Uncovering multiscale structure in the variability of larval zebrafish navigation.

Animals chain movements into long-lived motor strategies, exhibiting variability across scales that reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build Markov models of movement sequences that bridges across time scales and enables a quantitative comparison of behavioral phenotypes among individuals. Applied to larval zebrafish responding to diverse sensory cues, we uncover a hierarchy of long-lived motor strategies, dominated by changes in orientation distinguishing cruising versus wandering strategies. Environmental cues induce preferences along these modes at the population level: while fish cruise in the light, they wander in response to aversive stimuli, or in search for appetitive prey. As our method encodes the behavioral dynamics of each individual fish in the transitions among coarse-grained motor strategies, we use it to uncover a hierarchical structure in the phenotypic variability that reflects exploration-exploitation trade-offs. Across a wide range of sensory cues, a major source of variation among fish is driven by prior and/or immediate exposure to prey that induces exploitation phenotypes. A large degree of variability that is not explained by environmental cues unravels motivational states that override the sensory context to induce contrasting exploration-exploitation phenotypes. Altogether, by extracting the timescales of motor strategies deployed during navigation, our approach exposes structure among individuals and reveals internal states tuned by prior experience.

Long-wavelength traveling waves of vasomotion modulate the perfusion of cortex.

Brain arterioles are active, multicellular complexes whose diameters oscillate at ∼ 0.1 Hz. We assess the physiological impact and spatiotemporal dynamics of vaso-oscillations in the awake mouse. First, vaso-oscillations in penetrating arterioles, which source blood from pial arterioles to the capillary bed, profoundly impact perfusion throughout neocortex. The modulation in flux during resting-state activity exceeds that of stimulus-induced activity. Second, the change in perfusion through arterioles relative to the change in their diameter is weak. This implies that the capillary bed dominates the hydrodynamic resistance of brain vasculature. Lastly, the phase of vaso-oscillations evolves slowly along arterioles, with a wavelength that exceeds the span of the cortical mantle and sufficient variability to establish functional cortical areas as parcels of uniform phase. The phase-gradient supports traveling waves in either direction along both pial and penetrating arterioles. This implies that waves along penetrating arterioles can mix, but not directionally transport, interstitial fluids.

Uncovering multiscale structure in the variability of larval zebrafish navigation.

Animals chain movements into long-lived motor strategies, resulting in variability that ultimately reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build models that bridges across time scales that enable a quantitative comparison of behavioral phenotypes among individuals. Applied to larval zebrafish exposed to diverse sensory cues, we uncover a hierarchy of long-lived motor strategies, dominated by changes in orientation distinguishing cruising and wandering strategies. Environmental cues induce preferences along these modes at the population level: while fish cruise in the light, they wander in response to aversive (dark) stimuli or in search for prey. Our method enables us to encode the behavioral dynamics of each individual fish in the transitions among coarse-grained motor strategies. By doing so, we uncover a hierarchical structure to the phenotypic variability that corresponds to exploration-exploitation trade-offs. Within a wide range of sensory cues, a major source of variation among fish is driven by prior and immediate exposure to prey that induces exploitation phenotypes. However, a large degree of variability is unexplained by environmental cues, pointing to hidden states that override the sensory context to induce contrasting exploration-exploitation phenotypes. Altogether, our approach extracts the timescales of motor strategies deployed during navigation, exposing undiscovered structure among individuals and pointing to internal states tuned by prior experience.

Sticky issues in turbulent transport.

We investigate the role of partial stickiness among particles or with a surface for turbulent transport. For the former case, we re-derive known results for the case of the compressible Kraichnan model by using a method based on bi-orthogonality for the expansion of the propagator in terms of left and right eigenvectors. In particular, we show that enforcing the constraints of orthogonality and normalization yields results that were previously obtained by a rigorous, yet possibly less intuitive method. For the latter case, we introduce a general model of transport within the atmospheric boundary layer. As suggested by experimental observations on the transport of atmospheric tracers, both drift and diffusivity scale with the height to the ground. The strength of the drift is parameterized by a velocity V. We use the bi-orthogonality method to show that for V in the range -1 < V < 0 and 0 < V < 1 there is a one-parameter family of boundary conditions that are a priori admissible. Outside of that range, there is a single boundary condition that is admissible. In physical terms, the one-parameter family is parametrized by the degree to which particles stick to the ground.

Two-fluid dynamics and micron-thin boundary layers shape cytoplasmic flows in early Drosophila embryos.

Cytoplasmic flows are widely emerging as key functional players in development. In early Drosophila embryos, flows drive the spreading of nuclei across the embryo. Here, we combine hydrodynamic modeling with quantitative imaging to develop a two-fluid model that features an active actomyosin gel and a passive viscous cytosol. Gel contractility is controlled by the cell cycle oscillator, the two fluids being coupled by friction. In addition to recapitulating experimental flow patterns, our model explains observations that remained elusive and makes a series of predictions. First, the model captures the vorticity of cytosolic flows, which highlights deviations from Stokes' flow that were observed experimentally but remained unexplained. Second, the model reveals strong differences in the gel and cytosol motion. In particular, a micron-sized boundary layer is predicted close to the cortex, where the gel slides tangentially while the cytosolic flow cannot slip. Third, the model unveils a mechanism that stabilizes the spreading of nuclei with respect to perturbations of their initial positions. This self-correcting mechanism is argued to be functionally important for proper nuclear spreading. Fourth, we use our model to analyze the effects of flows on the transport of the morphogen Bicoid and the establishment of its gradients. Finally, the model predicts that the flow strength should be reduced if the shape of the domain is more round, which is experimentally confirmed in Drosophila mutants. Thus, our two-fluid model explains flows and nuclear positioning in early Drosophila, while making predictions that suggest novel future experiments.

Two-fluid dynamics and micron-thin boundary layers shape cytoplasmic flows in early Drosophila embryos.

Cytoplasmic flows are widely emerging as key functional players in development. In early Drosophila embryos, flows drive the spreading of nuclei across the embryo. Here, we combine hydrodynamic modeling with quantitative imaging to develop a two-fluid model that features an active actomyosin gel and a passive viscous cytosol. Gel contractility is controlled by the cell cycle oscillator, the two fluids being coupled by friction. In addition to recapitulating experimental flow patterns, our model explains observations that remained elusive, and makes a series of new predictions. First, the model captures the vorticity of cytosolic flows, which highlights deviations from Stokes' flow that were observed experimentally but remained unexplained. Second, the model reveals strong differences in the gel and cytosol motion. In particular, a micron-sized boundary layer is predicted close to the cortex, where the gel slides tangentially whilst the cytosolic flow cannot slip. Third, the model unveils a mechanism that stabilizes the spreading of nuclei with respect to perturbations of their initial positions. This self-correcting mechanism is argued to be functionally important for proper nuclear spreading. Fourth, we use our model to analyze the effects of flows on the transport of the morphogen Bicoid, and the establishment of its gradients. Finally, the model predicts that the flow strength should be reduced if the shape of the domain is more round, which is experimentally confirmed in Drosophila mutants. Thus, our two-fluid model explains flows and nuclear positioning in early Drosophila, while making predictions that suggest novel future experiments.

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.

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.

Manipulating the nature of embryonic mitotic waves.

Early embryogenesis is characterized by rapid and synchronous cleavage divisions, which are often controlled by wave-like patterns of Cdk1 activity. Two mechanisms have been proposed for mitotic waves: sweep and trigger waves.1,2 The two mechanisms give rise to different wave speeds, dependencies on physical and molecular parameters, and spatial profiles of Cdk1 activity: upward sweeping gradients versus traveling wavefronts. Both mechanisms hinge on the transient bistability governing the cell cycle and are differentiated by the speed of the cell-cycle progression: sweep and trigger waves arise for rapid and slow drives, respectively. Here, using quantitative imaging of Cdk1 activity and theory, we illustrate that sweep waves are the dominant mechanism in Drosophila embryos and test two fundamental predictions on the transition from sweep to trigger waves. We demonstrate that sweep waves can be turned into trigger waves if the cell cycle is slowed down genetically or if significant delays in the cell-cycle progression are introduced across the embryo by altering nuclear density. Our genetic experiments demonstrate that Polo kinase is a major rate-limiting regulator of the blastoderm divisions, and genetic perturbations reducing its activity can induce the transition from sweep to trigger waves. Furthermore, we show that changes in temperature cause an essentially uniform slowdown of interphase and mitosis. That results in sweep waves being observed across a wide temperature range despite the cell-cycle durations being significantly different. Collectively, our combination of theory and experiments elucidates the nature of mitotic waves in Drosophila embryogenesis, their control mechanisms, and their mutual transitions.

Alternation emerges as a multi-modal strategy for turbulent odor navigation.

Foraging mammals exhibit a familiar yet poorly characterized phenomenon, 'alternation', a pause to sniff in the air preceded by the animal rearing on its hind legs or raising its head. Rodents spontaneously alternate in the presence of airflow, suggesting that alternation serves an important role during plume-tracking. To test this hypothesis, we combine fully resolved simulations of turbulent odor transport and Bellman optimization methods for decision-making under partial observability. We show that an agent trained to minimize search time in a realistic odor plume exhibits extensive alternation together with the characteristic cast-and-surge behavior observed in insects. Alternation is linked with casting and occurs more frequently far downwind of the source, where the likelihood of detecting airborne cues is higher relative to ground cues. Casting and alternation emerge as complementary tools for effective exploration with sparse cues. A model based on marginal value theory captures the interplay between casting, surging, and alternation.

Cullin-5 mutants reveal collective sensing of the nucleocytoplasmic ratio in Drosophila embryogenesis.

In most metazoans, early embryonic development is characterized by rapid division cycles that pause before gastrulation at the midblastula transition (MBT).1 These cleavage divisions are accompanied by cytoskeletal rearrangements that ensure proper nuclear positioning. However, the molecular mechanisms controlling nuclear positioning are not fully elucidated. In Drosophila, early embryogenesis unfolds in a multinucleated syncytium. Nuclei rapidly move across the anterior-posterior (AP) axis at cell cycles 4-6 in a process driven by actomyosin contractility and cytoplasmic flows.2,3 In shackleton (shkl) mutants, this axial spreading is impaired.4 Here, we show that shkl mutants carry mutations in the cullin-5 (cul-5) gene. Live imaging experiments show that Cul-5 is downstream of the cell cycle but is required for cortical actomyosin contractility. The nuclear spreading phenotype of cul-5 mutants can be rescued by reducing Src activity, suggesting that a major target of cul-5 is Src kinase. cul-5 mutants display gradients of nuclear density across the AP axis that we exploit to study cell-cycle control as a function of the N/C ratio. We found that the N/C ratio is sensed collectively in neighborhoods of about 100 µm, and such collective sensing is required for a precise MBT, in which all the nuclei in the embryo pause their division cycle. Moreover, we found that the response to the N/C ratio is slightly graded along the AP axis. These two features can be linked to Cdk1 dynamics. Collectively, we reveal a new pathway controlling nuclear positioning and provide a dissection of how nuclear cycles respond to the N/C ratio.

Waves in Embryonic Development.

Embryonic development hinges on effective coordination of molecular events across space and time. Waves have recently emerged as constituting an ubiquitous mechanism that ensures rapid spreading of regulatory signals across embryos, as well as reliable control of their patterning, namely, for the emergence of body plan structures. In this article, we review a selection of recent quantitative work on signaling waves and present an overview of the theory of waves. Our aim is to provide a succinct yet comprehensive guiding reference for the theoretical frameworks by which signaling waves can arise in embryos. We start, then, from reaction-diffusion systems, both static and time dependent; move to excitable dynamics; and conclude with systems of coupled oscillators. We link these theoretical models to molecular mechanisms recently elucidated for the control of mitotic waves in early embryos, patterning of the vertebrate body axis, micropattern cultures, and bone regeneration. Our goal is to inspire experimental work that will advance theory in development and connect its predictions to quantitative biological observations.

Affinity maturation for an optimal balance between long-term immune coverage and short-term resource constraints.

In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its lymphocyte repertoire. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the encountered strain. This process of affinity maturation generates a memory pool whose diversity and size remain difficult to predict. We assume that the immune system follows a strategy that maximizes the long-term immune coverage and minimizes the short-term metabolic costs associated with affinity maturation. This strategy is defined as an optimal decision process on a finite dimensional phenotypic space, where a preexisting population of cells is sequentially challenged with a neutrally evolving strain. We show that the low specificity and high diversity of memory B cells-a key experimental result-can be explained as a strategy to protect against pathogens that evolve fast enough to escape highly potent but narrow memory. This plasticity of the repertoire drives the emergence of distinct regimes for the size and diversity of the memory pool, depending on the density of de novo responding cells and on the mutation rate of the strain. The model predicts power-law distributions of clonotype sizes observed in data and rationalizes antigenic imprinting as a strategy to minimize metabolic costs while keeping good immune protection against future strains.

Sector search strategies for odor trail tracking.

Ants, mice, and dogs often use surface-bound scent trails to establish navigation routes or to find food and mates, yet their tracking strategies remain poorly understood. Chemotaxis-based strategies cannot explain casting, a characteristic sequence of wide oscillations with increasing amplitude performed upon sustained loss of contact with the trail. We propose that tracking animals have an intrinsic, geometric notion of continuity, allowing them to exploit past contacts with the trail to form an estimate of where it is headed. This estimate and its uncertainty form an angular sector, and the emergent search patterns resemble a "sector search." Reinforcement learning agents trained to execute a sector search recapitulate the various phases of experimentally observed tracking behavior. We use ideas from polymer physics to formulate a statistical description of trails and show that search geometry imposes basic limits on how quickly animals can track trails. By formulating trail tracking as a Bellman-type sequential optimization problem, we quantify the geometric elements of optimal sector search strategy, effectively explaining why and when casting is necessary. We propose a set of experiments to infer how tracking animals acquire, integrate, and respond to past information on the tracked trail. More generally, we define navigational strategies relevant for animals and biomimetic robots and formulate trail tracking as a behavioral paradigm for learning, memory, and planning.

A Suite of Neurophotonic Tools to Underpin the Contribution of Internal Brain States in fMRI.

Recent developments in optical microscopy, applicable for large-scale and longitudinal imaging of cortical activity in behaving animals, open unprecedented opportunities to gain a deeper understanding of neurovascular and neurometabolic coupling during different brain states. Future studies will leverage these tools to deliver foundational knowledge about brain state-dependent regulation of cerebral blood flow and metabolism as well as regulation as a function of brain maturation and aging. This knowledge is of critical importance to interpret hemodynamic signals observed with functional magnetic resonance imaging (fMRI).

A mechanism for hunchback promoters to readout morphogenetic positional information in less than a minute.

Cell fate decisions in the fly embryo are rapid: hunchback genes decide in minutes whether nuclei follow the anterior/posterior developmental blueprint by reading out positional information in the Bicoid morphogen. This developmental system is a prototype of regulatory decision processes that combine speed and accuracy. Traditional arguments based on fixed-time sampling of Bicoid concentration indicate that an accurate readout is impossible within the experimental times. This raises the general issue of how speed-accuracy tradeoffs are achieved. Here, we compare fixed-time to on-the-fly decisions, based on comparing the likelihoods of anterior/posterior locations. We found that these more efficient schemes complete reliable cell fate decisions within the short embryological timescales. We discuss the influence of promoter architectures on decision times and error rates, present concrete examples that rapidly readout the morphogen, and predictions for new experiments. Lastly, we suggest a simple mechanism for RNA production and degradation that approximates the log-likelihood function.

Antagonistic odor interactions in olfactory sensory neurons are widespread in freely breathing mice.

Odor landscapes contain complex blends of molecules that each activate unique, overlapping populations of olfactory sensory neurons (OSNs). Despite the presence of hundreds of OSN subtypes in many animals, the overlapping nature of odor inputs may lead to saturation of neural responses at the early stages of stimulus encoding. Information loss due to saturation could be mitigated by normalizing mechanisms such as antagonism at the level of receptor-ligand interactions, whose existence and prevalence remains uncertain. By imaging OSN axon terminals in olfactory bulb glomeruli as well as OSN cell bodies within the olfactory epithelium in freely breathing mice, we find widespread antagonistic interactions in binary odor mixtures. In complex mixtures of up to 12 odorants, antagonistic interactions are stronger and more prevalent with increasing mixture complexity. Therefore, antagonism is a common feature of odor mixture encoding in OSNs and helps in normalizing activity to reduce saturation and increase information transfer.

Odorant Receptor Inhibition Is Fundamental to Odor Encoding.

Most natural odors are complex mixtures of volatile components, competing to bind odorant receptors (ORs) expressed in olfactory sensory neurons (OSNs) of the nose. To date, surprisingly little is known about how OR antagonism shapes neuronal representations in the detection layer of the olfactory system. Here, we investigated its prevalence, the degree to which it disrupts OR ensemble activity, and its conservation across phylogenetically related ORs. Calcium imaging microscopy of dissociated OSNs revealed significant inhibition, often complete attenuation, of responses to indole-a commonly occurring volatile associated with both floral and fecal odors-by a set of 36 tested odorants. To confirm an OR mechanism for the observed inhibition, we performed single-cell transcriptomics on OSNs exhibiting specific response profiles to a diagnostic panel of odorants and identified three paralogous receptors-Olfr740, Olfr741, and Olfr743-which, when tested in vitro, recapitulated OSN responses. We screened ten ORs from the Olfr740 gene family with ∼800 perfumery-related odorants spanning a range of chemical scaffolds and functional groups. Over half of these compounds (430) antagonized at least one of the ten ORs. OR activity fitted a mathematical model of competitive receptor binding and suggests normalization of OSN ensemble responses to odorant mixtures is the rule rather than the exception. In summary, we observed OR antagonism occurred frequently and in a combinatorial manner. Thus, extensive receptor-mediated computation of mixture information appears to occur in the olfactory epithelium prior to transmission of odor information to the olfactory bulb.

Chemotaxis as a navigation strategy to boost range expansion.

Bacterial chemotaxis, the directed movement of cells along gradients of chemoattractants, is among the best-characterized subjects in molecular biology1-10, but much less is known about its physiological roles11. It is commonly seen as a starvation response when nutrients run out, or as an escape response from harmful situations12-16. Here we identify an alternative role of chemotaxis by systematically examining the spatiotemporal dynamics of Escherichia coli in soft agar12,17,18. Chemotaxis in nutrient-replete conditions promotes the expansion of bacterial populations into unoccupied territories well before nutrients run out in the current environment. Low levels of chemoattractants act as aroma-like cues in this process, establishing the direction and enhancing the speed of population movement along the self-generated attractant gradients. This process of navigated range expansion spreads faster and yields larger population gains than unguided expansion following the canonical Fisher-Kolmogorov dynamics19,20 and is therefore a general strategy to promote population growth in spatially extended, nutrient-replete environments.

Progressive recruitment of distal MEC-4 channels determines touch response strength in C. elegans.

Touch deforms, or strains, the skin beyond the immediate point of contact. The spatiotemporal nature of the touch-induced strain fields depend on the mechanical properties of the skin and the tissues below. Somatosensory neurons that sense touch branch out within the skin and rely on a set of mechano-electrical transduction channels distributed within their dendrites to detect mechanical stimuli. Here, we sought to understand how tissue mechanics shape touch-induced mechanical strain across the skin over time and how individual channels located in different regions of the strain field contribute to the overall touch response. We leveraged Caenorhabditis elegans' touch receptor neurons as a simple model amenable to in vivo whole-cell patch-clamp recording and an integrated experimental-computational approach to dissect the mechanisms underlying the spatial and temporal dynamics we observed. Consistent with the idea that strain is produced at a distance, we show that delivering strong stimuli outside the anatomical extent of the neuron is sufficient to evoke MRCs. The amplitude and kinetics of the MRCs depended on both stimulus displacement and speed. Finally, we found that the main factor responsible for touch sensitivity is the recruitment of progressively more distant channels by stronger stimuli, rather than modulation of channel open probability. This principle may generalize to somatosensory neurons with more complex morphologies.