviour, the increased compressibility of wild isolates is not explained by the loss of function of the gene npr-1, which suggests that erratic locomotion is a laboratory-derived trait with a novel genetic basis. Because hierarchical compression can be applied to any sequence, we anticipate that compressibility can offer insights into the organization of behaviour in other animals including humans.

DNA Twist Stability Changes with Magnesium(2+) Concentration.

To understand DNA elasticity at high forces (F>30 pN), its helical nature must be taken into account, as a coupling between twist and stretch. The prevailing model, the wormlike chain, was previously extended to include this twist-stretch coupling. Motivated by DNA's charged nature, and the known effects of ionic charges on its elasticity, we set out to systematically measure the impact of buffer ionic conditions on twist-stretch coupling. After developing a robust fitting approach, we show, using our new data set, that DNA's helical twist is stabilized at high concentrations of the magnesium divalent cation. DNA's persistence length and stretch modulus are, on the other hand, relatively insensitive to the applied range of ionic strengths.

A place for time: the spatiotemporal structure of neural dynamics during natural audition.

We use functional magnetic resonance imaging (fMRI) to analyze neural responses to natural auditory stimuli. We characterize the fMRI time series through the shape of the voxel power spectrum and find that the timescales of neural dynamics vary along a spatial gradient, with faster dynamics in early auditory cortex and slower dynamics in higher order brain regions. The timescale gradient is observed through the unsupervised clustering of the power spectra of individual brains, both in the presence and absence of a stimulus, and is enhanced in the stimulus-locked component that is shared across listeners. Moreover, intrinsically faster dynamics occur in areas that respond preferentially to momentary stimulus features, while the intrinsically slower dynamics occur in areas that integrate stimulus information over longer timescales. These observations connect the timescales of intrinsic neural dynamics to the timescales of information processing, suggesting a temporal organizing principle for neural computation across the cerebral cortex.

Statistical thermodynamics of natural images.

The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding thermodynamics. We find evidence for criticality in a diverging specific heat, which corresponds to large fluctuations in how "surprising" we find individual images, and in the quantitative form of the entropy vs energy. We identify special image configurations as local energy minima and show that average patches within each basin are interpretable as lines and edges in all orientations.

Automated tracking of animal posture and movement during exploration and sensory orientation behaviors.

BACKGROUND: The nervous functions of an organism are primarily reflected in the behavior it is capable of. Measuring behavior quantitatively, at high-resolution and in an automated fashion provides valuable information about the underlying neural circuit computation. Accordingly, computer-vision applications for animal tracking are becoming a key complementary toolkit to genetic, molecular and electrophysiological characterization in systems neuroscience. METHODOLOGY/PRINCIPAL FINDINGS: We present Sensory Orientation Software (SOS) to measure behavior and infer sensory experience correlates. SOS is a simple and versatile system to track body posture and motion of single animals in two-dimensional environments. In the presence of a sensory landscape, tracking the trajectory of the animal's sensors and its postural evolution provides a quantitative framework to study sensorimotor integration. To illustrate the utility of SOS, we examine the orientation behavior of fruit fly larvae in response to odor, temperature and light gradients. We show that SOS is suitable to carry out high-resolution behavioral tracking for a wide range of organisms including flatworms, fishes and mice. CONCLUSIONS/SIGNIFICANCE: Our work contributes to the growing repertoire of behavioral analysis tools for collecting rich and fine-grained data to draw and test hypothesis about the functioning of the nervous system. By providing open-access to our code and documenting the software design, we aim to encourage the adaptation of SOS by a wide community of non-specialists to their particular model organism and questions of interest.

Active sampling and decision making in Drosophila chemotaxis.

The ability to respond to chemical stimuli is fundamental to the survival of motile organisms, but the strategies underlying odour tracking remain poorly understood. Here we show that chemotaxis in Drosophila melanogaster larvae is an active sampling process analogous to sniffing in vertebrates. Combining computer-vision algorithms with reconstructed olfactory environments, we establish that larvae orient in odour gradients through a sequential organization of stereotypical behaviours, including runs, stops, lateral head casts and directed turns. Negative gradients, integrated during runs, control the timing of turns. Positive gradients detected through high-amplitude head casts determine the direction of individual turns. By genetically manipulating the peripheral olfactory circuit, we examine how orientation adapts to losses and gains of function in olfactory input. Our findings suggest that larval chemotaxis represents an intermediate navigation strategy between the biased random walks of Escherichia Coli and the stereo-olfaction observed in rats and humans.

Emergence of long timescales and stereotyped behaviors in Caenorhabditis elegans.

Animal behaviors often are decomposable into discrete, stereotyped elements, well separated in time. In one model, such behaviors are triggered by specific commands; in the extreme case, the discreteness of behavior is traced to the discreteness of action potentials in the individual command neurons. Here, we use the crawling behavior of the nematode Caenorhabditis elegans to demonstrate the opposite view, in which discreteness, stereotypy, and long timescales emerge from the collective dynamics of the behavior itself. In previous work, we found that as C. elegans crawls, its body moves through a "shape space" in which four dimensions capture approximately 95% of the variance in body shape. Here we show that stochastic dynamics within this shape space predicts transitions between attractors corresponding to abrupt reversals in crawling direction. With no free parameters, our inferred stochastic dynamical system generates reversal timescales and stereotyped trajectories in close agreement with experimental observations. We use the stochastic dynamics to show that the noise amplitude decreases systematically with increasing time away from food, resulting in longer bouts of forward crawling and suggesting that worms can use noise to modify their locomotory behavior.